Stochastic Maximum-Likelihood DOA estimation in the presence of unknown nonuniform noise

This paper investigates the direction-of-arrival (DOA) estimation of multiple narrowband sources in the presence of nonuniform white noise with an arbitrary diagonal covariance matrix. While both the deterministic and stochastic Cramer-Rao Bound (CRB) and the deterministic Maximum-Likelihood (ML) DOA estimator under this model have been derived in [1], the stochastic NIL DOA estimator under the same setting is still not available in the literature. In this paper, a new stochastic ML DOA estimator is derived. Its implementation is based on an iterative procedure which step-wise concentrates the log-likelihood function with respect to the signal and noise nuisance parameters. A modified inverse iteration algorithm is also presented for the estimation of the noise parameters. Simulation results have shown that the proposed algorithm is able to provide significant performance improvement over the conventional uniform NIL estimator in nonuniform noise environments and require only a few iterations to converge to the nonuniform stochastic CRB.