Advances in Signal Processing for Maritime ...

EURASIP Journal on Advances in Signal Processing

Advances in Signal Processing for Maritime Applications Guest Editors: Frank Ehlers, Warren Fox, Dirk Maiwald, Martin Ulmke, and Gary Wood

Advances in Signal Processing for Maritime Applications


Advances in Signal Processing for Maritime Applications Guest Editors: Frank Ehlers, Warren Fox, Dirk Maiwald, Martin Ulmke, and Gary Wood

Copyright © 2010 Hindawi Publishing Corporation. All rights reserved. This is a special issue published in volume 2010 of “EURASIP Journal on Advances in Signal Processing.” All articles are open access articles distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Editor-in-Chief Phillip Regalia, Institut National des Télécommunications, France

Associate Editors Mohamed M. Alimi, Tunisia Kenneth Barner, USA Yasar Becerikli, Turkey Kostas Berberidis, Greece Jose Carlos Bermudez, Brazil Enrico Capobianco, Italy A. Enis Cetin, Turkey Jonathon A. Chambers, UK Mei-Juan Chen, Taiwan Liang-Gee Chen, Taiwan Huaiyu Dai, USA Satya Dharanipragada, USA Kutluyil Dogancay, Australia Florent Dupont, France Frank Ehlers, Italy Sharon Gannot, Israel Samanwoy Ghosh-Dastidar, USA Norbert Goertz, Austria M. Greco, Italy Irene Y. H. Gu, Sweden Fredrik Gustafsson, Sweden Ulrich Heute, Germany Sangjin Hong, USA Jiri Jan, Czech Republic

Magnus Jansson, Sweden Sudharman K. Jayaweera, USA Soren Holdt Jensen, Denmark Mark Kahrs, USA Moon Gi Kang, Republic of Korea Walter Kellermann, Germany Lisimachos P. Kondi, Greece Alex Chichung Kot, Singapore C.-C. Jay Kuo, USA Ercan E. Kuruoglu, Italy Tan Lee, China Geert Leus, The Netherlands T.-H. Li, USA Husheng Li, USA Mark Liao, Taiwan Y.-P. Lin, Taiwan Shoji Makino, Japan Stephen Marshall, UK C. Mecklenbräuker, Austria Gloria Menegaz, Italy Ricardo Merched, Brazil Marc Moonen, Belgium Christophoros Nikou, Greece Sven Nordholm, Australia

Patrick Oonincx, The Netherlands Douglas O’Shaughnessy, Canada Björn Ottersten, Sweden Jacques Palicot, France Ana Perez-Neira, Spain Wilfried Philips, Belgium Aggelos Pikrakis, Greece Ioannis Psaromiligkos, Canada Athanasios Rontogiannis, Greece Gregor Rozinaj, Slovakia Markus Rupp, Austria William Allan Sandham, UK Bulent Sankur, Turkey Erchin Serpedin, USA Ling Shao, UK Dirk Slock, France Yap-Peng Tan, Singapore João Manuel R. S. Tavares, Portugal George S. Tombras, Greece Dimitrios Tzovaras, Greece Bernhard Wess, Austria Jar Ferr Yang, Taiwan Azzedine Zerguine, Saudi Arabia Abdelhak M. Zoubir, Germany

Contents Advances in Signal Processing for Maritime Applications, Frank Ehlers, Warren Fox, Dirk Maiwald, Martin Ulmke, and Gary Wood Volume 2010, Article ID 512767, 5 pages Underwater Broadband Source Localization Based on Modal Filtering and Features Extraction, Maciej Lopatka, Grégoire Le Touzé, Barbara Nicolas, Xavier Cristol, Jérôme I. Mars, and Dominique Fattaccioli Volume 2010, Article ID 304103, 18 pages Simulation of Matched Field Processing Localization Based on Empirical Mode Decomposition and Karhunen-Loève Expansion in Underwater Waveguide Environment, Qiang Wang and Qin Jiang Volume 2010, Article ID 483524, 7 pages A Relative-Localization Algorithm Using Incomplete Pairwise Distance Measurements for Underwater Applications, Kae Y. Foo and Philip R. Atkins Volume 2010, Article ID 930327, 16 pages Acoustic Particle Detection with the ANTARES Detector, C. Richardt, G. Anton, K. Graf, J. Hößl, U. Katz, R. Lahmann, and M. Neff Volume 2010, Article ID 970581, 7 pages Masking of Time-Frequency Patterns in Applications of Passive Underwater Target Detection, Jüri Sildam Volume 2010, Article ID 298038, 10 pages An Underwater Acoustic Implementation of DFT-Spread OFDM, Yonghuai Zhang, Haixin Sun, En Cheng, and Weijie Shen Volume 2010, Article ID 572453, 6 pages Low Complexity Iterative Receiver Design for Shallow Water Acoustic Channels, C. P. Shah, C. C. Tsimenidis, B. S. Sharif, and J. A. Neasham Volume 2010, Article ID 590458, 13 pages Automatic Indexing for Content Analysis of Whale Recordings and XML Representation, Frédéric Bénard and Hervé Glotin Volume 2010, Article ID 695017, 8 pages Silent Localization of Underwater Sensors Using Magnetometers, Jonas Callmer, Martin Skoglund, and Fredrik Gustafsson Volume 2010, Article ID 709318, 8 pages Hausdorff-Based RC and IESIL Combined Positioning Algorithm for Underwater Geomagnetic Navigation, Yi Lin Volume 2010, Article ID 593238, 11 pages Realistic Subsurface Anomaly Discrimination Using Electromagnetic Induction and an SVM Classifier, Juan Pablo Fernández, Fridon Shubitidze, Irma Shamatava, Benjamin E. Barrowes, and Kevin O’Neill Volume 2010, Article ID 305890, 11 pages

CFAR Detection from Noncoherent Radar Echoes Using Bayesian Theory, Hiroyuki Yamaguchi and Wataru Suganuma Volume 2010, Article ID 969751, 12 pages Artificial Neural Network-Based Clutter Reduction Systems for Ship Size Estimation in Maritime Radars, ´ R. Vicen-Bueno, R. Carrasco-Alvarez, M. Rosa-Zurera, J. C. Nieto-Borge, and M. P. Jarabo-Amores Volume 2010, Article ID 380473, 15 pages An Evaluation of Pixel-Based Methods for the Detection of Floating Objects on the Sea Surface, Alexander Borghgraef, Olivier Barnich, Fabian Lapierre, Marc Van Droogenbroeck, Wilfried Philips, and Marc Acheroy Volume 2010, Article ID 978451, 11 pages Statistical Real-time Model for Performance Prediction of Ship Detection from Microsatellite Electro-Optical Imagers, Fabian D. Lapierre, Alexander Borghgraef, and Marijke Vandewal Volume 2010, Article ID 475948, 15 pages Techniques for Effective Optical Noise Rejection in Amplitude-Modulated Laser Optical Radars for Underwater Three-Dimensional Imaging, R. Ricci, M. Francucci, L. De Dominicis, M. Ferri de Collibus, G. Fornetti, M. Guarneri, M. Nuvoli, E. Paglia, and L. Bartolini Volume 2010, Article ID 958360, 24 pages Underwater Image Processing: State of the Art of Restoration and Image Enhancement Methods, Raimondo Schettini and Silvia Corchs Volume 2010, Article ID 746052, 14 pages A Fully Automated Method to Detect and Segment a Manufactured Object in an Underwater Color Image, Christian Barat and Ronald Phlypo Volume 2010, Article ID 568092, 10 pages

Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2010, Article ID 512767, 5 pages doi:10.1155/2010/512767

Editorial Advances in Signal Processing for Maritime Applications Frank Ehlers,1 Warren Fox,1 Dirk Maiwald,2 Martin Ulmke,3 and Gary Wood4 1 NATO

Undersea Research Centre (NURC), Viale S. Bartolomeo 400, 19126 La Spezia, Italy cables GmbH, Schanzenstraße 6-20, 51063 Köln, Germany 3 Fraunhofer FKIE, Neuenahrer Strasse 20, 53343 Wachtberg, Germany 4 Naval Systems Department, DSTL Portsdown West, Portsdown Hill Road, Fareham PO17 6AD, UK 2 nkt

Correspondence should be addressed to Frank Ehlers, [email protected] Received 23 March 2010; Accepted 23 March 2010 Copyright © 2010 Frank Ehlers et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction The maritime domain continues to be important for our society. Significant investments continue to be made to increase our knowledge about what “happens” underwater, whether at or near the sea surface, within the water column, or at the seabed. The latest geophysical, archaeological, and oceanographical surveys deliver more accurate global knowledge at increased resolutions. Surveillance applications allow dynamic systems to be accurately characterized. Underwater exploration is fundamentally reliant on the effective processing of sensor signal data. All maritime applications face the same difficult operating environment: fading channels, rapidly changing environmental conditions, high noise levels at sensors, sparse coverage of the measurement area, limited reliability of communication channels, and the need for robustness and low energy consumption, just to name a few. There are obvious technical similarities in the signal processing that have been applied to different measurement equipment, and this special issue aims to help foster cross-fertilization between these different application areas. The articles in this special issue cover the following topics: First, underwater acoustics: “Underwater broadband source localization based on modal filtering and features extraction”, “Simulation of matched field processing localization based on EMD denoising and Karhunen-Loève expansion in underwater waveguide environment,” “A relative-localization algorithm using incomplete pair-wise distance measurements for underwater applications,” “Acoustic particle detection with the ANTARES detector,” “Masking of time-frequency patterns in applications of passive underwater target detection,” “An

underwater acoustic implementation of DFT-spread OFDM,” “Low complexity iterative receiver design for shallow water acoustic channels,” and “Automatic indexing and content analysis of whale recordings and XML representation.” Second, underwater nonacoustics: “Silent localization of underwater sensors using magnetometers”, “Hausdorff-based RC and IESIL combined positioning algorithm for underwater geomagnetic navigation”, and “Realistic subsurface anomaly discrimination using electromagnetic induction and an SVM classifier”. Third, radar: “CFAR detection from non-coherent radar echoes using bayesian theory”, “Artificial neural network-based clutter reduction systems for ship size estimation in maritime radars.” Fourth, optics: “An evaluation of pixel-based methods for the detection of floating objects on the sea surface,” “Statistical real-time model for performance prediction of ship detection from micro-satellite electro-optical imagers,” “Techniques for effective optical noise rejection in amplitude-modulated laser optical radars for underwater three-dimensional imaging,” “Underwater image processing: state of the art of restoration and image enhancement methods,” and “A fully automated method to detect and segment a manufactured object in an underwater color image.”

2. Underwater Acoustics M. Lopatka et al. address the task of underwater broadband source localization based on modal filtering and features extraction. They focus on shallow water environment and broadband Ultra Low-Frequency acoustic sources. In this

2 configuration and at a long range the acoustic propagation can be described by normal mode theory. The propagating signal breaks up into a series of depth dependent modes. These modes carry information about the source position. Mode excitation factors and mode phases analysis allow, respectively, localization in depth and distance. The authors propose two different approaches to achieve the localization: multidimensional approach (using a horizontal array of hydrophones) based on frequency-wavenumber transform and monodimensional approach (using a single hydrophone) based on adapted spectral representation. For both approaches they propose first complete tools for modal filtering and then depth and distance estimators. Adding mode sign information improves considerably the localization performance in depth. They show also that an important issue is the source spectrum. They propose a simple method of source spectrum estimation and demonstrate how it can improve depth localization. The reference acoustic field needed for depth localization is simulated with a new realistic propagation model. The feasibility of both approaches is validated on data simulated in shallow water for different configurations. The performance of localization, both in depth and distance, is very satisfactory. Q. Wang et al. present a simulation of matched field processing (MFP) localization based on Empirical mode decomposition (EMD) denoising and Karhunen-Loève expansion in the underwater waveguide environment. The mismatch problem has been one of important issues of matched field processing for underwater source detection. Experimental use of MFP has shown that robust range and depth localization is difficult to achieve. In many cases this is due to uncertainty in the environmental inputs required by acoustic propagation models. The authors present a combined scheme with EMD denoising and KarhunenLoève expansion. Results on performance, robustness, and effectiveness of the proposed method are given for simulated data. K. Y. Foo et al. present a relative-localization algorithm using incomplete pairwise distance measurements for underwater applications. The task of localizing underwater assets involves the relative localization of each unit using only pair-wise distance measurements, usually obtained from time-of-arrival or time-delay-of-arrival measurements. In the fluctuating underwater environment, a complete set of pair-wise distance measurements can often be difficult to acquire, thus hindering a straightforward closed-form solution in deriving the assets’ relative coordinates. An iterative multidimensional scaling approach is presented based upon a weighted-majorization algorithm that tolerates missing or inaccurate distance measurements. Substantial modifications are proposed to optimize the algorithm, while the effects of refractive propagation paths are considered. A parametric study of the algorithm based upon simulation results is shown. An acoustic field-trial was then carried out, presenting field measurements to highlight the practical implementation of this algorithm. C. Richardt et al. present the acoustic particle detection with the ANTARES detector. The AMADEUS (Antares Modules for Acoustic Detection Under the Sea) system

EURASIP Journal on Advances in Signal Processing within the ANTARES (Astronomy with a Neutrino Telescope and Abyss environmental RESsearch) neutrino telescope is designed to investigate detection techniques for acoustic signals produced by particle cascades. While passing through a liquid a cascade deposits energy and produces a measurable pressure pulse. This can be used for the detection of neutrinos with energies exceeding 1018 eV. The AMADEUS setup consists of 36 hydrophones grouped in six local clusters measuring about one cubic meter each. The article focuses on acoustic particle detection, the hardware of the AMADEUS detector, and techniques used for acoustic signal processing. J. Sildam investigates the application of masking of timefrequency patterns in applications of passive underwater target detection. Spectrogram analysis of acoustical sounds for underwater target classification is utilized when loud nonstationary interference sources overlap with a signal of interest in time but can be separated in time-frequency (TF) domain. He proposes a signal masking method which in a TF plane combines local statistical and morphological features of the signal of interest. A dissimilarity measure D of adjacent TF cells is used for local estimation of entropy H, followed by estimation of ΔH = Htc − Hfc entropy difference, where Hfc is calculated along the time axis at a mean frequency fc, and Htc is calculated along the frequency axis at a mean time tc of the TF window, respectively. Due to a limited number of points used in ΔH estimation, the number of possible ΔH values, which define a primary mask, is also limited. A secondary mask is defined using morphological operators applied to, for example, H and ΔH. He demonstrates how primary and secondary masks can be used for signal detection and discrimination, respectively. He also shows that the proposed approach can be generalized within the framework of Genetic Programming. Y. Zhang et al. discuss the implementation of DFT-spread OFDM for underwater acoustics. The paper presents a design of DFT-spread OFDM system applied to an underwater acoustic channel. It not only combines all the advantages of a conventional OFDM system but also reduces the peakto-average power ratio of the transmit signal. Besides, the scheme spreads the information over several subcarriers as a result of the application of an additional DFT operation and leads to a diversity gain in a frequency-selective fading channel, which is one of the many challenges of communicating data through an underwater acoustic channel. Simulation results show that their proposal possess good bit-error-rate performance. The system has been tested in a real underwater acoustic channel—the experimental pool in Xiamen University. The experimental results show that the DFT-spread OFDM system can achieve better results than a simple OFDM system in a benign underwater channel. C. P. Shah et al. present a low complexity iterative receiver design for shallow water acoustic channels. An adaptive iterative receiver structure for the shallow underwater acoustic channel (UAC) is proposed using a decision feedback equalizer (DFE) and employing bit interleaved coded modulation with iterative decoding (BICM-ID) in conjunction with adaptive Doppler compensation. Experimental results obtained from a sea trial demonstrate that

EURASIP Journal on Advances in Signal Processing the proposed receiver not only reduces the inherent problem of error propagation in the DFE but also improves its convergence, carrier phase tracking, and Doppler estimation. Furthermore, simulation results are carried out on UAC, modelled by utilizing geometrical modelling of the water column that exhibits Rician statistics and a long multipath spread resulting in severe frequency selective fading and intersymbol interference (ISI). It has been demonstrated that there is a practical limit on the number of feedback taps that can be employed in the DFE and data recovery is possible even in cases where the channel impulse response (CIR) is longer than the span of the DFE. The performance of the proposed receiver is approximately within 1 dB when compared with the performance of the system employing DFE-turbo-BICM, however, at much lower computational complexity and memory requirements, features that are attractive for real-time implementation. F. Bénard et al. address the task of automatically indexing and analyzing whale recordings leading to an XML representation. The paper focuses on the robust indexing of sperm whale hydrophone recordings based on a set of features extracted from a real-time passive underwater acoustic tracking algorithm for multiple vocalizing whales using four or more omnidirectional widely spaced bottom mounted hydrophones. In past years, interest in marine mammals has increased leading to the development of robust and real-time systems. Acoustic localization permits the study of whale behavior in deep water (several hundreds of meters) without interfering with the environment. The authors recall and use a real-time multiple target tracking algorithm recently developed, which localizes one or more sperm whales. Given the position coordinates, they are able to generate different features such as the speed, energy of the clicks, and Interclick-Interval (ICI). These features allow the authors to construct different markers which allow them to index and structure the audio files. Thus, the behavior study is facilitated by choosing and accessing the corresponding index in the audio file. The complete indexing algorithm is processed on real data from the NUWC1 and the AUTEC2. Their model is validated by similar results from the US Navy3 and SOEST4 Hawaii university labs in a single whale case. Finally, as an illustration, they index a single whale sound file using the extracted whale’s features provided by the tracking, and they present an example of an XML script structuring it.

3 to localize the sensors. The trajectory of the vessel and the sensor positions are estimated simultaneously using an Extended Kalman Filter (EKF). Simulations show that the sensors can be accurately positioned using magnetometers. L. Yi presents a primitive solution with novel scheme and algorithm for Underwater Geo-magnetic Navigation (UMN), which now occurs as the hot-point in the research field of navigation. UMN as an independent or supplementary technique can theoretically supply accurate locations for marine vehicles, but in practice there are plenty of restrictions for UMN’s application (e.g., geomagnetic daily variation). After analysis about the theoretical model of geomagnetic positioning in the correlation-matching mode from the viewpoint of pattern recognition, the author proposes an appropriate matching scenario and a combined positioning algorithm for UMN. The subalgorithm of Hausdorff-based Relative Correlation (RC) corresponding to the pattern classification module implements the coarse positioning, and the subalgorithm of Isograms EquidistanceSegmenting the Intersection Lines (IESILs) associated with the module of feature extraction continues the fine positioning. The experiments based on the simulation platform and the real-surveyed data both validate the new algorithm, and its efficiency and accuracy are also discussed. It can be concluded that the work introduced in the paper gives an initial and real validation of UMN’s potentiality. J. P. Fernández et al. investigate realistic subsurface anomaly discrimination by using electromagnetic induction and an SVM classifier. The environmental research program of the United States military has set up blind tests for detection and discrimination of unexploded ordnance. One such test features data collected with the EM-63 sensor at Camp Sibert, AL. They review the performance on the test of a procedure that combines a field-potential (HAP) method to locate targets, the normalized surface magnetic source (NSMS) model to characterize them, and a support vector machine (SVM) to classify them. The HAP method infers location from the scattered magnetic field and its associated scalar potential, the latter reconstructed using equivalent sources. NSMS replaces the target with an enclosing spheroid of equivalent radial magnetization whose integral it uses as a discriminator. SVM generalizes from empirical evidence and can be adapted for multi-class discrimination using a voting system. The proposed method identifies all potentially dangerous targets correctly and has a false-alarm rate of about 5%.

3. Underwater Nonacoustics J. Callmer et al. present a silent localization procedure for underwater sensors using magnetometers. Sensor localization is a central problem for sensor networks. If the sensor positions are uncertain, the target tracking ability of the sensor network is reduced. Sensor localization in underwater environments is traditionally addressed using acoustic range measurements involving known anchor or surface nodes. They explore the usage of triaxial magnetometers and a friendly vessel with known magnetic dipole to silently localize the sensors. The ferromagnetic field created by the dipole is measured by the magnetometers and is used

4. Radar H. Yamaguchi et al. propose a new constant false alarm rate (CFAR) detection method from noncoherent radar echoes, considering heterogeneous sea clutter. It applies the Bayesian theory for adaptive estimation of the local clutter statistical distribution in the cell under test. The detection technique can be readily implemented in existing noncoherent marine radar systems, which makes it particularly attractive for economical CFAR detection systems. Monte Carlo simulations were used to investigate the detection performance and

4 demonstrated that the proposed technique provides a higher probability of detection than conventional techniques, such as cell averaging CFAR (CA-CFAR), especially with a small number of reference cells. R. Vicen-Bueno et al. present artificial neural networkbased clutter reduction systems for ship size estimation in maritime radars. The existence of clutter in maritime radars deteriorates the estimation of some physical parameters of the objects detected over the sea surface. For that reason, maritime radars should incorporate efficient clutter reduction techniques. Due to the intrinsic nonlinear dynamic of sea clutter, nonlinear signal processing is needed, what can be achieved by artificial neural networks (ANNs). In the paper, an estimation of the ship size using an ANN-based clutter reduction system followed by a fixed threshold is proposed. High clutter reduction rates are achieved using 1-dimensional (horizontal or vertical) integration modes, although inaccurate ship width estimations are achieved. These estimations are improved using a 2-dimensional (rhombus) integration mode. The proposed system is compared with a CA-CFAR system, denoting a great performance improvement and a great robustness against changes in sea clutter conditions and ship parameters, independently of the direction of movement of the ocean waves and ships.

5. Optics A. Borghgraef et al. discuss the evaluation of pixel-based methods for the detection of floating objects on the sea surface. Ship-based automatic detection of small floating objects on an agitated sea surface remains a hard problem. Their main concern is the detection of floating mines, which proved a real threat to shipping in confined waterways during the first Gulf War, but applications include salvaging, searchand-rescue, and perimeter or harbour defense. Detection in infrared (IR) is challenging because a rough sea is seen as a dynamic background of moving objects with size order shape and temperature similar to those of the floating mine. They have applied a selection of background subtraction algorithms to the problem, and they show that recent algorithms such as ViBe and behaviour subtraction, which take into account spatial and temporal correlations within the dynamic scene, significantly outperform the more conventional parametric techniques, with only little prior assumptions about the physical properties of the scene. F. D. Lapierre et al. present a statistical real-time model for performance prediction of ship detection from microsatellite electro-optical imagers. For locating maritime vessels longer than 45 meters, such vessels are required to set up an Automatic Identification System (AIS) used by vessel traffic services. However, when a boat is shutting down its AIS, there are no means to detect it in open sea. They use Electro-Optical (EO) imagers for noncooperative vessel detection when the AIS is not operational. As compared to radar sensors, EO sensors have lower cost, lower payload, and better computational processing load. EO sensors are mounted on LEO microsatellites. They propose a realtime statistical methodology to estimate sensor Receiver

EURASIP Journal on Advances in Signal Processing Operating Characteristic (ROC) curves. It does not require the computation of the entire image received at the sensor. The authors then illustrate the use of this methodology to design a simple simulator that can help sensor manufacturers in optimizing the design of EO sensors for maritime applications. R. Ricci et al. apply techniques for effective optical noise rejection in amplitude-modulated laser optical radars for underwater three-dimensional imaging. Amplitudemodulated (AM) laser imaging is a promising technology for the production of accurate three-dimensional (3D) images of submerged scenes. The main challenge is that radiation scattered off water gives rise to a disturbing signal (optical noise) that degrades more and more the quality of 3D images for increasing turbidity. The authors summarize a series of theoretical findings that provide valuable hints for the development of experimental methods enabling a partial rejection of optical noise in underwater imaging systems. In order to assess the effectiveness of these methods, which range from modulation/demodulation to polarimetry, they carried out a series of experiments by using the laboratory prototype of an AM 3D imager (λ = 405 nm) for marine archaeology surveys, in course of realization at the ENEA Artificial Vision Laboratory (Frascati, Rome). The obtained results confirm the validity of the proposed methods for optical noise rejection. R. Schettini et al. discuss the state of the art of restoration and image enhancement methods for underwater images. The underwater image processing area has received considerable attention within the last decades, showing important achievements. They review some of the most recent methods that have been specifically developed for the underwater environment. These techniques are capable of extending the range of underwater imaging, improving image contrast and resolution. After considering the basic physics of the light propagation in the water medium, the authors focus on the different algorithms available in the literature. The conditions for which each of them has been originally developed are highlighted as well as the quality assessment methods used to evaluate their performance. C. Barat et al. present a fully automated method to detect and segment a manufactured object in an underwater color image. They propose a fully automated and active contoursbased method for the detection and the segmentation of a moored manufactured object in an underwater image. Detection of objects in underwater images is difficult due to the variable lighting conditions and shadows on the object. The proposed technique is based on the information contained in the color maps and uses the visual attention method, combined with a statistical approach for the detection and an active contour for the segmentation of the object to overcome the above problems. In the classical active contour method the region descriptor is fixed and the convergence of the method depends on the initialization. With their approach, this dependence is overcome with an initialization using the visual attention results and a criterion to select the best region descriptor. The approach improves the convergence and the processing time while providing the advantages of a fully automated method.


Acknowledgments The guest editors of this special issue are much indebted to their authors and reviewers, who put a tremendous amount of effort and dedication to make this issue a reality. Frank Ehlers Warren Fox Dirk Maiwald Martin Ulmke Gary Wood

5


Research Article Underwater Broadband Source Localization Based on Modal Filtering and Features Extraction Maciej Lopatka,1 Grégoire Le Touzé,1 Barbara Nicolas,1 Xavier Cristol,2 Jérôme I. Mars,1 and Dominique Fattaccioli3 1 GIPSA-Lab,

Department of Image Signal, 961 rue de la Houille Blanche, 38402 St Martin d’Heres, France Underwater Systems S.A.S., 525 Route des Dolines BP 157, 06903 Sophia-Antipolis Cedex, France 3 CTSN-DGA Centre Technique des Systmes Navals, avenue de la Tour Royale BP 40915, 83050 Toulon Cedex, France 2 THALES

Correspondence should be addressed to Maciej Lopatka, [email protected] Received 7 July 2009; Accepted 11 January 2010 Academic Editor: Gary Wood Copyright © 2010 Maciej Lopatka et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Passive source localization is a crucial issue in underwater acoustics. In this paper, we focus on shallow water environment (0 to 400 m) and broadband Ultra-Low Frequency acoustic sources (1 to 100 Hz). In this configuration and at a long range, the acoustic propagation can be described by normal mode theory. The propagating signal breaks up into a series of depth-dependent modes. These modes carry information about the source position. Mode excitation factors and mode phases analysis allow, respectively, localization in depth and distance. We propose two different approaches to achieve the localization: multidimensional approach (using a horizontal array of hydrophones) based on frequency-wavenumber transform (F-K method) and monodimensional approach (using a single hydrophone) based on adapted spectral representation (FTa method). For both approaches, we propose first complete tools for modal filtering, and then depth and distance estimators. We show that adding mode sign and source spectrum informations improves considerably the localization performance in depth. The reference acoustic field needed for depth localization is simulated with the new realistic propagation modelMoctesuma. The feasibility of both approaches, F-K and FTa , are validated on data simulated in shallow water for different configurations. The performance of localization, in depth and distance, is very satisfactory.

1. Introduction Passive source localization in shallow water has attracted much attention for many years in underwater acoustics. In this environment and for Ultra-Low Frequency waves (1 to 100 Hz, denoted further ULF) classical beamforming techniques are inappropriate because they do not consider multipath propagation phenomena and ocean acoustic channel complexity. Indeed, ULF acoustic propagation in shallow water waveguides is classically based on normal mode theory [1]. ULF band is very attractive for detection, localization, and geoacoustical parameter estimation purposes, because propagating acoustic waves are almost not affected by absorption and thus can propagate at very long ranges. In this context, mainly two approaches are used: Matched-Field Processing (denoted MFP) [2, 3] and Matched-Mode Processing (denoted MMP) [4–6]. The com-

parative study of both approaches is given in [7]. MatchedMode approach can be considered as MFP combined with modal decomposition. The main difference is that MFP operates in receiver space and MMP in mode space. Both methods require a reference acoustic field (replica field) to be compared, generally by correlation techniques (building and maximizing an objective function), with the real acoustic field recorded on receiver(s). Another alternative to perform source localization is to use time reversal [8] which can be seen as a broadband coherent MFP. Some experiments have been performed showing the feasibility of the method [9]. The main drawback of the method is that a numerical backpropagation has to be computed which needs a good knowledge of the environment. As MMP is less sensitive to environmental mismatches than MFP and Time Reversal methods, this technique is more interesting for practical applications, and thus is used in our approach to estimate

2 the source depth. The access to modes not only allows estimation of mode excitation factors for depth localization, but also gives the possibility to analyze mode phase to extract information about the source distance. As a result, in this paper depth estimation is performed using MMP on the mode excitation factors and distance estimation is achieved by mode phase analysis. Consequently, the main issue to perform underwater localization for ULF sources in shallow water is to develop signal processing methods to accomplish modal filtering. These methods should be based on physics of wave propagation in waveguides, to be adapted to signals propagating in shallow water environment. In this context, we propose two complementary techniques to localize broadband impulsive source in depth and distance. The first method based on frequency-wavenumber transform and denoted F-K is a multidimensional approach based on array processing. The second method based on adapted Fourier transform and denoted FTa is a monodimensional technique used on a single hydrophone. Traditionally, matched-mode localization was applied on vertical line arrays (VLAs), and mode excitation factors were extracted by a spatial integration of pressure field. As proposed in [10, 11], we record the signal (represented in the space: radial distance r and time t) on a horizontal line array (HLA), as it is generally more practical in real applications (towing possibility, faster deployment, and stability). In this configuration, modes can be filtered in the frequencywavenumber plane ( f -k), which is a two-dimensional Fourier transform of radial distance-time section (signal r-t). For the mono-dimensional approach, modes cannot be filtered by conventional modal filtering techniques. As modes have nonstationary properties, the only way to filter modes is to integrate modal time-frequency characteristics [12] into modal filtering. The main idea is to deform a signal in such way that nonlinearities in the time-frequency plane become linear (according to the frequency domain). Consequently, the signal becomes stationary and classical filtering tools can be used to filter modes. Hereby, modal filtering in mono-dimensional configuration is done in an adapted frequency domain (Pekeris Fourier transform). The classical and adapted frequency domains are related by the unitary equivalence formalism [13]. After a brief presentation of modal propagation theory, we give a short description of the simulator Moctesuma-2006, which is used for simulation of acoustic replica fields and acoustic parameter computation. Then, we present details about the experimental configuration. Next, we describe mode filtering methods in the mono- and multidimensional cases to finally present estimators used for depth and distance localization. Finally, results of distance and depth localization for mono and multidimensional method are presented on simulated data.

2. Modal Propagation and Modes Acoustic propagation of Ultra-Low Frequency waves in shallow water waveguide can be modeled by normal mode theory. Propagating signal at long range is composed of

EURASIP Journal on Advances in Signal Processing dispersive modes. These modes are analyzed for depth (matched-mode processing) and distance (mode phase processing) localization. To demonstrate very succinctly the idea of localization using modes, we introduce the simplest model of oceanic waveguide—the perfect waveguide. Even if this model is a simplification of real complex waveguides, it reflects the most important waveguide phenomena: modal decomposition of the propagated signal. The perfect waveguide model is made of a homogeneous layer of water between perfectly reflecting boundaries (a pressure release surface and a rigid sea bottom). The water layer is characterized by depth D, velocity V1 , and density ρ1 . We consider an omnidirectional point source located at depth zs and at distance 0 radiating a signal s(t). The acoustic pressure field P(r, z, t) received at a reception point of coordinates (r, z), where r and z are, respectively, horizontal distance and depth, can be expressed by

P(r, z, t) =

f

p r, z, f · e−2iπ f t df ,

(1)

where t is the time, f is the frequency, and p(r, z, f ) satisfies the general Helmholtz equation. Using variable separation (in depth and in range) and boundaries conditions [1], the pressure p at long range becomes a sum of modes

p r, z, f = A · S f ·

∞

e−2iπkrm r ψm (zs )ψm (zr ) krm r m=1

(2)

with A a constant, S( f ) the source spectrum, ψm the modal function of mode m, and krm the horizontal spatial frequency of mode m. The spatial frequency k is defined by k = f /V1 and it corresponds to the classical wavenumber divided by 2π. In the following, for the sake of simplicity, we will call k the wavenumber with its horizontal and vertical components kr and kz (instead of spatial frequency). The mode wavenumber spectrum is discrete and each mode is associated with an unique wavenumber. The amplitude ψm (zs ) is a function of the source depth zs :

ψm (zs ) =

2 sin(kzm zs ) D

(3)

with kzm = (2m − 1)/4D. This short theoretical introduction of normal mode theory made on the example of perfect waveguide exposes the principle used for source depth estimation; mode amplitudes depend on source depth zs by the factor ψm (zs ). Then, let us demonstrate very shortly the principle of mode phase processing for distance estimation. Modes contain, besides depth information, also distance information about the source. This information is contained in mode phase. The phase of mode m at frequency f is defined by

Φm f =

π + φs f + 2π f t0 4

+ φ ψm (zs ) + φ ψm (zr ) + krm f r,

(4)

EURASIP Journal on Advances in Signal Processing Bathy: Mediterranean Sea-summer

0

Depth (m)

3

50

100 130 1505

1510

1515 1520 1525 Sound speed (m/s)

1530

1535

Figure 1: Sound speed profile of the water column for Mediterranean Sea in summer.

where (i) φs ( f ) is the phase of the source at frequency f ; (ii) 2π f t0 is a phase factor due to time delay t0 of the recorded signal; (iii) φ(ψm (zs )) depends on the modal function sign at the source depth zs ; it is π if ψm (zs ) < 0 and 0 if ψm (zs ) ≥ 0; (iv) φ(ψm (zr )) depends on the modal function sign at the receiver depth zr ; (v) krm ( f )r is a phase factor at frequency f linked to the propagation distance r between source and receiver. As one can notice, modal decomposition is a very useful theory for acoustic propagation in oceanic waveguide. Indeed, MMP uses this decomposition to perform localization [14]. In this section we demonstrated that by having access to modes, and more precisely to their excitation factors and phases, it is possible to localize source in depth and in distance. Moctesuma-2006. To perform the depth estimation using MMP, we need an acoustic model to generate replica fields. Several classical underwater acoustic propagation models exist in the literature and are used according to the seabed depth, the source range, and the frequency band. Models are based on different theories: ray theory, parabolic equation modeling, normal mode models, and spectral integral models [1]. Among the different models we choose the numerical model Moctesuma-2006—a realistic underwater acoustic propagation simulator developed by Thales Underwater Systems [15]. For the sake of simplicity Moctesuma2006 will be called further Moctesuma. This model, based on normal mode theory, simulates an underwater acoustic propagation for range-dependent environments. It is well adapted to transient broadband ULF signals for shallow and deep water environments. Moreover, we choose Moctesuma as it provides the acoustic parameters of the environment (wavenumbers) and the full acoustic field (time-series) [16]. The transmitted transient signal is first split into narrow subbands signals through a set of bandpass filters. Each

subband is associated with a central frequency for which acoustic modes are fully computed. For each mode in each subband, propagation consists in delaying the original signal. The summation is performed in the time domain, so the signal causality is necessarily satisfied. Moctesuma considers different acoustic signal phenomena such as penetration, elasticity, multiple interactions inside multilayered sea bottoms and water. The time and space structure of waves is analyzed beyond simple wavefronts and Doppler effect (moving source and/or receiver). A set of parameters is necessary to make a simulation with Moctesuma. The first parameter group concerns a description of the environment. As it is a range-dependent model, parameters are given for each environment sector. User has to provide following environmental parameters: sea state, temperature, sound speed profile, seabed type (or precise seabed structure). The second parameter group concerns the input signal and the experiment configuration (coordinates, depths, speeds and caps of the source and the antenna, antenna’s length, and sensors’ number). In our analysis, we use Moctesuma to simulate the reference acoustic field (in the MMP) and to access the acoustic parameters of the environment such as horizontal wavenumbers, group velocities, and mode excitation factors signs.

3. Experimental Configuration 3.1. Environment. The analysis presented in this paper is done in a simulated shallow water environment located in the Mediterranean Sea during a summer period. The environment is range independent with a water depth of 130 m. The sound speed profile of the water column (Figure 1) is characterized by a strong negative gradient of approximately 25 m/s. The highest gradient is located in the first half of the water column. The seabed parameters are presented in Figure 2. Modal functions no. 1 to 9 of the studied environment are presented in Figure 3. 3.2. Signal Sources and Reception Configurations. In this paper we consider two impulsive broadband sources in the ULF band: the first one ULF-1 lasts several tens of milliseconds and has a flat spectrum; the second source ULF-2 lasts several hundreds of milliseconds and is made

EURASIP Journal on Advances in Signal Processing 0

0

1

1

1

2

2

2

3

3

3

4

4

4

5 6

Depth (m)

0

Depth (m)

Depth (m)

4

5 6

5 6

7

7

7

8

8

8

9

9

9

10

10

1650 1750 · · · 6000 P-wave velocity (m/s)

10

0

0.5 1 P-wave attenuation (dB/m/kHz)

(a)

1

2 Density (kg/m3 )

(b)

3

(c)

0

0

20

20

20

40

40

40

60 80

Depth (m)

0

Depth (m)

Depth (m)

Figure 2: Vertical structure of the seabed: P-wave velocity (a), P-wave attenuation (b) and density (c).

60 80

60 80

100

100

100

120

120

120

−0.2

0 0.2 Amplitude

−0.1

Mode 1 Mode 2 Mode 3 (a)

0 0.1 Amplitude Mode 4 Mode 5 Mode 6 (b)

−0.1

0 0.1 Amplitude Mode 7 Mode 8 Mode 9 (c)

Figure 3: Theoretical modal functions no. 1 to 9 based on Moctesuma’s modelization. The frequency-dependent functions are calculated as a mean over frequency band 1 to 100 Hz.

of four band signals (“4 hills” spectrum). Both signals are presented in temporal and spectral domains in Figure 4. The source ULF-1 is used to validate the methods in a simple case. For a more complex situation source ULF-2 is then used in Section 6.3. Signals radiated by source are recorded on a horizontal line array (HLA) after acoustic propagation. The HLA is 800 m long and is composed of 240 omnidirectional equispaced hydrophones (separated by 3.347 m). The sampling frequency is 250 Hz. The experimental configuration is given on Figure 5. Three different source depths zs are studied: 40 m, 70 m, and

105 m. The horizontal distance between the source and the first sensor of HLA is equal to 10 km. The HLA is located on the sea bottom (zHLA = D). The HLA can be located at any depth, but this information has to be known. In our simulations the source and the HLA are motionless.

3.3. Data. Moctesuma simulator provides a section of the pressure recorded on the HLA P(r, zHLA , t) denoted signal r − t for the sake of simplicity in the following. It is a sampling of the pressure field in radial distance r and in time t. The size of the data is defined by


5 5 Amplitude

Amplitude

1 0.5 0 −0.5

50

100 150 200 250 300 350 400 Time (ms)

0 −5

450 500

50

100 150 200 250 300 350 400 Time (ms) (b)

Amplitude (dB)

Amplitude (dB)

(a)

0 −10 −20 −30

0

450 500

50

100

150

0 −20 −40 −60

0

20

40

Frequency (Hz)

60 80 Frequency (Hz)

(c)

100

120

(d)

Figure 4: ULF sources: waveforms and spectrums. The first signal (a) and (c), denoted as ULF-1, is a flat spectrum transient. The second signal (b) and (d), denoted as ULF-2, is a broadband comb-type (“4 hills” spectrum) transient.

0

zs D Depth z

zHLA

rHLA

Distance r

Source

L

Water HLA: NH receivers Sea bottom

Figure 5: Experimental configuration.

(i) number of hydrophones (traces) Nr ; (ii) duration and frequency sampling of the recording (number of samples nt ). The “real data” is obtained by adding a white bidimensional (in time and in space) Gaussian noise to the simulated data. Several signal-to-noise ratios (SNRs) are considered.

4. Filtering Methods In this paper, source localization in depth and distance is performed either by multi-dimensional or by monodimensional approach. The first one will be called F-K approach (as the method operates in the frequencywavenumber domain f -k) and the second one FTa approach (as the method is based on adapted Fourier transform). They both achieve modal filtering which is described in this section. For the first approach, in the frequency-wavenumber plane ( f -k) modes are separated and thus can be filtered. In the second approach, which is theoretically more difficult as we have a single hydrophone, modes are not easily separable and thus, cannot be filtered using classical signal

representations such as Fourier transform or time-frequency representation. As proposed in [12, 17], we use an adapted frequency representation in which modes are separable and consequently can be filtered. 4.1. Multi-Dimensional Approach. In the multi-dimensional case, the radial distance-time section P(r, t) is represented in the frequency-wavenumber plane f -k. The transformation, called F-K transform and denoted by P(kr , f ), is linked to P(r, t) via a two-dimensional Fourier transform (in radial distance r and in time t). The F-K transform of the signal P(r, t) is defined by

P f k kr , f =

t

r

P(r, t)e−2iπ( f t−kr r) dtdr .

(5)

To improve dynamics of modal representation and avoid spatial aliasing in the f -k plane, a Vref velocity correction on the section P(r, t) is applied before calculating F-K transform [11] (classical preprocessing technique used in array processing). This operation consists in applying to every trace of the section a time shift, so that the direct wave (traveling with speed Vref , equal to V1 in the perfect waveguide) arrives at every sensor at the same time (giving an apparent infinite velocity). Let us denote X(kr , f ) the F-K representation of the section x(r, t). Then, F-K representation of the section after velocity correction y(r, t) = x(r, (t + r)/Vref ) is

kr + f ,f . Y kr , f = X Vref

(6)

The consequence of this processing is a shifting of every point in the f -k plane in such way that the spatial aliasing is canceled and the representation space of modes is much larger (greater dynamics, simpler filtering).

6

EURASIP Journal on Advances in Signal Processing Dispersion curves Modes: 1–10 Cut at Vmax = 6000 (m/s)

Dispersion curves Modes: 1–10 Cut at Vmax = 2000 (m/s)

100

100

80

80

Frequency (Hz)

120

Frequency (Hz)

120

60

60

40

40

20

20

0

−0.03

−0.025

−0.02

−0.015

krm

−0.01

0

−0.005

−0.03

−0.025

−0.02

(m−1 )

(a)

−0.015 krm (m−1 )

−0.01

−0.005

(b)

Figure 6: Moctesuma’s dispersion curves no. 1 to 10 in frequency-wavenumber domain after Vref velocity correction (in plot, the mode number increases from (b) to (a)). Wavenumbers in (a) correspond to all propagating modes (water and seabed), and these in (b) plot correspond only to modes propagating in the water column.

Representation F-K Frequency-wavenumber

120

120

100

100 Frequency (Hz)

Frequency (Hz)

Representation F-K Frequency-wavenumber

80 60 40 20

80 60 40 20

0

−0.01

−0.006

−0.002

0.002 Wavenumber (m−1 )

0.006

0.01

0

−0.01

−0.006

−0.002

0.002 Wavenumber (m−1 )

(a)

0.006

0.01

(b)

Figure 7: F-K transforms of sections r-t simulated with source ULF-1 at 105 m (a) and source ULF-2 at 70 m (b).

If we consider a white broadband source radiating a transient signal in a perfect waveguide, the F-K transform of the pressure signal (see (2)) received on the HLA, at long range, can be approximated by Pfk

∞ kr , f ≈ B f · ψm (zs )ψm (z)δ(kr − krm ) m=1

(7)

with B( f ) a frequency dependent constant related to the source spectrum. The theoretical modal signal energy is located on the mode dispersion curves kr (m, f ) = krm ( f ) (the form of the mode dispersion curves is given in Figure 6). As one can notice, for each frequency the wavenumber spectrum is discrete. The F-K representations of two data sets are given in

Figure 7. The first plot shows a simulation done with signal ULF-1 (flat spectrum) at depth 105 m. The energy is spread across all the frequency band. The second plot presents a simulation with signal ULF-2 (“4 hills” spectrum) at depth 70 m. The F-K representation reflects exactly the spectrum of the source signal (see Figure 4). As the HLA is located at a known depth, values of the factors ψm (z) are known. For HLA located on the sea bottom |ψm (z)| ≈ 1 and expression (7) can be rewritten as P f k kr , f ≈ B f ·

∞ ψm (zs ) · δ(kr − krm ).

(8)

m=1

The amplitude of the F-K transform for each curve (dispersive mode) depends only on the mode excitation factor


7 Masks Modes: 1–14 120 100 f (Hz)

modulus. We use these curves to estimate the excitation factor modulus of each mode. For a perfect waveguide model there is no frequency dependence for modal functions, which is the case in reality. Therefore, excitation factor of mode m is estimated as the mean value across the frequency domain. Moreover, mode excitation factors at the bottom interface are not exactly equal to 1 and will slightly modify the estimation of the mode amplitude at the source depth. This phenomenon does not affect the result as the same methodology is applied for the replica data.

80 60 40 20 0

Mm kr , f =

dkm d f

−0.02

−0.015

−0.01 krm (m−1 )

−0.005

0

Figure 8: Set of binary masks in the f -k domain built from dispersion curves given in Figure 6 by bi-dimensional dilatation process. The set is complete for the studied environment.

100

f (Hz)

Mask Construction. Once F-K representation of the signal is calculated, a mask filtering has to be applied to filter modes. The mask is a binary image (with the same size as the F-K transform) and is used to extract a mode by a simple multiplication in the f -k domain. The mask built for each mode should “cover” the region occupied by this mode in the f -k plane. An initial mask of mode m is created using its wavenumbers. These can be computed theoretically by a propagation model if the environmental parameters are known. In our case they are given by Moctesuma (see Figure 6). Then, the mask of mode m is dilated independently in both domains (frequency and wavenumber) with the dilation parameter dk,m f = [dkm , d f ] according to the following formula:

−0.025

50

δ kr − krm f ± d f · Δ f ± dkm · Δk , (9)

dkm

where and d f denote, respectively, dilation sizes in wavenumber (dkm ∈ {1, . . . , dkmmax }) and frequency (d f ∈ {1, . . . , d fmax }) domains, and Δk and Δ f denote, respectively, the sampling period in wavenumber and frequency domains. The first parameter dkm determines the distances between successive masks (depends on mode number m) and the second parameter d f defines the distance of the mask for mode 1 to the frequency 0 Hz. This definition of dilation parameters makes the mask width in the frequency dimension adapted to the frequency (narrower masks at high frequencies for lower number modes and larger masks at lower frequencies for higher number modes). The dilation process is restricted by limitation that the masks for different modes must not overlap. These masks allow an efficient filtering even for higher modes which are usually more difficult to filter. The simulated environment has to be as close as possible to the real environment to achieve a good filtering of modes. Moreover, it is necessary to dilate the previous theoretical mask for two reasons: (i) the limited HLA length-mode energy spreads around dispersion curves in the f -k plane; (ii) the mismatch between real and simulated environments [11]. A total set of masks for the studied environment is given in Figure 8. This set contains 14 masks which corresponds to the total number of propagating modes in this environment. An example of the mask adapted to mode no. 4 is given in

0

−0.01

−0.005 krm (m−1 )

0

Figure 9: Binary mask used to filter mode no. 4.

Figure 9. The mask of mode no. 4 is built starting from its dispersion curve (see Figure 6, 4th trace counting from right to left) and then dilated according to (9). The energy spectrum of data in Figure 7 (a) is shown in Figure 10. For each mode the energy is calculated as a mean of the f -k region where this mode is present (after mask filtering). In Figure 11 we present the result of the mode filtering for modes nos. 1, 4 (mode with very low energy), and 6 (the mode with the highest energy). 4.2. Monodimensional Approach. In the mono-dimensional configuration, classical signal representations such as Fourier transform or short-time Fourier transform are not suited for description of a signal that can be decomposed in a sum of dispersive modes (nonstationary and nonlinear timefrequency patterns). Therefore, these techniques cannot correctly represent the signal having modal structures (see Figures 12(a) and 13(a)). This signal processing problem has attracted much interest for the last decades [13, 18, 19]. In this paper we based our monosensor approach on works [12, 17, 20]. The idea is to find a representation well adapted for modal signal structure to achieve modal filtering. The best way is to take into account the physics of oceanic

8


Normalised energy

1

As a result, the pressure signal of the perfect waveguide model is defined by

0.8

pparf (t) =

0.6

gm (t)e2πiνc (m)ξ(t)

m

0.4 0.2 0

1

2

3

4

5 6 7 8 Mode number

9

10

Figure 10: Energy spectrum in modal space (for modes no. 1 to 10).

waveguide propagation and build a representation adapted to the signal structure in the same way as Fourier transform is adapted to a monochromatic signal. Here, we discuss only an adapted frequency representation FTa . However, on the same rule an adapted time-frequency representation can be constructed and used [12, 17]. The adapted processing tools are based on the combination between acoustic wave propagation (waveguide propagation law) and signal processing theory (unitary equivalence). Building of the adapted frequency representation is based primary on definition of the unitary operator of transformation adapted to guided waves. This unitary operator is linked to the dispersion law νm = f (t), where ν is the instantaneous frequency and t is the time. For a perfect waveguide model and for each mode m the dispersion law is defined by parf νm (t) =

(2m − 1)V1 t

4D t 2 − (r/V1 )2

,

(10)

parf

φm (t) = 2π

t

parf

νm (t)dt

(2m − 1)V1 t2 − r = 2π 4D V1

2

(11)

= 2πνc (m)ξ(t)

with νc (m) the cut-off frequency of mode m defined by νc (m) =

(2m − 1)Vref . 4D

(12)

ξ(t) is called the general dispersive function and is defined as follows: 2 r 2 t − . ξ(t) =

V1

with gm (t) the envelope evolution of mode m. The unitary operator of transformation should transform nonlinear mode structures in linear ones (in time-frequency domain), and thus allow the use of classical Fourier filtering techniques. In construction of such representation, the unitary equivalence formalism is used [13]. One of the unitary operators is a warping operator Ww (applied to a signal x(t)) defined as follows: ∂w(t) 1/2 · x[w(t)]. ∂t

(Ww x)(t) =

(13)

(15)

The function w(t) has to be derivable and bi-univocal, and function w−1 (t) has to exist. The operator Ww is applied to the signal in order that (Ww pparf )(t) becomes a sum of linear structures

Ww p

parf

∂w(t) 1/2 Cm e2πiνc (m)ξ[w(t)] . (t) = ∂t

(16)

m

To do so, we deduce from (16), the deformation function w(t) defined on R+ → D f

r2 −1 2 (t) w(t) = ξ = t + 2 .

V1

(17)

Finally, the unitary operator of transformation adapted to a perfect waveguide is

where V1 is the sound speed in water, D is the waveguide depth, t is the time, and r is the distance. This relation defines temporal domain of group delay D f = (R+ /V1 , +∞], where R+ /V1 is arrival time of the wavefront. Starting from the dispersive relation given in 10, the instantaneous frequency νm is the derivative of the instanparf taneous phase φm (t):

(14)

Ww p

parf

(t) =

∂w(t) 1/2 2πiνc (m)t . ∂t Cm e

(18)

m

Note that this tool is reversible, so one can go back to the initial representation space (time or frequency). In this short presentation of adapted transformation for the perfect waveguide we demonstrated the principal idea of this technique which consists in transformation of modes into linear structures. In our work we use a method adapted to Pekeris waveguide model, as it is a more complex model (closer to reality) taking into account the interaction with the sea bottom (described in details in [12]). As the non-linear time-frequency signal structures become linear after this transformation, the signal becomes stationary (see Figures 12(b) and 13(b)). In this case, one can use classical frequency filtering tools to filter modes. The modal filtering is then done in the adapted frequency domain (Pekeris frequency) by a simple bandpass filtering defined by the user.

5. Estimators In Section 4 we demonstrated how extracting modes from the recorded signal by multi and mono-dimensional approaches. In this section we discuss depth and distance


9

Filtered Mode 1

Filtered Mode 4

Filtered Mode 6

100

100

100

80

80

80

60

f (Hz)

120

f (Hz)

120

f (Hz)

120

60

60

40

40

40

20

20

20

0

−0.01

−0.005

0

−0.01

−0.005

0

krm (m−1 )

krm (m−1 )

−0.005 krm (m−1 )

(a)

(b)

(c)

0

−0.01

0

0

Figure 11: Modes nos. 1, 4, and 6 extracted from F-K representation given in Figure 7(a) by mask filtering.

60 Pekeris frequency (Hz)

Frequency (Hz)

150

100

50

0

0.2

0.3

0.4 0.5 Time (s)

0.6

50 40 30 20 10 0

0.7

1

(a)

1.5 2 Pekeris time (s)

2.5

3

(b)

Figure 12: Classical STFT and adapted STFT (matched to Pekeris model) of a signal recorded on a single hydrophone. The simulation is given for the source ULF-1 at 40-m depth and 10 km distant from hydrophone.

Classical FT modulus

100

Adapted FT Modulus Warping −→ Pekeris model

140 120

80 Amplitude

Amplitude

100 60 40

80 60 40

20 0

20 0

20

40

60 80 Frequency (Hz) (a)

100

120

0

0

10

20 30 40 Pekeris frequency (Hz)

50

60

(b)

Figure 13: Classical Fourier spectrum and adapted Fourier spectrum of a signal recorded on a single hydrophone (the same as in Figure 12).

10

EURASIP Journal on Advances in Signal Processing Table 1: Values of Δφ(m, n, z).

Table 2: Absolute mode sign choice rule: the absolute sign of mode n Sabs (n, zs ) depends on the absolute sign of mode m Sabs (m, zs ) and n, zs ) (where n > m). the pass function Δφ(m,

Sign of ψn (z) Sign of ψm (z)

−

+ 0 π

+ −

Δφ(m, n, zs ) 0 π 0 π

Sabs (m, zs ) + +

π 0

−

estimators based on modal processing. For depth estimation, we use a matched-mode technique, and for distance estimation our approach is based on mode phase analysis. For both approaches, F-K and FTa , we use the same estimators for localization in depth and distance. The only difference is the representation space of modal filtering: frequencywavenumber for F-K method and adapted Fourier spectrum for FTa method. 5.1. Range Estimation. The range estimation is combined with the mode sign estimation; therefore we call the estimator sign-distance estimator. The estimator applied only on the real data is based on mode phase analysis and calculates a cost function C based on two mode phases (m and n, where n > m) extracted from the data. Modes are not necessarily consecutive; however their numbers and associated wavenumbers (calculated by Moctesuma) have to be known. The sign-distance estimator is originally based on a work published in [20]. We present this estimator very succinctly, more details can be found in [21]. The principle is based on the definition of mode phase given in (4). To suppress the unknown parameters in this equation, the initial estimator ΔΦ uses the difference between two mode phases:

ΔΦ m, n, f = Φm f − Φn f

= Δφ(m, n, zs )+Δφ(m, n, zHLA )+rΔkr m, n, f

(19) with

−

Δφ(m, n, z) = φ ψm (z) − φ ψn (z)

= πδsign(ψm (z)),− sign(ψn (z)) (mod(2π)),

(20)

(ii) Δkr (m, n, f ) = krm ( f ) − krn ( f ). The estimation is done in sequential way; that is, superior mode signs (of order n) are estimated using inferior mode signs (of order m). The starting point is the absolute mode sign of mode no. 1 which is always positive: Sabs (1, zs ) → +. For example to estimate the sign of mode n = 5, one can use in theory modes m = {1, 2, 3, 4}. As the frequency band shared by two modes (m and n) has to be maximized for the estimation performance, we propose the following rule to

− −

+

choose inferior mode number (m) for estimation of superior sign mode number (n): m = {n − 3, n − 2, n − 1}.

(21)

The sign of Δφ(m, n, zHLA ) is known as the depth z of HLA is known (in our case it is D). To estimate mode signs for real data, for each frequency f the quantity ΔΦexp is measured, and then we calculate the cost function C defined as

C r, Δφ(m, n, zs ) =

2 d(ΔΦexp (m, n, f ), ΔΦ(m, n, f ) , f

(22) where d is the distance function defined as

d φ1 , φ2 = arg exp i φ1 − φ2

(23)

with arg defined on a basic interval (−π, π]. The signdistance estimator is found by the minimization of the cost function C:

r, Δφ(m, n, zs ) =

arg min

C r, Δφ(m, n, zs ) , (24)

r,Δφ(m,n,zs )={0,π }

where r ∈ rmin , rmax and Δφ(m, n, zs ) =

(i) Δφ(m, n, z) being difference between two mode phases at depth z; the values of this parameter are defined by (for details see Table 1):

Sabs (n, zs ) +

⎧ ⎨0 ⎩

π

if modes m and n have the same signs, if modes m and n have opposite signs. (25)

The sign-distance estimator is calculated for 2 possible values of Δφ(m, n, zs ): 0 and π. By minimizing C, we find the searched value of Δφ(m, n, zs ) (using (25), the relative sign between modes m and n is estimated) and also the distance. As we know the absolute sign Sabs (m, zs ) of inferior mode m (known or estimated in previous step of estimation) and n, zs ) betwen the estimated value of the pass function Δφ(m, modes m and n, we can find the absolute sign of mode n → Sabs (n, zs ). The rule of mode sign estimation is given in Table 2. The mode sign estimation for N mod = K takes at least K − 1 steps as the first mode sign is always positive and as the estimator works sequentially on mode couples. 5.2. Depth Estimation. Source depth estimation is based on Matched-Mode Processing. The principle of MMP is

EURASIP Journal on Advances in Signal Processing Ambiguity function (dB) −→ without mode signs Mode number : 5, fHz ∈ (5, 95)

11 Ambiguity function (dB) −→ with mode signs Mode number : 5, fHz ∈ (5, 95)

50

120

50

120

45

45

40

40 100

35 80

30 25

60 20 40

15

Estimated depth source (m)

Estimated depth source (m)

100

35 80

30 25

60 20 40

15

10 20

10 20

5 20

40 60 80 100 Real depth source (m)

120

0

(a)

5 20

40 60 80 100 Real depth source (m)

120

0

(b)

Figure 14: Theoretical ambiguity functions for matched-mode localization. Results obtained for the set of modes 1 to 5 and frequency band (5, 95) Hz. In (a) the contrast function G is calculated at the basis of mode excitation factor modulus, and in (b) the mode sign information is integrated.

to compare modes in terms of excitation factors extracted from the real data with those extracted from the replica fields. The modeled acoustic field (replica) is simulated with Moctesuma. The depth estimator is based on a correlation which measures a distance between mode excitation factors estimated from real and from simulated data (for a set of investigated depths). The depth for which this correlation reaches maximum (the best matching) is chosen as the estimated source depth. The mode excitation factors are extracted by F-K or TFa approach on real and replica data in the same manner. They are positive as they are extracted from positive value spaces (F-K transform or modulus of the adapted Fourier transform). Their signs are then obtained using the signdistance estimator presented in the previous section. The mode signs are estimated only for real data. For the reference data, as the simulations are done for a set of determined source depths, mode signs are known. The combination of mode excitation factors with mode signs allows canceling secondary peaks in the correlation function. These peaks are due to “mirror solutions” of modal functions for some depths when considering only mode excitation factor modulus (see Figure 14). Therefore, adding mode sign information to mode excitation factor modulus improves significantly the performance of depth localization (shown on examples in Section 6). The localization performance is strongly dependent of the matching accuracy between real and simulated acoustic fields. Study of the influence of environmental and system

effects on the localization performance is presented in [11, 22]. The dilation used to build masks in the f -k plane makes the method more robust against these errors. To compare mode excitation factors extracted from real and simulated data, a normalization based on the closure relationship is applied:

2 (zs ) = 1, cm

(26)

m

where cm is an excitation factor of mode m. Then, the comparison between mode excitation factors extracted from real and replica data csimul is made using the the real data cm m contrast function G: ⎛

GN mod (zs ) = −10 log⎝

N mod m=1

2 ⎞

real − csimul (z ) cm s m ⎠, N mod

(27)

where N mod is the number of analyzed modes zs = arg max GN mod (zs ). zs

(28)

The maximum of G indicates the estimated depth of the source. In matched-mode localization, modes for which the function G defined by (27) is calculated are theoretically unrestricted. However, in case of ULF localization, only the first modes are used. The upper mode number limit is given by the environment and existence of cut-off frequencies as

12


the methods presented in this paper are based on broadband signal processing. In our analysis the number of used modes is between 5 and 7. Theoretical performances of depth localization for the studied environment and for all source depths are presented in Figure 14 (each vertical line corresponds to a contrast function G). The figure presents two plots: for the method without mode signs (a) and for the method with mode signs (b). The result is obtained by the application of (27) to mode excitation factors directly taken from Moctesuma simulations. For the method without mode signs, one can notice the existence of “mirror solutions” which is a line of secondary peaks intersecting with the primary peaks line indicating the true source positions. That line does not exist for the method with mode signs, as the “mirror solutions” are cancelled by adding mode signs to mode excitation factor modulus. In such way, one can remove the localization ambiguity, which is problematic especially in low signal-tonoise conditions. 5.3. Source Spectrum Estimation. To perform matched-mode localization, knowledge (at least partial) of quantities such as geoacoustical parameters of the environment and spectral characteristics of the source is crucial. This results from the fact that the simulated acoustic field should be simulated in geoacoustical conditions similar (as much as possible) to the real conditions existing in the location of interest. In general, environmental parameters can be estimated using inversion methods [23, 24]. Unluckily, in passive approach the knowledge of the source spectrum remains notwithstanding problematic. As the influence of the source spectrum is relevant (see (2) and (7)), we propose an estimator of source spectrum based on the analysis of the first mode (most horizontal), as this mode is always excited. The property of distinct attenuation of signal frequencies (growing non linearly with the frequency) is taken into account by the estimator in order to improve estimation quality. The proposed estimator can be formulated as follows:

Xs f = A f ·

1 r mod {1} X f , Nr n=1 n N

(29)

where Xs ( f ) is the estimated source spectrum, A( f ) is a spectral factor correcting the signal attenuation over frequency, Nr is a number of hydrophones, and Xnmod {1} ( f ) is the spectrum of the first mode on hydrophone n estimated from the f -k plane. For better performance the correction factor A( f ) can be measured in the field (by recording a known broadband signal at some distance). As we do not operate on real field data, to calculate A( f ) we use theoretical values of spectral attenuation (for frequency range of interest).

6. Localization We present some examples of source localization using methods described in Sections 4 and 5. First, examples of localization in distance and in depth are presented using a

single hydrophone, and then using a horizontal hydrophone array (HLA). Moreover, we show the interest of mode signs and source spectrum estimations in case of depth localization by F-K and FTa approaches. Due to limited paper’s length, we do not expose here the study of the robustness of the methods against noise. These considerations have been studied in [11, 25]. We give only some most important conclusions. The simulations on source depth estimation demonstrate that to obtain the primary peak-to-secondary peak ratio of 10 dB the signal-to-noise ratio has to be superior to −5 dB for F-K method and 5 dB for FTa method. The impact of noise on source range estimation seems to be more relevant. These considerations concern white (in time and in space) gaussian model of local (non propagating) noise. 6.1. One Hydrophone. The objective of this section is to show performance of FTa localization method using a single hydrophone. The methods are validated for the environment and configuration described in Section 3 for a signal-to-noise ratio of 15 dB. The distance between source and hydrophone is equal to 10 km. Source is deployed at 40 m of depth and the hydrophone is on the seabed. We first apply the deformation of the signal described in Section 4.2 for the Pekeris model. The parameters used to warp the modal signal are (i) water column depth: 130 m; (ii) sound speed velocity in water: 1500 m/s; (iii) sound speed velocity in sediments: 2000 m/s; (iv) water density: 1 kg/m3 ; (v) sediment density: 2 kg/m3 . Within the parameters, the water column depth is a correct value, and other parameters are approximations of the real values to demonstrate robustness of the method. Then, the FTa method allows a filtering of modes (classic bandpass filter applied on spectral representation given in Figure 13(b)), and these modes are analyzed for distance and depth estimation. 6.1.1. Distance. For the distance localization an access to mode phases is essential. First, a modal filtering by FTa is performed and then for each analyzed mode, its phase is calculated through a Fourier transform. Wavenumbers needed by the estimator defined in (19) are provided by Moctesuma. In Figure 15 we show the cost function C corresponding to several distance estimations. As the distance estimator works on mode couples, we present five distance estimations for mode couples: (2, 1), (3, 1), (4, 2), (5, 3), and (6, 4) and research area r ∈ (8, 13) km with a step Δr = 25 m. The estimated distances are given in Table 3 (the real distance is 10 km). The first 4 estimations are correct, and the last one is false, which is due to limited frequency band of mode 6. Moreover, the sign-distance estimator provides mode signs. For this example, the mode signs were estimated on the same mode couples as distance. The estimation of mode signs no.

EURASIP Journal on Advances in Signal Processing Sign and distance estimation −→ Modes: 2 and 1

6 4 2 0

8

9

10 11 Distance (km)

Sign and distance estimation −→ Modes: 3 and 1

8 Estimation error

8 Estimation error

13

12

6 4 2 0

13

8

9

10 11 Distance (km)

(a)

Estimation error

Estimation error

4 2

8

9

10 11 Distance (km)

12

13


8

6

0

13

(b)


8

12

12

6 4 2 0

13

8

9

10 11 Distance (km)

(c)

(d) Sign and distance estimation −→ Modes: 6 and 4

Estimation error

5 4.5 4 3.5 3 2.5 2

8

9

10 11 Distance (km)

12

13

(e)

Figure 15: Cost functions C of sign-distance estimator in a single hydrophone scenario. The results are given for mode couples: (2, 1), (3, 1), (4, 2), (5, 3), and (6, 4) and radial distance search zone r ∈ (8, 13) km. The source is 10 km distant from the hydrophone. Solid and dashed n, zs ): 0 and π. lines are given for two possible values of Δφ(m,

1 to 6 is correct and the absolute signs are 1 → +, 2 → −, 3 → +, 4 → +, 5 → −, and 6 → +. 6.1.2. Depth. For depth localization an estimation of mode excitation factors is needed. First, a modal filtering is performed on real and simulated data by FTa approach, and then for each analyzed mode, its mode excitation factor modulus is calculated as a mean over frequency. Moreover, mode signs estimated above can be used in the contrast function G. In Figure 16 we show the result of depth localization. The performance is given for the methods “without mode

signs” and “with mode signs.” The difference in performance between two methods is relevant which results from the importance of taking into account mode signs when calculating the contrast function G. The method “with mode signs” eliminates the “mirror solutions” (decrease of the contrast function G from 22.5 dB to 4.5 dB for a secondary peak at 105 m by adding mode signs). Figure 17 highlights also a problem that can appear when adding mode signs: if the mode sign estimation is false (here, sign of mode 3 is false), then the localization performance decreases significantly. However, as one can choose between 3 options when estimating mode signs (the current mode sign n is


40

35 30 25 20

35 30 25 20

Contrast G (dB)

Contrast G (dB)

14

15 10 5 0

0

10 20 30 40 50 60 70 80 90 100 110 120 130 Depth (m)

15 10 5 0

0

10 20 30 40 50 60 70 80 90 100 110 120 130 Depth (m)

No sign Sign

No sign Sign

Figure 16: Contrast functions G for depth source localization by FTa approach. The results are given for methods: without mode signs (circles) and with mode signs (squares). The source is located at 40 m of depth. The vertical resolution is 5 m.

Figure 17: Contrast functions G for depth source localization by FTa approach with false mode sign estimation. The mode sign no. 3 is estimated with an error (estimated as negative, but should be positive). The configuration localization is the same as in Figure 16.

estimated using three inferior modes m = {n − 3, n − 2, n − 1}), the probability of this error should decrease (if the signal-to-noise ratio is sufficiently high). Due to the oscillating character of modal functions and because we consider only modal function modulus, there exist “mirror” depths which give secondary peaks in the contrast function G (Figure 14(a)). To explain this fact and the reason why they disappear when integrating mode signs in the depth estimation, let us present an example. Figure 18 shows 6 mode excitation factors extracted from simulated data at two different source depths: 40 m and 105 m. For these two depths the mode excitation factor moduli are almost the same (Figure 18(a)), and so the difference in the contrast function for these depths is not relevant. When the complete information about mode excitation factors (i.e., modulus and sign) is considered (Figure 18(b)), these depths become discriminated. This is due to especially modes no. 2, 6, but also 4. In the mono-dimensional configuration in lower signalto-noise ratio conditions the mode sign and distance estimations can be inaccurate. Also, the depth localization performance cannot be satisfied. Therefore, we propose the multi-dimensional configuration that is more robust and efficient due to a richer information about the source and the environment recorded on the HLA.

Table 3: Results of the source distance estimation for FTa approach.

6.2. Horizontal Line Array. This section presents results of localization in distance and in depth using F-K approach. The objective is to show the performance of F-K localization method. The methods are validated in the environment and configuration described in Section 3 for a signal-to-noise ratio of 5 dB. The distance between the source and the first hydrophone of HLA is 10 km. The source depth is 105 m and the HLA is on the seabed. According to the Shannon theorem and for the ULF band ( fmax = 100 Hz) the maximal spatial sampling should be done every 7.5 m. Thus, in theory we could consider every second HLA hydrophone without any information lost (as the whole HLA samples linearly the space every

Mode couple 2 and 1 3 and 1 4 and 2 5 and 3 6 and 4

Estimated distance (km) 9.925 10 10 10 9.625

3.347 m). However, with a higher space sampling, better noise canceling algorithms can be implemented. What is more important, is a length of the HLA. When the length of HLA reduces, the localization performance decreases. This is provoked by a spreading of the signal in the f -k plane which results from a not sufficiently long radial distance sampling of the modal signal [16]. Different issues of the use of HLA are discussed in [10]. The first step of the method is a Vref velocity correction which is done with the minimum value of the sound speed profile in water Vmin = 1508.4 m/s. Then, the F-K transform is calculated and this representation is used for mode filtering. These modes are then analyzed for distance and depth estimations. 6.2.1. Distance. After F-K filtering, the phase of each mode is calculated through a Fourier transform. The wavenumbers needed by the estimator defined in (19) are provided by Moctesuma simulator. This estimation is applied to each hydrophone of the HLA (240 estimations) [16]. We apply the estimator on five different mode couples: (2, 1), (4, 1), (4, 2), (5, 2), (6, 4), and (7, 4), and research erea r ∈ (8, 13) km with step Δr = 25 m. The estimated distance values are given in Figure 19 and its mean values are given in Table 4. Moreover, the sign-distance estimator gives as a result mode sign. In multi-dimensional case, we dispose of Nr estimations of mode signs for each mode couple option. For a mode number equal to 7, the sign-distance estimator is applied on following mode couples: (2, 1) (for mode 2),

EURASIP Journal on Advances in Signal Processing Mode excitation factors −→ without signs Modes : 1–6

0.5 0 −0.5 −1

1

1.5

2

2.5

3 3.5 4 Mode number

4.5

5

Mode excitation factors −→ with signs Modes : 1–6

1 Mode amplitude

1 Mode amplitude

15

5.5

0.5 0 −0.5 −1

6

1

Simulation for 40 m Simulation for 105 m

1.5

2

2.5

3 3.5 4 Mode number

4.5

5

5.5

6

Simulation for 40 m Simulation for 105 m

(a)

(b)

Figure 18: Mode excitation factors extracted from 2 simulations: source at 40 m and 105 m of depth. (a) represents the mode excitation factor modulus (no sign information) and (b) shows the mode excitation factor modulus combined with sign information.

Histogram Modes: 2 and 1

15

10

Counts

Counts

15

5 0 9.95

9.975

10 Distance (km)


10.025

10 5 0 9.95

10.05

9.975

(a)

Counts

Counts 9.975

10 Distance (km)

10.025

0 9.95

10.05

9.975


Counts

Counts 10 Distance (km) (e)

10.05

10.025

10.05


20

5

9.975

10 Distance (km) (d)

10

0 9.95

10.025

5

(c)

15

10.05


10

10

0 9.95

10.025

(b)


20

10 Distance (km)

10.025

10.05

10

0 9.95

9.975

10 Distance (km) (f)

Figure 19: Results of distance estimation by F-K method for 6 mode couples. For each mode couple the estimation is done for all HLA hydrophones (240 distance estimations). The true value of distance is 10 km.

16


Mean distance value (km) 10.01 10.01 10.005 10 10.005 10.005

(3, 1), (3, 2) (for mode 3), (4, 1), (4, 2), (4, 3) (for mode 4), (5, 2), (5, 3), (5, 4) (for mode 5), (6, 3), (6, 4), (6, 5) (for mode 6), (7, 4), (7, 5), and (7, 6) (for mode 7) and the user has to select the couple he wants to use. This information is used here to maximize the probability of correct choice within available options for each estimation step. As the mode sign estimation is sequential it is primordial to not commit an error at the beginning to avoid its propagation. At each step (for each mode sign estimation) a series of 3 parameters is calculated to help the user in taking the decision. For the first step these parameters are calculated once (for the couple (2, 1)), for the second step we dispose of two set of parameters (for the couples (3, 1) and (3, 2)), and for the following steps we have always three sets of parameters. These parameters are defined as follows. (i) Choice reliability: |N − floor(Nr /2 + 1)|

floor(Nr /2 + 1)

∗ 100,

(30)

where N is a number of sign changes (N ∈ [0, Nr ]). This criteria should be maximal. (ii) Estimation variability: 2 (re )

, Nr

(31)

where re denotes a set of Nr distance estimations and

denotes a second derivative with respect to the hydrophone number. For the no-error estimation of distance the first derivative is equal to interhydrophone distance. Then, the second derivative is equal to zero as the first derivative is a constant function. This criterion allows to measure the variability of distance estimations across all hydrophones and should be minimal. (iii) Error distance estimation:

40 30 20 10 0

0

10 20 30 40 50 60 70 80 90 100 110 120 130 Depth (m) No sign Sign

Figure 20: Contrast functions G for depth source localization by F-K approach. The results are given for methods: without mode signs (circles) and with mode signs (squares). The source is located at 105 m of depth. The vertical resolution is 5 m.

0 Amplitude (dB)

Mode couple 2 and 1 3 and 1 4 and 3 5 and 2 6 and 5 7 and 6

Contrast G (dB)

Table 4: Mean values of source distance estimation for multidimensional approach. The bin width is 5 m.

−20 −40 −60

0

20

40

60 80 Frequency (Hz)

100

120

Figure 21: Result of the source spectrum estimation for source ULF-2 (to be compared with Figure 4(d)).

For the example presented here, the mode signs were estimated on the same mode couples as distance. The estimation of signs of modes no. 1 to 7 is correct and the absolute signs are 1 → +, 2 → +, 3 → +, 4 → −, 5 → −, 6 → −, and 7 → −.

(32)

6.2.2. Depth. After modal filtering, the mode excitation factor modulus of each mode is calculated as a mean over the f -k region. Moreover, the sign-distance estimator can be used for mode signs estimation. In Figure 20 we show the result of depth localization. The performance is given for method “without mode signs” and “with mode signs.” The difference between both methods is relevant which confirms the importance of taking into account mode signs when calculating the contrast function G. The method “with mode signs” eliminates the “mirror solutions” (decrease of the contrast function from 21 dB to 6 dB for a secondary peak at 35 m by adding mode signs).

where ren,i+1 denotes a distance estimation for nth hydrophone at actual step analysis (i + 1) and rei denotes the final estimation of distance from previous step (i). This criterion allows cancel secondary peak solutions for which the first two criteria gave good results and should be obviously minimal.

6.3. Source Spectrum Issue. In Section 5.3 we described a simple method of estimation of the source spectrum. Now, we quantify the impact of this estimation on depth localization. Let us consider an example of depth localization in the environment described in Section 3. The source ULF-2 is

1/Nr

Nr n,i+1 − rei n=1 re , rei

Contrast G (dB)


45 40 35 30 25 20 15 10 5 0

Depth localisation by F-K Contrast function −→ no sign

10 20 30 40 50 60 70 80 90 100 110 120 130 Depth (m)

(a)

Contrast G (dB)

Nevertheless, our method is designed for broadband sources. Therefore, even if spectral characteristics of the source are perfectly known, but present narrowband or comb-type structures, the localization performance decreases. The performance decrease due to nonbroadband source is higher than the gain due to acquaintance of source spectral characteristics.

7. Conclusion

No spectrum estimation Spectrum estimation

45 40 35 30 25 20 15 10 5 0

17

Depth localisation by F-K Contrast function −→ sign

10 20 30 40 50 60 70 80 90 100 110 120 130 Depth (m) No spectrum estimation Spectrum estimation (b)

Figure 22: Contrast functions G for depth source localization by F-K approach combined with source spectrum estimation. The simulation is given for source ULF-2 located at 70 m of depth and 10 km distant from the HLA. (a) shows the gain given by taking into account the estimated spectrum of an unknown source for localization method without mode signs. (b) shows this gain in case of localization algorithm with integrated mode signs into the contrast function.

located at 70 m of depth. As we do not know the spectral properties of the localized source we consider two cases. (i) We use a source with flat spectrum for simulation of the replica field (source ULF-1)-common approach when unknown source. (ii) We estimate a source spectrum by the method defined in (29) and use it to simulate the replica field. In Figure 21, we present spectrum of the source ULF2 estimated by the proposed method (compare with Figure 4(d)). The results of localization without and with source spectrum estimation are shown in Figure 22. We can note that estimating the source spectrum improves considerably the localization performance (of about 20 dB in the example).

In this paper we propose passive source localization in shallow water based on modal filtering and features extraction. The depth and distance of an Ultra Low Frequency source are estimated in the mono-dimensional configuration (a single hydrophone) and in the multi-dimensional configuration (a horizontal line array). The localization techniques are, respectively, based on adapted Fourier transform and frequency-wavenumber transform. In both representations modes are separable and thus can be filtered. We discuss modal filtering tools, then the localization itself is performed. For distance estimation, we base our localization method on the analysis of mode phases. The proposed distance estimator is naturally combined with mode sign estimator. For depth localization, we use matched-mode processing, a technique that widely demonstrated its performance in a shallow water environment. The principle is based on comparison (by a contrast function) of mode excitation factors extracted from real data with a set of mode excitation factors (for simulated source depths) extracted from replica data (modeled with Moctesuma). We demonstrate that adding the mode signs to the mode excitation factor modulus improves significantly the localization performance in depth. We also propose a method of estimation of the source spectrum, which is very important for depth localization using Matched-Mode Processing. The localization results, in depth and distance, obtained on signals simulated with Moctesuma in realistic geophysical conditions are very satisfactory and demonstrate the performance of the proposed methods.

Acknowledgment This work was supported by Project REI 07.34.026 from the Mission pour la Recherche et l’Innovation Scientifique (MRIS) of the Delegation Generale pour l’Armement (DGAFrench Departement of Defense).

References [1] F. B. Jensen, W. A. Kuperman, M. B. Porter, and H. Schmidt, Computational Ocean Acoustics, AIP Press, New York, NY, USA, 1994. [2] A. B. Baggeroer, W. A. Kuperman, and P. N. Mikhalevsky, “An overview of matched field methods in ocean acoustics,” IEEE Journal of Oceanic Engineering, vol. 18, no. 4, pp. 401–424, 1993. [3] J. A. Fawcett, M. L. Yeremy, and N. R. Chapman, “Matchedfield source localization in a range-dependent environment,” The Journal of the Acoustical Society of America, vol. 99, no. 1, pp. 272–282, 1996.

18 [4] G. R. Wilson, R. A. Koch, and P. J. Vidmar, “Matched-mode localization,” The Journal of the Acoustical Society of America, vol. 104, no. 1, pp. 156–162, 1998. [5] E. C. Shang, C. S. Clay, and Y. Y. Wang, “Passive harmonic source ranging in waveguides by using mode filter,” The Journal of the Acoustical Society of America, vol. 78, no. 1, pp. 172–175, 1985. [6] N. E. Collison and S. E. Dosso, “Regularized matchedmode processing for source localization,” The Journal of the Acoustical Society of America, vol. 107, no. 6, pp. 3089–3100, 2000. [7] C. W. Bogart and T. C. Yang, “Comparative performance of matched-mode and matched-field localization in a rangedependent environment,” The Journal of the Acoustical Society of America, vol. 92, no. 4, pp. 2051–2068, 1992. [8] W. A. Kuperman, W. S. Hodgkiss, and H. C. Song, “Phase conjugation in the ocean: experimental demonstration of an acoustic time-reversal mirror,” The Journal of the Acoustical Society of America, vol. 103, no. 1, pp. 25–40, 1998. [9] C. Prada, J. de Rosny, D. Clorennec, et al., “Experimental detection and focusing in shallow water by decomposition of the time reversal operator,” The Journal of the Acoustical Society of America, vol. 122, no. 2, pp. 761–768, 2007. [10] C. W. Bogart and T. C. Yang, “Source localization with horizontal arrays in shallow water: spatial sampling and effective aperture,” The Journal of the Acoustical Society of America, vol. 96, no. 3, pp. 1677–1686, 1994. [11] B. Nicolas, J. I. Mars, and J.-L. Lacoume, “Source depth estimation using a horizontal array by matched-mode processing in the frequency-wavenumber domain,” EURASIP Journal on Applied Signal Processing, vol. 2006, Article ID 65901, 16 pages, 2006. [12] G. Le Touzé, B. Nicolas, J. Mars, and J.-L. Lacoume, “Matched representations and filters for guided waves,” IEEE Signal Processing Letters. In press. [13] R. G. Baraniuk and D L. Jones, “Unitary equivalence: new twist on signal processing,” IEEE Transactions on Signal Processing, vol. 43, no. 10, pp. 2269–2282, 1995. [14] T. C. Yang, “A method of range and depth estimation by modal decomposition,” The Journal of the Acoustical Society of America, vol. 82, no. 5, pp. 1736–1745, 1987. [15] X. Cristol, J.-M. Passerieux, and D. Fattaccioli, “Modal representations of transient sound pulses in deep and shallow environments, with investigations about detailed space and time correlation of propagated waves,” MAST, 2006. [16] M. Lopatka, B. Nicolas, G. Le Touzé, et al., “Robust underwater localization of ultra low frequency sources in operational context,” in Proceedings of the Uncertainty Analysis in Modelling (UAM ’09), Nafplion, Greece, 2009. [17] G. Le Touzé, B. Nicolas, J. I. Mars, and J.-L. Lacoume, “Timefrequency representations matched to guided waves,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP ’06), vol. 3, pp. 440–443, 2006. [18] A. Papandreou-Suppappola, R. Murray, B.-G. Iem, and G. F. Boudreaux-Bartels, “Group delay shift covariant quadratic time-frequency representations,” IEEE Transactions on Signal Processing, vol. 49, no. 11, pp. 2549–2564, 2001. [19] M. McClure and L. Carin, “Matching pursuits with a wavebased dictionary,” IEEE Transactions on Signal Processing, vol. 45, no. 12, pp. 2912–2927, 1997. [20] G. Le Touzé, localisation de source par petits fonds en UBF (1−100Hz) a` l’aide d’outils temps-frequence, Ph.D. dissertation, INP, Grenoble, France, 2007.

EURASIP Journal on Advances in Signal Processing [21] B. Nicolas, G. Le Touzé, and J. I. Mars, “Mode sign estimation to improve source depth estimation,” in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP ’08), pp. 2437–2440, Las Vegas, Nev, USA, 2008. [22] S. M. Jesus, “Normal-mode matching localization in shallow water: environmental and system effects,” The Journal of the Acoustical Society of America, vol. 90, no. 4, pp. 2034–2041, 1991. [23] J. H. Wilson, S. D. Rajan, and J. M. Null, “Inversion techniques and the variability of sound propagation in shallow water,” IEEE Journal of Oceanic Engineering, vol. 21, no. 4, p. 321, 1996. [24] B. Nicolas, J. Mars, and J. L. Lacoume, “Geoacoustical parameters estimation with impulsive and boat-noise sources,” IEEE Journal of Oceanic Engineering, vol. 28, no. 3, pp. 494–501, 2003. [25] G. Le Touzé, J. I. Mars, and J.-L. Lacoume, “Matched timefrequency representations and warping operator for modal filtering,” in Proceedings of the European Signal Processing Conference (EUSIPCO ’06), Florence, Italy, September 2006.


Research Article Simulation of Matched Field Processing Localization Based on Empirical Mode Decomposition and Karhunen-Loève Expansion in Underwater Waveguide Environment Qiang Wang1 and Qin Jiang2 1 Department 2 College

of Quality and Safety Engineering, China Jiliang University, Hangzhou, Zhejiang 310018, China of Metrology and Measurement Instrument, China Jiliang University, Hangzhou, Zhejiang 310018, China

Correspondence should be addressed to Qiang Wang, [email protected] Received 1 July 2009; Revised 26 November 2009; Accepted 22 February 2010 Academic Editor: Frank Ehlers Copyright © 2010 Q. Wang and Q. Jiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Mismatch problem has been one of important issues of matched field processing for underwater source detection. Experimental use of MFP has shown that robust range and depth localization is difficult to achieve. In many cases this is due to uncertainty in the environmental inputs required by acoustic propagation models. The paper presents that EMD (Empirical mode decomposition) processing underwater acoustic signals is motivated because it is well suited for removing specific unwanted signal components that may vary spectrally. And the Karhunen-Loève expansion is applied on sample covariance matrix to gain a relatively uncorrupted signal. The EMD denoising scheme is combined with Karhunen-Loève expansion to improve underwater target localization performance of matched field processing (MFP). The robustness and effectiveness of the proposed method is tested by the benchmark cases numerical simulation when there had large environmental parameter uncertainties of the acoustic waveguide.

1. Introduction Matched field processing has been extensively explored for use in detecting and localizing underwater sources. MFP uses ocean propagation models to account for multipath when generating replica vectors [1–3]. Typically, matched field source localization involves fitting measured narrowband vertical array outputs with versions of the field, predicted by a full wave deterministic normal mode model, for a set of hypothesized source ranges and depths [4]. If accurate environmental information is available, sources can be localized in range, depth, and bearing. Under practical circumstances, ocean environmental parameters such as sound speed profile, water depth, and bottom density, may have significant spatial and temporal variability. But a major difficulty facing this approach is that the localization process is extremely sensitive to errors in the assumed propagation model and array calibration. Accurately modeling multipath can also yield mismatch reduction and detection gains as compared to direct-path beamformers. Because of the limitation of

inaccurate measurement as well as all kinds of noises and perturbs in underwater environment, it is inevitable for us to receive the desirable signal with noise and have the uncertainties in modeling real ocean environment [2]. As a result it would be better to find a new robust matched field processor based on denoising scheme. MFP exploits the complex multipath structure to generate the signal replica or the so-called steering vector. The steering vector is the spatial point source response of the medium (Green’s function), thus depending on not only the source location but also the environmental parameters. It is very common that the assumed environmental parameters differ from the true ones, and thus sensitivity to mismatch is the most important liability with matched-field methods [1]. To overcome the mismatch problem, many researchers have proposed some robust algorithms, and sector-focused processing was applied to the test data cases devised for the MFP. Sector-focused processor located the source with robustness similar to the replica correlator processor, but with the higher resolution characteristic of Minimum

2 variance distortionless response (MVDR) [3]. A broadband MAP estimator for robust MFP termed the wideband optimum uncertain field processor (OUFP) was presented in [4]. A contrast-maximized optimization scheme was introduced to the MFP in order to reduce the sidelobe level of ambiguity surfaces [5]. The Karhunen-Loève expansion, also called feature extraction method, has been proposed with an improvement of robustness on environmental mismatch. It is one of robust MFP algorithm, which is based on the eigenvector estimation [6]. The MFP results were presented in real ocean experimental data using KarhunenLoève expansion and MVDR with white noise constrain [7]. The coherent white noise constraint processor has also been shown through simulation to perform better than the conventional and MVDR estimators at low SNR [8]. The last two decades have seen tremendous activity in the development of new mathematical and computational tools based on multiscale ideas (wavelet). Then Ding and Gong had also proposed multiresolution processing method for source detection and localization. It improves the MFP ambiguity surface performance with analysis of shallow water trial data [9]. Based on wavelet transform and feature extraction scheme, a robust MFP was proposed by G. Gong and X. Gong [10]. The main drawback of this method is that a mother wavelet has to be defined a priori. But in the end, it would seem that the wavelet family is specifically related to the analyzed dataset because certain authors have systematically chosen different wavelet families for underwater signal analyses. Recently, a new data-driven technique, referred to as empirical mode decomposition (EMD), has been introduced by Huang et al. [11] for analyzing data from nonstationary and nonlinear processes. The EMD has received more attention in terms of applications and interpretations [12]. The major advantage of the EMD is that the basis functions are derived from the signal itself. Hence, the analysis is adaptive in contrast to the traditional methods where the basis functions are fixed. The EMD is based on the sequential extraction of energy associated with various intrinsic time scales of the signal, starting from finer temporal scales (high-frequency modes) to coarser ones (low-frequency modes). The total sum of the intrinsic mode functions (IMFs) matches the signal very well and, therefore, ensures completeness [11]. To the nonlinear and nonstationary signals analysis, the EMD method gave promising results and has advantages when compared with the wavelet transform [12]. Flandrin et al. have proposed the signal-filtering method based on EMD to process the fractional Gaussian noise [12]. Boudraa and Cexus proposed the consecutive mean square error (CMSE) criteria to differentiate IMFs of main signal component and IMFs of noise, that does not require any knowledge of y(t), and use the main IMFs to reconstruct signal and performed denoising functions [13]. To represent underwater target echo involving broadband noise, our main work in this paper is the application of EMD scheme to deal with underwater acoustic signals. Then based on Karhunen-Loève expansion, robust matched field processor was constructed. The robustness and effectiveness

EURASIP Journal on Advances in Signal Processing of the suggested algorithm has been illustrated through the numerical simulation of MFP benchmark shallow water data [14].

2. Underwater Acoustic Signals Denoising Scheme Based on EMD 2.1. The Empirical Mode Decomposition. Traditional data analysis methods, like Fourier and wavelet-based method, require some predefined basis functions to represent a signal. The EMD relies on a fully data-driven mechanism that does not require any a priori known basis. It is especially well suited for nonlinear and nonstationary signals, such as underwater acoustic signals. The EMD consists of the decomposition of the original signal in successive modes. The decomposition does not require specific vectors: the signal is decomposed on itself. Obtaining a mode from the original signal is called the sifting process. The decomposition of the signal s is written as s(n) =

M

ci (n) + TM (n)

(1)

i=1

with ci being the ith mode of the signal. c is also called intrinsic mode functions (IMF), and TM is the residue. The result of the EMD produces M IMFs and a residue signal. The lower-order IMFs capture fast oscillation modes while higher-order IMFs typically represent slow oscillation modes. If we interpret the EMD as a time-scale analysis method, lower-order IMFs and higher-order IMFs correspond to the fine and coarse scales, respectively. The decomposition following the sifting process is complete; that is, the sum of all IMFs is exactly equal to the original signal. These IMFs are deduced from the signal’s extrema. Each IMF has to verify the following two conditions: (1) the number of maxima and minima has to be the same or having a difference ±1, and (2) the envelope from the minima and the envelope from the maxima must have a null mean. In the end, the residue has no more than two extrema. Because the number of the signal extrema is finite, it is important to note that the number of IMF is consequently finite, regardless of the features of the signal to be analyzed. Selecting certain IMF is equivalent to filtering the signal. And the filtered signal is the result of the sum of the selected IMF [12]. The highband and lowband filtered signal will be, respectively, defined as sh f ,k (n) =

k

ci (n) ,

i=1

sb f ,k (n) =

M+1

ci (n),

(2)

i=k

if we note cM+1 [n] = TM [n]. 2.2. EMD Denoising Scheme. Noise is always present in recorded underwater acoustic signals and is contingent upon meteorological conditions, underwater noise from human activities, signal propagation, echoes, and electronic characteristics of the material for recording. The EMD does not use any predetermined filter or wavelet function and it is a fully data-driven method.


3

The EMD involves the decomposition of a given signal into a series of IMFs, through the sifting process, each with distinct time scale. The EMD method can decompose any complicated signal into its IMFs which reflect the intrinsic and reality information of the signal. The performance of the denoising methods is evaluated from the CMSE: EMD has the equivalent filter bank structure with binary wavelet [12]. The signal is decomposed as (1) . Each IMF stands for certain frequency band signal information, such as (2) , and small scale IMF stands for high-frequency component, means spiking signal and noise. Large-scale IMF stands for low-frequency band signal. The EMD method is employed for decomposing the input signal into IMFs (IMF1 , . . . ,IMFN , where N is the number of IMFs). These IMFs are soft-thresholded, yielding tIMF1 , . . . , tIMFN , which are thresholded versions of the original components. The filtered signal is obtained as a linear summation of thresholded IMFs. A smooth version of the input data can be obtained by thresholding the IMFs before signal reconstruction: EMDsoft [13]. Donoho and Johnstone have proposed a universal threshold for removing added Gaussian noise given by τ j [15]: #

MAD j , (3) 0.6745 where σ j is the noise level of the jth IMF, and L stands for the length of IMF. The MAD j represents the absolute median deviation of the jth IMF and is defined by τ j = σ j 2 log(L),

σj =

MAD j = Median IMF j (t) − Median IMF j (t) . (4)

Instead of using a global thresholding, level-dependent thresholding uses a set of thresholds, one for each IMF (scale level). The soft-thresholding method shrinks the IMF samples towards zero as follows: ⎧ ⎪ ⎨IMF j (t) − τ j

if IMF j (t) ≥ τ j ,

c j (t) = ⎪ ⎩0

if IMF j (t) < τ j .

(5)

2.3. MFP Based on K-L Expansion after Denoising Scheme. Karhunen-Loève expansion method was applied to estimate eigenvector by Seong and Byun to build robust MFP in [6]. They applied empirical orthogonal function in matched field processing area and used it to estimate the eigenvectors that constitute the field in an ocean acoustic waveguide. For received field data P, snapshot averaged sampling covariance matrix, R, can be decomposed as follows: snapshot

R=

PPH =

i=1

N

λri ri H .

(6)

i=1

We used eigenvector decomposition of snapshotaveraged sampling covariance matrix in order to construct the signal vector P, and then received signal vector which is averaged over snapshots is represented as [7] P=

N #

λi ri .

i=1

(7)

In (7) , where λ is the simulated snapshot ri (1 ≤ i ≤ N) number, ri are the eigenvectors of the covariance matrix of received signal, and superscript H denotes complex conjugate transpose. Seong and Byun have proved that the eigenvector with relatively large eigenvalues can be said to be the main features of the pressure field generated by a source located at the assumed replica position. Then eigenvalue decomposition was applied to R and gains the eigenvector corresponding to the largest eigenvalue. As mentioned in [2, 16], this eigenvector can be used to represent the desirably received signal. For the real data situation where multisnapshots are given, if the EMD denoising for each snapshot ri (1 ≤ i ≤ N) can be performed before R is determined, a better data processing ability may be obtained. Conveniently, the eigenvector r corresponding to maximum eigenvalue represents the desirably received signal. To achieve the radiated signal from the sources EMD is performed with respect to r and the reduced noise r of desirably received signal is defined as r = r − r ,

(8)

where r is the reconstructed signal of r obtained from EMD denoising scheme. It is known that most replicas obtained from possible candidate environment positions contain model errors because of inaccurate environment parameters, therefore replica vector p also is considered to consist of noise and uncorrupted signal, and the reduced of replica signal is defined as noise p p = p − p ,

(9)

where p is the reconstructed signal of p after EMD denoising. The new MFP processor is constructed by EMD denoising scheme and Karhunen-Loève expansion, which is presented as

EMD-MFP = r H p

N/2 · rH p .

(10)

where · denotes inner product. This processor can be illuminated that if the signal factors r and p are perfectly are perfectly matched as well as noise factors r and p matched, r and p are perfectly matched so that the source location that produces the best match between the measured and predicted fields corresponds to the true source position. In addition, the exponent N/2 is used to control sidelobe level. Therefore the EMD-MFP estimates of underwater object in range r and depth z are obtained by solving the optimization problem: %

'

r&, z& = arg max r H p

{(r,z)∈D}

N/2 · rH p ,

(11)

where D denotes the sources of all the candidate positions.

3. Numerical Simulation To validate EMD-MFP robustness and effectiveness furthermore, simulation results are discussed under conditions of

4


MFP benchmark cases in [17], which supply a quantitative numerical simulation comparison of MFP performance with various schemes. The normal-mode propagation model KRAKEN was used in this study [16]. The selected cases of different kinds of mismatch situations are called briefly COLNOISE, SSPMIS, and GENLMIS. In benchmark cases, underwater source frequency is 250 Hz in shallow water environment, whose signals are received on a vertical array of 20 receivers spanning the water column. The first case adds colored noise, the second case introduces uncertain ocean sound speed profile (SSP) data plus white noise, and the third has both colored noise and uncertainty in virtually every environmental parameters. For the colored noise case (COLNOISE) we use a noise model that is most appropriate for treating surface noise due to breaking waves. The noise sources are then modeled as a uniform distribution of monopoles located at a small distance below the surface. The noise field is then calculated using a normal mode model to propagate the monopole sources to the receiving array. The detailed discussion is provided in [17]. The precise environment is described in [17] and the actual parameters are intended to be realistic. Figure 1(a) is the true environment parameters of ocean waveguide. Figure 1(b) is the environmental information provided for SSP mismatch case (SSPMIS) and true environment for SSPMIS (c(0) = 1499.4 m/s c(D− ) = 1481.6 m/s). Figure 1(c) is the Ocean waveguide for general mismatch case (GENLMIS). True environment is c(0) = 1499.9 m/s, c(D− ) = 1478.7 m/s c(D+ ) = 1574 m/s, c(200) = 1694 m/s, α = 0.19 dB/λ, ρ = 1.79.

0m

3.1. COLNOISE Case. The Bartlett processor (linear MFP) is typically the cross-correlation between data and model predictions for that data resulting in a scalar output indicating the agreement between data and model. Its ambiguity surfaces typically are incoherently averaged across frequency when performing matched field processing on a broadband source. It assumes that the true source location at each frequency remains fixed, while the sidelobes will appear at different locations at different frequencies and thus will be suppressed by the average. Replicas of the field were computed for 50 m increments in range from 100 to 10000 m, and for 2 m increments in depth from 1 to 100 m. These replicas were matched with the simulated covariance data using the different beamformers. For the COLNOISE case the localization performance is very good for 40 dB SNR case and therefore results are only presented for the lower two SNR values. Then, we compared the underwater target localization performance of this processor with Bartlett processor to get the source location in the low SNR case. From Figures 2(a) and 2(b), the EMD-MFP and Bartlett processor localization results are all able to accurately localize target too, when SNR is 10 dB. The true source location range is r = 9100 m, and depth is z = 66 m. It is clear that EMD-MFP owns robust sidelobe suppression ability. For very low −5 dB SNR case, the location results of Bartlett and EMD-MFP are in Figures 3(a) and 3(b), and the true location range equals 9700 m, and depth is z = 58 m. The Bartlett processor cannot locate

D = 100 m

D = 200 m

c(0) = 1500 m/s

r

c(D− ) = 1480 m/s c(D+ ) = 1600 m/s

c(200) = 1750 m/s α = 0.2 dB/λ ρ = 1.8

z (a)

0m

D = 100 m

D = 200 m

c(0) = 1500 ± 2.5 m/s

r

c(D− ) = 1480 ± 2.5 m/s c(D ) = 1600 m/s

c(200) = 1750 m/s α = 0.2 dB/λ ρ = 1.8

z (b)

0m

D = 100 m

D = 200 m

c(0) = 1500 ± 2.5 m/s

r

c(D− ) = 1480 ± 2.5 m/s c(D+ ) = 1600 ± 50 m/s

c(200) = 1750 ± 100 m/s α = 0.35 ± 0.25 dB/λ ρ = 1.75 ± 0.25

z (c)

Figure 1: Environmental information provided for true environmental parameters (a), SSPMIS (b), and GENLMIS (c).

the source. Its sidelobes even own the same level with main lobe. Though the EMD-MFP located target correctly, it also has higher sidelobe than the localization results under SNR which is 10 dB condition. Naturally, the sidelobe levels tend to increase as the SNR decreases. 3.2. SSIPMIS Case. The SSPMIS represents a low level of environmental mismatch. In addition, white noise was added to the data vectors. As seen in Figure 1(a), the only source of mismatch is in the sound speed within the water column where both its gradient and mean level were randomized. Figure 4 shows the results of EMD-MFP for SSIPMIS. The 10 random samples over the environmental parameter space were used, where they are assumed as uniformly distributed over the possible interval. Under SSIPMIS (true source position r = 9300 m, z = 78 m) condition, for −5 dB low


5

1

N normalised power

N normalised power

1 0.8 0.6 0.4 0.2 0 100

0.8 0.6 0.4 0.2 0 100

De

50 pth (m

)

0

5000

6000

7000

8000

9000

10000 De

) e (m Rang

50 pth (m

)

0

(a)

5000

6000

7000

8000

9000

10000

) e (m Rang

(b)

Figure 2: Bartlett ambiguity surface for COLNOISE with SNR of (a) and EMD-MFP ambiguity surface (b) for COLNOISE (SNR = 10 dB).

1

N normalised power

N normalised power

1 0.8 0.6 0.4 0.2

0.8 0.6 0.4 0.2 0 100

0 100 De 50 pth (m )

0

5000

6000

7000

8000

9000

10000 De

) e (m Rang

pth

50 (m

)

0

(a)

5000

6000

7000

8000

9000

10000

) e (m Rang

(b)

Figure 3: Bartlett ambiguity surface (a) and EMD-MFP ambiguity surface (b) for COLNOISE (−5 dB SNR case).

1

N normalised power

N normalised power

1 0.8 0.6 0.4 0.2 0 100

0.8 0.6 0.4 0.2 0 100

De

50 pth (m

)

0

5000 (a)

6000

7000

8000

9000

) e (m Rang

10000 De

50 pth (m

)

0

5000

6000

7000

8000

9000

) e (m Rang

(b)

Figure 4: The EMD-MFP ambiguity surface (a) 10 dB SNR case and (b) −5 dB SNR case for SSIPMIS.

10000

6

EURASIP Journal on Advances in Signal Processing However, we saw that strong differences were evident in ambiguity surface. Noticeable difference between different SNRs is shown in Figure 5. It reveals that EMD-MFP locates the true source position under the very low −5 dB SNR condition. The eigenvalues of sampling covariance matrix spread out and so signal P has relatively large noise components as well as source signal components. After the proposed scheme processing, the total performance of processor is satisfied under GENLMIS condition.

N normalised power

1 0.8 0.6 0.4 0.2 0 100 De

50 pth (m

)

0

5000

6000

7000

8000

9000

10000

) e (m Rang

(a)

N normalised power

1 0.8 0.6 0.4 0.2 0 100 De

pth

50 (m

)

0

5000

6000

7000

8000

9000

10000

) e (m Rang

(b)

Figure 5: Ambiguity surface for GENLMIS using EMD-MFP localization computationally test case: (a) (SNR = 10 dB) and (b) (SNR = −5 dB).

SNR case, location results are in Figure 4(a), r = 9300 m, and z = 78 m. Though the location is correct, the sidelobe level is high. When SNR = 10 dB (true position r = 9300 m, z = 78 m), the simulation results are presented in Figure 4(b). Simulation localization results are correct, but there also exist some high sidelobes in ambiguity surface. 3.3. GENLMIS Case. The general mismatch (GENLMIS) case was intended to include many problems typical of real world scenarios. It combines both mismatch and colored noise. In particular, both ocean and sediment sound speeds were randomized, the sediment attenuation and density were randomized, and the depth of the ocean/sediment interface was randomized. For GENLMIS conditions, simulation results indicate that EMD-MFP accurately localizes the source, but the sidelobe level increases with decreasing the same compared with the COLNOISE case. When SNR is −5 dB, we compute the target location results of the case. In Figure 5, true target source position is r = 6200 m, z = 92 m, the EMD-MFP localization results r = 6200 m, and depth z = 92 m are correct. For −5 dB low SNR case, EMD-MFP is also able to localize true source.

4. Conclusion The eigenvector of sample covariance matrix corresponding to the maximum eigenvalue is seen as the desirably received signal; however this desirably received signal is still considered to contain the signal from the radiated source and noise, so EMD denoising method is performed to denoise the underwater acoustic signals. Simulation which is similar to the environmental parameters presented in the MFP benchmark workshop was carried out, and the results showed that the proposed method owns robustness source detection performance and effective sidelobe suppression in spite of severe environmental mismatches. These results are encouraging since they imply that detailed environmental knowledge may not be a prerequisite for source localization with MFP. In GENLMIS mismatch environment, after EMD denoising, we selected the largest dominant eigenvector generated by perturbing environment to replace replica field vector in MFP that can provide robust localization performance. For relatively low-level signal, source detection was performed but peak-to-noise field ratio was low. Especially, in the test cases of slight environmental mismatches, it localized the true source location with low sidelobes.

Acknowledgments The authors thank Dr. Gong G. Y. for her help and the anonymous reviewers for their useful comments, which lead to a better presentation of this paper. The work was supported by the National Nature Science Foundation of China under Grant 60902095 and funded by Zhejiang Provincial Natural Science Foundation of China under Grant no. Y1090672.

References [1] A. Tolstoy, “Matched field processing: a powerful tool for the study of oceans and scatterers,” in Acoustic Interactions With Submerged Elastic Structures, G. Ardéshir, M. Gérard, E. Juri, and W. Michael, Eds., vol. 5, pp. 84–111, World Science, Singapore, 2001. [2] A. B. Baggeroer, W. A. Kuperman, and P. N. Mikhalevsky, “Overview of matched field methods in ocean acoustics,” IEEE Journal of Oceanic Engineering, vol. 18, no. 4, pp. 401–424, 1993. [3] G. B. Smith, H. A. Chandler, C. Feuillade, and D. J. Morris, “Sector focusing for robust high resolution analysis of the


[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

matched field processing workshop data set,” Journal of Computational Acoustics, vol. 2, no. 3, pp. 199–215, 1994. J. A. Shorey and L. W. Nolte, “Wideband optimal a posteriori probability source localization in an uncertain shallow ocean environment,” Journal of the Acoustical Society of America, vol. 103, no. 1, pp. 355–361, 1998. K. C. Shin and J. S. Kim, “Matched field processing with contrast maximization,” Journal of the Acoustical Society of America, vol. 118, no. 3, pp. 1526–1533, 2005. W. Seong and S.-H. Byun, “Robust matched field-processing algorithm based on feature extraction,” IEEE Journal of Oceanic Engineering, vol. 27, no. 3, pp. 642–652, 2002. K. S. Kim, W. Seong, and C. Lee, “Matched field processing: analysis of feature extraction method with ocean experimental data,” in Proceedings of the International Symposium on Underwater Technology (UT ’04), pp. 181–185, Taipei, Taiwan, 2004. C. Debever and W. A. Kuperman, “Robust matched-field processing using a coherent broadband white noise constraint processor,” Journal of the Acoustical Society of America, vol. 122, no. 4, pp. 1979–1986, 2007. F. Ding and X. Y. Gong, “Multiresolution processing for source detection and localization,” Acta Acustica, vol. 28, no. 1, pp. 40–44, 2003. G. Gong and X. Gong, “Robust matched field processor based on wavelet denoising and feature extraction,” Chinese Journal of Electronics, vol. 16, no. 4, pp. 683–687, 2007. N. E. Huang, Z. Shen, S. R. Long, et al., “The empirical mode decomposition and the Hilbert spectrum for non-linear and non-stationary time series analysis,” Proceedings of the Royal Society of London A, vol. 454, no. 1971, pp. 903–995, 1998. P. Flandrin, G. Rilling, and P. Goncalves, “Empirical mode decomposition as a filter bank,” IEEE Signal Processing Letters, vol. 11, no. 2, pp. 112–114, 2004. A.-O. Boudraa and J.-C. Cexus, “EMD-based signal filtering,” IEEE Transactions on Instrumentation and Measurement, vol. 56, no. 6, pp. 2196–2202, 2007. F. B. Jensen, W. A. Kuperman, M. B. Porter, and H. Schmidt, Computational Ocean Acoustics, AIP Press, Woodbury, NY, USA, 1994. D. L. Donoho and I. M. Johnstone, “Ideal spatial adaptation by wavelet shrinkage,” Biometrika, vol. 81, no. 3, pp. 425–455, 1994. M. B. Porter, “The KRAKEN normal mode program,” Tech. Rep. SM-245, SACLANT Undersea Research Centre, La Spezia, Italy, 1991. M. B. Porter and A. Tolstoy, “The matched field processing benchmark problems,” Journal of Computational Acoustics, vol. 2, no. 3, pp. 161–185, 1994.

7


Research Article A Relative-Localization Algorithm Using Incomplete Pairwise Distance Measurements for Underwater Applications Kae Y. Foo and Philip R. Atkins School of Electronic, Electrical and Computer Engineering, University of Birmingham, Edgbaston, B15 2TT, UK Correspondence should be addressed to Kae Y. Foo, [email protected] Received 1 July 2009; Revised 5 December 2009; Accepted 13 January 2010 Academic Editor: Martin Ulmke Copyright © 2010 K. Y. Foo and P. R. Atkins. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The task of localizing underwater assets involves the relative localization of each unit using only pairwise distance measurements, usually obtained from time-of-arrival or time-delay-of-arrival measurements. In the fluctuating underwater environment, a complete set of pair-wise distance measurements can often be difficult to acquire, thus hindering a straightforward closed-form solution in deriving the assets’ relative coordinates. An iterative multidimensional scaling approach is presented based upon a weighted-majorization algorithm that tolerates missing or inaccurate distance measurements. Substantial modifications are proposed to optimize the algorithm, while the effects of refractive propagation paths are considered. A parametric study of the algorithm based upon simulation results is shown. An acoustic field-trial was then carried out, presenting field measurements to highlight the practical implementation of this algorithm.

1. Introduction The capability of reliable underwater modem technology [1, 2] has led to a growing number of emerging underwater applications, presenting with them new possibilities and challenges. One of these applications is the deployment of a cluster of underwater sensors [3], which offers benefits ranging from oil-platform monitoring [4] to ecosystem monitoring, surveillance, and early warning systems for tsunami. A typical application of a sensor deployment generally involves the collection of data and the delivery of these data [5, 6]. In the former, the knowledge of sensor positions may play an important role in aiding the interpretation of the recorded data or in improving the performance of signal processing algorithms such as in array processing [7]. In the latter, where the collected data are sent or relayed to a destination, the estimation of sensor position enables the implementation of more energy and latency efficient routing and channelaccess protocols [8, 9]. Therefore, in situations where the positional information are not available to the sensors prior to deployment, or that it changes after deployment, there exists the

motivation to localize the sensors with existing modem capabilities. The aim of this paper is to present and evaluate an algorithm using the weighted-majorization [10, 11] multidimensional scaling (MDS) approach for the localization of sparsely deployed sensors within the underwater environment. Based on extensive study of sensor localization in the radio frequency domain, the underpinning methodology can be broadly categorised into range-free and rangebased schemes [12]. Range-free schemes are effective in obtaining estimated positions for applications requiring limited accuracies but usually impose constraints on the flexibility of deployment. Range-based schemes are based upon the accurate measurements of Euclidean distances between the sensors, which can be derived from two-way ranging delays, time-of-arrivals, angles-of-arrival, or received signal strength indicator (RSSI). In the underwater environment, RSSI measurements are affected by multipaths and back-scattering especially in a shallow water environment such as in coastal waters or within a busy harbour. Also, acoustic modems generally operate within a frequency band that captures many external sources of noise, varying from shrimps [13]

2 (in tropical waters) to breaking waves in a stormy weather [14], thus contributing to a high and fluctuating level of ambient noise. These factors can potentially lead to inconsistency in RSSI measurements. Similarly, measuring anglesof-arrival to a high accuracy may prove prohibitive unless every node is equipped with the necessary hydrophone array. The viable methods are therefore by using time-of-arrival measurements which require strict synchronization amongst all the nodes or by two-way ranging. The latter method requires no synchronization and operates by measuring the two-way propagation time assuming that the queried modem sends a reply packet after a fixed time-delay. The task of underwater sensor localization can be considered as a two-step process; first by the localization of the sensors in the 3D Euclidean space with respect to one another using measurements of internode distances only, and then, if necessary, the anchoring of these positions to a reference or geodetic coordinate system. A relatively straightforward method of resolving the sensors’ relative locations using only pairwise distance measurements is by metric multidimensional scaling, as a special case where one assumes that the measure of dissimilarities is represented by Euclidean distances, and that a set of coordinates within the relevant dimensions explain the observed distances. This concept has its roots in the field of psychometrics [15], in which an early analytical solution was presented by Torgerson [16] and referred to as classical MDS. In order to apply classical MDS to the problem of sensor localization, all the pairwise distances between the nodes need to be obtained [17]. This implies that every node needs to have acoustic visibility to all the other nodes. Such a requirement may often be difficult to meet in practice, as ranging measurements may be erroneous or unsuccessful between nodes that are further apart, as well as nodes that are partially obstructed (such as by harbour walls) and have no complete visibility to all the other nodes. The contribution of this article is in addressing the problem of relative localization using incomplete pairwise distance measurements. By applying a robust approach based upon an iterative, weighted, cost-minimization algorithm known as stress-majorization [18, 19], it is shown that a cluster of sensor nodes can be efficiently localized in the absence of complete pairwise distance measurements. The key improvements introduced herein are a robust and effective method of initialization of the algorithm, a parametric study of the proposed approach, and a case-study of its practical application based upon experimental field measurements. The next section relates the contribution of this paper with regard to previous research effort within similar domain. Section 3 presents the analytical formulation of the problem and the algorithm of the proposed approach. In Section 4, simulation results provide a parametric evaluation on the algorithm’s performance. Section 5 describes a field trial being conducted with 12 nodes using acoustic timeof-arrival measurements, capturing the issues related to the implementation of this algorithm and verifying the results predicted in the simulation study. Section 6 presents a short discussion on the scope of this article while Section 7 draws the conclusion from this work.


2. Related Work Sensor localization is an area of active research in both the radio [20–24] and underwater domains [25–29], where various solutions based on different levels of constraints and assumptions on infrastructure availability have been studied. Broader reviews on this subject can be found in [12, 30]. In [23], Patwari et al. applied maximum likelihood estimation techniques to approximate a node’s relative location, but the accuracy of the approximations (and the validity of the derived lower Cramer-Rao bounds) depends on having complete pairwise distances for all the nodes and knowledge of the probability distribution underlying the observed data. Although one can assume that the pairwise distances are Gaussian distributed (the validity of which increases with higher signal-to-noise ratios [31]), the requirement of obtaining all pairwise distances may introduce a challenging constraint in practice for the application scenario considered in this article. In [22], Moses et al. also presented a selflocalization approach method using a maximum-likelihood estimator, relying on both time-of-arrival measurements and angle-of-arrival measurements. It is also acknowledged that with incomplete data measurements, the maximum likelihood estimator may not yield a unique solution. In [17], Shang et al. applied classical-MDS by eigenvalue decomposition (EVD) for the localization of nodes using distance measurements. It is demonstrated that closed-form solutions can be obtained without the need for iterative computations, but this is restricted by the condition that global information of pairwise distances in the network needs to be made available to a central processor or to all individual nodes. Ji and Zha [32] applied a majorizationMDS approach for sensor localization, allowing for missing pairwise distances. This removes the requirement for complete pairwise distance measurements. However, a random start configuration is applied for the estimation of the initial point coordinates, and the possible existence of nonlinear propagation paths was not discussed. The work is extended by Costa et al. in [33], where arbitrary non-negative weightings can be applied to distance measurements, such that adaptive weightings can be applied to account for different levels of confidence amongst the pairwise distances. The proposed algorithm is decentralised such that each node estimates its local cost function iteratively, then communicates this to their neighbours in order to achieve cost minimization globally across all the nodes. However, there is little emphasis on the method for estimating initial node positions, and the algorithm similarly assumes that the measured distances are an accurate representation of Euclidean distances between the nodes. Also, since the focus is on adaptively choosing neighbours based upon the quality of measurements by allocating the appropriate weightings, the work did not investigate the tolerance of the algorithm to varying levels of missing pairwise measurements. An experimental study of sensor self-localization in the free-space outdoor environment was conducted using acoustic ranging by Kwon et al. in [34]. In addressing the issue of missing and noisy distance measurements, a weighting function that was coupled with a soft constraint

EURASIP Journal on Advances in Signal Processing of minimum distances were introduced. The key difference in their approach is in that a gradient descent algorithm was applied in the process of minimization, and that a multiple restart scheme was used to avoid local minima. Separately, an alternative method of addressing missing distances within a 3D environment was studied by Birchfield [35], which iteratively uses a subset of points (up to 4 for 3D) with the highest availability of distance measurements to derive an estimate of local coordinates, until all the coordinates based on relative distances are obtained. Simulation results showed that this can effectively mitigate the need for classical MDS in cases where the condition, that each node has a minimum of m + 1 unique distance measurements to nodes that satisfies the same condition, is met, where m is the total number of dimensions. This condition is more easily met when the total number of sensors is high compared to the number of dimensions which is usually only up to 3 in a Euclidean space. The focus of this work is on a majorization-MDS algorithm for the relative localization of underwater sensors, or nodes, by using only incomplete inter-node distance measurements, given no other a priori information. Central to this approach is the application of classical-MDS using approximated distances in replacement of missing pairwise distances for obtaining the initial estimates of coordinates for the majorization algorithm. This is shown to be effective in avoiding local minima, and mitigates the need for multiple restarts with different sets of random estimates.

3. A Weighted and Iterative Minimization Approach Iterative majorization, a term coined by Heiser [11], is a minimization method formulated in the field of geometric data representation [10, 18], and can be applied to multidimensional scaling [19, 36]. One of the attractive features of this algorithm is that a non-increasing sequence of function values are yielded, implying a quick and guaranteed convergence. However, it is worth noting that the algorithm does not necessarily converge at the global minimum. On the contrary, the point of convergence would, in most cases, be at a local minimum [37], hence the importance of having an effective approach to find the global minimum when applying this algorithm. The sensor nodes are assumed to be stationary, or drifting at such a rate that the change in position during localization is negligibly small. Nodes are also assumed to have protocols to broadcast their presence to the other nodes, to perform mutual ranging measurements, and to share their range measurements with the other nodes. This assumption does not reduce the practicality of the algorithm proposed herein. In its simplest form, this can be based on a classical time-division protocol, where nodes broadcast their ID and any known pairwise measurements before performing ranging measurements to any previously unknown nodes, and repeating the process several times. Time-slots can be uniquely allocated based upon each node’s unique ID [38], while the slot length is defined in order to mitigate the need for strict time-synchronization across all the nodes. Optimized distributed protocols can be found in [33, 39].

3 3.1. Problem Formulation. Relative-localization involves calculating a set of relative coordinates in the relevant dimensions of the Euclidean space for all the nodes within a cluster, such that their corresponding pairwise distances closely match the measured pairwise distances. Given n number of sensor nodes, the coordinates of these nodes are represented by an n × m matrix X where m is the number of dimensions. The pairwise distance between any two nodes is a function of the set of coordinates X, and for a Euclidean space can be expressed as ⎡

di j (X) = ⎣

m

⎤1/2

(xia − x ja )

2⎦

,

(1)

a=1

where di j is the pairwise distance between nodes i and j, calculated using their respective m dimensional coordinates. The elements di j form a symmetrical n × n pairwise distance matrix, D. Similarly, the measured distances between nodes i and j, δi j , form a symmetrical pairwise distance matrix Δ. The mismatch between the measured distances and those which are calculated for the approximated coordinates Xmaj can be expressed as σ(X) =

2

wi j δi j − di j (X) ,

(2)

i< j

where wi j is the weighting for the distance between node i and j that corresponds to element (i, j) in both the matrices Δ and D. The condition of i < j denotes the elements in the upper triangle of the symmetrical matrices. The weightings are normalized to values between 0 and 1 where a 0 represents a missing distance measurement. The function σ is commonly referred to as the stress function in related literatures [40]. The remaining task is to approximate the coordinates of the nodes, Xmaj , such that the value of σ is minimized. 3.2. Classical-MDS. When all the pairwise distance measurements are available, classical-MDS offers a solution without iterative computations. Using the matrix Δ, the computation steps for classical-MDS [16, 24] are given as follows. (1) Calculate a covariance matrix, Z, from the square of the distance matrix, Δ2 by multiplication with centring matrices, producing a centred matrix Z = (−1/2)JΔ2 J where J = I − L/n, I is an identity matrix of size n, and L is a square matrix of ones of size n. (2) Compute the eigenvalues, G, and eigenvectors, Q, by applying eigen-decomposition on Z. (3) The approximated coordinates, Xc , is then given by Qn,m Gn,n 1/2 where Qn,m is the first n × m elements of Q, while Gn,n is the first n × n elements of G that usually correspond to the non-negative eigenvalues in the diagonal. 3.3. Iterative Majorization Initiated by Approximated Classical-MDS. If some of the pairwise range measurements cannot be obtained, for example as a result of obstruction

4


to the line-of-sight, then the measured pairwise distance matrix Δ will be incomplete (in which the elements δi j that correspond to the unavailable measurements are 0). In such cases, the function in (2) can be iteratively minimized by updated approximations of Xmaj . This is achieved by using a majorization function that satisfies a chain of inequality towards the stress function, resulting to new approximations of Xmaj that yield a smaller value for the stress function. The derivation of the majorization function is well documented in [36]. For the purpose of clarity in describing the proposed modifications, the usual procedures of the algorithm are herein described. (1) Set the weights wi j corresponding to the i- j pairwise distances, using 0 for missing measurements and 1 otherwise, or, if a priori knowledge is available to provide indication towards the relative levels of confidence in the measurements, positive ratios of up to 1 are allocated. (2) Initialize Xmaj,0 to a set of random coordinates, and the number of iterations, k = 0, then calculate σ0 using (2). (3) Calculate an update for Xmaj,k by using the relationship:

Xmaj,k+1 = V + Bk Xmaj,k Xmaj,k ,

(3)

where V + = (V + L)−1 , V is a matrix with elements vi j formed from the allocated weightings such that n vi j = −wi j if i = / j and vii = j =1, j = / i wi j for the diagonal elements. Recall that L is a square matrix of ones of size n. Bk contains elements bi j calculated in the following manner: bi j =

w i j δi j

di j Xmaj,k

for i = / 0, / j, di j Xmaj,k =

bi j = 0 for i = / j, di j Xmaj,k = 0, bii =

n

bi j

(4)

for the diagonal elements.

j =1, j = /i

(4) Calculate σk+1 and repeat from step 3 if σk+1 − σk > h, where h is an arbitrarily small positive constant acting as a threshold beyond which is indicative of a convergence, or if k ≤ K, where K is the maximum number of iterations allowed. Otherwise, the relative locations are given by the coordinates in Xmaj,k+1 . The corresponding distance matrix is Dmaj,RandInit . The value of h can be set as σ0 /105 , such that it is suitably small to indicate that any further iterations yield negligible minimisation of the error parameter σ, hence no further improvements to the estimate of relative positions.

3.4. Algorithm Optimization. A common method to optimise the iterative algorithm in Section 3.3 is to apply multiple restarts (i.e., performing the complete iterative algorithm repetitively) using different sets of random initial coordinates in order to avoid local minima. This may be computationally intensive for embedded processors on deployable nodes, which usually implies greater power consumption. An alternative method is herein proposed for mitigating random restarts, and is shown in Section 4 to have comparable performance but with a significant reduction in computation requirement. Central to the proposed approach is the observation that, albeit with poor results, classical-MDS can be performed on a distance matrix with missing measurements. One may choose to obtain a relatively inaccurate, but rapid, approximation of the missing measurements by taking the mean of available pairwise distances corresponding to both i and j nodes (i.e., mean of available measurements across the rows of i and j). The algorithm of classical-MDS described in Section 3.2 can be applied to Δ, but m is set to n so that Xc,n is a set of coordinates in a larger number of dimensions than the Euclidean space. By principle component analysis [41], one then notes that the columns of Xc,n that have larger values of standard deviations would represent the more principal axes, or dimensions, in the data. It is then possible to discard the dimension with the least standard deviation, recalculate an updated distance matrix, and obtain a new Xc,n−1 with a smaller number of dimensions, until the coordinates in 3dimensional space are obtained. This is applicable because distance measurements corresponding to the Euclidean space are often restricted to within 2 or 3 dimensions, such that m n. However, the final result is often a few orders of magnitude inferior to the results obtained from iterative majorization with multiple restarts. This is because some useful information in the discarded axes is inevitably lost during dimensionality reduction. A more robust approach therefore is to merge this technique with the iterative majorization algorithm, such that the coordinates Xc,n can be used as the initial estimates for the iteration. The complete steps are described as follows. (1) Obtain rapid approximations of the missing pairwise distances using simple averaging for available measurements corresponding to the pair of nodes, yielding Δapprox . (2) Perform classical-MDS on Δapprox to obtain Xc,n such that the coordinates have n number of dimensions. (3) Set Xmaj,0 = Xc,n and perform the majorization algorithm in Section 3.3 using the original Δ and corresponding weightings. (4) Upon convergence, calculate a new set of distances, Δconv , by using Xma j,k+1 . (5) Perform classical-MDS on Δconv with m = 2 or 3 depending on the desired number of dimensions. (6) Using the obtained Xc as initial estimates, perform the majorization algorithm to obtain the final coordinates. The corresponding distance matrix is Dmaj,MDSInit .


5 Difference between estimated ray path and shortest distance 8

r

θl

r TX a s RX

Estimated error, s − a (m)

θl

7 6 5 4 3 2 1 0 0

Figure 1: Refracted path modelled as an arc of curvature given the assumption of constant sound velocity gradient.

1

2

3 4 5 6 7 Distance from source, s (m)

8

9

10 ×103

Figure 2: Error from shortest distance due to refracted propagation path.

To distinguish between the two approaches, this approach is named as MDSInit while the random multiple restart approach is named as RandInit. The results from a parametric study comparing MDSInit and RandInit are shown in Section 4. 3.5. Issues Related to Underwater Sound Propagation. There are two issues related to underwater sound propagation that have a direct impact on the measurement of pairwise distances. The first is the estimation of sound velocity. The distances are usually obtained from the time or timedelay-of-arrival measurements using an estimated sound velocity. However, this estimated velocity may contain an error if the sound speed profile is not measured prior to localization of the assets. By making the assumption that the estimated velocity is the velocity at the corresponding depth of the node, the error can be compensated using a simple scaling factor. However, the accurate scaling factor cannot be directly optimized using the implied distances because the actual path of sound propagation is usually greater than the shortest Euclidean internode distance assumed by MDS algorithms, which leads to the second issue. The refraction experienced by a sound wave is proportional to the gradient of velocity with respect to depth. Although the modelling of the precise path is more involved, it is possible to approximate a relationship between the shortest distance and the non-linear path using the Ray theory [42], which in the underwater environment is applicable for higher frequencies of a few kHz and above. This is applicable for underwater modems that have effective range of up to a few kilometres, hence operating within a relatively high frequency band, typically from 2 to 20 kHz. If the operating environment is assumed to have a depth of not more than 100 m, the velocity gradient can be treated as quasi-constant such that there is no significant fluctuation in the underlying trend [43]. This is usually representative of shallow coastal waters, and may not encapsulate all possible deployment environments for underwater sensor networks. Given this assumption, the non-linear path then becomes an arc of curvature for a circle with a radius r as shown in Figure 1,

expressed as (by Snell’s law): r=

c , g cos(θ)

(5)

where c is the velocity of sound corresponding to the depth of the source, g is the gradient of the velocity variation, and θ is the launch angle of the ray. The relationship between the length of the refracted ray, s, and the shortest distance a can be stated as (by trigonometry of an isosceles triangle):

a = 2r sin

s . 2r

(6)

As an example, if the ray is horizontally launched by a node at 50 m depth, and the velocity profile has a gradient of 2 ms−1 /100 m, the relationship between (s − a) and s is shown in Figure 2, indicating that for the assumed environment, the error introduced by sound refraction is mild for ranges under 4000 m. With time-delay-of-arrival measurements, this error is doubled due to the two-way propagation path. Compensating for this error requires the availability of sound velocity profile data during localisation. Figure 2 shows that in very shallow water environments with relatively benign velocity profiles and short ranges (i.e., under 4000 m), the error caused by sound refraction is relatively small (i.e., 0.02% of the range) compared to the ambiguity errors that are potentially introduced by a large percentage of missing pairwise distances (typically in the order of 10 to 20% of range). Another common compensation approach is by using a set of available anchor points of which the precise coordinates, and hence shortest inter-node distances, are used to predict a best-fit velocity profile by matching against ranging measurements. These anchor points are also used for mapping the relative locations onto geo-coordinates by using m-axis vector translations along with m-axis rotations. It must be noted that the nonlinearity of the propagation path is only insignificant in very shallow waters where the variation of sound velocity with respect to depth is small. However, this assumption is no longer valid in deeper waters, and therefore, it is important in such cases to compensate for the associated errors. An effective numerical solution is

6 presented by Berger et al. [44] that evaluate and compensate for the stratification effect of the depth-dependent sound velocity by using only the depth and sound velocity profile information, and allows for noisy (Gaussian) time-of-arrival and depth measurements. 3.6. Weighting Matrix. The weighting matrix can be used to set the level of influence exerted by the corresponding distances in the outcome of the algorithm. Intuitively, the weightings are a representation of confidence in the measured data, and with the appropriate levels that best matches the actual underpinning conditions, one seeks to obtain an optimal weighting matrix that produces the relative locations with the smallest error. A priori data can be used to guide the allocation of weighting. As an example, if a modem is known to produce an error that is proportional to the measured distance, then one would penalise the weighting for a larger distance measurements. Such information can also come from detailed channel modelling for a known environment. Without a priori data, the estimation of an optimal weighting matrix relies heavily on the availability of statistical information that can be extracted from the measured data. With both time-of-arrival measurements and timedelay-of-arrival measurements, it is possible to obtain multiple measurements, and adjust the weighting based upon the standard deviations of these repetitive measurements, such that data with large standard deviations are allocated smaller weights. This assumes that the error influencing the deviations has a nonzero mean. Otherwise, taking the average of a sufficiently large number of repetitive measurements would give a similarly confident result. In the case of time-of-arrival measurements, the difference between the measurements in opposite directions provides an indicator to the bias in the distance measurement. For the acoustic experiments detailed in Section 5, the wind speed was estimated using the differences in time-of-arrival measurements, and the weighting matrix is adjusted based upon the standard deviations of repetitive measurements.

4. Parametric Simulations Simulations were carried out in order to obtain a comparison between the initialization approaches. The approach of using MDS and dimensionality reduction to initialize points is named as MDSInit, while RandInit denotes the use of multiple sets of random initial points. The environment was a 10000 × 10000 × 3000 m 3-D space. As the purpose of the simulation is to carry out a parametric and comparative study of the algorithms within a 3-D space, using a very shallow environment (i.e., kthr . Another approach is the balloon estimator, in which the window size h is increased until a minimum number of samples from X are covered. In this case the acceptance criterion depends on the window volume: hd < Vthr . Updating a sample-based model is simple: a pixel classified as background is added to the sample set X, and the oldest samples in the set are removed. Still, some methods split their sample set into two subsets: one for describing long-term background phenomena, and one for dealing with short-term, high frequency change in the background. The ViBe [7] method we used, implements a fairly simple kernel density estimator but uses an innovative approach to the model update by including spatial information. Classification of the incoming pixel is done by counting the samples in a fixed-size window around it, with the threshold being 2 samples out of a set of 20. The sample set is not divided in a long- and short-term memory, but the bias of single sample set methods towards recent data is alleviated by a random replacement update scheme. To ensure spatial correlation, when data is inserted into a pixel model, it is also added to a randomly selected neighbouring pixel model. This allows for the spatial correlation between pixels to be taken into account by the model, greatly improving the method’s ability to deal with noise and small camera movements. One should note that the ViBe algorithm does not need to be trained as it can be instantaneously initialized using a single image.

4. Movement-Based Methods 4.1. Introduction. The background subtraction methods described above are capable of extracting anomalous objects, even from a moving background. However, they still have trouble with the worst case mine detection scenario we assumed, where a high sea state causes the scene to be filled with moving objects of similar scale, shape, and intensity as the foreground target. Inherently, all anomaly detection methods make tradeoffs regarding computational cost and memory usage, trying to maintain an up-to-date background model with a description length as small as possible. Algorithms such as EGMM discard both temporal and spatial information, retaining only image intensity statistics; whereas the samplebased ViBe method introduces some spatial information. Given the tendency of floating mines to converge to thermal equilibrium with the surrounding sea water, even spatially correlated intensity statistics will not suffice. We stated that the object’s motion provides a better detection characteristic, and in the previous research we showed that the short-term motion information provided by an optical flow algorithm was capable of detecting floating objects [4, 5]. Still, this method, which includes both spatial and temporal information, proved to be slow and restricted to the extrema of the objects motion. Therefore we intend to look at longer-term motion information for more reliable detection. When looking at long-term motion information, keeping track of spatial information becomes difficult, since the

EURASIP Journal on Advances in Signal Processing background waves will traverse across the entire image. This would require an object-based approach, in which waves are identified as such and tracked throughout the video sequence. In a confused sea state, it is hard to figure out which wave is which, and intersecting wave trains can seem to break up or merge, which seriously complicates tracking them. In this paper, we restrict ourselves to a low-level, pixelbased approach, meaning that spatial information will be lost, and that detection will have to be based upon temporal characteristics. 4.2. Behaviour Subtraction. An interesting approach can be found in the behaviour subtraction method described by Jodoin et al. [8]. This generic technique was developed for the detection of abnormal behaviour in surveillance footage and is not tied to the physical properties of the sea surface scene. Interesting is also that Jodoin et al. demonstrate their algorithm on video sequences of water surfaces, in which the regular surface waves are included in the background; whereas extraordinary events such as ripples from a stone thrown in the water, or a passing boat, are detected as abnormal events. The behaviour subtraction method functions by monitoring the level of scene activity in a sliding time window of length W, and by comparing this observed activity to a background behaviour model derived from a training We explained before that this sort of approach sequence I. has considerable memory and computational requirements, making real-time implementation difficult. Jodoin et al. solve this problem by significantly reducing the information processed on two levels. For one, frames are compared to a conventionally obtained background model b (which we calculated using a running mean algorithm). This preprocessing step transforms an integer frame It to an image consisting of binary activity labels, thus significantly reducing the required storage space Lt = | I t − b | > θ .

(12)

The second reduction occurs when the label sequence Lt is evaluated in time window of length W. Jodoin et al. reduce the dimensionality of this 3D space-time volume by defining “behaviour descriptors,” compressing the dynamics of a pixel into a single value. One behaviour descriptor proposed is the maximum activity descriptor. In this case, an excessively high level of activity is considered to be a sign of abnormal behaviour. Therefore, a background behaviour image B is defined as the maximum level of activity encountered in any of the windows throughout the training sequence I of length N: ⎡

B = max⎣ k

k τ =k−W+1

⎤ τ ⎦, L

W ≤ k ≤ N.

(13)


7

(a)

(b)

Figure 5: MW01 sequence in the 3–5 μm band. From left to right, (a): original, mean, gmm. (b): EGMM, ViBe, behaviour subtraction.

(a)

(b)


With this background image obtained, the incoming video stream can be evaluated through comparing B to the observed behaviour image vt at time t: vt =

t τ =t −W+1

Lτ .

(14)

This comparison can subsequently be used to detect abnormal behaviour, for example, by defining a “negatives-tozero” distance function D t = vt − B 0 ,

(15)

8


(a)

(b)


(a)

(b)

(c)

Figure 8: MW08 sequence in the 3–5 μm band. From left to right, (a): original, mean.(b): gmm, EGMM, (c): ViBe, behaviour subtraction.

where a0 = 0 if a < 0. Similarly to (1), a binary mask Mt can be obtained by thresholding this distance function, effectively subtracting the background behaviour and detecting foreground objects. Realistic assessment of background behaviour requires a fairly large time window W to be chosen. In [8] the

authors use W = 100 for the maximum activity descriptor. The activity images’ binary nature significantly mitigates this large storage requirement, but a conventional high-level implementation still suffers from the number of required memory access operation. A solution can be found in the following writing of (14):


9

(a)

(b)


5. Experiments

100

80

B(y)

60

40

20

0

0

50

100

150

200

250

y

Figure 10: Maximum activity descriptor B for MW01 trained on a vertical line (parallel to the y-axis) in the sequence, showing clearly the gaps in the model due to short training sequence. This causes the horizontal streaks of false positive detections by the behaviour subtraction algorithm in Figure 5.

We used six infrared video sequences of floating test targets taken in various environmental conditions to evaluate the algorithms described above. These sequences are between 300 and 2000 frames long, have been taken in coastal waters using stationary thermal cameras, and have been annotated with groundtruth data for the purpose of detection performance evaluation. On these measurements we tested a number of pixelbased background subtraction methods described above. We used a running mean, a simple GMM, the extended EGMM algorithm, the ViBe sample-based method, and an adaptation of the behaviour subtraction method. We obtained precision and recall values for the last three algorithms, as seen in Table (1). Precision represents the probability that a detected pixel belongs to a target;whereas recall represents the probability that a target pixel will be detected by the algorithm. This can be expressed in terms of true and false positives (tp, fp) and of false negatives (fn) by the following formula: Precision =

tp , tp + fp

tp Recall = . tp + fn vt = vt−1 − Lt−W + Lt .

(16)

Here we see that only 3 images have to be kept in memory at any iteration: the first one of the previous time window Lt−W , the previous activity descriptor vt−1 , and the current activity image Lt . This keeps memory requirements low for large W and reduces the amount of redundant calculation during summation.

(17)

For the behaviour subtraction implementation, we use the output of the running mean filter to determine the initial background. We also used the prior assumption of spatial invariance in sea surface statistics, which translates into a horizontal invariance of the background behaviour for the scene. This assumption holds in the absence of land, ships, or direct solar glint in the frame. This allowed us to train the behaviour model on a single vertical line of the image, instead of on the entire image. Furthermore we used the

10 maximum activity descriptor, on a time window of 100 frames and a θ = 10. When looking at the qualitative results in Figures 5–9, we see ViBe and behaviour subtraction clearly outperforming the parametric models. The classic GMM has few false positives but fails to detect the target in all but one case (video sequence MW33, Figure 9) in which the target intensity is clearly much higher than its surroundings. EGMM, which assigns multiple foreground classes, has the inverse problem: it gets drowned in false positives, only performing reasonably well in one sequence (MW03, Figure 6). We also see this in the quantitative analysis: while EGMM has relatively high recall values, indicating successful detection of the targets, its low precision shows that extracting these targets from the cloud of false positives will be difficult. It is peculiar that the recall values in Table 1 are all fairly low, which would indicate a low probability of target detection, yet when we look at the images, the targets are clearly visible in the detection results. The reason for this is that our validation is pixel-based, and none of the algorithms registers the full target, but only parts of it, so a number of pixels in the groundtruth data remain undetected. This problem can be avoided by applying postprocessing methods, and by, for example, defining detection by coinciding bounding boxes. We chose not to do this, as it would lead us away from the pixel-based paradigm in which the evaluated algorithms were defined. The sample-based ViBe algorithm performs better overall than the parametric models, though it still has its limitations. It performs exceptionally well in the sequences where there is a significant thermal contrast between target and background (MW01, MW03, and MW05: Figures 5–7), resulting in the heighest precision of all three algorithms, and succeeds in providing a learned model capable of dealing with a very dynamic background. However, when the sea state worsens, and the thermal distinction between the target and the breaking waves diminishes, ViBe’s performance weakens (Figures 8 and 9). This was to be expected: ViBe only models the background intensity, which means that it does not possess the temporal information required to distinguish between background and foreground. Behaviour subtraction on the other hand renders the best performance of all three for high sea state, achieving both high precision and recall in these sequences. It manages to classify all but a few exceptional waves as background, and it identifies the target’s behaviour as anomalous in all examples, though only in a part of the target’s composing pixels. However, in Figure 5, we show a peculiar failure mode of the algorithm (which performs better later on in the same sequence). We see several series of false positives stringed along horizontal lines. Upon closer inspection, this was caused by the gaps in the behaviour model B which was trained along a vertical line in the image sequence. This lack of smoothness as seen in Figure 10 allows for horizontal zones where the behaviour threshold is lower than in the surroundings, allowing for the strings of false positives to occur. While behavioural variation along the vertical axis is expected due to the difference in range, there is no physical reason for these gaps to occur. This leads us to conclude that

EURASIP Journal on Advances in Signal Processing Table 1: Sequence average precision-recall pairs for behaviour subtraction, ViBe, and EGMM. MW01 MW03 MW05 MW08 MW33

Behaviour .29;.40 .36;.20 .25;.62 .77;.79 .46;.71

ViBe .30;.42 .90;.20 .86;.49 .69;.75 .30;.49

EGMM .27;.66 .34;.29 .09;.29 .69;.57 .29;.67

smoothness should be imposed on the model, either through longer training times, or by application of a smoothening function to the model. Finally, we would like to indicate a point where all algorithms failed. Sequence MW01 contains two targets, one spherical target in the upper left corner, and a cylindrical one lying in the surf mid-front. None of the algorithms, including behaviour subtraction, succeed in detecting this target, which is the reason for the low precision values measured.

6. Conclusions In this paper we described the problems involved in the automatic detection of small floating targets on the sea surface, and this in the context of the detection of drifting mines. We described the state of the art in the domain of pixel-based background subtraction algorithms, including the innovative ViBe method, and compared this with the more complex behaviour subtraction method which includes temporal information to address the specific problems of the dynamic background provided by the sea surface. The sample-based ViBe algorithm performs significantly better than the parametric methods we applied to our test sequences, which is particularly interesting given its complete lack of prior assumptions regarding the scene. In rough seas, the method performs less ideally due to the great similarity between waves and target. While the algorithm could be adapted to incorporate these waves into the background model, this would not allow it to detect targets at thermal equilibrium with the ocean. On the other hand, the algorithm would be exceptionally fit to the detection of targets radiating at a different temperature than the surface, such as swimmers, shipwreckees, small boats, or a semisubmersible’s exhaust. The behaviour subtraction method outperforms all of the background subtraction algorithms presented here, because of its inclusion of temporal information in the model. It deals better with heavy seas than the others and has no trouble detecting targets at equilibrium with their surroundings. This comes at the cost of a heavier computational load, and the need for a long training sequence, which needs to be updated over time. The method shares with ViBe an interesting lack of prior assumptions, allowing it to be applied to a wide range of applications. We have shown that pixel-based masking techniques such as background and behaviour subtraction can be used to detect anomalous objects in the very dynamic environment provided by an agitated sea surface. While

EURASIP Journal on Advances in Signal Processing not suited as stand-alone detection algorithms in all cases, these methods can provide regions of interest with sufficiently high confidence to allow higher-level, object-based classification methods to use them as prior input. In future research we intend to evaluate the alternative “average activity descriptor” described in [8], to obtain groundtruth data for a quantitative validation of the algorithms’ detection performance. We also need to improve upon the training procedure for the behaviour subtraction method, guaranteeing a smooth model and allowing for continuous update. Behaviour subtraction also does not use spatial correlation the way ViBe does, which indicates an interesting approach to improving the method. Lastly, since theoretical models of the sea surface describe a spectral distribution, we would like to look into activity descriptors which makes explicit use of frequency information.

Acknowledgments This research resides within the framework of the MRN06 project sponsored by the Belgian Ministry of Defence and was conducted at the Royal Military Academy (RMA), at Université de Liège (ULg), and at Ghent University (UGent).

References [1] D. Comaniciu, V. Ramesh, and P. Meer, “Kernel-based object tracking,” IEEE Transactions Pattern Analysis and Machine Intelligence, vol. 25, pp. 564–577, 2003. [2] Z. Khan, T. Balch, and F. Dellaert, “An MCMC-based particle filter for tracking multiple interacting targets,” in Proceesdings of the European Conference on Computer Vision, vol. 4, pp. 279– 290, 2004. [3] J. Cheng and J. Yang, “Real-time infrared object tracking based on mean shift,” in Proceedings of the Iberoamerican Congress on Pattern Recognition, pp. 45–52, 2004. [4] A. Borghgraef and M. Acheroy, “Using optical flow for the detection of floating mines in IR image sequences,” in Proceedings of the SPIE Optics and Photonics in Security and Defence, vol. 6395, Stockholm, Sweden, September 2006. [5] A. Borghgraef, F. D. Lapierre, and M. Acheroy, “Motion segmentation for tracking small floating targets in IR video,” in Proceedings of the 3rd International Target and Background Modeling and Simulation Workshop (ITBMS ’07), Toulouse, France, 2007. [6] Z. Y. Wei, D. J. Lee, D. Jilk, and R. Schoenberger, “Motion projection for floating object detection,” in Proceedings of the 3rd International Symposium on Advances in Visual Computing, vol. 4842 of Lecture Notes in Computer Science, pp. 152– 161, 2007. [7] O. Barnich and M. Van Droogenbroeck, “ViBe: a powerful random technique to estimate the background in video sequences,” in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP ’09), pp. 945– 948, April 2009. [8] P. M. Jodoin, J. Konrad, and V. Saligrama, “Modeling background activity for behavior subtraction,” in Proceedings of the 2nd ACM/IEEE International Conference on Distributed Smart Cameras (ICDSC ’08), pp. 1–10, 2008. [9] A. D. Forsyth and J. Ponce, Computer Vision: A Modern Approach, Prentice-Hall, New York, NY, USA, 2002.

11 [10] M. Piccardi, “Background subtraction techniques: a review,” IEEE Transactions Systems, Man and Cybernetics, pp. 3099– 3104, 2004. [11] S. Y. Elhabian, K. M. El-Sayed, and S. H. Ahmed, “Moving object detection in spatial domain using background removal techniques—state-of-art,” in Proceedings of the Recent Patents on Computer Science, vol. 1, pp. 32–54, 2008. [12] Y. Benezeth, P.-M. Jodoin, B. Emile, H. Laurent, and C. Rosenberger, “Review and evaluation of commonly-implemented background subtraction algorithms,” in Proceedings of the IEEE International Conference on Pattern Recognition (ICPR ’08), pp. 1–4, 2008. [13] Z. Zivkovic., “Improved adaptive gausian mixture model for background subtraction,” in Proceedings of the International Conference on Pattern Recognition, pp. 28–31, 2004. [14] Z. Zivkovic and F. van der Heijden, “Efficient adaptive density estimation per image pixel for the task of background subtraction,” Pattern Recognition Letters, vol. 27, no. 7, pp. 773–780, 2006. [15] K. M. Ochi, Ocean Waves, Cambridge University Press, Cambridge, UK, 1998. [16] W. P. Pierson and L. Moskowitz, “A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigordskii,” Journal of Geophysical Research, vol. 69, pp. 5181–5190, 1964. [17] K. Hasselmann, T. P. Barnett, E. Bouws, D. E. Carlson, P. Hasselmann, K. Eake, et al., “Measurements of wind-wave growth and swell decay during the joint north sea wave project (JONSWAP),” Deutsche Hydrographische Zeitschrift, vol. 8, no. 12, 1973. [18] R. Stewart, Introduction to Physical Oceanography, Texas A & M University, 2008. [19] K. Toyama, J. Krumm, B. Brumitt, and B. Meyers, “Wallflower: principles and practice of background maintenance,” in Proceedings of the 7th IEEE International Conference on Computer Vision, vol. 1, pp. 255–261, 1999. [20] C. Wren, A. Azarbayejani, T. Darrell, and A. Pentland, “Pfinder: real-time tracking of the human body,” in Proceedings of the IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 19, pp. 780–785, 1997. [21] C. Stauffer and E. Grimson, “ Adaptive background mixture models for real-time tracking,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, vol. 6, pp. 246–252, 1999. [22] R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, Wiley-Interscience, 2nd edition, 2000. [23] E. Parzen, “On estimation of a probability density function and mode,” The Annals of Mathematical Statistics, vol. 33, no. 3, pp. 1065–1076, 1962.


Research Article Statistical Real-time Model for Performance Prediction of Ship Detection from Microsatellite Electro-Optical Imagers Fabian D. Lapierre, Alexander Borghgraef, and Marijke Vandewal CISS Department, Royal Military Academy, Avenue de la Renaissance, 30, 1000 Brussels, Belgium Correspondence should be addressed to Fabian D. Lapierre, [email protected] Received 1 July 2009; Revised 13 October 2009; Accepted 5 November 2009 Academic Editor: Frank Ehlers Copyright © 2010 Fabian D. Lapierre et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For locating maritime vessels longer than 45 meters, such vessels are required to set up an Automatic Identification System (AIS) used by vessel traffic services. However, when a boat is shutting down its AIS, there are no means to detect it in open sea. In this paper, we use Electro-Optical (EO) imagers for noncooperative vessel detection when the AIS is not operational. As compared to radar sensors, EO sensors have lower cost, lower payload, and better computational processing load. EO sensors are mounted on LEO microsatellites. We propose a real-time statistical methodology to estimate sensor Receiver Operating Characteristic (ROC) curves. It does not require the computation of the entire image received at the sensor. We then illustrate the use of this methodology to design a simple simulator that can help sensor manufacturers in optimizing the design of EO sensors for maritime applications.

1. Introduction Since a couple of years, the number of illegal acts for taking control of maritime vessels has increased. For search-andrescue reasons, it is suitable to find efficient sensor systems for detecting vessels. Vessel candidates for illegal acts are often commercial vessels with great dimensions. Such vessels (and all vessels with length greater than 45 m) are required to set up an Automatic Identification System (AIS) used by vessel traffic services for identifying and locating vessels. However, when a ship is shutting down its AIS due to illegal acts or material defects, there are no means to detect it in open sea. Spaceborne sensors are a valuable tool for noncooperative ship detection when the AIS is not operational. Two classes of spaceborne sensors exist: radar and electro-optical (EO) sensors. As compared to radar sensors, EO sensors have lower cost, lower payload, and better computational processing load. To have a high revisiting time, a constellation of LEO micro-satellites is used. Micro-satellites limit the sensor payload to a few kilograms. Currently, EO sensors are then the best candidate for spaceborne applications. To have daynight capabilities, infrared (IR) sensors are used.

Optimum design of such sensors implies to be capable of simulating the evolution of sensor performance as a function of sensor or scene parameters before manufacturing the sensor. Sensor performance is often expressed using Receiver Operating Characteristic (ROC) curves representing the evolution of the probability of detection with respect to the probability of false alarms. So far, these curves are computed using results of detection algorithms applied to the image received by the sensor. This implies the simulation of these images and the choice of detection algorithms. For our application, since the payload is very limited, the Ground Sampling Distance (GSD) is large (about 100 m). Hence, ship detection cannot solely be pixel-based. This indeed leads to an important rate of false alarms. One possible solution is to detect wakes behind the ship. At large GSD, the turbulent wake is the most visible. It appears bright in optical images (Figure 1) and dark in long-wave IR (LWIR) images (Figure 2). Computing the evolution of ROC curves with sensor or scene parameters is then computationally intensive. This paper proposes a methodology having real-time capabilities for helping sensor manufacturers in optimizing the design of new EO sensors for maritime (ship detection) applications. This implies to be able to test, in real-time,

2


1 km

Spot 2 275.547

96-10-11

0339.2 2 P/5

Figure 1: Example panchromatic (optical) SPOT image of moving ships. Source: [2]. Turbulent wake appears bright.

We emphasize that our aim is not to provide a very accurate, validated simulator. Hence, in this paper, performance of the proposed tool is not deeply examined and this tool is not validated using real data. This will be the subject of further research. Our aim is only to propose a real-time methodology for assessing EO sensor performance and to illustrate this methodology by the design of a simple simulator for ship detection using MWIR sensors. Remember that this methodology is inspired from [3, 4]. Section 2 describes the wakes generated behind a moving ship. Section 3 defines ROC curves. Section 4 presents models used for the sea surface and for the turbulent wake. Sections 5 and 6 explain the model of the signal received at the sensor. Section 7 presents the real-time statistical simulator. Section 8 studies its performance. Section 9 concludes.

2. Wakes behind Moving Ships

Figure 2: Example thermal infrared (LWIR) LANDSAT image of moving ships. Turbulent wake appears dark. Colors correspond to normalized radiance received by the sensor.

the effect of sensor or scene parameters on ROC curves. In IR, near real-time simulators exist [1]. However, they were designed for airborne applications, for which ship detection is done using the contrast between ship and sea background pixels. This cannot be used for spaceborne EO sensors with large GSD. Hence, to our knowledge, there are no real-time tools available for simulating performance of spaceborne EO sensors with large GSD in a maritime environment. Our approach is based on the one described in [3, 4], where real-time capabilities are obtained by computing ROC curves from a model of the probability density function (pdf) of pixels contained in the image. This avoids simulating the image received by the sensor. In [3, 4], this idea was developed for land-cover scene modeling using hyperspectral sensors. In a maritime environment, a very first attempt to model sea pixels with a pdf was described in [5] for LWIR airborne sensors. To our knowledge, such methodology has not yet been considered for ship detection. This is the subject of the present paper. Our real-time statistical methodology is described in the case of a mid-wave IR (MWIR) sensor. The result is a simple simulator that produces ROC curves in realtime. The proposed statistical methodology can be applied to other EO sensors and even to radar sensors, if appropriate models for the pdfs are used. Such a tool can be very useful for ship detection using Synthetic Aperture Radar (SAR), for which the simulation of SAR images is time consuming [6, 7].

If a ship is moving, wakes are generated behind it. These wakes are observed for any vessel speed and dimensions and can persist for hours and grow several tens of kilometers long, making it a feature which can easily be detected using spaceborne sensors. It can also provide information on the vessel’s heading, speed, and potentially its hull dimensions, which makes it a very desirable feature for detection and tracking purposes. Therefore, wake detection is often used either in combination with or even instead of other ship detection methods. A ship produces two types of wakes [8]. The turbulent wake, a zone of reduced sea surface roughness which appears as a long bright (optical sensors) or dark (LWIR sensors) streak behind the ship, bounded by a v-wake, and the Kelvin wake, a system of ripples occurring inside a cone of 39 degrees originating at the ship’s bow. The Kelvin wake’s wave spectrum can be analyzed for determining the ship’s speed and heading, and its dimensions. Figure 3 shows a typical wakes pattern. 2.1. Kelvin Wake. The Kelvin wake consists of two systems of ripples, the transverse and divergent waves. These systems [9] are bounded by two cusp-lines separated by an angle of 39 deg. On the cusp-line, a wave propagates with a √ wavelength λ depending upon the ship speed V : λ = 4πV 2 / 3g with g being the gravity constant. 2.2. Turbulent Wake. The turbulent wake is a zone of highfrequency low-amplitude waves behind the ship’s stern. It behaves like a flat but rough surface, therefore contrasting with its surroundings. Hence, the physical quantities of interest are the width and the length of the wake. The turbulent wake’s width W depends upon ship dimensions, more specifically its beam (width) B, and its length L. We have W(r) ≈

w0 Bα−1 r 1/α , (r 0 L/B)1/α

(1)

where r is the distance from the ship stern. Here r 0 ≈ 4 and w0 ≈ 4 are derived from an empiric approximative


3 Cusp wave Kelvin envelope

Stern wave v

Turbulent wake

Ship hull Transverse wave Divergent wave Local wave disturbance region

3.1. Signal and Noise Pdfs. In our application, the target signal is the turbulent wake radiance, and the noise signal is the open-sea radiance. Each signal is characterized by a pdf. We thus have two pdfs representing the statistical distribution of the wake signal and of the open-sea signal. They are, respectively, denoted pw (S) and ps (S), where S is the level of the signal displayed by the sensor. 3.2. ROC Curves and Detection Algorithm. The detection algorithm works as follows. The value of each pixel in the image received at the sensor is a realization of either pw (S) or of ps (S) (or a mix of both pdfs). The mean of each pdf is denoted mw and ms , respectively. To perform the detection, we apply a threshold Trh to the pixels in the signal image. If mw > ms , all pixels greater than Trh are classified as target pixels and other pixels as noise pixels. However, among target pixels, some of them are noise pixels and thus correspond to false alarms. Below, we describe how to evaluate the rate of false alarms. For a given Trh , we can define a probability of detection pd (Trh ) and a probability of false alarms pfa (Trh ). If mw > ms , pd (Trh ) and pfa (Trh ) are given by

pfa (Trh ) =

∞

pw (S)dS, (2)

∞

Trh

Figure 3: Different types of wakes appearing behind a moving vessel.

120

Wake width versus range for ships with L/B = 10 L = 300 m

100

Wake width (m)

ROC curves are an important signal processing tool for assessing the performance of a sensor or an algorithm. They rely on the definition of a probability density function (pdf) for the signal and the noise [11].

Trh

Free wave pattern region

Crest Trough

3. Definition of ROC Curves

pd (Trh ) =

19.5 deg

formula for the turbulent wake width at four ship lengths. Experimental data show that α ≈ 5 is a good approximation, though α can vary between 4 and 5. In general, L/B = 10 is a good approximation which varies very little for common ship designs [9], resulting in further simplification: W(r) ≈ 1.9B4/5 r 1/5 . The wake length is a more difficult problem and depends upon sea state. The turbulent wake is caused by water displacement due to the ship’s hull and propulsion system. This water displacement has a kinetic energy decreasing according to r −4/5 [10]. As long as this kinetic energy is significantly larger than the energy of the top water layers, the turbulent wake remains detectable. Typically, turbulent wakes exist during a long period of time. Their length is typically a few kilometers. Figure 4 shows example simulated turbulent wake widths.

80

60 L = 100 m 40 L = 45 m 20 0

200

400 600 Range from ship (m)

800

1000

Figure 4: Width of the turbulent wake as a function of the distance behind the ship for various ship dimensions.

all possible values of Trh . We can repeat the reasoning if mw < ms . These curves serve as basis for discussing sensor performance: for a given pfa , pd should be as high as possible. Below, we describe a model for ps (S) and pw (S).

ps (S)dS.

Hence, pfa (·) represents the probability that an opensea pixel is classified as a wake pixel and pd (·) represents the probability that a wake pixel is effectively classified as a wake pixel. pd (Trh ) and pfa (Trh ) are represented graphically in Figure 5. Hence, for each Trh , we have one pd and one pfa . ROC curves are obtained by plotting pd versus pfa for

4. Sea and Turbulent Wake Surface Models Finding ps (S) and pw (S) implies to compute the signal received at each pixel in the detector plane of the spaceborne sensor. There are mainly two classes of pixels: open-sea and wake pixels, respectively, containing open-sea and turbulent wake radiances. We first describe how the geometrical

4

EURASIP Journal on Advances in Signal Processing Pdf pw (S)

by a value for A, k, and φ. The wave height zw (r, t) at location r and time t is found by integrating the plane waves over the entire space spanned by k. We thus have

ps (S)

A (k, t)e jk·r dk,

(4)

A (k, t) = A(k)e j(ω(k)t+φ(k)) .

(5)

zw (r, t) =

k

where Threshold Trh

S (signal)

pd (a) Probability of detection Pdf pw (S)

Hence, zw (r, t) is the inverse Fourier Transform (FT) of A (k, t). Modeling gravity waves is done by specifying a model for A(k) and for φ(k). Modeling swells is done in the same way. The only difference is the model for A(k) and φ(k). For gravity waves, in the case where capillarity waves can be neglected, we have the dispersion relationship [12] ω2 (k) = gk, where g is the gravity constant. φ(k) is modeled as a random process (RP) that determines the random character of wind-generated waves. Here, φ(k) is modeled as a Gaussian RP with zero mean and unit variance. The model of A(k) depends upon wind speed v and wind direction θw . We can write A(k) as

ps (S)

Threshold Trh

S (signal)

pfa (b) Probability of false alarms

#

A(k) = P(k)cos2 Δθ,

Figure 5: Probability of detection and probability of false alarms.

models of the sea surface and of the turbulent wake surface are obtained.

where Δθ = θ − θw and P(k) is the power spectrum often given by the Pierson-Moskowitz spectrum [14], that is, P(k) = P(ω(k)) =

4.1. Open-Sea Surface Modeling. Our model is based on the model presented in [12, 13]. In realistic sea surface models, we consider three classes of waves: (1) capillarity waves with small wavelength (λ < 5 cm) influenced by viscosity and surface tension, (2) gravity waves that are wind-driven waves with wavelength λ > 5 cm and smaller than a few meters, (3) swells being waves with great wavelength, that is, λ is greater than a few meters (these waves originate due to the presence of wind. However, they remain active for a long time after the wind has blown), (4) choppy waves appearing for high wind speed and introducing nonlinearities in the sea surface model (they are the starting point of breaking waves and of the apparition of foam). We only consider gravity waves and swells. To obtain the sea surface model, we divide the sea surface in small facets. Then, vertical displacements are applied to these facets. These displacements are obtained by modeling the sea surface as a superposition of linear plane waves [14]. A plane wave is given as z(r, t) = Ae j(ωt+k·r+φ) ,

(3)

where A is the wave amplitude, t is time, r = (x, y) is the position vector, φ is the phase, and k is the wave vector given by k = k(cos θ, sin θ), where k = 2π/λ is the wave number where λ is the wavelength. θ is the direction of propagation of the plane wave. Gravity waves are modeled as a superposition of a great number of plane waves. Each wave is characterized

(6)

αg 2 (−β(ω0 /ω)4 ), e ω5

(7)

#

where ω = gk, α = 8.110−3 , β = 0.74, and ω0 = g/v19.5 , where v19.5 is the wind speed at 19.5 m above the sea level. There exist other spectra that are tailored to a particular sea [14]. In practice, zw (r, t) in (4) is computed using the 2D inverse FFT (IFFT). Indeed, by discretizing k = (kx , k y ) as km1 m2 = (m1 Δkx , m2 Δk y ), where m1 ∈ [0, Nx ] and m2 ∈ [0, N y ] and r = (rx , r y ) as r n1 n2 = (n1 Δrx , n2 Δr y ), where n1 ∈ [0, Nx ] and n2 ∈ [0, N y ], (4) becomes

zw r n1 n2 , t =

A km1 m2 , t e j2π(m1 n1 /Nx +m2 n2 /N y ) .

m1,m2

(8)

The length of the patch where the IFFT is computed is given by (Lx , L y ) = (Nx Δrx , N y Δr y ). The periodicity of the IFFT can be used to replicate the zw (·)’s in both spatial directions. Hence, we can compute sea heights zw (r, t) for extended surfaces at an acceptable computation cost. Figure 6 shows examples of sea surface heights generated with the previous model. Only considering gravity waves and swells for modeling sea surface is valid for low sea states. For high sea states (typically > 5), breaking waves appear due to gravity. These waves are not handled in this model. The presence of breaking waves only modifies the model for ps (S); the principles of the method remain unchanged.


5

0

0 3.2

2 1.5

0 −0.5

150

0.8 y (m)

y (m)

0.5

100

0 −0.8 −1.6

150

−1

−2.4

−1.5 −2

200 0

50

100 x (m)

150

−3.2

200

200

Sea heights (m)

1.6

1 100

2.4

50 Sea heights (m)

50

0

50

100 x (m)

(a)

150

200

(b)

Figure 6: Examples simulated color-coded sea heights for a wind speed of 11 m/s: (a) gravity waves and (b) gravity waves and swells. x-axis and y-axis are labeled in meters. Color indicates sea heights (in meters). Sea height zero is the mean sea level.

4.2. Turbulent Wake Surface Model. A turbulent wake is modeled as a very rough flat surface [9, 10]. Hence, we model this wake as a flat sea. This flat sea is divided into microfacets (to simulate turbulences), the orientation of these microfacets being uniformly distributed between 0 and π/2 to simulate surface roughness. In Section 5, we see that sea water emissivity (resp., reflectivity) goes down (resp., up) as the angle of arrival of the optical beam on a sea facet increases. Hence, wakes can be distinguished from open-sea thanks to a change in the emissivity (or reflectivity) between wake and open-sea pixels. For optical sensors, the wake appears bright (Figure 1) due to a higher value (higher reflectivity) of the sun glint for wake than for open-sea pixels. For LWIR sensors, the wake appears dark due to a reduction in the emissivity of the sea surface in the wake compared to its value for open-sea pixels. For MWIR sensors, there is a competition between reflection (sun glint and sky irradiance) on sea facets and self-emission of sea facets. This is discussed further below.

5. Radiance Received at the Sensor Below, we present a model for computing the radiance received at the entry of the sensor. This model can be applied to open-sea and wake pixels. 5.1. Radiance at the Sea Surface (One Sea Facet). We first describe the method for computing the radiance leaving one sea facet n. The radiance Rn (λ)[W/m2 · sr μm] leaving n for wavelength λ is computed using the following equation [12, 13, 15]: n n n n (λ) + Esky (λ) + Ediff (λ) + Eglint (λ). Rn (λ) = Esea

(9)

We describe below a real-time model for each term in (9). Figure 7 defines useful variables relative to n.

nn

Sensor vector s

θn βs,n

v(θ, φ)

θs,n θs Facet n

Figure 7: Useful variables for a sea facet n.

n represents the radiance 5.1.1. Emitted Radiance. In (9), Esea emitted by n due to its nonzero temperature. It is computed using Planck’s law [16], that is, n (λ) = Vn εsea (λ)Mbb (λ, Tsea ), Esea

(10)

where εsea (λ) is the open sea water emissivity at λ, Tsea is the absolute open sea surface temperature, and Mbb (·) is the blackbody radiance [16]. Vn = 1 if s · nn > 0, zero otherwise. n with n is mainly due to the variation The variation of Esea of εsea (λ) with the elevation angle βs,n of the optical beam s that goes to the sensor. Neglecting the dependence upon wavelength, we have [17]

εsea λ, βs,n = 0.98 1 − 1 − cos βs,n

5

.

(11)

For wake pixels, εwake (λ) is the mean of εsea (λ, βs,n ) for βs,n ∈ [0, π/2]. Hence, εwake (λ) = 0.87. Hence, for wake facets, εwake < εsea for most values of βs,n . n 5.1.2. Sky Radiance. In (9), Esky is the irradiance produced by the sky. It is present at any time. There are two models. n as a blackbody at sky temperature Tsky The first model Esky (depending upon weather parameters) [18, 19], that is,

n (λ) = Fn ρsea λ, βs,n Mbb λ, Tsky , Esky

(12)

6


where ρsea (λ, βs,n ) = 1 − εsea (λ, βs,n ) is the sea reflectivity and Fn is a visibility factor representing the portion of the sky hemisphere seen by n. This model is realistic under clearsky conditions. The second model uses MODTRAN [20]. However, it is computationally intensive. To have a real-time model, we use the blackbody model. 5.1.3. Solar Irradiance. The solar extraterrestrial radiation not back-scattered to space reaches the ground in two ways. The radiation reaching the ground directly is the beam irradiance. The scattered radiation reaching the ground is the diffuse irradiance. Below, we assume clear-sky conditions. (For images containing clouds, we assume that cloud masking algorithms [21, 22] have been applied prior to ship detection.) The beam irradiance incident on a surface of 1 m2 on the earth’s ground is

n,n n,n n (λ) = Eb,sol (λ)v θ, φ · nn = Eb,sol (λ) cos θs,n , Eb,sol

5.3. Radiance at the Spaceborne Sensor. To obtain the radiance Rs,i arriving at the entrance of the spaceborne sensor, we multiply R p by the solid angle of the sensor (using the radius r p of the entrance pupil and the satellite height Hs ). We obtain Rs,i (λ) =

πr p2 p , R (λ)c(λ) + Lpath (λ) W/μm , 2 Hs

(18)

where Lpath represents the radiance received on the path between the sea surface and the sensor and c(λ) is the atmospheric transmittance. For MWIR sensors, Lpath represents the radiance emitted by the atmosphere on the path between n and the sensor. It can then be modeled as the integral of a blackbody with height-dependent temperature. We then approximate Lpath using a blackbody at a temperature being the mean of the air temperature along the path to the sensor.

(13)

6. Signal Displayed by the Sensor

where (14)

We describe the model for converting Rs,i (λ) to the signal displayed at each pixel of the sensor.

where α is a proportionality constant and c(λ) is obtained from MODTRAN and accounts for propagation through the atmosphere. Msol (λ) is the spectral radiance of the sun computed either using a blackbody at Tsun = 5760 K or using n (λ) corresponds to MODTRAN (more accurate). In (9), Eglint the reflected beam solar irradiance, that is, the solar glint. Assuming that n is a Lambertian (diffuse) reflector (diffuse solar glint), we have

6.1. Model for the Displayed Signal (No Noise). Rs,i (λ) is transferred by the sensor optics to the detector focal plane where the image is formed. The spectral irradiance at the entry of a detector located on the optical axis is related to Rs,i (λ) by the camera equation [15]

n,n (λ) = αVn c(λ)Msol (λ), Eb,sol

n n (λ) = ρsea λ, βs,n Eb,sol (λ). Eglint

(15)

n Ediff is the diffuse irradiance reflected by n. Since we conn since it is a small sider clear-sky conditions, we neglect Ediff n,n n at all fraction of Eb,sol . To reduce computation time, Eb,sol zenith angles are precomputed and the value corresponding to a given zenith angle is obtained by interpolation of the n,n ’s. pre-computed Eb,sol

5.2. Radiance at Sea Level (One Pixel). The radiance R p (λ) leaving an open-sea pixel corresponding to the IFOV of the sensor is R p (λ) = Sh

,

2 √ , 1 + erf(ν) + (1/ν π)e−ν2

Rb = Iτ aqe

(16)

where An is the area of n and Sh is a shadowing coefficient smaller than one if the satellite is not at zenith. Indeed, in this case, some sea facets are shadowed by other sea facets. Modeling of Sh implies to resort to ray-tracing algorithms (highly time-consuming). Here, we use a simplified, but realistic expression [12], that is, (17)

where erf(·) is the error function, ν ≡ tan θ/σ, where θ is the satellite look angle and σ is the RMS slope of the facets [23], 2 , where v12.5 is the average that is, σ 2 = 0.003 + 0.00512v12.5 wind speed at 12.5 m above sea level.

πτo (λ) s,i , R (λ) W/μm , 2 4N

(19)

where τo (λ) is the optical system transmittance (often 90% and nearly flat), N is the f -number. Then, the detector converts collected photons in an electrical current [A] (photo-electric effect). The efficiency of this transformation is aqe ∈ [0, 1]. Next, Rs (λ) is spectrally filtered by the spectral response Sb (λ). The resulting signal Rb is the integration of Rs (λ) over the spectral interval [λ1 , λ2 ] corresponding to the bandpass of the detector. To increase the SNR, the signal is temporally integrated over a time interval (integration time) specified by Iτ . Hence,

-

Rn (λ)An W/ sr μm ,

n

Sh (ν) =

Rs (λ) =

λ2 λ1

Sb (λ)Rs (λ)dλ · [C].

(20)

Here, we assume that τo (λ) = τo and Sb (λ) = 1 for all λ ∈ [λ1 , λ2 ]. Rb is expressed in Coulomb (C). Dividing Rb by the electrical charge e− of an electron, we get the number N b of electrons collected by the detector, that is, N b = Rb /e− . If the imaged scene is a point source, the image produced at the detector is a blurred point due to diffraction. The resulting image is called the Point Spread Function (PSF) PSF(x, y). For any other imaged scene, the signal Rbl (x, y) at each pixel (x, y) on the detector plane is given by a convolution of Rb (x, y) with PSF(x, y), that is,

Rbl x, y =

α

β

Rb α, β PSF x − α, y − β dα dβ.

(21)


7

For real systems, the PSF also includes nonideal effects. With each effect, a PSF is associated. The global PSF is the convolution of all PSFs. Typical nonidealities are the following. First, the optics induce blurring by the optical PSF as explained above. The image formed by the optics may move during the integration time; this introduces image motion PSF (also called smearing PSF). High-frequency (resp., low frequency) vibrations of the satellite also imply a degradation of the signal. We then associate to these vibrations a jitter (resp., pointing) PSF. The detector also adds additional blurring due to the detector PSF. Finally, the detected signal is further degraded by the electronics PSF. Computation of (21) is computationally intensive. One alternative is to compute the FT of the PSFs. The convolution becomes a product. The FT of a PSF is called a Modulation Transfer Function (MTF). Hence,

Rbl x, y = F −1 MTF(u, v)F Rb x, y

,

(22)

where F ( f (x)) (resp., F −1 ( f (x))) is the FT (resp., inverse FT) of f (x). In practice, Rbl (x, y) is a discrete function since the number of detectors in the detector plane is finite. Rbl [i, j] represents the current received at detector located at position (i, j). Similarly, N bl [i, j] = Rbl [i, j]/e− is the number of electrons collected at (i, j). 6.2. Inclusion of Noise. So far, the proposed model for Rbl does not include noise present in the detector. In EO sensors, the most important noise sources are the following: (1) the photon (shot) noise associated with the nonequilibrium conditions in a potential energy barrier of a photovoltaic detector through which a dc current flows; (2) the thermal (Johnson) noise associated to fluctuations in the voltage current caused by the thermal motion of charge carriers in resistive materials, (3) the multiplexer (read out) noise. Each noise is modeled as a random process (RP) with 2 (photon noise), σ 2 (thermal zero mean and variance σpn tn 2 (multiplexer noise). Models for these variances noise), or σmn can be found in [24]. Each noise is expressed in number of electrons. The total detector noise variance σn2 is then the sum 2 , σ 2 , and σ 2 , so that of σpn tn mn #

2 + σ2 + σ2 . σn = σpn tn mn

(23)

There exist two other noise sources (the quantization noise and bit errors) [3]. However, they are not considered here. Notice that these noises only modify the value of σn ; the reasoning remains unchanged. The signal Sbl [i, j] displayed by the sensor at detector [i, j] is then , bl

-

S i, j = N

, bl

-

, n

-

i, j + N i, j ,

(24)

where N n [i, j] is a realization of the zero-mean Gaussian RP with variance σn2 .

7. Real-Time Simulator Evaluating sensor performance implies first to simulate Sbl [i, j] for all detectors in the detector plane. This is

computationally intensive due to the inclusion of the PSF (or MTF). Hence, evaluating sensor performance using this approach is not possible in real-time. Below, we propose an efficient, real-time strategy. First, observe that, for an image in the open-sea, we have three classes of pixels: (1) pixels only composed of open-sea radiance, (2) pixels only composed of wake radiance, and (3) mixed pixels composed partially of open-sea radiance and of wake radiance. For each class of pixels, we propose below an RP for the received signal. Hence, instead of simulating the entire image, we only have to find a model for the pdf of the three classes of pixels. Indeed, the entire image is found by considering realizations of these three RPs. To summarize, we propose to reduce the computation of the entire image to the computation of three pdfs, one for each class of pixels. ROC curves are then obtained as discussed in Section 3. 7.1. Probability Density Function for Rb . We first consider the pdf of an open-sea pixel. Then, we consider a wake pixel and finally, a mixed pixel. 7.1.1. Open-Sea Pdf. The signal Rb corresponding to an open-sea pixel is denoted Rbs and is given by (20) using the geometric model of Section 4.1. Rbs mainly depends on satellite position ss , sun location v(θ, φ), and wind speed v. Consider that ss , v(θ, φ), and v are fixed. Consider a great open-sea area divided in small planar facets for which we compute sea heights (see Section 4). We then compute the received Rbs for each facet, and we plot the corresponding histogram. This gives an idea of the pdf of Rbs for opensea pixels. Results are shown for various sea states (various wind speeds) in Figure 8 for MWIR sensors. Figure 8 shows normalized Rbs ’s, denoted as R&bs , that is, R&bs ∈ [0, 1], obtained as R&bs =

Rbs − Rbs,min , Rbs,max − Rbs,min

(25)

where Rbs,min and Rbs,max are, respectively, the minimum and the maximum values of Rbs for all sea facets. Histograms of R&bs all have the shape of a beta statistical distribution. The pdf pβ (r) of this distribution has two free parameters θ1 and θ2 and is given by

pβ R&bs , θ1 , θ2 =

θ1 −1 θ2 −1 1 R&bs 1 − R&bs , B(θ1 , θ2 )

(26)

where B(θ1 , θ2 ) = Γ(θ1 )Γ(θ2 )/Γ(θ1 + θ2 ), where Γ is the gamma function. To find the pβ (R&bs , θ1 , θ2 ) that best fits the R&bs ’s, we estimate θ1 and θ2 using the mean mr and the variance σr2 of the R&bs ’s. We have [25]

mr (1 − mr ) θ1,s = mr −1 , 2

σr

θ2,s = (1 − mr )

(27)

mr (1 − mr ) −1 . σr2

(28)

8


Sea state 1 (v = 0.5 m/s)

250

250 R&bs histogram

R&bs histogram

200 150 100 50 0

Sea state 2 (v = 1 m/s)

300

200 150 100 50

0

0.2

0.4 0.6 R&bs (open-sea)

0.8

0

1

0

0.2

(a)

0.8

1

0.8

1

500 R&bs histogram

250 R&bs histogram

1


600

300

200 150 100

400 300 200 100

50 0

0.8

(b)


350


0

0.2


0.8

0

1

0

0.2

(c)

(d)


450

0.4 0.6 R&bs (open-sea) Sea state 6 (v = 17.5 m/s)

1400

400

1200 1000

300

R&bs histogram

R&bs histogram

350

250 200 150

800 600 400

100 200

50 0

0

0.2


0.8

1

0

0

0.2


Beta distribution

Beta distribution

(e)

(f)

Figure 8: Histogram of R&bs ’s and corresponding beta distributions.


9

Hence, the pdf ps,b (Rbs ) of the Rbs ’s is pβ (R&bs , θ1 , θ2 ), where R&bs is replaced by Rbs using (25) and θ1 and θ2 are, respectively, replaced by θ1,s and θ2,s , that is, ps,b Rbs

= pβ

Rbs − Rbs,min , θ1,s , θ2,s . Rbs,max − Rbs,min

15

(29)

The reason why the open-sea Rbs ’s can be modeled as a beta distribution is currently not well understood. 7.1.2. Turbulent Wake Pdf. We consider a model for the pdf pw,b of the signal Rbw corresponding to a wake pixel given by (20) with the geometrical model of Section 4.2. We consider that ss , v(θ, φ), and v are fixed. In Section 4, we saw that Rbw corresponds to the radiance of a flat sea with important roughness. This roughness is modeled by dividing the wake pixel in microfacets with arbitrary orientation. (For computing Rbw , we consider that the wake surface temperature Tw is equal to Tsea . However, in practice, Tw < Tsea [26]. Modeling this temperature difference is outside the scope of this paper.) The simplest model for pw,b thus considers a uniform pdf for the emissivity leading to a uniform distribution of Rbw . However, this is not realistic since having microfacets with arbitrary orientation is more probable than having microfacets with horizontal orientation. One solution is to use a beta distribution with high probability density near the signal corresponding to microfacets with orientation uniformly distributed between 0 and π/2 (denoted as Rbwu ) and a very small probability density near the signal corresponding to a flat sea (denoted as Rbflat ). If Rbflat > Rbwu , we have

pw,b Rbw = pβ

Rbw − Rbwu , θ1,w , θ2,w , Rbflat − Rbwu

(30)

where θ1,w and θ2,w are such that pβ (ε) 1 and pβ (1 − ε) 0, with ε 1. Simulations show that θ1,w = 1 and θ2,w = 20 lead to a meaningful pdf. Figure 9 shows pw,b . 7.1.3. Mixed Pdf. Some pixels, called mixed pixels and located at the edge of the wake, are composed of a portion of wake and a portion of open-sea (Figure 10). The signal Rbm corresponding to a mixed pixel is then Rbm = αRbw + (1 − α)Rbs ,

(31)

where α is the portion of wake signal in the pixel. We then have to find a model for the pdf pm,b of Rbm . Computing the analytical expression of the pdf of a linear combination of different beta distributions is challenging. In Section 7.2.3, we propose a method for computing this pdf. We use this method here with weights α and 1 − α. The resulting pdf is then a beta distribution (see Section 7.2.3) given by

pm,b Rbm = pβ

Rbm − Rbm,min , θ1,m , θ2,m , Rbm,max − Rbm,min

(32)

where Rbm,min and Rbm,max are, respectively, the minimum and the maximum values of Rbm , obtained using the minimum

Pdf values

20

10

5

0

0

0.2

0.4 0.6 R&bw (turbulent wake)

0.8

1

Figure 9: Pdf of R&bw : beta distribution with θ1,w = 1 and θ2,w = 20.

Mixed pixel

Mixed pixel

(a) Edge pixel

(b) Overlapping pixel

Figure 10: Mixed pixels: (a) Edge and (b) overlapping mixed pixels.

and the maximum values of Rbs and Rbw . Coefficients θ1,m and θ2,m are obtained as explained in Section 7.2.3. An example of mixed pixel pdf is given in Figure 11. 7.2. Statistical Model for Rbl . Below, we describe the model for the pdf pbl of Rbl for a mixed pixel. The approach is similar for open-sea and wake pixels. Finding a model for pm,bl (Rbl m ) implies to include the effect of the PSF. We can either compute the convolution of the PSF with the image pixels or perform the FT of the image and multiply the resulting image by the MTF. Both methods are computationally intensive: they require the computation of the entire image. Below, we propose an efficient method to include the effect of the PSF without computing the entire image. Moreover, to simulate the effect of changing the PSF (or MTF) of one particular nonideality on sensor performance, we should first be able to easily change the shape of the PSF (or MTF) and second to update ROC curves in real-time. Hence, we propose to represent each PSF (or MTF) with one scalar value: the MTF at Nyquist. This allows to rapidly update sensor performance.

10

EURASIP Journal on Advances in Signal Processing 0.3

where x and y are normalized detector locations (with respect to d). PSFG (x, y) is used to compute Rbl m in (21).

Wake pixel Mixed pixel

0.25

Pdf values

0.2

7.2.3. Model for Rbl m . Consider a detector (i, j). Hence, discretizing integrals in (21), we obtain

Open-sea pixel

,

-

Rbl m i, j =

0.15 0.1 0.05 0 2464900

2560900 Signal received by the sensor (eV)

2656900

Figure 11: Example pdf of a mixed pixel for α = 0.4, sea state 5, GSD of 100 m, and wake width of 40 m. Simulation corresponds to sunlight dominating (bright) wake.

Rb [k, l]PSFG i − k, j − l ,

(35)

k∈K l∈L

where K and L are the sets of pixel indexes centered on (i, j) and for which PSFG has a nonnegligible value. With typical values of MTFN , the sizes of K and L are about 3 to 4. Hence, Rbl m is evaluated by summing signals of about 9 to 16 pixels, which is very efficient. Now, we describe a model for the pdf bl pm,bl of Rbl m . Rm in (35) is a weighted sum of RPs. Indeed, each Rb in (35) is the signal corresponding either to an open-sea pixel or to a wake pixel or to a mixed pixel that all are RPs. Hence, we can compute mean mbl [i, j] and variance σbl2 [i, j] of Rbl m [i, j]. We have ,

-

mbl i, j =

mb [k, l]PSFG i − k, j − l ,

k∈K l∈L

7.2.1. MTF at Nyquist. If a sensor is looking at a scene, each detector of the sensor senses a pixel of size equal to the GSD. For a line of detectors, the values received at these detectors correspond to the sampling of a continuous signal corresponding to the radiance produced by all patches on the ground line corresponding to the detector line. Hence, the maximum frequency of the signal that can be sensed is f = 1/2GSD. Signals with higher frequencies produce aliasing. Hence, the MTF MTFN at Nyquist frequency fN = 2 f = 1/GSD plays an important role in evaluating sensor performance. fN is often expressed using the detector size d to be independent upon the GSD. Hence, MTFN = 1/d. The MTF can then be characterized by one scalar value, that is, MTFN . 7.2.2. Model for the MTF. Each MTF is then described by its MTFN . For each nonideality ni , we have a value of MTFN , denoted MTFN,i . The global MTFN is the product of the MTFN,i ’s. Sensor designers provide two MTF functions: the along-track and the across-track MTF. Both MTF are combined to give the 2D MTF. We thus have two MTFN , that is, the along-track MTFN (MTFN,al ) and the across-track MTFN (MTFN,ac ). We make the reasonable assumption that the 2D MTF is Gaussian [15]. This allows to compute the inverse FT analytically, saving computation time. Hence,

MTFG (u, v) = e−π

2 u2 /a

e−π

2 v 2 /b

,

(33)

where u and v are normalized frequency variables (with respect to d) and a and b are determined using MTFN,al and MTFN,ac . Estimates a and b of a and b are a = = −π 2 / ln(MTFN,ac ). PSFG (x, y) is −π 2 / ln(MTFN,al ) and b the inverse FT of MTFG (u, v), which is also a Gaussian, that is,

PSFG x, y =

⎛

a −by 2 ⎝ e π

⎞

b −ax2 ⎠ , e π

(36)

where mb [k, l] is the mean of Rb [k, l]. For σbl2 [i, j], we have ,

-

σbl2 i, j =

k∈K l∈L

σb2 [k, l]PSF2G i − k, j − l ,

(37)

where σb2 [k, l] is the variance of Rb [k, l]. Using mbl [i, j] and σbl2 [i, j], we can model pm,bl as a beta distribution with parameters θ1,bl and θ2,bl , respectively, given by (27) and (28), where mr and σr2 are, respectively, replaced by mbl [i, j] and σbl2 [i, j]. Hence, pm,bl is

pm,bl Rbl m

= pβ

bl Rbl m − Rm,min , θ1,bl , θ2,bl , bl Rbl m,max − Rm,min

(38)

bl where Rbl m,min and Rm,max are the minimum and the maximum bl values of Rm , obtained using the minimum and maximum values of each Rb [k, l] with k ∈ K and l ∈ L. Figure 12 compares (a) ps,b and pm,b (Figure 12(a)) ps,bl and pm,bl (Figure 12(b)). We first conclude that ps,bl and pm,bl are close to a Gaussian distribution. This is a consequence of the Central Limit Theorem. Second, the separation between ps,bl and pm,bl is smaller than the one between ps,b and pm,b indicating that the MTF degrades detection performance.

7.3. Statistical Model for Signal Sbl . We propose a model for the pdf of Sbl for the three classes of pixels. Since the method is similar for these three classes, we only consider a mixed bl pixel, that is, Sbl m . Sm for detector [i, j] is given by (24) where Nmbl is modeled as a beta distribution with parameters θ1,bl and θ2,bl and where N n is modeled as a zero-mean Gaussian RP with variance σn2 . The pdf pm,s (S) of the RP Sbl m is then the sum of a beta distribution and a Gaussian pdf. The mean ms and the variance σs2 of Sbl m are, respectively, given by (36) and (37), that is, ms = mbl ,

(34)

σs2 = σbl2 + σn2 ,

(39)


11

pm,s (S) = pβ

S − Sm,min , θ1 , θ2 , Sm,max − Sm,min

Open-sea pixel

(40)

0 2220000

2260000 2320000 Signal values (eV)

bl bl where Sm,min Nm,min and Sm,max Nm,max .

2340000

(a) ×10−4

3 Pdf values

Mixed pixel Open-sea pixel

0 1310000


1370000

(b)

Figure 12: Comparison between (a) ps,b and pm,b and (b) ps,bl and pm,bl for sea state 5 and α = 0.4. Simulation corresponds to sunlight dominating (bright) wake. ×10−4

6

Mixed pixel 5 4 Pdf values

7.4. Line Detection Algorithms. Since we consider low payload sensors, the spatial resolution is small. Hence, the IR ship-only signature is spread between a small number of pixels. Using pixel-based ship detection algorithms thus gives high pfa . A ship pixel is indeed easily confused with opensea pixels with sun glint or open-sea pixels corresponding to swells or cloud pixels. (For ship detection, we assume that cloud masking algorithms have been applied prior to detection [21, 22].) We then have to use more than one pixel for ship detection. Below, we investigate how to detect ships using their turbulent wake. Indeed, this wake can persist a few kilometers away from the ship, making their detection with low-resolution sensors possible. The wake appears either as a curved or a straight line (Figures 1 and 2). Curve tracing and curve detection algorithms can then be used to detect and separate wakes [27, 28], reducing pfa . Since we want to develop a real-time methodology for evaluating sensor performance, computing the entire image and the corresponding curve detection algorithms is time consuming. Below, we propose a statistical, real-time approach. We describe the algorithm principles in the case of a straight line. The methodology is easily generalized to curved wakes. Consider a ship moving in a given direction and the corresponding wake. A line is then visible in the image. Consider the application of a line-detection algorithm to the center pixel of the ship. There are an infinite number of lines passing through this pixel. These lines generate a curve in the line-space. Each point on this curve is weighted by the percentage of the length of the line in the original image that effectively crosses a line in the original image. Hence, this curve exhibits a maximum when the line is confounded with the wake. Instead of thresholding the contrast between two pixels, we threshold the contrast between two lines of pixels; the first line is the wake (or a mix between the wake and an open-sea line) and the second line is an open-sea line. Hence, if we are able to compute the pdf psL,N of the signal of a line of N open-sea pixels and the pdf pwL,N of the signal of a line of N wake (or mixed) pixels, we can compute ROC curves after the application of line-detection algorithms. Below, we L,N (S) of the signal of a explain how to compute the pdf pm line of N mixed pixels. The same method is used to compute psL,N (S) and pwL,N (S). Consider N mixed pixels. Each pixel is an RP described with the same pdf pm,s (S). One realization of the RP of the line is obtained by performing the mean between N realizations of the RP with pdf pm,s (S). Hence, using (36) and 2 of the line RP are (37), the mean mL,N and the variance σL,N

No MTF

Mixed pixel

MTF included

×10−5 12

Pdf values

where mbl and σbl2 are the mean and the variance of Nmbl . Using ms and σs2 , we can model pm,s (S) as a beta distribution with parameters θ1 and θ2 , respectively, given by (27) and (28), where mr and σr2 are, respectively, replaced by ms and σs2 . Hence, pm,s (S) is

Open-sea pixel

3 2 1

0 2300000

2320000


2380000

L,N for sea state 5 and N = 10. Simulation Figure 13: Pdfs psL,N and pm corresponds to sunlight dominating (bright) wake.

2 2 /N, where m 2 given by mL,N = mm,s and σL,N = σm,s m,s and σm,s are, respectively, the mean and the variance of pm,s (S). Using (27) and (28), we, respectively, obtain estimates θ1,L and θ2,L of the parameters θ1 and θ2 of the resulting beta distribution. Hence,

L,N (S) pm

= pβ

S − Sm,min , θ1,L , θ2,L . Sm,max − Sm,min

(41)

L,N for N = 10. We first conFigure 13 shows psL,N and pm L,N L,N clude that ps and pm are close to a Gaussian distribution.

12


Table 1: Value of all parameters for the MWIR scenario. Value 100 1024 × 1024 15 9.8 × 9.8 102 × 102 10 90 30 0.6 0.75

0.998 Probability of detection

MWIR sensor GSD (m) # pixels pixel size (μm) FOV (◦ ) Swath (km) Integration time (ms) Focal length (mm) Entrance pupil (mm) Transmittance τo Average QE

0.996 0.994 0.992 0.99 0.988 0.986 0.984 10−4

10−3

10−2

10−1

Probability of false alarms (a) No MTF

This is a consequence of the Central Limit Theorem. Second, L,N is greater than the one the separation between psL,N and pm between ps,bl and pm,bl (see Figure 12(b)) illustrating that the line-detection algorithm enhances detection performance. Probability of detection

In this section, we illustrate the use of the presented simulator to assess sensor performance using ROC curves. The set of simulations is chosen as broad as possible in order to show that this simulator can be used in realistic scenarios. Remember that our aim is not to present validation results of the simulator. We consider the scenario of Table 1 with the MTFN ’s and the noise variances of Table 2. We first illustrate ROC curves for three cases: (a) no MTF (Figure 14(a)), (b) MTF included (Figures 14(b) and 14(c)) line detection + MTF (Figure 14(c)). We see the degradation of performance due to the inclusion of the MTF. The ROC curve for line detection shows the important gain obtained with such algorithms. In practice, performance is more degraded due to the presence of nondiffuse sun glint that increases pfa . Second, Figures 15(a) and 15(b), respectively, show the evolution of sensor performance for different wake widths and different satellite look angles. This illustrates the fact that sensor performance degrades as wake width decreases and as satellite looks at the sea with an angle closer to the horizontal direction. We assume that the sensor FOV is small enough so that each pixel sees the sensor with the same angle. These results were obtained in real-time. Next, we consider the difference between day and night conditions. During the night, sun glint is absent. Figure 16(a) compares sea, wake, and mixed pixels pdfs. For MWIR sensors, there is a competition between reflections on the sea surface (reflection of the sun and the sky irradiances) and self-emission of the sea surface facets [15]. During the day, due to the presence of sun glint, reflections dominate over self-emission and then the wake appears bright (the wake pdf is located at the right of the open-sea pdf). During the night, the absence of sun glint reduces the importance of reflections and self-emission dominates. Then, the wake appears dark

0.9 0.8 0.7 0.6 0.5 0.4 0.3 10−5

10−4

10−3

10−2

10−1

100

Probability of false alarms (b) MTF included

1 0.99 Probability of detection

8. Performances

1

0.98 0.97 0.96 0.95 0.94 0.93 10−5

10−4

10−3

10−2

10−1

100

Probability of false alarms (c) MTF and line detection included

Figure 14: ROC curves for scenario of Tables 1 and 2 (wake width of 40 m and sea state 5). (a) MTF not included in the model, (b) MTF included, and (c) MTF and line detection algorithm included.


13

ROC curves Wake Mixed

0.8

Wake

Mixed

Sea

Pdf values

Pdf values

1

Sea

0.6 Pds

2220000


0.4

2300000 Signal values (eV)

(a) 1

0.2

0

0

0.002

0.004

0.006

0.008

0.01

Pfas Wake width 8 Wake width 25 Wake width 50

Probability of detection

0.8 Night 0.6

0.4 Day

0.2

(a) ROC curves

1

10−5

10−4

0.8

10−3 Probability of false alarms

10−2

(b)

Figure 16: Sensor performance day versus night: (a) Wake, sea, and mixed pixel pdfs during the day (left) and the night (right) and (b) ROC curves before line detection. Sea state is 5. Wake length is 1 km.

Pds

0.6

0.4

Table 2: MTF budget at Nyquist and noise variances. 0.2

0

(a)

0

0.002

0.004

0.006

0.008

0.01

Pfas ROC sat2 ROC sat3

ROC sat0 ROC sat1 (b)

Figure 15: Evolution of sensor performance with (a) wake width and (b) satellite look angle (sat 0 = Nadir, sat 1 = 0.47 rad, sat 2 = 0.93 rad, and sat 3 = 1.4 rad from Nadir). Sea state is 5. Wake length is 2 km.

(the wake pdf is now located at the left of the open-sea pdf). Figure 16(b) compares detection performance during day (“−” curve) and night (“−.” curve). Night detection performances are better. Indeed, it is well known that sun glint introduces false alarms. Finally, we briefly examine performance obtained with the simulator when false alarms are present. We consider the presence of swells as a candidate for false alarms. Figure 17

MTF at Nyquist Optical MTF Detector MTF Smearing MTF Jitter MTF Pointing MTF Across-track MTF Along-track MTF

Value 0.4 0.64 0.82 0.9 0.9 0.21 0.17 (b)

Noise (eV) Photon Thermal Read out

Value 2007 1107 420

compares ROC curves when the sea model contains gravity waves (“−” curve) and when both gravity waves and swells are present (“−.” curve). As expected, performances with swells are degraded.

14


Probability of detection

1

0.95

[6] 0.9

Gravity waves Gravity waves + swells

[7] 0.85

[8] 0.8 10−5

10−4

10−3

10−2

10−1

100

Probability of false alarms

Figure 17: Sensor performance when the sea surface model includes (a) gravity waves and (b) gravity waves and swells after line detection. Sea state is 5. Wake length is 1 km.

9. Conclusions This paper was devoted to the design of a real-time methodology for assessing detection performance of spaceborne sensors. Real-time capabilities are obtained by representing pixels in the images with random processes with given probability density functions. It was described in the case of mid-wave infrared (MWIR) sensors. However, its principles are applicable to any electro-optical sensor and even to radar sensors, provided that adequate models for the random processes are inserted into the model. Using this methodology to study sensor performance was then studied for a particular scenario.

[9]

[10]

[11] [12]

[13]

[14] [15]

Acknowledgment This paper was a part of the project ESPAIS financed by the European Space Agency (ESA).

References [1] S. E. Lagaras and N. K. Uzunoglu, “A model for the passive infrared detection of naval targets through FLIR: model description and preliminary results applicable in the eastern Mediterranean Sea,” International Journal of Infrared and Millimeter Waves, vol. 29, no. 6, pp. 596–607, 2008. [2] C. Melsheimer, H. Lim, and C. Shen, “Observation and analysis of ship wakes in ERS-SAR and spot images,” in Proceedings of the 20th Asian Conference on Remote Sensing (ACRS ’99), pp. 554–559, November 1999. [3] J. P. Kerekes and J. E. Baum, “Spectral imaging system analytical model for subpixel object detection,” IEEE Transactions on Geoscience and Remote Sensing, vol. 40, no. 5, pp. 1088–1101, 2002. [4] J. Kerekes and J. Baum, “Fully-spectrum spectral imaging system analytical model,” IEEE Transaction on Geoscience and Remote Sensing, vol. 43, no. 3, pp. 571–580, 2005. [5] M. Bernhardt, M. I. Smith, P. G. Whitehead, L. N. Hunt, D. L. Hickman, and C. Dent II, “A statistical sea-surface

[16] [17] [18] [19] [20] [21]

[22]

[23]

clutter model in the long-wave infrared,” in Targets and Backgrounds X: Characterization and Representation, W. R. Watkins, D. Clement, and W. R. Reynolds, Eds., vol. 5431 of Proceedings of SPIE, pp. 270–278, Orlando, Fla, USA, April 2004. C. Cochin, T. Landeau, G. Delhommeau, and B. Alessandrini, “Simulator of ocean scenes observes by polarimetric SAR,” in Proceedings of the 5th International Conference on Radar Systems, pp. 17–21, Brest, France, May 1999. D. Crisp, “The state-of-the-art in ship detection in synthetic aperture radar imagery,” Tech. Rep., DSTO Information Sciences Laboratory, Edinburgh, South Australia, 2004. I. Hennings, R. Romeiser, W. Alpers, and A. Viola, “Radar imaging of Kelvin arms of ship wakes,” International Journal of Remote Sensing, vol. 20, no. 13, pp. 2519–2543, 1999. G. Zilman, A. Zapolski, and M. Marom, “The speed and beam of a ship from its wake’s SAR images,” IEEE Transactions on Geoscience and Remote Sensing, vol. 42, no. 10, pp. 2335–2343, 2004. A. Benilov, G. Bang, A. Safray, and I. Tkachenko, “Ship wake detectability in the ocean turbulent environment,” in Proceedings of the 23rd Symposium on Naval Hydrodynamics, pp. 687–703, 2001. M. Barkat, Signal Detection and Estimation, Artech House, Boston, Mass, USA, 1991. F. Schwenger and E. Repasi, “Sea surface simulation for testing of multiband imaging sensors,” in Targets and Backgrounds IX: Characterization and Representation, vol. 5075 of Proceedings of SPIE, pp. 72–84, Orlando, Fla, USA, April 2003. F. Schwenger and E. Repasi, “Sea surface simulation in the infrared modeling and validation,” in Targets and Backgrounds XII: Characterization and Representation, vol. 6239 of Proceedings of SPIE, Orlando, Fla, USA, April 2006. M. K. Ochi, Ocean Waves the Stochastic Approach, Cambridge University Press, London, UK, 1998. R. A. Schowengerdt, Remote Sensing: Models and Methods for Image Processing, Academic Press Elsevier, San Diego, Calif, USA, 2007. R. Siegel and J. Howell, Thermal Radiation Heat Transfer, Hemisphere, Washington, DC, USA, 3rd edition, 1992. I. Wilf and Y. Manor, “Simulation of sea surface images in the infrared,” Applied Optics, vol. 23, no. 18, pp. 3174–3180, 1984. J. Duffie and W. Beckman, Solar Engineering of Thermal Processes, John Wiley & Sons, New York, NY, USA, 1980. G. Walton, Thermal Analysis Research Program, U.S. Government, Washington, DC, USA, 1983. O. Corp, “The MODTRAN software,” http://www.modtran .org/. M. Suh and K. Park, “A simple method for the cloud detection over land using daytime AVHRR data,” in Proceedings of the 18th Asian Conference on Remote Sensing, Kuala Lumpur, Malaysia, October 1997. A. Benbouzid, K. Laidi, and A. Rachedi, “Hardware mask for cloud detection approach,” in Proceedings of the 2nd International Symposium on Communications, Control and Signal Processing (ISCCSP ’06), Marrakech, Morocco, March 2006. C. Cox and W. Munk, “Measurement of the roughness of the sea surface from photographs of the sun’s glitter,” Journal of the Optical Society of America, vol. 44, no. 11, pp. 838–850, 1954.

EURASIP Journal on Advances in Signal Processing [24] A. Daniels, Field Guide to Infrared Systems, SPIE Press, Bellingham, Wash, USA, 2007. [25] NIST SEMATECH, Engineering Statistics Handbook, http:// www.itl.nist.gov/div898/handbook/. [26] R. D. Peltzer, W. D. Garrett, and P. M. Smith, “A remote sensing study of a surface ship wake,” International Journal of Remote Sensing, vol. 8, no. 5, pp. 689–704, 1987. [27] G. Du and T. S. Yeo, “A novel radon transform-based method for ship wake detection,” in Proceedings of the International Geoscience and Remote Sensing Symposium (IGARSS ’04), vol. 5, pp. 3069–3072, September 2004. [28] K. Raghupathy, Curve tracing and curve detection in images, M.S. thesis, Cornell University, Ithaca, NY, USA, 2004.

15


Research Article Techniques for Effective Optical Noise Rejection in Amplitude-Modulated Laser Optical Radars for Underwater Three-Dimensional Imaging R. Ricci,1 M. Francucci,2 L. De Dominicis,1 M. Ferri de Collibus,1 G. Fornetti,1 M. Guarneri,1 M. Nuvoli,1 E. Paglia,1 and L. Bartolini3 1 ENEA,

Dipartimento Tecnologie Fisiche e Nuovi Materiali, Centro Ricerche Frascati, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy 2 ENEA fellow, Dipartimento Tecnologie Fisiche e Nuovi Materiali, Centro Ricerche Frascati, Via. Enrico Fermi 45, 00044 Frascati, Rome, Italy 3 ENEA guest, Dipartimento Tecnologie Fisiche e Nuovi Materiali, Centro Ricerche Frascati, Via. Enrico Fermi 45, 00044 Frascati, Rome, Italy Correspondence should be addressed to R. Ricci, [email protected] Received 30 July 2009; Accepted 13 December 2009 Academic Editor: Martin Ulmke Copyright © 2010 R. Ricci et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Amplitude-modulated (AM) laser imaging is a promising technology for the production of accurate three-dimensional (3D) images of submerged scenes. The main challenge is that radiation scattered off water gives rise to a disturbing signal (optical noise) that degrades more and more the quality of 3D images for increasing turbidity. In this paper, we summarize a series of theoretical findings, that provide valuable hints for the development of experimental methods enabling a partial rejection of optical noise in underwater imaging systems. In order to assess the effectiveness of these methods, which range from modulation/demodulation to polarimetry, we carried out a series of experiments by using the laboratory prototype of an AM 3D imager (λ = 405 nm) for marine archaeology surveys, in course of realization at the ENEA Artificial Vision Laboratory (Frascati, Rome). The obtained results confirm the validity of the proposed methods for optical noise rejection.

1. Introduction The growing interest for underwater 3D imaging, with applications ranging from the monitoring of submarine archaeological sites to the inspection of submerged structures for industrial and scientific purposes, has stimulated in recent years the development of 3D optical imagers specifically designed to operate underwater [1]. A promising category of underwater 3D imagers is represented by continuous-wave amplitude-modulated laser optical radars [2, 3], whose overland counterparts can achieve—in air—a line-of-sight accuracy of hundreds of micrometers at tens of meters of distance. These systems belong to the class of incoherent rangefinders. Distance d is determined indirectly through the measurement of the phase difference Δφ between the modulated intensity of a laser

beam-used as the carrier of a radio-frequency modulating signal- and a reference signal: d=

v Δφ, 4π fm

(1)

where v is the light speed in the medium and fm the modulation frequency. The uncertainty σ in distance measurements, in regime of shot noise dominance, can be estimated by means of the formula v , (2) σ= √ 2 2πm fm Ri where m is the modulation depth and Ri the current signalto-noise ratio, depending, among others, on the received power and measurement integration time.

2


The advantage of this approach is that it requires continuous-wave, low power laser light, making it possible to realize more robust, affordable and non-invasive devices. It also natively enables one to acquire, in a single scan, selfregistered range—that is, geometric- and reflectivity/color— that is, imaging-information. All pieces of information, recorded in the form of two-dimensional arrays of structured data, are then integrated and transformed into 3D images by means of dedicated software. These features make AM laser optical radars particularly well suited for applications in the field of cultural heritage cataloguing and conservation, where they are widely used for the 3D digitization of both single artworks (paintings, sculptures, pottery) and entire sceneries (façades and interiors of historical buildings, archaeological sites). While AM rangefinding in air is nowadays a mature technology, the development of underwater AM optical radars is still an important scientific and technological challenge, which poses several problems in terms of reliability and attainable accuracy. This is mainly due to the noncooperative nature of water, a much more absorbing and scattering medium than air. The intensity I0 of a light beam propagating through water is attenuated because of absorption and scattering events due to dissolved molecules and suspended particles. In the regime of single scattering dominance, the rate of attenuation is well described by the Lambert-Beer law, which for a homogenous medium of thickness z is written as I(z) = I0 e−kz .

(3)

Here I(z) is the intensity of transmitted radiation and k the total attenuation coefficient. The latter—which depends in general on the radiation wavelength as well as, for inhomogeneous media, on space coordinates—accommodates for intensity losses due to both absorption and scattering, and can be expressed as k = ka + ks , where ka and ks denote the absorption and scattering coefficients, respectively. In underwater laser imaging applications, the effect of light absorption can in principle be reduced by properly selecting the laser wavelength in the region where transmission has a maximum. For pure water, light absorption is minimal in the blue-green region of the visible spectrum (350 nm ≤ λ ≤ 550 nm) [4, 5]. In particular, the use of green laser light permits to reduce absorption for turbid water with a relatively abundant chlorophyll concentration, typical of coastal seawater. In the case of interest for the present work-open sea characterized by rather clean seawater-the minimum of absorption is better matched by using laser light in the violet-blue region of the visible spectrum (λ = 405 nm). The other phenomenon affecting the performances of underwater laser imagers is scattering. Light backscattered by water and falling into the angular field of view of the receiver gives rise to an undesirable signal (optical noise), which combines with the target signal that carries the information necessary to image reconstruction. (Because of its deleterious effects on 3D imaging measures, the signal due to light backscattered by water is often referred to as optical noise

in this work-although it cannot be considered noise in strict sense.) The result is a reduction of the accuracy of range measurements, as well as a degradation of image contrast. It follows that optical noise has to be strongly reduced, in order to obtain 3D images of high contrast, resolution and accuracy. A partial reduction can be achieved by means of a bistatic optical layout, that is, by increasing the spatial separation between the launching and receiving stages [6]. The main drawback of this method is that it does not guarantee an effective filtering of the radiation backscattered by the initial part of the water column, which otherwise provides the most important contribution to the total noise. So, most effective rejection methods are necessary. In this article, we present the results of research recently carried out in the ENEA Artificial Vision Laboratory (Frascati, Rome, Italy) on scattered light rejection using modulation/demodulation and polarization techniques. The Artificial Vision Laboratory comprises researchers with a long-dating experience in the development of both coherent and incoherent optoelectronic devices, and dedicated software for artificial vision applications. The line of research on optical noise rejection is specifically targeted at the realization of a new underwater 3D imager, the AM Underwater Laser Optical Radar (AMULOR), which is at the moment of writing in course of advanced development. The first AMULOR operational system will be released in late 2009 as a deliverable of the BLU-Archeosys national project, funded by the Italian Ministry for University and Research. The final system will be mounted on a remotely operated vehicle and used for the survey of submerged archaeological sites at depths of a few tenths of meters, so in conditions of rather clear seawater. As a preparatory step to the realization of the AMULOR 3D imager, an experimental test bed has been set up in the ENEA Frascati research center, comprising a couple of tanks (1.56 m and 25 m long, resp.) equipped with an antireflection coated entrance window, and a laboratory prototype of the imager itself, supplemented, in case, by a polarizationsensitive receiving stage. The test bed was used to carry out various series of measurements in conditions of clean and relatively turbid water, obtained by adding proper amounts of a diffusing element— such as skim milk and Maalox —to tap water. Different scattering regimes (Rayleigh, intermediate or quasi-Mie) were explored, mainly in the limit of optically thin medium, where single scattering prevails on multiple scattering and polarization memory effects are negligible. The results of these experiments, reported in the present work, provided useful insights for the design and optimal configuration of the AMULOR. The paper is organized as follows. In the first part, we set up a simple theoretical framework, by summarizing results that help shed light on the characteristics of optical noise in underwater imaging systems. In particular, in Sections 2 and 3 we develop a simplified model of water backscattering that specifically applies to the case of AM laser imagers, by providing an analytical solution to the corresponding radiative transfer problem in the small angle

EURASIP Journal on Advances in Signal Processing diffusion approximation. The model is exploited in Section 4 to outline some possible modulation/demodulation experimental procedures, that enable the cancellation of optical noise by exploiting the existence of an interference-like effect between water and target signals. A complementary polarimetric approach is described in Section 5, where we briefly introduce the Muller-Stokes formalism, and use it to give grounds for the different polarization characteristics of light scattered by the medium and the target, respectively. In the second part of the article, we assess the effectiveness of the optical noise rejection techniques suggested by theory, by describing a number of experiments purposely carried out in the ENEA laboratories. Specifically, the experimental apparatus is briefly described in Section 6. In Section 7 we verify the low-pass filter behavior of water backscattering as a function of the modulation frequency in AM systems [7–9]. The analysis of how the water backscattering signal affects the performance of AM laser 3D imagers in turbid water—firstly published in [10] and then further explored in [11, 12]—is given in Section 8, where methods for the direct cancellation of the optical noise are also suggested. Finally, in Section 9 results obtained by using a specific polarimetric technique [13] for optical noise reduction are presented and discussed, followed by conclusions and acknowledgments. 1.1. Part I Theory. We provide in the following a simplified theoretical description of the most relevant properties that characterize the optical noise revealed by 3D laser imagers. The treatment is aimed at emphasizing those aspects that can be utilized for the reduction of optical noise effects in real conditions. In Sections 2 and 3 we derive a simple theoretical model, that incorporates the most important physical processes involved in the operation of a typical underwater AM laser 3D imager. The model permits to calculate, within the framework of the radiative transfer theory [14, 15] and in idealized yet still sufficiently realistic conditions, the power falling onto the system’s receiver when an AM laser beam is shot in open water. This result is used, in Section 4, to predict the observation of an interference-like pattern in the signal detected by an underwater AM 3D imager. The logical steps of the derivation are the following. Using the Multi-Component Approach (MCA) [14, 16, 17], the initial problem is firstly split into a system of Radiative Transfer Equations (RTEs), admitting a clearer physical interpretation in terms of forward and diffuse components. The Small Angle Approximation (SAA) is then used to simplify the equations [14, 18]. The SAA can be applied whenever the scattering probability strongly favors forward scattering events at small angles, that is, the phase function is strongly peaked in the forward direction. This condition is generally met by natural waters—such as seawater— where the angular deviation of light rays from their initial directions after a scattering event is usually very small and directed forwards. Finally, the Small Angle Diffusion Approximation (SADA) is applied [14, 17]. This enables a further simplification of the mathematical problem, which can then be explicitly solved. The resulting model takes into

3 account single backscattering events, as well as the spread of the laser beam due to multiple scattering events in the forward direction at small angles. In Section 5, finally, we use the Stokes-Muller formalism for demonstrating some important polarization properties of backscattered radiation, that permit to motivate the use of polarimetry as a means for optical noise rejection.

2. Optical Noise and Radiative Transfer Equation in Underwater AM Imagers Consider a point-like, perfectly collimated, AM laser source located at the origin of a Cartesian system with coordinates R = (r, z). Let the plane z = 0 coincide with the separation interface between air (z < 0) and water (z > 0). The laser starts shooting at t = 0 along the positive z axis with power ,

P(t) = P0 1 + m cos 2π fm t

-

≡ P0 + mPm (t),

(4)

where fm is the modulation frequency and m the modulation depth (0 ≤ m ≤ 1). A receiver, also located on the plane z = 0, but centered around the point rrec at a distance rrec = |rrec | from the origin, collects the radiation backscattered by the medium and falling onto the sensitive area Σrec and within the acceptance solid angle Ωrec . We aim at calculating the received power as a function of all intrinsic and extrinsic parameters of the imaging system, comprising light source, medium and receiver. It is convenient to model the imager’s receiving stage with ≡ ϕrec (r, Ω)δ(z), which represents the a function Φrec (R, Ω) receiver’s normalized spatial-angular sensitivity pattern to radiation falling at point R in the direction identified by the The received power is then given by versor Ω.

t Φrec R, Ω dRdΩ, Prec (t) = Σrec Ωrec I R, Ω,

(5)

t) is the radiance of the optical field (power where I = I(R, Ω, per unit projected area and unit solid angle). Once a suitable sensitivity pattern is assumed for the receiver, the problem is thus reduced to the determination of the radiance I, that is, to solving the following non-stationary, linear, integrodifferential radiative transfer equation: 7

8 1 ∂ t + Ω · ∇R + k I R, Ω, v ∂t

ks = 4π

4π

I R, Ω , t dΩ + S R, Ω, t . ·Ω p Ω

(6)

(We neglect thermal emission as not particularly relevant for the problem considered in this article.) Here v is the speed of light in the medium, and k = ka + ks is the attenuation coefficient (ka and ks are the absorption and scattering coefficients, respectively), which is constant all over the medium, supposed homogeneous. ∇R represents ) is the scattering phase ·Ω the gradient operator and p(Ω function, which we assume depending only on the scattering ≡ cos θs . · Ω angle θs (0 ≤ θs ≤ π) through Ω

4


)/4π is ·Ω With the chosen conventions, the quantity p(Ω naturally interpreted as the probability density that radiation is scattered in direction Ω . The last propagating along Ω term in (6) is an external source term modeling the injected t) ≡ light, which in the case at hand can be written as S(R, Ω, t)δ(z). s(r, Ω, Equation (6) represents the law of radiant energy conservation and provides an appropriate description of the interaction of light with matter as long as propagation distances are much larger than the wavelength. Analytical solutions to this equation can only be found in very specific cases, corresponding to well specified simplifying assumptions. It is firstly convenient to reduce the non-stationary problem to a stationary one, by taking the Fourier transform with respect to time of (6):

· ∇R + k + i Ω

ks = 4π

2π f I R, Ω, f v

(7) p Ω · Ω I R, Ω , f dΩ + S R, Ω, f ,

(8)

It is worth noticing that f appears in (7) only as a parameter. In order to keep notations simple, we are thus allowed to ignore the dependence on f initially, with the assumption to restate it at the end of the calculation. Thus, we are led to seek a solution to the following stationary RTE:

= ks · ∇R + k I R, Ω Ω 4π

4π

f

p = a f p f + ad pd .

(10)

f

f

· ∇R + k Id R, Ω Ω

ks Id R, Ω dΩ + T R, Ω , ·Ω p Ω 4π

I f R, Ω

R , Ω S R , Ω dR dΩ , G R, Ω;

=

Id R, Ω

R , Ω G R, Ω;

ksd I f R , Ω dΩ dR dΩ , ·Ω pd Ω 4π (13)

its definition in terms of where we substituted to T(R, Ω) I f (R, Ω). It is possible to derive an elegant, symmetric expression for the power falling onto the receiver by substituting the second of (13) into (5), and using the property

R , Ω G R, Ω;

; R, −Ω , = G R , −Ω

(14)

which is a direct consequence of the optical reciprocity theorem [14, 19]. After a few manipulations, one obtains

ks I f R, Ω dΩ + S R, Ω , ·Ω pf Ω = 4π

(12)

It is important to notice that both I f and Id obey now to the same RTE, yet with different source terms. If we manage to calculate the corresponding Green’s function R , Ω ), the forward and diffuse radiance compoG(R, Ω; nents can be immediately recovered as

· ∇R + k I f R, Ω Ω

ks Id R, Ω dΩ + T R, Ω . ·Ω pf Ω 4π

=

×

Here 1 > a f ad > 0 (a f + ad = 1), and p f and pd are legitimate phase functions describing the scattering over small forward- and large backward angles, respectively. This enables one to rewrite (7) as

· ∇R + k Id R, Ω Ω

(9)

The first step consists in applying the MCA, in order to distinguish between forward and diffuse radiation, I = I f + Id , by assuming that

ks I f R, Ω dΩ + S R, Ω , ·Ω pf Ω = 4π

=

I R, Ω dΩ ·Ω p Ω

. + S R, Ω

=

· ∇R + k I f R, Ω Ω

4π

I(. . . , t) = I . . . , f e2πi f t df .

(In order to simplify the notations, if not explicitly stated otherwise, we adopt the convention to distinguish functions and their Fourier transforms only from the list of arguments.) I(. . . , t) is eventually recovered from I(. . . , f ) by taking the inverse transform:

f

where we have introduced the quantities ks = a f ks and f ≡ ksd = ad ks (ks ≡ ks + ksd ). The new source term T(R, Ω) < d )I f (R, Ω ·Ω )dΩ is completely determined (ks /4π) pd (Ω after solving the first equation. The system of (11) is so far equivalent to (7). A first simplifying approximation can be made at this point by expanding Id in powers of ksd and only retaining terms of order ksd in the corresponding equation. This amounts to modifying the initial problem into a new one, where only single backscattering events are considered. No approximation is made in the equation for the forward component, which thus encompasses forward scattering at all orders. The new equations read

(11)

kd

Prec = I f R, Ω

s

4π

·Ω I&f R, Ω dRdΩdΩ . pd −Ω

(15) Here, I f is given by the first of (13), while I&f is obtained → S(R, ≡ & Ω) by the latter with the substitution S(R, Ω)


5

can be & Ω) Σrec Ωrec Φrec (R, −Ω). The new quantity S(R, interpreted as a fictitious source with an emission spatialangular pattern identical to the reception pattern of the receiver. In order to find explicit expressions for I f and I&f , and further simplify (15), we make the reasonable assumption that the underlying RTE-see (12)-admits a formulation in terms of the so-called small angle approximation. This amounts to assuming that the angles θ formed by forward scattered radiation with the incidence direction of the laser beam are very small, so that the following substitutions can be made:

4π

·Ω θs ≡ arccos Ω

(16)

+∞

−∞

du,

+∞

−→ u − u

0

pdb (|u|) J(z, u)du, 4π −∞

(17)

J(z, u) ≡ I f (r, z, u )I&f (r, z, u + u )drdu .

(18)

Each of the forward radiance functions entering (18) obeys a SAA radiative transfer equation of the form 8

ks = p f u − u I f (r, z, u )du + s(r, u)δ(z). 4π

(19)

Equation (19) can be solved analytically after applying 2D Fourier transforms in both r and u. Assuming that q and p are the Fourier conjugates of r and u, respectively, the solution reads [18]