An asymptotic maximum likelihood for estimating the nominal angle of a spatially distributed source

Abstract

This paper proposes a large-sample approximation of the maximum-likelihood estimator for direction finding in the presence of a spatially spread source. The key idea is to replace the parametric estimate of the four-dimensional nuisance parameter vector with the approximate one that depends on just one parameter of interest, called the nominal angle, thus permitting the use of one-dimensional optimization techniques. The proposed estimator is shown to be strongly consistent and asymptotically efficient, and the Cramér–Rao bound on its standard deviation is derived. Simulations show the estimator to outperform previously proposed estimators, such as the subspace-based estimator and others based on one-dimensional search.