点击次数：

论文类型： 期刊论文

发表时间： 2019-11-15

发表刊物： IEEE TRANSACTIONS ON SIGNAL PROCESSING

收录刊物： SCIE

卷号： 67

期号： 22

页面范围： 5746-5760

ISSN号： 1053-587X

关键字： Covariance matrices; Manifolds; Linear matrix inequalities; Sea measurements; Estimation; Clutter; Detectors; Adaptive radar signal processing; matrix manifold; geometric measure; mean matrix; matrix spectral norm

摘要： 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.