An asymptotic maximum likelihood for localizing multiple spatially-distributed sources

Abstract

Summary form only given. This paper proposes a large-sample approximation of maximum likelihood (ML) criterion for joint estimation of nominal directions and angular spreads in the presence of multiple spatially spread sources. The key behind the idea is to concentrate on the exact likelihood function by replacing the parametric nuisance estimate, which depends itself at the critical point on all model parameters, with one that relies only on angles of interest. Rather than (3N/sub S/ + 1) dimensions as the exact ML estimation required, this large-sample approximation allows us to only 2N/sub S/-dimensional search, where N/sub S/ signifies the number of sources. Since it is an asymptotic approximation of the ML estimator, its standard deviation of estimate error is derivable to attain the Cramer-Rao bound in large number of temporal snapshots. To validate the new estimator, numerical results are performed and also compared with other previous approaches.