Robust tracking of a mobile receiver using unsynchronized time differences of arrival

Localization based on the time difference of arrival (TDoA) has turned out to be a promising approach for indoor environments, especially in combination with innovative self-calibrating TDoA algorithms that eliminate the need to measure the positions of reference receivers. We consider the previously unsolved problem of locating a moving target receiver by discrete signals from stationary beacons at unknown locations. We assume that the beacons are small and inexpensive and they require no further communication, i.e. they are unsynchronized. They only emit short discrete signals at regular intervals, of which we assume that they can be distinguished. The moving target travels on an unknown trajectory, receiving signals from the beacons and calculating the TDoA of the signals. First, we discuss adaptions of two TDoA algorithms by which the senders can be located from unknown signals. Second, we propose two novel approaches based on probabilistic state estimation to enable robust localization of the mobile receiver using the discrete arrival times, once the senders have been located. The probabilistic algorithms use the particle filter and the unscented Kalman filter to estimate the position and velocity of the target, as well as the unknown synchronization offsets of the senders. We provide a motion model and a sensor model for which we take into account that the signals of the beacons are received as singles, each at a different time. We verify the feasibility and robustness of our approach in extensive simulations, where we analyze the reliability of localization and compare both algorithms.