Theoretical Lower Bound for UWB TDOA Positioning

Abstract

Indoor radio channels suffer multipath and non- line-of-sight (NLOS) fading, which is undesirable for accurate indoor positioning. High bandwidth of Ultra-wideband (UWB) implies high temporal resolution and hence high ranging accuracy. Furthermore, its robustness to multipath fading makes UWB perfect for indoor applications. This paper analyses the theoretical bounds of position estimation based on UWB time-difference-of-arrival (TDOA) measurements in multipath and NLOS environments. The TDOA range errors are modeled as range dependent, where the variance of the range errors is a function of the interested TDOA range. Cramer-Rao Lower Bound (CRLB) for distance- independent and distance-dependent TDOA range errors has been derived and compared.