Abstract
Scatter matrix estimation and hypothesis testing are fundamental inference problems in a wide variety of signal processing applications. In this paper, we investigate and compare the matched, mismatched, and robust approaches to solve these problems in the context of the complex elliptically symmetric (CES) distributions. The matched approach is when the estimation and detection algorithms are tailored on the correct data distribution, whereas the mismatched approach refers to the case when the scatter matrix estimator and the decision rule are derived under a model assumption that is not correct. The robust approach aims at providing good estimation and detection performance, even if suboptimal, over a large set of possible data models, irrespective of the actual data distribution. Specifically, due to its central importance in both the statistical and engineering applications, we assume for the input data a complex t-distribution. We analyze scatter matrix estimators derived under the three different approaches and compare their mean square error (MSE) with the constrained Cramer-Rao bound (CCRB) and the constrained misspecified Cramer-Rao bound (CMCRB). In addition, the detection performance and false alarm rate (FAR) of the various detection algorithms are compared with that of the clairvoyant optimum detector.
Highlights
This paper deals with two common inference problems in radar signal processing, namely the estimation of the disturbance covariance matrix and the adaptive detection of a radar target
We address the mismatched case where, following the approach discussed in our recent work [14], the performance of the mismatched maximum likelihood (ML) (MML) scatter matrix estimator derived under Gaussian assumption is evaluated and its mean square error (MSE) compared with the constrained misspecified Cramér-Rao bound (CMRB) [15]
6 Conclusions This paper focused on two inference problems, the scatter matrix estimation and the adaptive detection of radar targets in complex t-distributed data
Summary
This paper deals with two common inference problems in radar signal processing, namely the estimation of the disturbance covariance matrix and the adaptive detection of a radar target. From a practical point of view, this means that we can use the simpler mismatched estimator based on the Gaussian model assumption to estimate the scatter matrix and the average power of a set of complex t-distributed data since it converges to the true required quantities. It is natural to ask if it is possible to establish a lover bound on the estimation performance in the mismatched estimation framework In his seminal working paper [37], Vuong proposed the misspecified Cramér-Rao bound (MCRB) and showed that it represents a lower bound on the error covariance matrix of any unbiased (in a proper sense) estimator of a deterministic parameter vector under misspecification of the true data model.
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