Robust Covariance Estimation under Imperfect Constraints using an Expected Likelihood Approach (original) (raw)
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Constrained ML estimation of structured covariance matrices with applications in radar STAP
2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), 2013
The disturbance covariance matrix in radar space time adaptive processing (STAP) must be estimated from training sample observations. Traditional maximum likelihood (ML) estimators are effective when training is generous but lead to degraded false alarm rates and detection performance in the realistic regime of limited training. We exploit physically motivated constraints such as 1.) rank of the clutter subspace which can be inferred using existing physics based models such as the Brennan rule, and 2.) the Toeplitz constraint that applies to covariance matrices obtained from stationary random processes. We first provide a closed form solution of the rank constrained maximum likelihood (RCML) estimator and then subsequently develop an efficient approximation under joint Toeplitz and rank constraints (EASTR). Experimental results confirm that the proposed EASTR estimators outperform stateof-the-art alternatives in the sense of widely used measures such as the signal to interference and noise ratio (SINR) and probability of detection-particularly when training support is limited.
2012 IEEE Radar Conference, 2012
We consider here the continually important problem of radar target detection in the presence of clutter, noise and jamming. Under complex Gaussian noise statistics, the optimal detection statistic relies on an inversion of the disturbance (clutter + noise and jamming) covariance matrix. The disturbance (and hence clutter) covariance must be estimated in practice from sample, i.e. training observations. Traditional maximum likelihood (ML) estimators are effective when training is abundant but lead to poor estimates and hence high detection error in the realistic regime of limited or small training. The problem is exacerbated by recent advances which have led to high dimensionality N of the observations arising from increased antenna elements (J) as well as higher temporal resolution (P time epochs and finally N = J.P). This work introduces physically inspired constraints into ML estimation. In particular, we exploit both the structure of the disturbance covariance and importantly the knowledge of the clutter rank to yield a new rank constrained maximum likelihood (RCML) estimator of clutter/disturbance covariance. Experimental validation on the KASSPER data set (where ground truth covariance is made available) shows that the proposed estimator vastly outperforms state-of-the art alternatives in the sense of: 1.) higher normalized signal to interference and noise ratio (SINR), and 2.) lower variance of target amplitude estimators that utilize disturbance covariance. Crucially the proposed RCML estimator can excel even for low training including the notoriously difficult regime of K ≤ N training samples.
Expected likelihood approach for determining constraints in covariance estimation
IEEE Transactions on Aerospace and Electronic Systems, 2016
Recent covariance estimation methods for radar space-time adaptive processing exploit practical constraints such as the rank of clutter subspace and the condition number of disturbance covariance to estimate accurate covariance even when training is not generous. While rank and condition number are very effective constraints, often practical nonidealities make it difficult to know them precisely using physical models. Therefore, we propose a method to determine constraints in covariance estimation for radar space-time adaptive processing via an expected likelihood approach. We analyze three cases of constraints: 1) a rank constraint, 2) both rank and noise power constraints, and 3) a condition number constraint. In each case, we formulate precise constraint determination as an optimization problem. For each of the three cases, we derive new analytical results which allow for computationally efficient, practical ways of determining these constraints with formal proofs. Through experimental results from a simulation model and the KASSPER data set, we show that the estimator with optimal constraints obtained by the expected likelihood approach outperforms state-of-the-art alternatives.
Numerical performances of low rank stap based on different heterogeneous clutter subspace estimators
2014 International Radar Conference, 2014
Space time Adaptive Processing (STAP) for airborne RADAR fits the context of a disturbance composed of a Low Rank (LR) clutter, here modeled by a Compound Gaussian (CG) process, plus a white Gaussian noise (WGN). In such context, the corresponding LR adaptive filters used to detect a target require less training vectors than classical methods to reach equivalent performance. Unlike the classical filter which is based on the Covariance Matrix (CM) of the noise, the LR filter is based on the clutter subspace projector, which is usually derived from a Singular Value Decomposition (SVD) of a noise CM estimate. Regarding to the considered model of LR-CG plus WGN, recent results are providing both direct estimators of the clutter subspace [1][2] and an exact MLE of the noise CM . To promote the use of these new estimation methods, this paper proposes to apply them to realistic STAP simulations.
Radar Clutter Covariance Estimation: A Nonlinear Spectral Shrinkage Approach
ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
In this paper, we exploit the spiked covariance structure of the clutter plus noise covariance matrix for adaptive radar signal processing. Using state-of-the-art techniques from mathematical finance and high dimensional statistics we propose a nonlinear shrinkage-based rotation invariant spiked covariance matrix estimator. We compare the proposed estimator with Rank Constrained Maximum Likelihood (RCML)-Expected Likelihood (EL) covariance estimator using the Challenge dataset generated from RFView. We demonstrate that the computation-time for the proposed estimator is less than the RCML-EL estimator with identical Signal to Clutter plus Noise (SCNR) performance for the Challenge dataset. We derive the lower bound and upper bound for the normalized SCNR and empirically show that RCML-EL and the proposed estimator perform within these derived bounds for the Challenge dataset. We state the convergence for the spiked eigenvalues of the estimator.
Clutter Subspace Estimation in Low Rank Heterogeneous Noise Context
IEEE Transactions on Signal Processing, 2015
This paper addresses the problem of the Clutter Subspace Projector (CSP) estimation in the context of a disturbance composed of a Low Rank (LR) heterogeneous clutter, modeled here by a Spherically Invariant Random Vector (SIRV), plus a white Gaussian noise (WGN). In such context, the corresponding LR adaptive filters and detectors require less training vectors than classical methods to reach equivalent performance. Unlike classical adaptive processes, which are based on an estimate of the noise Covariance Matrix (CM), the LR processes are based on a CSP estimate. This CSP estimate is usually derived from a Singular Value Decomposition (SVD) of the CM estimate. However, no Maximum Likelihood Estimator (MLE) of the CM has been derived for the considered disturbance model. In this paper, we introduce the fixed point equation that MLE of the CSP satisfies for a disturbance composed of a LR-SIRV clutter plus a zero mean WGN. A recursive algorithm is proposed to compute this solution. Numerical simulations validate the introduced estimator and illustrate its interest compared to the current state of art.
2010 IEEE International Conference on Acoustics, Speech and Signal Processing, 2010
By incorporating a priori knowledge into radar signal processing architectures, knowledge-aided space-time adaptive processing (KA-STAP) algorithms can offer the potential to substantially enhance detection performance and to combat heterogeneous clutter effects. In this paper, we develop a KA-STAP algorithm to estimate directly the interference covariance matrix inverse rather than the covariance matrix itself, by using a linear combination of inverse covariance matrices (LCICM), which leads to an equivalent expression of the combination of two filters. The computational load is greatly reduced due to the avoidance of the matrix inversion operation. The performance of the LCICM scheme can be further improved by applying a modification. Moreover, adaptive algorithms for the mixing parameters are developed using affine combinations (AC). Numerical examples show the potential of our proposed algorithms for substantial performance improvement.
IEEE Transactions on Signal Processing, 2000
Recently, a new adaptive scheme [Conte et al. (1995), Gini (1997)] has been introduced for covariance structure matrix estimation in the context of adaptive radar detection under non-Gaussian noise. This latter has been modeled by compound-Gaussian noise, which is the product c of the square root of a positive unknown variable (deterministic or random) and an independent Gaussian vector x, c = x. Because of the implicit algebraic structure of the equation to solve, we called the corresponding solution, the fixed point (FP) estimate. When
2012
In a previous work, we have developed a low-rank (LR) spatiotemporal adaptive processing (STAP) filter when the disturbance is modeled as the sum of a low-rank spherically invariant random vector (SIRV) clutter and a zero-mean white Gaussian noise. This LR-STAP filter is built from the normalized sample covariance matrix (NSCM) and exhibits good robustness properties to secondary data contamination by target components. In this correspondence, we derive the bias of the NSCM with this noise model. We show that the eigenvectors estimated from the NSCM are unbiased. The new expressions of the expectation of NSCM eigenvalues are also given. From these results, we also show that the estimate of the clutter subspace projector based on the NSCM used in our LR-STAP is a consistent estimate of the true one. Results on numerical data validates the theoretical approach.
Robust adaptive signal processing methods for heterogeneous radar clutter scenarios
Signal Processing, 2004
This paper addresses the problem of radar target detection in severely heterogeneous clutter environments. Speciÿcally, we present the performance of the normalized matched ÿlter test in a background of disturbance consisting of clutter having a covariance matrix with known structure and unknown scaling plus background white Gaussian noise. It is shown that when the clutter covariance matrix is low rank, the (LRNMF) test retains invariance with respect to the unknown scaling as well as the background noise level and has an approximately constant false alarm rate (CFAR). Performance of the test depends only upon the number of elements, the number of pulses processed in a coherent processing interval, and the rank of the clutter covariance matrix. Analytical expressions for calculating the false alarm and detection probabilities are presented. Performance of the method is shown to degrade with increasing clutter rank especially for low false alarm rates. An adaptive version of the test (LRNAMF) is developed and its performance is studied with simulated data from the KASSPER program. Results pertaining to sample support for subspace estimation, CFAR, and detection performance are presented. Target contamination of training data has a deleterious impact on the performance of the test. Therefore, a technique known as self-censoring reiterative fast maximum likelihood/adaptive power residue (SCRFML/APR) is developed to treat this problem and its performance is discussed. The SCRFML/APR method is used to estimate the unknown covariance matrix in the presence of outliers. This covariance matrix estimate can then be used in the LRNAMF or any other eigen-based adaptive processing technique.