A Matrix Information Geometry Detector Based on Riemannian Gaussian Distribution for Radar Detection in Clutter Backgrounds

Detectors based on matrix information geometry have been developed recently and demonstrated advantages against conventional methods for detection of targets within nonhomogeneous clutter backgrounds. However, existing methods employing geometric measures to distinguish target and clutter lack sufficient consideration of statistical distribution of covariance matrices on manifold. In this article, a detector is proposed utilizing the statistical characteristic of covariance matrices on the Riemannian manifold, which is modeled by the Riemannian Gaussian distribution. A second-order detection problem is formulated utilizing sample covariance matrices. The statistical characteristic of sample covariance matrices on the symmetric positive-definite matrix manifold is analyzed to address the detection problem. It is verified that the distribution of the sample covariance matrix of multivariate Gaussian observations can be well approximated by Riemannian Gaussian distribution when the number of samples is large. Then, the likelihood ratio test (LRT) detector based on Riemannian Gaussian distribution is derived according to the Neyman–Pearson principle. In practical applications, the unknown parameter of clutter distribution in the LRT detector is substituted by the geometric mean of samples in reference cells, which is the maximum likelihood estimate of the mean of Riemannian–Gaussian distribution. The above results and the theoretical performance of the proposed detector have been validated through numerical simulations. Experiments based on real weather clutter, ground clutter, and sea clutter demonstrate that the proposed detector outperforms conventional detectors and existing detectors using geometric metrics.