An Information Geometric Viewpoint on the Detection of Range Distributed Targets

The paper adopts the information geometry, to put forward a new viewpoint on the detection of range distributed targets embedded in Gaussian noise with unknown covariance. The original hypothesis test problem is formulated as the discrimination between distributions of the measurements and the noise. The Siegel distance, which is exactly the well-known geodesic distance between images of the original distributions via embedding into a higher-dimensional manifold, is given as an intrinsic measure on the difference between multivariate normal distributions. Without the assumption of uncorrelated measurements, we propose a set of geometric distance detectors, which is designed based on the Siegel distance and different from the generalized likelihood ratio algorithm or other common criterions in statistics. As special cases, the classical optimal matched filter, Rao test, and Wald test, which have been proven to have the CFAR property, belong to the set. Moreover, it is also accessible to an intuitively geometric analysis about how strongly the data contradict the null hypothesis.