Sensitivity analysis of the maximum likelihood direction-finding algorithm

A first-order analysis is performed of the sensitivity of the maximum likelihood (ML) direction-finding algorithm to system errors which cause differences between the array manifold used by the algorithm and the true array manifold. The effect of such errors on the directions-of-arrival (DOA) estimates is investigated. The ability of the ML algorithm to resolve two closely spaced sources in the presence of phase and gain errors in the array elements or in the receivers, or errors in the element locations, is analyzed. A formula for computing the failure threshold of the algorithm as a function of source separation and other system parameters is derived and tested by simulation. The analysis assumes that the exact covariance matrix of array element outputs is known