Approximate maximum likelihood direction of arrival estimation for two closely spaced sources

Most high resolution direction of arrival (DoA) estimation algorithms exploit an eigen decomposition of the sample covariance matrix (SCM). However, their performance dramatically degrade in case of correlated sources or low number of snapshots. In contrast, the maximum likelihood (ML) DoA estimator is more robust to these drawbacks but suffers from a too expensive computational cost which can prevent its use in practice. In this paper, we propose an asymptotic simplification of the ML criterion in the case of two closely spaced sources. This approximated ML estimator can be implemented using only 1-D Fourier transforms. We show that this solution is as accurate as the exact ML one and outperforms all high-resolution techniques in case of correlated sources. This solution can also be used in the single snapshot case where very few algorithms are known to be effective.