Maximum likelihood localization of sources in noise modeled as a stable process

Abstract

This paper introduces a new class of robust beamformers which perform optimally over a wide range of non-Gaussian additive noise environments. The maximum likelihood approach is used to estimate the bearing of multiple sources from a set of snapshots when the additive interference is impulsive in nature. The analysis is based on the assumption that the additive noise can be modeled as a complex symmetric /spl alpha/-stable (S/spl alpha/S) process. Transform-based approximations of the likelihood estimation are used for the general S/spl alpha/S class of distributions while the exact probability density function is used for the Cauchy case. It is shown that the Cauchy beamformer greatly outperforms the Gaussian beamformer in a wide variety of non-Gaussian noise environments, and performs comparably to the Gaussian beamformer when the additive noise is Gaussian. The Cramer-Rao bound for the estimation error variance is derived for the Cauchy case, and the robustness of the S/spl alpha/S beamformers in a wide range of impulsive interference environments is demonstrated via simulation experiments.