Joint position and clock tracking of wireless nodes

Abstract

In this paper we consider the problem of joint position and clock tracking of a mobile wireless node by a set of reference nodes. Imperfections of the mobile clock are characterized by its skew and offset, which are assumed to change with time according to simple random walk models. We put forth a measurement protocol, similar to that used in two-way ranging, and apply extended and unscented Kalman filters to estimate the position and the velocity of the mobile, and the skew and offset of its clock. We analyze the performance of the algorithms by means of extensive simulations, where the mobile's velocity is assumed to follow a random walk. Simulation results are compared to the Cramér–Rao bound for a simplified model of a mobile with constant velocity. We show that estimation errors are largely independent of the mean values of the offset and the skew, but they increase with the mean speed. We also study how estimation errors are influenced by other factors such as the number of reference nodes. We believe these results to be of relevance, specially, in indoor positioning applications.