m Likelihood Localization of Sources oise Modeled as a Stable Process
Panagiotis Tsakalides, Chrysostomos L. Nikias · 1995
This paper introduces a new class of robust beam- formers 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 b impulsive in nature. The analysis is based on the assumption that the additive noise can be modeled as a complex symmetric a-sfable (SaS) process. Transform-based approximations of the likelihood estimation are used for the general SaS 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 Cram&-Rao bound for the estimation error variance is derived for the Cauchy case, and the robustness of the SnS beamform- ers in a wide range of impulsive interference environments is demonstrated via simulation experiments. I. INTRODUCTION The importance of the ML technique comes from the math- ematical property that under certain regularity conditions, the ML estimator is known to be asymptotically efficient, i.e., it achieves the Cram&-Rao bound (CRB) for the estimation error variance. In this sense, ML has the best possible asymptotic properties. Many researchers have studied the ML technique as a means of approachmg the source localization problem in the presence of Gaussian additive noise. Stoica and Nehorai examined the ML performance and its asymptotic properties, derived expressions for the CRB, and established some of its properties (Z). Additionally, they investigated the relationship between the ML and large sample approximation methods such as MUSIC. With high computational cost constituting the main shortcoming of the ML technique, Ziskind and Wax introduced a computationally attractive method for calculating the ML estimator (3). Their method was based on an iterative