Iterative methods for DOA estimation of correlated sources in spatially colored noise fields

Direction of arrival (DOA) estimation in the presence of correlated sources and unknown spatially colored noise field is concerned in this paper. We develop two iterative approaches to jointly estimate the angle parameters and unknown nonuniform noise covariance matrix from multi-snapshot sensor array data. Specifically, we show that both methods allow to obtain the estimates by explicit formulas: i) By concentrating the ML estimation problem with regard to all nuisance parameters, the proposed method provides a concise derivation of the concentrated likelihood function; ii) compact expressions of the estimates of the parameters of interest from sparse Bayesian learning (SBL) principle are also presented. This technique can be deemed as an alternative to ML estimation, and it provides better accuracy often at a lower computational cost. In spatially colored noise fields, the proposals are free of any further structural constraints that are usually imposed on the received signals in most existing direction finding approaches. Extensive simulations and experimental results are presented to demonstrate the satisfying performance of the proposed methods.