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Maximum likelihood (ML) direction-of arrival (DOA) estimation of multiple narrowband sources in unknown nonuniform white noise is considered. A new iterative algorithm for stochastic ML DOA estimation is presented. The stepwise concentration of the log-likelihood (LL) function with respect to the signal and noise nuisance parameters is derived by alternating minimization of the Kullback-Leibler divergence between a model family of probability distributions defined on the unconditional model and a desired family of probability distributions constrained to be concentrated on the observed data. The new algorithm presents the advantage to provide closed-form expressions for the signal and noise nuisance parameter estimates which results in a substantial reduction of the parameter space required for numerical optimization. The proposed algorithm converges only after a few iterations and its effectiveness is confirmed in a simulation example.