A Large-Sample Approximate Maximum Likelihood for Localizing A Spatially Distributed Source

Abstract:
This paper proposes a large-sample approximation of the maximum likelihood (ML) criterion for estimating the nominal direction of a spatially spread source. The likelihood function is concentrated on at the critical point. The parametric nuisance estimate, which depends on all model parameters, is replaced by one that relies only on the nominal angle of interest. Rather than the four-dimensional optimization required in the exact ML estimation, this large-sample approximation allows us to obtain only one-dimensional search. Since it is an asymptotic approximation of the exact ML estimator, the standard deviation of its estimate error attains the Cramér-Rao bound for a large number of temporal snapshots. To validate the asymptotic efficiency, numerical simulations are performed and also compared with previous approaches. The well-behaved results show that the asymptotic ML estimator outperforms several sub-optimal criteria in non-asymptotic region, both extreme SNR situations, and for large angular spread.