Radar detection and track in presence of impulse

E UROPEAN M ICROWAVE A SSOCIATION

Radar detection and track in presence of impulse interference by using the polar hough transform Ivan Garvanov1 and Christo Kabakchiev2 Abstract – In this paper, the polar Hough transform (PHT) is considered as a track initiator in a track before detect (TBD) system. The study is performed in the presence of impulse interference. The algorithm under study includes a parametric CFAR detector, which works successfully in conditions of impulse interference and uses the polar Hough transform. The proposed Hough detector improves the detection probability in conditions of both Poisson and binominal random impulse flows. The usage of both CFAR and Hough transforms materially reduces the requirements to the input SNR in conditions of impulse noise. Another important advantage of PHT is that it is stability when the target velocity and azimuth vary in the time. Index Terms – Radar signal processing, Polar Hough transform, Track before detect, CFAR processor, Binary integration, Randomly arriving impulse interference.

I. Introduction The standard Hough transform and the related Radon transform have aroused much interest in recent years. The use of them makes possible the transformation of twodimensional images with lines into a domain of possible line parameters, where each image line corresponds to a peak, positioned at the respective line parameters. For these reasons, many line detection applications are considered within the image processing, computer vision and seismic research areas. Firstly, the use of the standard Hough transform (SHT) for target detection and track determination in white Gaussian noise is introduced by Carlson in [1]. The presence of randomly arriving impulse interference in the radar resolution cells can cause drastic degradation in the performance of a CFAR processor, and of the SHT detector. False alarms resulted from that make difficult the track detection. The improvement in the target detection and trajectory detection on the non-homogeneous background (impulse interference) is possible by using an approach for CFAR detection by means of the HT [2-4]. The Hough detection scheme includes a CFAR detector for signal detection in the scan area, the HT for mapping the target distance measurements from the scan area into the parameter space, binary integration of data in the parameter space and linear trajectory detection. These CFAR Hough detectors have been studiedin cases when the target moves in the same azimuth cell and the target velocity is constant [2-6]. There are modifications where the HT is used for the image processing after the conversion of radar data from the range-azimuth coordinate system to the Cartesian system associated with radar [7-9]. A polar Hough (PH) transform, which is more suitable for search radar applications, is proposed in [10]. This transform is analogous to the standard Hough transform, where

the input parameters are the target distance and azimuth measured by search radar. The technique converts the data obtained from previous search scans into one large multidimensional polar data map. This transform is suitable in radar detection and track determination, when both the target velocity and the target azimuth vary in time. The possibility to minimize time of radar signal detection providing the required values of the probabilities of false alarm and detection has appeared in result of the sequential analysis that has been developed in [11]. The priority of the sequential detector over the conventional detector is in the radar energy reduction at the stage of target detection. In this paper, a new CFAR polar Hough detector that can be used in a TBD system in conditions of randomly arriving impulse interference is proposed and evaluated. In this two-stage detector, the Hough detector removes all false alarms, which are resulted from the CFAR detector. The general structure of an adaptive polar Hough detector with binary integration is similar to that of a standard Hough detector. The difference between them is that the polar detector uses (range-azimuth-time) space while the SHT employs (range-time) space. The detection probability of a polar Hough detector can be calculated by Brunner’s method as for a standard Hough detector. In our previous algorithms described in [2-6], the use of the PHT instead of the SHT for track and target detection in the presence of randomly arriving impulse interference, allows employing them in real practical situations when the target moves with variable velocity along arbitrary linear trajectories.

II. Signal model It is assumed that the target is fluctuating according to the Swerling II case. It is also assumed that the total background environment includes the binomial distribution of impulse interference-plus-noise situation. The Binomial model describes a situation when the impulse noise is derived from two independent and identical impulse-noise sources, each of which generates a random impulse sequence with the same power intensity and the same average repetition frequency [12]. The probability of occurReceived December 8th, 2006. Revised April 6th, 2007. Institute of Information Technologies (IIT), Bulgarian Academy of Science. Bulgaria, Sofia 1113, Akad. G. Bonchev Str,. bl.2. Phone: +359 29792928; E-mail:1 [email protected]; 2 [email protected]

Proceedings of the European Microwave Association Vol. 3; March 2007; 170–175

I. GARVANOV AND C. KABAKCHIEV

rence (e) of a random pulse generated by each impulsenoise source in each range resolution cell can be expressed as e=F j• tc , where F j is the average pulse repetition frequency of and tc is the transmitted pulse duration.This means that the elements of the reference window are drawn from three classes. The first class represents the receiver noise only with probability (1-e)2 . The second class represents a situation when the signal samples are corrupted by a random impulse generated by one or the other impulse-noise source. This situation occurs with probability 2e(1-e). The third class represents a situation when the signal samples are corrupted by a total random pulse that is a sum of pulses generated by the two impulse-noise sources. This situation occurs with probability e2 . According to the theorem of total probability, the elements of the reference window are independent random variables distributed with the following probability density function (PDF): −x (1 − e)2 f (x) = exp + λ (1 + S) λ (1 + S) 2e (1 − e) −x (1) + exp + λ (1 + I + S) λ (1 + I + S) e2 −x + exp λ (1 + 2I + S) λ (1 + 2I + S) where λ is the average power of the receiver noise, I is the average interference-to-noise ratio (INR) of impulse interference, S is the average signal-to-noise ratio (SNR). The probability density function of Poisson distribution can be obtained under the assumption that e2 →0, 2e(1-e)→e0 and (1-e)2 →(1-e0 ) [6, 12]. It is the case when the probability of co-occurrence of the two random pulses in each range resolution cell becomes negligible, i.e. e2 tends to 0, but the probability of occurrence of a random pulse derived from one of two impulse-noise sources is non-zero, i.e. 2e(1e)>0.

In such a detector, target detection is declared if the signal value x0 exceeds a preliminary determined adaptive threshold H D . Incase of Poisson and binominal distribution of impulse interference, the analytical expressions for calculating of detection and false alarm probability are obtained in [2-6, 13-16]. B) Polar Hough transform The output data after each radar scan forms the polar data space (r -a), where r and a are the target range and azimuth. There are two approaches for Hough transformation of data - standard and polar Hough transforms (SHT and PHT). The SHT is more suitable for image transformation, while the PHT is very convenient for the use in radar because the output radar parameters (range and azimuth) are the input parameters of the transform. One trajectory is formed in a polar data map (r -a) after N S radar scans (fig. 1).

III. Hough detector with binary integration The algorithm proposed in this section is the improved modification of the algorithm for target detection and track initiation with the Hough transform, proposed by Carlson, Evans and Wilson in [1]. In order to keep the false alarm constant rate in conditions of impulse interference, a CFAR processor replaces the detector with fixed detection threshold in the range-time space. For determination of the non-radial trajectory, the standard Hough transform is replaced by the polar Hough transform [10]. The algorithm under study includes a CFAR processor, which works in the scan area, a polar Hough transform of the target distance measurements into the parameter space, a binary integrator of data and a detector of linear trajectory in the parameter space. A) CFAR processor The CFAR processor is a detector, which maintains the constant false alarm rate in the process of target detection.

Proceedings of the European Microwave Association

Fig. 1. Geometry in polar coordinate system, showing ten data points and defining parameters of line through them.

The point coordinates in the (r -a) space form the polar parameter space. The PHT maps points (targets) from the observation space (polar data map) into curves in the polar Hough parameter space, termed as the (rho-theta) space, by: (2)

r ho = r cos (a − theta) , 0 < (a − theta) ≤ π

where r and a are the target range and azimuth, theta is the angle and rho is the smallest distance to the origin of polar coordinate system. The mapping can be viewed as stepping through theta from 0. ˚ to 180. ˚ and calculating the corresponding rho. The result of transformation is a sinusoid with unit magnitudes. Each point in the polar Hough parameter space

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RADAR DETECTION AND TRACK IN PRESENCE OF IMPULSE INTERFERENCE BY USING THE POLAR HOUGH TRANSFORM

corresponds to one line in the polar data space with parameters rho and theta. A single rho-theta point in the parameter space corresponds to a single straight line in the r − a data space with these rho and theta values. Each cell from the polar parameter space is intersected by a limited set of sinusoids obtained by PHT.

IV. Probability characteristics The detection probability of the polar Hough detector cannot be presented in the form of a simple Bernoulli sum as for a standard Hough detector. During the target movement, the SNR of the received signal changes depending on the distance to the target, and as a consequence, the probability of target detection changes as well. Therefore, H ough the probability PD can be calculated by Brunner’s method [1]. For Ns scans, the detection probability is: (3)

H ough

PD

=

NS

PD (i, N S )

i=TM

Fig. 2. Hough parameter space showing ten sinusoids corresponding to ten data point of Fig. 1. Point of intersection defines r ho and theta of line in polar data space through the ten data point.

Each sinusoid corresponds to a set of possible lines through the point. If a line exists in the polar data space, by means of PHT it is represented as a point of intersection of sinusoids defined by PHT. The polar data space is built from range-azimuth cells, containing the coordinates of targets after N scans. The parameters rho and theta have the linear trajectory in the polar Hough parameter space and can be transformed back to the polar data space showing the current distance to the target. If the number of binary integrations (BI) of data in the polar Hough parameter space (of intersections in any of the cells in the parameter space) exceeds the detection threshold, both target and linear trajectory detection are indicated. Target and linear trajectory detection are carried out for all cells from the polar Hough parameter space.

Fig. 3. Binary integration of data in Hough parameter space for example show on Fig. 2.

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where TM is the binary threshold in the polar Hough parameter space, PD is the cumulative probability of getting exactly i detections from Ns looks at the target. The PD is obtained in [2-6,13-15] for different CFAR detectors and in the presence of non-homogeneous background, including homogeneous and randomly arriving impulse interference. The probability of false alarm is evaluated by (2), where PD is calculated for SNR=0 dB.

V. Simulation example and experiment description Using simple examples, we illustrate the advantages of the PHT in situations, when the target moves with variable velocity along arbitrary linear trajectories. The polar Hough transform is very convenient for the use in radar detection and track determination because the input parameters of the transform are the output parameters of the search radar. The input data for the CFAR processor is simulated by using the equation (1), where the average power of the receiver noise is .λ=1, the signal-to-noise ratio is 20dB, the probability impulse noise appearance is 0.1 and the average interference-to-noise ratio is I =30dB (fig. 4).

Fig. 4. Range-azimuth matrix obtained after radar scan and includes noise, randomly arriving impulse interferences, and target signal. This is the input matrix for the Cell Averaging CFAR processor.



The situation is additionally complicated by returns from interferences and the receiver noise. After CFAR processing, the output matrix includes 1 or 0 depending on that whether the target signal or false alarm are detected or not. (fig. 5). The heavy interference environment can be described in terms of the probability of false alarm.

Fig. 7. An observation of a target in polar coordinate system after N radar scans. Fig. 5. Range-azimuth matrix obtained after CFAR processing. It includes ) and 1 in cases of target detection and false alarm.

The target changes its velocity and moves at different azimuths. After N radar scans, as a result of CFAR processing the matrix of target detections in the range-azimuth plane is formed (fig. 6).

Fig. 8. Hough parameter space showing the sinusoids corresponding to the data point from Fig. 7.

Fig. 6. An observation of a target in the range-azimuth plane after N radar scans.

The matrix includes the true points of the target trajectory and false alarms. This information fills the range-azimuth space, which is the input for the polar Hough transform. The positions of a target in the polar coordinate system after N radar scans are shown on fig. 7. This result is equivalent to fig. 6. The polar Hough transform maps points (targets and false alarms) from the observation space (polar data map) into curves in the polar Hough parameter space, termed as the (rho-theta) space (fig. 8).


The results of transformation are sinusoids with unit magnitudes. Each point in the polar Hough parameter space corresponds to one line in the polar data space with parameters rho and theta. A single rho-theta point in the parameter space corresponds to a single straight line in the range-azimuth data space with these rho and theta values. Each cell from the polar parameter space is intersected by a limited set of sinusoids obtained by PHT. The sinusoids obtained by the transform are integrated in the Hough parameter space after each radar scan (fig. 9). In each cell of the Hough parameter space is performed binary integration and comparison with the detection threshold. If the number of binary integration (BI) of data in the polar Hough parameter space (of intersections in any of the cells in the parameter space) exceeds the detection threshold, both target and linear trajectory detection are indicated.

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RADAR DETECTION AND TRACK IN PRESENCE OF IMPULSE INTERFERENCE BY USING THE POLAR HOUGH TRANSFORM

Target and linear trajectory detection are carried out for all cells from the polar Hough parameter space.

BI processor and by 17 dB - for the Hough detector with API CFAR processor toward the Hough detector with fixed threshold (TM /N S =7/20 and 13/20). The results obtained show that in situations when the impulse interference occurs with the probability of 0.1, the Hough detector with API CFAR processor is the most effective.

Fig. 9 Binary integration of data in Hough parameter space for example show on Fig. 8.

The Hough detector with fixed threshold is compared to another three two-dimensional Hough CFAR detectors proposed in [16] – Hough CFAR BI (Binary Integration) detector, Hough EXC CFAR BI detector and Hough API (Adaptive censoring Post detection Integration) CFAR detector. In order to analyze the quality of the polar Hough detector we consider radar with parameters, similar to those in [1-6]: the search scan time is 6s; the range resolution is .δR=3nmi; the beam range-time space has 128 range cells and 20 time slices. In [16] we consider straightline trajectory, incoming target with a speed of Mach 3 and 1 sq. m radar cross-section. In the analysis, the average SNR is calculated as S = K /R 4 , where K=0.16*1010 is the generalized energy parameter of the radar and R is the distance to the target measured in nautical miles. The experimental results are obtained for the following input parameters: the average power of the receiver noise I λ=1; the average interference-to-noise ratio is I =30dB; the probability of appearance of impulse noise is 0.1; the number of reference cells is N =16; the CFAR binary decision rule “M-out-of-N” is 16/16; the probability of false alarm is PF A =10−4 , the excision threshold is Be=2; the number of scans is N =20, the binary detection threshold in the Hough parameter space is TM =13. The Hough detector with fixed threshold and the Hough detectors with CFAR BI, EXC CFAR BI, API CFAR processors, with different thresholds in the Hough parameter space - TM are presented on fig.10. The results show losses in the SNR by about 7 dB - for the Hough detector with EXC CFAR

References [1] Carlson, B.; Evan, E.; Wilson, S.: Search Radar Detection and Track with the Hough Transform. IEEE Trans., AES (1994), Part I, 102-108; Part II, 109-115; Part III, 116-124.

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Fig. 10 Probability of detection for Hough detectors with API, BI and EXC BI CFAR processors.

VI. Conclusion In this paper, a track before detect (TBD) radar system, with application of the polar Hough transform is proposed. It is shown, that the Hough detection algorithm is suitable for using in many practical situations when the target moves with variable velocity along arbitrary linear trajectories in the presence of randomly arriving impulse interference. The proposed Hough detector improves the detection probability in conditions of both Poisson and binominal random impulse flows. The usage of both CFAR and Hough transforms reduces the requirements to the input SNR in conditions of impulse noise. By using N radar scans, the average detection threshold (ADT) of this detector is improved. As a consequence, the proposed polar Hough detector can be used successfully in different radar systems and secondary applications of communication technologies.

Acknowledgment This work was partially supported by projects: IIT 010059/2004, MPS Ltd. - Grant IF-02-85/2005 and by Bulgarian NFSR - Grant TH-1305/2003.

[2] Behar, V.; Kabakchiev, Chr.; Doukovska, L.: Target Trajectory Detection in Monopulse Radar by Hough Transform. Compt. Rend. Acad. Bulg. Sci., 53 (2000), 45-48. [3] Behar, V.; Vassileva, B.; Kabakchiev, Chr.: Adaptive



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Hough Detector with Binary Integration in Pulse Jamming, Proc.ECCTD’97, Budapest, 1997, 885 - 889. Behar, V.; Kabakchiev, Chr.: Hough Detector with Adaptive Non-coherent Integration for Target Detection in Pulse Jamming, Proc. ISSSTA’98, South Africa, 1998, 10031008. Kabakchiev, Chr.; Doukovska, L.; Garvanov, I: Hough Radar Detectors in Conditions of Intensive Pulse Jamming, S&T e-Didest, ISSN 1726-5479, 2005, 381-389. Kabakchiev, Ch.; Garvanov, I; Doukovska, L.: Excision CFAR BI Detector with Hough Transform in the Presence of Randomly Arriving Impulse Interference, Proc. of the International Radar Symposium – IRS 2005, Berlin, Germany, 06-08 September 2005, 259-264. Grishin Y.; Swiercz, E.; Janczak, D.: Using The Hough Transform as A Track Initiator in A TBD System, Proc. IRS 2004, Warszawa, Poland, 2004, 291-296. Lazarov, A.; Minchev, Ch.: ISAR Image Reconstruction Technique With Stepped Frequency Modulation and Multiple Receivers, Proc. DASC’05, Washington, 2005, CD14E2-115. Semerdjiev, E.; Alexiev, K; Bojilov, L.: Multiple Sensors Data Association Using Hough Transform for Track Initiation, Proc. Fusion’98, Las Vegas, II (1998), 980-985. Garvanov, I.; Kabakchiev, Chr.; Rohling, H.: Detection Acceleration in Hough Parameter Space by K-stage Detector,

Ivan Ganchev Garvanov was born in Popintsi, Bulgaria, on June 10, 1973. He received two M.S. degrees in the Technical University – Sofia, Bulgaria, as follow: first, in the Faculty Automatic, specialization ”Systems and Management” (1997) and second, in the Transport Faculty, specialization ”Exploitation of Electric and Aeronautical Techniques” (1998). He received the Ph.D. degree at the Institute of Information Technologies, Bulgaria in 2003. The dissertation title is: “Methods and Algorithms for Keeping Constant False Alarm Rate in the Presence of Pulse Jamming”. Since 2006 he is Associate Professor in Institute of Information Technologies, Bulgarian Academy of Sciences.His research experience is in CFAR radar signal detection; radar signal and jamming simulation; clutter and jamming cancellation and adaptive filtering; radar signal transform (Hough); statistical analysis and Monte Carlo simulation.


[11]

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6th International Conference “Numerical Methods and Applications” NM&A-2006, August 20-24, 2006, Borovets, Bulgaria, (in print). Garvanov, I.; Kabakchiev, Chr.: Radar Detection and Track Determination with a Transform Analogous to the Hough Transform, Proc. of International Radar Symposium – IRS 2006, Krakow, Poland, 24-26 May, 2006, 121-124. Akimov, P.; Evstratov, F.; Zaharov, S.: Radio Signal Detection, Moscow, Radio and Communication, (1989), 195-203 (in Russian). Garvanov, I.: CFAR BI Detector in Binomial Distribution Pulse Jamming, Comptes Rendus de l’Academie Bulgare des Sciences, 56 (2003), 37-44. Kabakchiev, Chr.; Doukovska, L.; Garvanov, I.: Hough Radar Detectors in Conditions of Intensive Pulse Jamming, Sensors & Transducers Magazine (S&T e-Didest), Special Issue, August 2005, 381 – 389. Kabakchiev, Chr.; Doukovska, L.; Garvanov, I.: Adaptive Censoring CFAR PI Detectors with Hough Transform in Multipath Situation, Cybernetics and Information technologies, 5 (2005), 115-126. Doukovska, L.; Kabakchiev, Chr.: Performance of Hough Detectors in Presence of Randomly Arriving Impulse Interference, Proc. of the International Radar Symposium IRS, Krakow, Poland, 22-26 May, 2006, 473-476.

Christo Avgustov Kabakchiev received his MSc. and Ph.D. degrees in Radio Engineering from the Air Force Engineering Academy, Moscow, Russia, in 1970 and 1975 respectively. He obtained his D.Sc. degree in Radar Signal Processing from the Institute of Defence Electronics “Electron”, Sofia, Bulgaria, in 1986. From 1977 to 1989, he was an Assistant Researcher and Associate Professor, at the Institute of Defence Electronics “Electron” in 1984. From 1994 to 1995 he was an Associate Professor. Since 1995 he is Professor, Head of Research Group in Institute of Information Technologies, Bulgarian Academy of Sciences. Since 1996 he is Visitor Professor, Technical University, Sofia. Since 2005 he is Professor, Software Technology Department, Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”. Prof. Kabakchiev participated in 12 scientific research projects, leading 6 of them. Since 2005 he is a member of the Scientific Commission “Military and Military Engineering Science”, the Highest Certification Commission to the Bulgarian Government, and Scientific Council to the Highest Certification Commission to the Bulgarian Government, “Radio electronics and communication technique”, “Information Sciences”. Professor Kabakchiev’s current research interests include target detection performance calculation, CFAR technique, real time radar signal processing, parallel algorithm, systolic, and multiprocessor architecture.

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