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Spectral Norm Based Mean Matrix Estimation and Its Application to Radar Target CFAR Detection

The estimation of mean matrix for a set of Hermitian positive definite (HPD) matrices can be considered based on a geometric framework. This kind of estimator is closely related to geometric measures, which can be established to measure the dissimilarity between two matrices on the matrix manifold. In this paper, the matrix spectral norm is exploited to derive a new geometric measure on the matrix manifold consisting of all HPD matrices. Correspondingly, the mean matrix associated with the new geometric measure on the matrix manifold is considered via two effective solution techniques. More specifically, the first method transforms the mean matrix estimation into a semidefinite programming problem solved by the interior point method; the second method exploits joint approximate diagonalization to diagonalize the given covariance matrices and then recasts the mean matrix estimation into an optimization problem with linear inequality constraints. Furthermore, two matrix detectors employing the proposed mean matrix estimators are designed for target detection using pulse Doppler radar with a small bunch of pulses. At the analysis stage, we show that the proposed matrix detector can guarantee the bounded constant false alarm rate property in terms of the clutter covariance matrix. Finally, numerical experiments based on simulated clutter data and real sea clutter data are performed to verify the effectiveness and robustness of the proposed matrix detectors.