Fast approximate maximum likelihood algorithm for single source localisation

The authors present an approximation for the deterministic maximum likelihood (ML) method for estimating the direction of arrival of a signal from a single source. To apply the proposed approximate ML (AML) method one has to compute the principal eigenvector of the sample covariance matrix, i.e. the unit eigenvector corresponding to the largest eigenvalue. Surprisingly, the AML method coincides with the principal eigenvector method of Evans, Johnson and Sun (1982) that was derived based on the unnecessary assumption of high signal-to-noise ratio. Next, the authors present for the AML method a fast and simple explicit method for computing the principal eigenvector of the sample covariance matrix as well as an explicit estimator for the signal-to-noise ratio. The proposed explicit AML (EAML) method is faster than the ML method in carrying out the maximisation step. Simulations reveal that AML and ML methods have similar performance, while EAML performance is only slightly inferior to the ML method