Performance Prediction of Maximum-Likelihood Direction-of-Arrival Estimation in the Presence of Modeling Errors

This paper provides new analytic expressions for the root mean-square (RMS) error and bias of the maximum-likelihood (ML) direction-of-arrival (DOA) estimator in the presence of steering vector modeling errors. Previous work has provided a first-order approximation of these performance measures, which is valid for small modeling errors. In order to take into account larger errors and provide tools for designing an experimental setup, a more accurate (but still easy-to-use) performance analysis is necessary. For such an investigation, the DOA estimation errors are expressed as a Hermitian form with a stochastic vector composed of the modeling errors. Closed-form expressions relating the bias and RMS errors to the statistical moments of the modeling error are then deduced from the statistics of this Hermitian form. Simulations are provided to illustrate the usefulness of the theoretical results.