Detection of Ground Moving Targets for Two-Channel Spaceborne SAR-ATI
© Zhen Dong et al. 2010
Received: 9 March 2009
Accepted: 1 April 2010
Published: 10 May 2010
Many present spaceborne synthetic aperture radar (SAR) systems are constrained to only two channels for ground moving target indication (GMTI). Along-track interferometry (ATI) technique is currently exploited to detect slowly moving targets and measure their radial velocity and azimuth real position. In this paper, based on the joint probability density function (PDF) of interferogram's phase and amplitude and the two hypotheses "clutter" and "clutter plus signal", several constant false alarm rate (CFAR) detection criteria are analyzed for their capabilities and limitations under low signal-to-clutter ratio (SCR) and low clutter-to-noise ratio (CNR) conditions. The CFAR detectors include one-step CFAR detector with interferometric phase, two-step CFAR detectors, and two-dimensional (2D) CFAR detector. The likelihood ratio test (LRT) based on the Neyman-Pearson (NP) criterion is exploited as an upper bound for the performance of the other CFAR detectors. Performance analyses demonstrate the superiority of the 2D CFAR techniques to detect dim slowly moving targets for spaceborne system.
Many present spaceborne synthetic aperture radar (SAR) systems, such as TerraSAR-X and RADARSAT-2, are constrained to two channels to detect slowly moving targets on the ground. The two channels, which aligned in the flight direction of the same or different platform(s), observe the same terrain at different times under identical geometry. The radial velocities of the ground moving targets lead to the phase difference of the two registered SAR images whereas the two channel signals for stationary scene are identical and can be canceled out by computing the phase difference. Along-track interferometry (ATI) technique exploits the interferogram of the two channel SAR images to perform moving target detection, radial velocity measurement, and azimuth relocation.
Traditional SAR-ATI detection techniques only used the interferometric phase as the constant false alarm rate (CFAR) detection metric to separate moving target from clutter. Gierull [1, 2] derived the theoretical joint (PDF) probability density function (PDF) of interferogram's phase and amplitude for the hypotheses "clutter" and "clutter plus signal" under the assumption of Gaussian backscatter. A two-step CFAR detector  is also proposed by computing the magnitude and phase thresholds separately based on the marginal PDFs of magnitude and phase. Chiu  proposed a nonparametric CFAR detector using histogram approximation to the theoretical joint PDF for the clutter interferogram. Meyer et al.  integrated a prior information into a likelihood ratio detector, which include road network database and the radar cross-section (RCS) of the moving targets. This new hypothesis-test framework is fit for public traffic monitoring applications, where the vehicles are assumed to travel strictly on streets or roads.
In fact, two-channel ATI technique is not a clutter-cancellation technique, which only nulls the clutter interferometric phase but does not improve the signal-to-clutter ratio (SCR) as other clutter suppression techniques. For decreasing SCR values, the interferometric phase of the "clutter plus target" migrate from the true target phase value towards zero on one hand, and increase in variance on the other hand. The nonnegligible clutter contamination to target signal may lead to significant decrease of performance for target detection and velocity estimation . Cross-channel decorrelations of clutter returns, such as channel unbalance or the additive receiver thermal noise, are other limitations to ATI detection performance, but some of them can be remedied using suitable calibration techniques [2, 5]. At low clutter-to-noise ratio (CNR) patches, such as smooth roads or water surfaces, the correlation value may be lower to 0.8. Due to the low coherence, the wide phase distribution of the clutter interferogram induces that the phase detection threshold becomes too large, and prohibits almost any detection . In this paper, under low SCR or low CNR conditions, several CFAR techniques are analyzed for their capabilities and limitations.
In this paper, based on the joint probability density function (PDF) of interferogram's phase and amplitude and the two hypotheses "clutter" and "clutter plus signal", several constant false alarm rate (CFAR) detection criteria are analyzed for their capabilities and limitations under low signal-to-clutter ratio (SCR) and low clutter-to-noise ratio (CNR) conditions. The CFAR detectors include one-step CFAR detector with interferometric phase, two-step CFAR detectors and two-dimensional (2D) CFAR detector. The likelihood ratio test (LRT) based on the Neyman-Pearson (NP) criterion is exploited as an upper bound for the performance of the other CFAR detectors.
The paper is organized as follows. Section 2 reviews the statistics of the multilook interferograms' magnitude and phase for the hypotheses "clutter" and "clutter plus moving target" under Gaussian assumption of the clutter. Section 3 describes the CFAR detection techniques and the likelihood ratio test (LRT) under the NP (Neyman-Pearson) criterion. Performance analysis and comparison are given in Section 4. Section 5 gives the conclusion.
2. Statistics of Multilook Interferograms' Magnitude and Phase for the Hypotheses "Clutter" and "Clutter Plus Moving Target"
where is the interferometric phase of moving target and is the signal-to-clutter ratio (SCR). are defined in (1). The analytical integration of (4) with respect to the magnitude or phase to get the marginal PDF is extremely difficult or even impossible. Alternatively, numerical integration can be used to calculate the theoretical PDF of phase or magnitude.
3. CFAR Detectors and Likelihood Ratio Test Based on the Optimum NP Criterion
3.1. One-Step CFAR Detector with Interferometric Phase
3.2. Two-Step CFAR Detectors
3.3. Two-Dimensional (2D) CFAR Detector
3.4. The Likelihood Ratio Test Based on NP Criterion
Simplification of the LRT function is a very difficult task and the numerical integration can be exploited to compute the , and . Unfortunately, since the threshold curves for fixed depend on the signal parameters SCR and , the LRT under the NP criterion does not possess the CFAR property.
4. Performance Analysis and Comparisons
4.1. Receiver Operating Characteristics
4.2. Probability of Detection versus Radial Velocities of Moving Target
In this paper, based on the theoretical PDF of interferogram's amplitude-phase for the two hypotheses, several ATI CFAR detectors are analyzed under low SCR or low CNR conditions. The LRT based on the NP criterion yields an upper bound performance for the other detectors. The 2D CFAR detector shows a close performance to the optimum LRT detector, which is also ease to be applied to process the real data. In , the author also proposed the theoretical joint PDF for the heterogeneous clutter and the extremely heterogeneous clutter regions. The CFAR detectors analyzed in the paper can also be used under these conditions.
The authors wish to thank Dr. C. H. Gierull and Dr. S. Chiu for their important comments and discussions to our paper. This work is supported by the preresearch foudation of equipment for China under Grant no. 9140A21020609KG01 and no. 51321030101.
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