Asymptotic and empirical results on approximate maximum likelihood and least squares estimates for sensor array processing

The problem of source location estimation in the presence of partly unknown noise fields is addressed. A novel two-stage procedure is developed which combines the conditional maximum-likelihood estimate and the conditional marginal maximum-likelihood estimate for the signal parameters and the noise parameters, respectively. The strong consistency and asymptotic normality of the conditional maximum-likelihood estimates for location parameters and noise parameters in the case of not necessarily normal and independent distributed observations are proved. Alternatively, different least squares criteria fitting a parametric model of the spectral density matrix to a nonparametric consistent estimate of the spectral density matrix are investigated and their asymptotic behaviors are mentioned briefly. Results of numerical experiments are presented to show the performance of the different estimates