Bayesian signal subspace estimation with compound Gaussian sources

Abstract

In this paper, we consider the problem of low dimensional signal subspace estimation in a Bayesian context. We focus on compound Gaussian signals embedded in white Gaussian noise, which is a realistic modeling for various array processing applications. Following the Bayesian framework, we derive two algorithms to compute the maximum a posteriori (MAP) estimator and the so-called minimum mean square distance (MMSD) estimator, which minimizes the average natural distance between the true range space of interest and its estimate. Such approaches have shown their interests for signal subspace estimation in the small sample support and/or low signal to noise ratio contexts. As a byproduct, we also introduce a generalized version of the complex Bingham Langevin distribution in order to model the prior on the subspace orthonormal basis. Finally, numerical simulations illustrate the performance of the proposed algorithms.