Performance Analysis of Covariance Matrix Estimates in Impulsive Noise

Abstract

This paper deals with covariance matrix estimates in impulsive noise environments. Physical models based on compound noise modeling (SIRV, Compound Gaussian Processes) allow to correctly describe reality (e.g., range power variations or clutter transitions areas in radar problems). However, these models depend on several unknown parameters (covariance matrix, statistical distribution of the texture, disturbance parameters) which have to be estimated. Based on these noise models, this paper presents a complete analysis of the main covariance matrix estimates used in the literature: four estimates are studied, the well-known Sample Covariance Matrix M SCM and a normalized version M N , the Fixed Point (FP) estimate M F P , and a theoretical benchmark M T F P . Among these estimates, the only one of practical interest in impulsive noise is the FP. The three others, which could be used in a Gaussian context, are, in this paper, only of academic interest, i.e., for comparison with the FP. A statistical study of these estimates is performed through bias analysis, consistency, and asymptotic distribution. This study allows to compare the performance of the estimates and to establish simple relationships between them.Finally, theoretical results are emphasized by several simulations corresponding to real situations.

Detection of Range Migrating Targets in Compound-Gaussian Clutter

“…Moreover, real fast moving targets, observed by a wideband radar, are both extended and range migrating, as shown in Figure 1, d. However, the detection of extended target is not considered in this study, so we focus on the model shown in Figure 1, b. Finally, in practical applications, the aforementioned detectors exploit CM estimated from the reference cells, resulting in the appropriate change of the threshold [28], [29]. Coming back to the problem of migrating target detection in a highly inhomogeneous clutter, the GLRT for the CompoundGaussian model can be written in the following form:…”

“…In particular it can influence the number of iterations required for convergence. Recall that in both cases the iterative procedure is applied to obtain an estimation ofα present in the scene under H 1 , see (16) and (28). In this light, both algorithms should be initialized with some non-iterative estimation ofα.…”

“…[11], [13], [18], [32], [37]. The modern trend is to model high resolution radar clutter as a compound-Gaussian process (which belongs to the class of spherically invariant random vectors (SIRV) [11], [27], [28]) i.e. a Gaussian process with power varying from one range cell to another, but sharing the same correlation structure in slowtime [11], [36].…”

“…Moreover, for long CPI the distribution-free test has been shown to approach the performance of the optimal one, as shown in [8], [34]. The recent studies [5], [16], [28], [29] are focused on implementation of adaptive CFAR detector 2 in compound-Gaussian clutter, which exploits the estimated covariance matrix (CM) of clutter. The discussion there is focused on strategies for CM estimation from the reference cells in spiky clutter and on the threshold setting for the adaptive detector.…”

A test statistic for high resolution polarimetric SAR data classification

“…Existence and uniqueness of the above equation solution T F P , the Fixed Point (FP) estimate, have been investigated in [3], and its statistical properties (consistency, unbiasedness and asymptotic Gaussianity) have been studied in [4]. In practice, it is obtained by the associated recursive algorithm which converges whatever the initialization (see for details [3]).…”