An MSE Approximation for Grid-Based Maximum Likelihood Direction-of-Arrival Estimators

In this work, we derive a mean squared error (MSE) approximation for maximum likelihood (ML) estimators for direction finding that evaluate the likelihood function only on a grid. Such estimators are encountered if the array manifold is only known for a finite set of angles, or as an initialization for a gridless ML approach. As has been shown in previous works, the MSE can be decomposed into a local error part and a portion that accounts for outliers. We develop tight approximations for both parts, as is confirmed by our simulations.