Approximate maximum likelihood estimation of two closely spaced sources

The performance of the majority of high resolution algorithms designed for either spectral analysis or Direction-of-Arrival (DoA) estimation drastically degrades when the amplitude sources are highly correlated or when the number of available snapshots is very small and possibly less than the number of sources. Under such circumstances, only Maximum Likelihood (ML) or ML-based techniques can still be effective. The main drawback of such optimal solutions lies in their high computational load. In this paper we propose a computationally efficient approximate ML estimator, in the case of two closely spaced signals, that can be used even in the single snapshot case. Our approach relies on Taylor series expansion of the projection onto the signal subspace and can be implemented through 1D Fourier transforms. Its effectiveness is illustrated in complicated scenarios with very low sample support and possibly correlated sources, where it is shown to outperform conventional estimators.