Approximate Calibration-Free Trajectory Reconstruction in a Wireless Network

The problem of location tracking of a mobile station in a wireless network has received considerable attention in recent literature. In many installations, a mobile station transmits a radio frequency signal which is received at a number of base stations, from which location estimation follows. Such an application requires some form of signal-distance calibration, either an empirical signal map, or a model-based method which relies on functional relationships between signal and distance derivable from physical principles. In this paper, we propose an alternative approach in which a time series of received signal strength (RSS) measurements is mapped onto a plane in a manner which preserves the general topological and directional properties of any trajectory of a mobile station. This is accomplished without requiring a signal-distance calibration, or even exact knowledge of the base station locations. A detailed proof of the stability properties of the mapping is given. An implementation protocol is developed, and illustrated with numerical examples.