Cramer-Rao bound for TOA estimations in UWB positioning systems

Abstract

This paper deals with time delay estimation for a UWB positioning system. We consider the a priori model in which the distributions of path gain and the desired time delay are known. Joint probability density functions for both parameters are cast into explicit form. Then, we address parameter estimations based on maximum likelihood as well as maximum a posteriori. The Fisher information matrix (FIM) of the ordinary Cramer-Rao bound (CRB) is available from maximum likelihood criterion. For three possible cases of a priori knowledge, the inherent accuracy are provided by a posteriori CRBs, which can be derived from three possible assumptions. All theoretical results are unconditioned on any specification of UWB pulse and hence are plausible to extend to further performance analysis.