Abstract
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.
Highlights
The estimation of the disturbance covariance matrix is an important subject in the field of advanced radar signal processing
We extend the definition of total Bregman divergence (tBD) to the Riemannian manifold of Hermitian positive-definite (HPD) matrices
This section is devoted to analyzing the robustness of total Bregman divergence median and arithmetic mean via the influence function
Summary
The estimation of the disturbance covariance matrix is an important subject in the field of advanced radar signal processing. Many covariance estimation algorithms derived from the geometry of matrix space, not resorting to the statistical characterization of sample data, are reported in the literature. The Riemannian mean and median of covariance matrices is proposed to design the radar target detector [12,13,14,15,16]. The geometric approach is used in many other applications; for instance, the Bhattacharyya mean and median are exploited for diffusion tensor magnetic resonance (DT-MRI) image segmentation [30,31] In these contexts, the geometric approaches have achieved good performances. As the geometric medians are not relying on the statistical characteristics of the sample data in heterogeneous clutter, the performance of covariance estimation can be improved.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
