A Geometric Approach to Covariance Matrix Estimation and its Applications to Radar Problems

Abstract

Abstract-A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample covariance matrix projection into a specific set of structured covariance matrices. Regardless of the considered norm, an efficient solution technique to handle the resulting constrained optimization problem is developed. Specifically, it is shown that the new family of distribution-free estimators shares a shrinkagetype form; besides, the eigenvalues estimate just requires the solution of a one-dimensional convex problem whose objective function depends on the considered unitary norm. For the two most common norm instances, i.e., Frobenius and spectral, very efficient algorithms are developed to solve the aforementioned one-dimensional optimization leading to almost closed form covariance estimates. At the analysis stage, the performance of the new estimators is assessed in terms of achievable Signal to Interference plus Noise Ratio (SINR) both for a spatial and a Doppler processing assuming different data statistical characterizations. The results show that interesting SINR improvements with respect to some counterparts available in the open literature can be achieved especially in training starved regimes.

Generalized Ambiguity Function for MIMO Radar Systems

“…Specifically, the authors in [31] proposed a maximum likelihood estimator for the covariance matrix of radar signals by applying a special structure assumption and a condition number upper-bound constraint. Additionally, in [32] a geometric approach to the covariance matrix estimation problem was introduced based on the projection of the sample covariance matrix into a specific set of structured covariance matrices. Results in [31] and [32] demonstrated respectively that closed and almost closed form estimates can be provided, facilitating also high computational efficiency.…”

“…Additionally, in [32] a geometric approach to the covariance matrix estimation problem was introduced based on the projection of the sample covariance matrix into a specific set of structured covariance matrices. Results in [31] and [32] demonstrated respectively that closed and almost closed form estimates can be provided, facilitating also high computational efficiency.…”

“…The resulting conditions are similar to those presented in [1], scaled however by the time scaling factor and more importantly having dependency on the target's position. Using (32) and (33), and assuming a sub-reference coordinate system with centre of axes the target's centre of gravity and α j,i ≈ 1 for all transmitter-receiver pairs, these conditions can also be expressed as:…”

A Geometric Barycenter-Based Clutter Suppression Method for Ship Detection in HF Mixed-Mode Surface Wave Radar

“…The similarity detector (SD) algorithm [16][17][18][19] selects the samples with waveforms that are similar to the CUT. Recently, the information geometry-based SD algorithm has drawn more attentions on covariance estimation and target detection processing [20][21][22][23][24]. A class of covariance matrix estimators, which are associated with suitable distances in the considered space and defined as the geometric barycenter, are proposed to exclude the outliers and clutter for target detection in [25,26].…”

Deterministic-aided single dataset STAP method based on sparse recovery in heterogeneous clutter environments

“…And some STAP detection methods, which allow one to identify the degree of accuracy of the prior knowledge and combine the prior information with the secondary data in an appropriate way, were proposed in [21,22]. To further deal with the training-limited problem, a detection scheme using a linear combination of some available a priori models to model the inverse covariance matrix was reported in [23], a newly proposed detection method using two sets of training data are not limited by the conventional constraint on the cardinality of the classic training dataset [24], and a geometric approach to covariance matrix estimation can also achieve considerable SINR improvement in training-starved regimes [25]. Some other related applications to MIMO radar can be found in [26,27].…”