A generalized sample weighting method in heterogeneous environment for space-time adaptive processing
Introduction
As a well-established technique in application of ground moving target indication (GMTI), space-time adaptive processing (STAP) is a powerful filtering method for clutter (or dense interferences) suppression with an airborne array surveillance radar system [1]. The fundamental and core problem for STAP is always the accurate estimate of clutter-plus-noise covariance matrix (CCM). For side-looking airborne radar, the classical STAP method, i.e., sample covariance matrix (SCM) method [2], [3], can obtain a significant performance in clutter suppression by exploiting the independent and identically distributed (IID) training samples adjacent to the range cell under test (RCUT). However, the limitations of its application in practice lie in two major issues. First, it is difficult to obtain enough IID training samples support (if not impossible) for an accurate CCM estimation, especially in the case of complicated and heterogeneous clutter scenarios. Second, a huge computational burden makes the fully adaptive algorithms impractical. During recent several decades, to address the aforementioned issues, many corresponding solution schemes from different perspectives have attracted much attention.
For a joint-domain optimal processor, the large spatiotemporal degrees of freedom (DOFs) may make it difficult to be applied in real-time applications. Thus, to reduce the adaptive processing dimensions of a STAP algorithm as well as the target-free and homogeneous training samples support, the dimension-reduced techniques are developed including the fixed dimension-reduced architectures (i.e., data-independent transformation matrices) and the adaptive dimension-reduced architectures or the rank-reduced algorithms. The auxiliary channel processor [4], a cascaded time-space method (F$A) [5], extended FA (EFA) [6], [7] (or m-Doppler transformation-space adaptive processing (mDT-SAP) [7]), joint domain localized (JDL) [8], [9], and ΣΔ-STAP [10] are the typical dimension-reduced approaches. Additionally, the data-dependent transformations are adopted in rank-reduced algorithms by virtue of the low rank characteristic of clutter, such as the eigencanceler [11], the principle component inverse method [12], the cross-spectral metric method [13], and Krylov subspace methods that include the multi-stage Wiener filter [14] and the auxiliary vector filtering algorithm [15]. Furthermore, the parametric methods mainly contain the space-time autoregressive filter (STAR) [16] and the parametric adaptive matched filter (PAMF) [17], where the basic idea is that an autoregressive (AR) model is exploited to describe the CCM characteristics to achieve the reduction of dimensions and ranks. On one hand, some special CCM properties, such as Toeplitz structure, low rank structure, condition number constraint, persymmetry property, and Kronecker product structure [18], [19], [20], [21], [22], [23], can be utilized to improve the estimate accuracy. On the other hand, some knowledge-aided (KA) algorithms [24], [25], [26] directly estimate the CCM via some priori information about the radar system. Also, note that Saleh et al. introduce a new multistage STAP approach that significantly reduces the required sample support while still processing all available DOFs [27] in recent work.
The clutter non-homogeneity is another crucial factor to limit the practical application for STAP. In fact, the non-homogeneity of clutter mainly includes two aspects [28]: structure variation of angle-Doppler spectrum (i.e., non-stationary clutter) induced by radar array geometry and clutter heterogeneity due to both dense-target environment and complex terrains, including land/sea interface, urban–rural fringes, and mountains. For the problem of non-stationary clutter, in the STAP literatures, the core ideas of methods based on clutter compensation are to regain performance by compensating the training data to mitigate their range-dependence, such as adaptive angle Doppler compensation (A2DC) method [29], derivative based updating (DBU) method [30], space-time interpolation transformation (STINT) method [31], and registration based compensation (RBC) method [32], etc. Another type of typical methods also referred as the deterministic STAP approaches [33], [34], [35], [36], are considered instead of the statistical STAP algorithms. The well-known direct data domain (DDD) methods [34] and the maximum likelihood estimation detector (MLED) algorithms [35] only operate with RCUT, and thus, they can remove all the undesired impacts due to the non-stationary clutter and circumvent the problem of the required homogeneous training samples support.
To address the heterogeneous clutter and target rich environments, in [37] the authors develop the non-homogeneity detector (NHD) based on the generalized inner product (GIP) to enhance clutter suppression performance by detecting and eliminating the nonhomogeneous training samples and obtaining a good CCM estimate. A censored fast maximum likelihood (CFML) method which leads to a performance improvement [38] is presented. Besides, sample weighting methods are proposed as discussed in [39], [40], where the data-dependent weighting coefficient for each sample measures the contribution of each sample to the CCM estimation. In the literatures [41] and [42], knowledge-aided STAP (KA-STAP) approaches are proposed by exploiting the digital terrain maps to select representative training data. As a result, KA-STAP will suppress the terrain clutter more effectively. However, the performance of clutter cancellation depends mainly on the accurate prior knowledge on the clutter statistics. In other words, using inaccurate prior knowledge due to environmental changes or outdated intelligence information may degrade rather than improve STAP performance.
In this paper, we mainly pay attention to the problem of the CCM estimation in heterogeneous clutter and target rich environments for side-looking airborne radar. As mentioned above, the SCM method and its developments, including sample weighting and selecting methods, where the weighting coefficients are restricted to be one or zero [43], are here consolidated as the weighting sample covariance matrix (WSCM)-type method and can improve the STAP performance by providing a little or zero weighting coefficient to adjust the contribution of each nonhomogeneous sample to the CCM estimation. However, the WSCM-type method is confronted with the problem of valid training samples lack (or the information loss of sample clutter components available), especially for samples contaminated by target signal. Inspired by the idea that the distinction between samples can be measured with localized angle-Doppler plane, we propose a new scheme for STAP based on generalized sample weighting method in angle-Doppler domain (GSWADD) to mitigate information loss of sample clutter components for accurate CCM estimation as well as the need for training samples. Simulation results and experiments on measured real data show that the proposed method may obtain a significant performance improvement.
The remainder of this paper is organized as follows. In Section 2, a brief description of the space-time signal model is introduced as well as some fundamentals of STAP and the limitations of the WSCM-type method are explained in theory from the perspective of angle-Doppler localization. Section 3 is devoted to the proposed algorithm for STAP based on GSWADD. In Section 4, numerical results are given to verify the effectiveness of our approach with both simulated data and real measured synthetic aperture radar data with four-channel airborne radar. Finally, the conclusions are drawn in Section 5.
Section snippets
Signal model
The geometry of side-looking array radar is shown in Fig. 1. Without loss of generality, we consider a uniform linear array (ULA) and the radar antenna consists of N elements with an identical space of d. The platform velocity is . The variables θ and φ denote the azimuth angle and elevation angle of a clutter scatter relative to the antenna array, respectively. The variable represents the velocity cone angles of a clutter scatter relative to the along-track direction. The wave length of
Principle
Motivated by the idea of angle-Doppler localized processing, we can measure the non-homogeneity of training sample data and achieve the CCM estimation or reconstruction in the angle-Doppler 2-D domain to overcome the drawbacks of the WSCM-type method due to the single weighting coefficient.
Fig. 2 illustrates the distribution characteristics of clutter and a moving target in angle-Doppler 2-D spectrum plane for side-looking array radar configuration [46]. It can be seen that the angle-Doppler
Performance evaluation and numerical results
In this section, the numerical results are processed based on simulated data to verify the robustness and practicability of the proposed method. Besides, the four-channel real measured data of airborne radar for synthetic aperture radar (SAR) experiments will be described in the subsequent subsection in detail.
In what follows, aiming at exploring the advantages of the proposed method which is noted as GSWADD, three classical WSCM-type approaches are performed for comparisons, including standard
Conclusions
In this paper, we have proposed a generalized sample weighting approach for STAP called as GSWADD, which is proved to be a generalization of sample weighting algorithms from the CCM reconstruction's perspective in angle-Doppler domain, to mitigate the performance degradation of conventional WSCM-type method. The core problem of proposed method is to get the clutter angle-Doppler spectrum by using GSWADD. On the basis, the CCM can be estimated accordingly. Experiments on both simulated data and
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China under Grant 61671352 and 61231017, the Chinese Defense Advance Research Program of Science and Technology under Grant 9140xxx005, the Innovational Foundation of Shanghai Academy of Space Technology under Grant SAST2016027 and SAST2016033, and the Foundation of Key Laboratory of Cognitive Radio and Information Processing, Ministry of Education (Guilin University of Electronic Technology) under Grant CRKL160206.
Huajian Xu was born in Fujian, China, in 1990. He received the B.S. degree in electrical engineering from Xidian University, Xi'an, China, in 2013, where he is currently working toward the Ph.D. degree in the National Laboratory of Radar Signal Processing, Xidian University. His research interests include synthetic aperture radar (SAR), ground moving target indication (GMTI), and space-time adaptive processing (STAP).
References (54)
- et al.
Screening among multivariate normal data
J. Multivar. Anal.
(1999) - et al.
Covariance matrix estimation for CFAR detection in correlated heavy tailed clutter
Signal Process.
(2002) - et al.
Theory of adaptive radar
IEEE Trans. Aerosp. Electron. Syst.
(Mar. 1973) Space-Time Adaptive Processing for Airborne Radar
(1994)Principles of Space-Time Adaptive Processing
(2002)Space-Time Adaptive Processing: Principles and Applications
(1998)- et al.
Comparison of space-time adaptive processing approaches using experimental airborne radar data
Extended factored space-time processing for airborne radar system
- et al.
Review of reduced rank space-time adaptive processing for airborne radar
- et al.
On adaptive spatial-temporal processing for airborne surveillance radar systems
IEEE Trans. Aerosp. Electron. Syst.
(Jul. 1994)
Joint domain localized adaptive processing in homogeneous and non-homogeneous environments, part I: homogeneous environments
IEE Proc. Radar Sonar Navig.
STAP for clutter suppression with sum and difference beams
IEEE Trans. Aerosp. Electron. Syst.
The eigencanceler: adaptive radar by eigenanalysis methods
IEEE Trans. Aerosp. Electron. Syst.
Adaptive detection using low rank approximation to a data matrix
IEEE Trans. Aerosp. Electron. Syst.
Reduced-rank STAP performance analysis
IEEE Trans. Aerosp. Electron. Syst.
Adaptive widely linear reduced-rank interference suppression based on the multi-stage Wiener filter
IEEE Trans. Signal Process.
An iterative algorithm for the computation of the MVDR filter
IEEE Trans. Signal Process.
Maximum-likelihood estimation for covariance matrix in compound-Gaussian clutter via autoregressive modeling
Parametric adaptive matched filter for airborne radar applications
IEEE Trans. Aerosp. Electron. Syst.
Structured covariance estimation for space-time adaptive processing
Expected likelihood approach for determining constraints in covariance estimation
IEEE Trans. Aerosp. Electron. Syst.
Maximum Likelihood Covariance Estimation with a Condition Number Constraint
Improving EFA-STAP performance using persymmetric covariance matrix estimation
IEEE Trans. Aerosp. Electron. Syst.
On Kronecker and linearly structured covariance matrix estimation
IEEE Trans. Signal Process.
Robust SAR STAP via Kronecker decomposition
IEEE Trans. Aerosp. Electron. Syst.
Knowledge-based systems for adaptive radar: detection, tracking, and classification
IEEE Signal Process. Mag.
Robust fast maximum likelihood with assumed clutter covariance algorithm for adaptive clutter suppression
IET Radar Sonar Navig.
Cited by (0)
Huajian Xu was born in Fujian, China, in 1990. He received the B.S. degree in electrical engineering from Xidian University, Xi'an, China, in 2013, where he is currently working toward the Ph.D. degree in the National Laboratory of Radar Signal Processing, Xidian University. His research interests include synthetic aperture radar (SAR), ground moving target indication (GMTI), and space-time adaptive processing (STAP).
Zhiwei Yang was born in Sichuan, China, in 1980. He received M.S. and Ph.D. degrees in electrical engineering from Xidian University, Xi'an, China, in 2005 and 2008 respectively. He is currently an associate professor with the National Laboratory of Radar Signal Processing, Xidian University. His current work includes adaptive array signal processing, space-time-polarmetric adaptive processing and designed the ground moving target indication algorithms for the space-borne SAR/GMTI systems in China.
Shun He was born in Hunan, China, in 1980. She received the B.S. degree from Guilin University of Electronic Technology, Guangxi, China, in 2005, and her Ph.D. degree in the National Laboratory of Radar Signal Processing, Xidian University, Xi'an, China, in 2016. Her current research interests include adaptive array signal processing, wideband signal processing.
Min Tian was born in Henan, China, in 1993. She received the B.S. degree in communication engineering from Nanchang Hangkong University, Nanchang, China, in 2014. She is currently working toward the Ph.D. degree in the National Laboratory of Radar Signal Processing, Xidian University, Xi'an. Her research interests include space-time adaptive processing, ground moving target identification, and maritime target detection.
Guisheng Liao was born in Guiling, China. He received the B.S. degree from Guangxi University, Guangxi, China, and the M.S. and Ph.D. degrees from Xidian University, Xi'an, China, in 1985, 1990, and 1992, respectively. He is currently a Professor with Xidian University, where he is also Dean of School of Electronic Engineering. He has been a Senior Visiting Scholar in the Chinese University of Hong Kong, Hong Kong. His research interests include synthetic aperture radar (SAR), space-time adaptive processing, SAR ground moving target indication, and distributed small satellite SAR system design. Prof. Liao is a member of the National Outstanding Person and the Cheung Kong Scholars in China.
Yongyan Sun was born in Shandong, China, in 1978. He received the M.S. degree in computer application from Shanghai JiaoTong University, Shanghai, China, in 2008. He is currently a research fellow at Shanghai Institute of Satellite Engineering. His current work includes satellite general design and optimization technology, spacecraft configuration and layout design, spacecraft orbit and constellation design in China.
- 1
Senior Member, IEEE.