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

Area of Science:

• Signal Processing
• Information Geometry
• Statistical Inference

Background:

• Covariance matrix estimation is crucial for radar and sensor systems, especially in complex environments.
• Traditional methods like Sample Covariance Matrix (SCM) struggle with heterogeneous clutter.
• Information geometry offers a powerful framework for analyzing matrix-structured data.

Purpose of the Study:

• To develop a robust covariance matrix estimation method for heterogeneous clutter using information geometry.
• To reformulate covariance estimation as a geometric median computation on the manifold of Hermitian positive-definite matrices.
• To improve the performance of adaptive detection algorithms in challenging environments.

Main Methods:

• Introduction of a new class of total Bregman divergence on the Riemannian manifold of Hermitian positive-definite (HPD) matrices.
• Derivation of total Bregman divergence medians as estimators, replacing the traditional Sample Covariance Matrix (SCM).
• Utilizing the geometric structure of matrix space rather than solely relying on statistical sample characteristics.

Main Results:

• The proposed geometric median estimators demonstrate improved performance in heterogeneous clutter compared to SCM.
• Numerical results validate the enhanced detection performance of an adaptive normalized matched filter using the new estimator.
• The method effectively leverages the geometric properties of covariance matrices.

Conclusions:

• The information geometry-based covariance estimation method offers a significant advancement for signal processing in heterogeneous clutter.
• The proposed approach provides a more robust and accurate alternative to traditional SCM methods.
• This work paves the way for enhanced detection and performance in complex sensing scenarios.