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Detection and Extraction of Target With Micromotion in Spiky Sea Clutter via Short-Time Fractional Fourier Transform Xiaolong Chen, Jian Guan, Member, IEEE, Zhonghua Bao, and You He Abstract— In order to effectively detect moving targets in heavy sea clutter, the micro-Doppler (m-D) effect is studied and an effective algorithm based on short-time fractional Fourier transform (STFRFT) is proposed for target detection and m-D signal extraction. Firstly, the mathematical model of target with micromotion at sea, including translation and rotation movement, is established, which can be approximated as the sum of linearfrequency-modulated signals within a short time. Then, due to the high-power, time-varying, and target-like properties of sea spikes, which may result in poor detection performance, sea spikes are identified and eliminated before target detection to improve signal-to-clutter ratio (SCR). By taking the absolute amplitude of signals in the best STFRFT domain (STFRFD) as the test statistic, and comparing it with the threshold determined by a constant false alarm rate detector, micromotion target can be declared or not. STFRFT with Gaussian window is employed to provide time-frequency distribution of m-D signals, and the instantaneous frequency of each component can be extracted and estimated precisely by STFRFD filtering. In the end, datasets from the intelligent pixel processing radar with HH and VV polarizations are used to verify the validity of this proposed algorithm. Two shore-based experiments are also conducted using an X-band sea search radar and an S-band sea surveillance radar, respectively. The results demonstrate that the proposed method not only achieves high detection probability in a lowSCR environment but also outperforms the short-time Fourier transform-based method. Index Terms— Linear frequency modulated (LFM) signal, micro-Doppler (m-D), moving target detection, sea spike, shorttime fractional fourier transform (STFRFT).
I. I NTRODUCTION
R
OBUST detection of weak targets, especially “low attitude, slow, and small” targets, in sea clutter is always a challenging subject in the field of radar signal processing, which is important for military and civil use [1]. Sea clutter is a complex phenomenon influenced by environmental
Manuscript received June 23, 2012; revised December 18, 2012; accepted February 1, 2013. Date of publication May 21, 2013; date of current version December 12, 2013. This work was supported in part by the National Natural Science Foundation of China under, Grant 61002045, Grant 61179017, and Grant 61201445, and the Mountain Tai Scholars of China. The authors are with the Department of Electronic and Information Engineering, Naval Aeronautical and Astronautical University, Shandong 264001, China (e-mail:
[email protected];
[email protected];
[email protected];
[email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TGRS.2013.2246574
conditions (sea state decided by wind speed, wave height, tide, etc.), parameters of the radar system (transmitting frequency, resolution, polarization), and site configuration (height, grazing angle). To a high-resolution radar working at a low grazing angle, sea clutter usually shows nonhomogeneous, nonstationary, and time-varying properties especially in case of high sea state. Also, on a radar display, sea echoes generally have higher power and “spikier” appearance than the receiver noise [2], which may result in poor detection performance. Consequently, a careful study of sea clutter is necessary and important for weak target detection [3]. The total field scattered from an extended rough sea surface is the sum of elementary waves scattered from many parts of the surface. If the incident field is time coherent and the surface is not in motion, then one component of the scattered field above the surface must be time-invariant with a single frequency relative to the incident wave frequency and the incident angle, which is called the classical Bragg scattering mechanism. However, it has been shown for some time that models for low-grazing-angle radar backscatter from the sea surface based solely on the Bragg resonant scattering cannot fully explain experimental observations of Doppler spectrum or radar cross-section (RCS) values. Long [4] proposed a twoscatterer theory of sea echo, which suggests that sea echo is divided into fast fluctuations from wind ripples and slow fluctuations dependent on sea structure. Later, it was found that, in general, sea clutter consists of two parts: tilt modulated Bragg scattering and so-called sea spikes with large Doppler velocity caused by the scattering on breaking waves [5]. Lee et al. [6] observed through laboratory experiments with a water tank as well as measurements on sea surface that, in addition to the Bragg scattering associated with the scattering of small centimeter-scale waves, there were nonBragg components which resulted from “fast backscatter” composed of disordered mass of water, foam, bubbles, such as bursts (crests of waves just before they break) and whitecaps (very rough surface of waves as they break). Sea spikes, a term to describe the strong and rapidly fluctuating events caused by the scattering on “fast backscatter,” are point-like echoes occurring especially with high frequency, high resolution, low grazing angles, and horizontal polarization. It has been shown that sea spikes may lead to widened Doppler spectrum, Doppler shift, and target-like returns which will degrade the detection performance of radar detectors [7], [8].
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CHEN et al.: DETECTION AND EXTRACTION OF TARGET WITH MICROMOTION
Traditional detection methods based on statistics, which model as a stochastic process, depend on the prior knowledge of clutter distribution [9]. A lot of efforts have been made to fit various distributions to the observed sea clutter data, including Rayleigh, Weibull, log-normal, and the K distributions [10], [11]. However, these distributions do not address the extended tail region well when sea spikes are present with low signalto-clutter ratio (SCR). Hence, the nonGaussian property of heavy sea clutter makes it difficult for classical statistical mathematics to represent sea clutter accurately [12]. Another popular technique is the fractal-based detection method proposed by Haykin [13]. Fractal characteristics such as Fractal dimension, multifractal correlation, and fractal Poisson model, and so on, have been employed for target detection at sea [14], [15]. However, in a low-SCR environment, the fractal technique fails to detect the target covered by heavy sea clutter and cannot acquire the state of the moving target. A set of primitive signal processing techniques, including signal averaging, time-frequency representation, and morphological filtering are proposed in [2]. Nonetheless, these techniques are either time consuming or a rough estimation of Doppler frequency. When the sea is calm (corresponding to the sea state below two), the relative translation movement of radar to target at sea plays a dominant role in the Doppler shift. However, under high oceanic conditions, the attitude of target may vary with the fluctuation of sea surface, which induces the effect of power modulation on radar echo. Then the Doppler exhibits time-varying and nonstationary properties due to the simultaneous translation and rotation movements, that is, roll, pitch, and yaw movements [16], [17]. As a result, effective detection algorithm should be good at processing time-varying signals and reflect more detailed features of the radar echo. In recent years, the micro-Doppler (m-D) effect has attracted extensive attention worldwide for accurate description of movement information of a target [18], which has been applied to imaging, recognition and classification, and so on [19], [20]. M-D signature can be regarded as a unique signature of the target and provides additional information which is complementary to those made available by existing methods. Since m-D might induce frequency modulation on the returned signal, the m-D signature of target at sea may result from the nonuniform translation movement and the rotation movement. Consequently, m-D theory is quite helpful for weak target detection and recognition at sea indicating the subtle changes of frequency. However, lots of theoretical problems still remain to be solved. Time-frequency analysis provides an image of frequency contents as a function of time, which reveals how a signal changes over time. The Fourier transform (FT)-based analysis used in m-D processing is incapable of solving such nonstationary signals [18]. Thus, linear and nonlinear timefrequency distributions have been proposed to analyze the m-D effect [21]. Linear methods such as short-time Fourier transform (STFT) can be explained by showing the spectral characteristics as a function of time but it is limited by low time-frequency resolution. Wigner-related distributions, as the representative of nonlinear methods, can achieve high
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resolution; however, they suffer from cross-term interference in case of multiple m-D signals, which makes them less attractive for many practical purposes. Empirical mode decomposition is also used for micromotion target imaging with rotating parts, whereas it is more complicated with low efficiency [20]. The fractional FT (FRFT) is a generalization of the FT and it was first introduced by V. Namias in 1980 [22]. For a given chirp signal, it can achieve the best energy concentration in FRFT domain (FRFD) with a certain order, hence, FRFT is a powerful tool for the analysis of nonstationary, timevarying signals and has been applied in radar signal processing [23]. However, it only reveals the overall FRFD contents for the global kernel and fails to show the frequency changes. This leads to a new hybrid time-frequency transform, that is, the short-time FRFT (STFRFT), which displays the time and FRFD information jointly in the time–FRFD plane without cross-term interference [24]. It has the property of additivity of rotation and provides the frequency-modulated (FM) signal with a horizontal oriented support, which is helpful for the analysis and processing of m-D signals. In this paper, m-D theory is introduced to weak target detection in spiky sea clutter, which can expand the dimension of signals with more information. Automatic sea spikes suppression method is proposed by the identification criteria and the minimum power segment selection. Then detection and extraction of m-D signals are conducted with sea spikes removed based on STFRFT and STFRFD filtering. The performance of the proposed algorithm is demonstrated by simulations using real sea clutter data collected by the popular intelligent pixel (IPIX) processing radar, X-band sea search radar, and S-band sea surveillance radar. The remainder of this paper is organized as follows. In Section II, the mathematics of m-D effect induced by micromotion dynamics at sea are introduced. Section III presents the identification method of sea spikes and also discusses the properties with IPIX radar data. In Section IV, we propose the detection and extraction method of m-D signals based on STFRFT followed by performance analysis. Then, three kinds of real sea clutter datasets are used for verification, and simulations are provided in Section V. Finally, some concluding remarks are presented in Section VI. II. M ATHEMATICAL M ODEL OF TARGET W ITH M ICROMOTION AT S EA When ground-based radar observes a target at sea, such as ship, boat, and float, the target can be modeled as a rigid body with multiple scatterers. Therefore, the motion between radar and scatterers on target is decomposed into translation movement of reference point on ship and rotation movement around that reference point including pitch, roll, and yaw movements in three dimensions induced by sea wave. In the following discussions, we will take a ship sailing at sea as an example to represent the micromotion target and establish m-D signal model with two assumptions. 1) The radar echo of the ship is assumed to be a sum of single-scattering objects, that is, the point-scattering model. 2) Due to the small observation time and range resolution, the ship will stay within one range bin for the short
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z ωz
Cref =(X,Y,Z) Cmov =(x,y,z) Crlos=(q,r,h)
Z Ship
X
r
h
φ x
ωy
ωx q
RLOS
y
Y
Radar
Fig. 1.
Geometry of a ground-based radar and target at sea.
observation time (0.5 s in the simulations). (Even if the range migration exists, excellent algorithms such as Keystone and Radon-Fourier transform [RFT] algorithm can be used for range compensation [25], [26].) The geometry model and three corresponding observation coordinate systems are illustrated in Fig. 1, that is, Cref (reference coordinate), Cmov (movement coordinate), and Crlos (radar line-of-sight [RLOS] coordinate). The origin point (0, 0, 0) in the reference coordinate system Cref = (X, Y, Z ) is assumed to be stationary with respect to radar and is fixed on the ship’s center. The movement coordinate Cmov = (x, y, z) centers on the ship and moves along it with three rotation movements, that is, roll, pitch, and yaw movements. The positive axis x is toward the sailing direction and the absolute of (x, y, z) represents length, width, and height of the ship, respectively. If there is no rotation movement, then Cmov is coincident with Cref . The RLOS coordinate is denoted as Crlos = (q, r, h), where r is the RLOS range, h is orthogonal to the r -axis on the plane (X, Y ), and q meets the right-hand screw rule.
where v is the speed of the ship. Then (3) can be seen as a uniformly accelerated radial motion by taking the first three terms of (3) 1 (4) Rs (t) = R0 − v 0 t − as t 2 2 where v 0 is the radial velocity and as is the radial acceleration. Assume that the time and frequency synchronization meets the system performance, so the transmitted signal can be used as the reference signal. After the demodulation process, the intermediate frequency signal is obtained as sIF (t) = sr (t) · st∗ (t) t −τ exp (−j2πktτ ) exp (−j2π f c τ ) (5) = σr rect Tp where * denotes the complex conjugate. After range compression, (5) can be rewritten as t −τ sPC ( f, τ ) = σr rect sinc T p ( f + kτ ) exp (−j2π fc τ ). Tp (6) Substitute τ = 2Rs (t)/c into (6) and take the time derivative of the phase, we obtain the instantaneous frequency induced by the uniformly accelerated movement
2 2 d R0 − v 0 t − as t 2 /2 = (v 0 + as t) (7) ft = − λ dt λ where λ = c/ f c is the radar wavelength. We can deduce from (7) that after demodulation and range compression, the signal echo is modulated by the velocity and acceleration, which is approximated as a first-order polynomial, that is, LFM signal. Also, from (7), one can conclude that the Doppler can be regarded as a kind of m-D signal due to the time-varying frequency. B. Rotation Movement
A. Translation Movement To obtain high range resolution and reduce the effective bandwidth, the normalized linear frequency modulated (LFM) signal is transmitted, which has the form t 1 exp j2π f c t + kt 2 (1) st (t) = rect Tp 2 1, |u| ≤ 1/2 where, rect(u) = , f c denotes the carrier 0, |u| > 1/2 frequency, T p is the pulsewidth, and k = B/T p is the chirp rate with bandwidth B. Then the returned signal is represented as t −τ k 2 exp j2π f c (t − τ ) + (t − τ ) sr (t) = σr rect Tp 2 (2) where σr is the scattering coefficient and the time delay is τ = 2Rs (t)/c, c denotes the light speed. Suppose a ship is sailing toward the radar and only the radial velocity is considered. The range is a function of time, and can be expanded in Taylor series as 1 1 (3) Rs (t) = R0 − vt − v t 2 − v t 3 − · · · 2 3
The ship’s rotation movement around its center can be described by a rotation matrix R z−y−x , which is represented by a product of three elemental rotations with three rotation angles R z−y−x = R(θx )R(θ y )R(θz ) (8) where R(θx ), R(θ y ), and R(θz ) represent the roll matrix, pitch matrix, and yaw matrix, respectively, with their corresponding rotation angles θx , θ y , and θz [18] ⎤ ⎤ ⎡ ⎡ 1 0 0 cos θ y 0 sin θ y 1 0 ⎦ R(θx ) = ⎣0 cos θx − sin θx ⎦ , R(θ y ) = ⎣ 0 0 sin θx cos θx − sin θ y 0 cos θ y ⎡ ⎤ cos θz − sin θz 0 R(θz ) = ⎣ sin θz cos θz 0 ⎦ . (9) 0 0 1 For the requirement of movement status in the RLOS coordinate Crlos , the movement coordinate Cmov should firstly be transformed to the reference coordinate Cref by R z−y−x ⎡ ⎤ a11 x + a12 y + a13 z Cref = Rz−y−x Cmov = ⎣ a21 x + a22 y + a23 z ⎦ . (10) a31 x + a32 y + a33 z
CHEN et al.: DETECTION AND EXTRACTION OF TARGET WITH MICROMOTION
Then, based on the geometric relation in Fig. 1, the Crlos is obtained by transforming the Cref with R(ϕ) ⎡ ⎤ q Crlos = ⎣ r ⎦ = R(ϕ)Cref h ⎡ ⎤ ⎤⎡ cos ϕ − sin ϕ 0 a11 x + a12 y + a13 z = ⎣ sin ϕ cos ϕ 0 ⎦ ⎣ a21 x + a22 y + a23 z ⎦. (11) 0 0 1 a31 x + a32 y + a33 z Assume that the radar and the ship are in the same plane and the height is ignored, then the RLOS distance can be derived from the second row of (11) r (t) = sin ϕ(a11 x + a12 y + a13 z) + cos ϕ(a21 x + a22 y + a23 z) (12) where aii is calculated by (9) and (11) and is shown as follows: ⎧ a11 = cos θ y cos θz ⎪ ⎪ ⎪ ⎪ a ⎪ 12 = − cos θ y sin θz ⎪ ⎨ a13 = sin θ y (13) a21 = sin θx sin θ y cos θz + cos θx sin θz ⎪ ⎪ ⎪ ⎪ a22 = − sin θx sin θ y sin θz + cos θx cos θz ⎪ ⎪ ⎩ a23 = − sin θx cos θ y . The m-D due to the rotation movement is obtained as follows by taking the time-derivative of (12): 2 dr (t) 2vr (t) = . (14) λ λ t For the convenience of calculation, we will analyze the three kinds of rotation movement separately with their corresponding angular velocities ωx = θx /t, ω y = θ y /t, ωz = θz /t, ω = ϕ/t. 1) Roll Movement: In this case, θ y = θz = 0, and r (t) is rewritten as fr =
r (t) = sin ϕ · x + cos ϕ(cos θx · y − sin θx · z).
3) Yaw Movement: In this case, θx = θ y = 0, and the m-D due to the yaw movement can be derived as 2 f rz ≈ cos ϕ ωx + ωz x − ωωz yt − ωz2 yt . (19) λ If the roll, pitch, and yaw movements exist simultaneously, the m-D is combined by the three. Together with the nonuniform translation movement, the Doppler frequency is 2 f d = f t + fr ≈ v 0 + at + cos ϕ 3ωx − ωx z + ωz x λ + ωω y z −ωωz y −ω2x y −ωz2 y t . (20) From the above analysis, on condition that radar transmits LFM signal to a point-scattering target at sea, m-D due to the nonuniform translation and rotation movements can be modeled as the sum of FM signals, whose amplitude and frequency relate to the sea state. In the case of a short-time window, the FM signals can be approximately combinations of amplitude modulation and LFM signal with three parameters, that is, amplitude, initial velocity, and acceleration. Also, as the RCS of the micromotion target varies with visual angle and course, it will be more practical and effective to use a fluctuant model. Then, within observation time T , the model of a single micromotion target in sea clutter is characterized as follows: x(t) = s(t) + c(t) Ai (t) exp j2π f i t +jπki t 2 + c(t), |t| ≤ T =
(21)
i
where Ai (t) is the signal amplitude of the i th m-D signal, the center frequency and the chirp rate are f i and ki , and sea clutter is denoted as c(t). III. S EA S PIKES I DENTIFICATION AND DATA S ELECTION
(15)
Then, the frequency shift becomes fr x =
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2 cos ϕ · ωx − sin ϕ · ω (cos θx · y − sin θx · z) λ − cos ϕ (sin θx · ωx y + cos θx · ωx z) . (16)
In a short time, the rotation angular ϕ is quite small and the trigonometric functions can be approximated by the Taylor series expansion, that is, cos ϕ sin ϕ, sin θx ≈ ωx t, and cos θx ≈ 1. We can rewrite (16) as 2 f rx ≈ cos ϕ ωx − ωx z − ω2x yt . (17) λ Equation (17) indicates that the m-D of roll movement can be expressed as a FM signal whose frequency is related to the angular velocity and the ship’s movement coordinate (x, y, z). 2) Pitch Movement: Similar to the roll movement, θx = θz = 0 and we also carry out the approximate calculation. Then the m-D induced by the roll movement can be obtained as 2 (18) fry ≈ cos ϕ(ωx + ωω y zt) λ which shows that the Doppler is expanded by a chirp rate.
A. Description of IPIX Radar Database The experimental data presented in this paper were collected by the McMaster University IPIX radar at the east coast of Canada, from a clifftop near Dartmouth, Nova Scotia, in 1993. The IPIX radar is an instrumentation-quality, coherent, dual-polarized X-band radar, working at low grazing angles, designed for the purpose of identifying sea clutter features that are most useful for the research of weak target detection in sea clutter. A complete description of the IPIX radar can be found in [27]. To perform the simulations with real sea clutter, we have selected two representative datasets collected in November 1993, one with higher sea state (19931107_135603_starea.cdf, the average peak-totrough height of the highest on third of the waves, defined as significant wave height, is around 2.1 m, rough sea surface) named as dataset_17 and the other with lower sea state (19931108_220902_starea.cdf, a significant wave height of 1.0 m, slight sea surface) named as dataset_26. The detailed features of the two datasets are summarized in Table I. The sea surface of dataset_26, compared with that of dataset_17, is smoother because of the lower significant wave height and downwind observed direction. Fig. 2 shows the radar returns of the two datasets without target for HH and VV polarizations.
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TABLE I D ESCRIPTION OF IPIX R ADAR D ATA Significant Wave Height (m)
Observation Direction
Dataset_26
1.0
Downwind
