Prior mismatch in Bayesian direction of arrival estimation for sparse arrays

We study the mean-squared-error (MSE) performance of Bayesian direction-of-arrival (DOA) estimation for sparse linear arrays in which prior belief about the target location is incorporated into the estimation process. We utilize a recent extension of the method of interval errors (MIE) to the case of maximum a posteriori (MAP) direction-of-arrival estimation to more accurately predict low-medium MSE values in the presence of prior mismatch. We also develop a misspecified Cramér-Rao bound on MAP estimation that can improve the performance of MIE. We specialize to log-periodic arrays to conduct a notional trade study in which we consider the trade in improved estimation performance potentially possible with larger sparser arrays vs the increased sensitivity to incorrectly specified priors.