An Importance Sampling Maximum Likelihood Direction of Arrival Estimator

We present a new implementation for maximum likelihood (ML) estimation of the direction of arrival (DOA) of multiple narrow-band plane waves in noise. The proposed estimator can be applied to the estimation of DOAs of both deterministic and stochastic signals. In this paper, we discuss the estimation of DOAs for stochastic signals only. The proposed method uses a global optimization procedure to maximize the compressed likelihood function, which is a function of only the DOAs. The procedure is based on Monte Carlo importance sampling. It is shown via simulations that the method allows for estimation of DOAs at low angular separation and in situations for which other suboptimal techniques may fail. The improved performance of this method is due to its guaranteed convergence to a global maximum, which is not true for the iterative ML methods, as, for example, the WSF, MODE(X), and EM algorithms. We compare our method to the latter algorithms to show that the proposed method outperforms the iterative approaches for closely spaced narrow-band sources.