Performance bound for Target Localization under Model Misspecification

In positioning problems, the assumed data distribution could differ from the true one, leading to inaccurate target position estimation. Cramér-Rao bound (CRB), a lower bound on the variance of estimators that requires the parametric model to be correctly specified, malfunctions in such a misspecified model problem. To illustrate the limits on achievable positioning accuracy under model misspecification, this paper derives the performance bound of a typical positioning scenario using time-difference-of-arrival (TDOA) measurements under misspecification of the target altitude. Specifically, the misspecified Cramér-Rao bound (MCRB) on the error covariance matrix of a misspecified-unbiased estimator is developed in detail, and the positioning performance loss subject to the model misspecification is given by comparing it and CRB under true model. The simulation results of the performance bound and comparisons with the performance of the misspecified maximum likelihood (MML) estimator verify the correctness of theoretical derivation.