A Mismatched Bound for Stochastic DOA Estimation
Gerald LaMountain, Pau Closas · 2020
Model misspecification occurs when the assumed model on which an estimator is derived differs from the true underlying model for a given set of data. This often occurs when, for reasons of practicality, it is not reasonable to account for all of the real-world factors affecting a given signal. In the context of radio direction-of-arrival (DOA) estimation this can occur due to interference, multipath or other unanticipated phenomena, or due to modelling assumptions that are made in order to utilize computationally efficient array processing algorithms. In this contribution we address the problem of model misspecification in the context of multi-antenna stochastic direction-of-arrival estimation. We present this problem as an application for the Misspecified Cramér-Rao lower bound (MCRB) and derive a set of general models and expressions for computing the MCRB for the misspecified stochastic DOA problem. These models are compared against the convergent results of the stochastic maximum-likelihood (ML) estimation to show that the performance of an asymptotically optimal unbiased estimator does converge to the value predicted by the MCRB.