Posterior CRLB for tracking a mobile station in NLOS multipath environments

In this paper we investigate the posterior Cramer-Rao lower bound for tracking a mobile station in a non-line-of-sight multipath localization scenario. The posterior Cramer-Rao lower bound is the mean-square estimation error lower bound of a random scalar or vector parameter in linear/nonlinear filtering problems. A practical system model is chosen to represent the non-line-of-sight multipath propagations. A recursive formulation of the posterior Cramer-Rao lower bound is developed for tracking a mobile station in a non-line-of-sight multipath localization scenarios when the observations are the time-of-arrival, the angle-of-departure, the angle-of-arrival and the Doppler shift. The lower bound is also shown for a subset of these observations. The developed lower bound can be used to analyze the achievable performance of a tracking system designed for use in a non-line-of-sight multipath localization scenarios.