An optimization approach for robust transformation of measured range data into position estimates in wireless networks

This paper introduces a generalized framework for positioning mobile nodes in a wireless network. The transformation of the range data measured between pairs of network nodes into a spatial position is a very challenging task if the range measurements are distorted. Typical distortions in wireless ranging systems are caused by an imperfect clock synchronization or by multipath reflection. The positioning method proposed in this paper overcomes problems of the traditional circular or hyperbolic methods and allows for the detection and elimination of distorted measurements. The positioning is done in a non-Markovian manner, which is an advantage over other available methods, especially the Kalman-based positioning methods, since linear assumptions in the dynamics are avoided. Another advantage of the proposed method is that the two tasks positioning and smoothing are carried out separately. Hence, smoothing of the position data, e.g. by means of a Kalman filter, is possible without the well documented problems in conventional methods induced by the usually applied simplifying assumptions of linear dynamics. The very good performance of the presented approach is demonstrated by real life results obtained in industrial environments.