Information Geometry for Covariance Estimation in Heterogeneous Clutter with Total Bregman Divergence

This paper presents a covariance matrix estimation method based on information geometry in a heterogeneous clutter. In particular, the problem of covariance estimation is reformulated as the computation of geometric median for covariance matrices estimated by the secondary data set. A new class of total Bregman divergence is presented on the Riemanian manifold of Hermitian positive-definite (HPD) matrix, which is the foundation of information geometry. On the basis of this divergence, total Bregman divergence medians are derived instead of the sample covariance matrix (SCM) of the secondary data. Unlike the SCM, resorting to the knowledge of statistical characteristics of the sample data, the geometric structure of matrix space is considered in our proposed estimators, and then the performance can be improved in a heterogeneous clutter. At the analysis stage, numerical results are given to validate the detection performance of an adaptive normalized matched filter with our estimator compared with existing alternatives.

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