Optimal and suboptimal broad-band source location estimation

Two maximum-likelihood (ML) estimators are considered for direction-of-arrival (DOA) estimation of broadband sources with unknown spectral parameters. One is based on the assumption that the sources radiate stochastic-Gaussian signals and therefore is called the stochastic-Gaussian ML (SGML) estimator; the other, using estimates of the actual signals (not their assumed distribution), is called the conditional ML (CML) estimator. Neither is efficient if the source spectral parameters are completely arbitrary and unknown, but the problem can be avoided for a version of the SGML estimation if the signal and noise spectra are known to satisfy certain smoothness conditions. While this version of the SGML is formally superior to the CML, it is demonstrated that the performance difference is small with underconditions not infrequently encountered in practice. When these are satisfied, the computationally simpler CML can be used without significant loss. The required conditions become more stringent as the source separation decreases or correlation between sources increases. A closed-form analytic expression is obtained for the small-error variance of the CML estimator of the DOA of the nth source in the presence of N-1 other sources