Mean-Squared-Error Prediction for Bayesian Direction-of-Arrival Estimation

In this article, we study the mean-squared-error performance of Bayesian direction-of-arrival (DOA) estimation in which prior belief about the target location is incorporated into the estimation process. Our primary result is an extension of the method of interval errors (MIE) to the case of maximum a posteriori (MAP) direction-of-arrival estimation. We work in a general framework in which the prior information used in the MAP estimation may not match the actual target distribution. In particular, when the prior is incorrect, the MAP estimator degrades relative to the performance of a MAP estimator with the correct prior. Our methods are able to accurately predict the performance of a MAP estimator in this more general situation. We apply our methods to investigate the sensitivity of MAP direction-of-arrival estimation to mismatches between the chosen prior and the actual angular distribution of the target.