# Positioning and Tracking in Asynchronous Wireless Sensor Networks

[Licentiatavhandling]

This thesis deals with the problem of locating mobile nodes in an asynchronous wireless communication network, i.e., a wireless network of mobile terminals where some or all nodes do not have access to a global time reference. A strong focus lies on reducing the complexity associated with straight forward classical algorithms of node coordinate estimation. The thesis is based on a number of previously published papers, listed in the introductory chapter.

Two complexity reducing data preprocessing methods are presented. Both preprocessors achieve a complexity reduction through a cancellation of unknown clock-offsets from the estimation problem. Based on a concept of invariant preprocessors, we show how the individual unknown clock-offsets at some or all nodes in the network may be discarded from the estimation problem, without any degradation of the asymptotic performance bounds of the positioning problem.

We further present two, fully distributed, sub-optimal positioning algorithms that operate on a set of asynchronous delay measurements. The first, called the kernel algorithm, reduces complexity by a divide and conquer approach. The second algorithm is based on a mechanical analogy of the positioning problem. We evaluate the performance of both algorithms, in terms of the mean-squared positioning error, by computer simulation. The performance of the kernel algorithm is found to lie on the order of the delay measurement accuracy, while the second algorithm is shown to attain the Cramér-Rao lower bound under a set of reasonable assumptions.

In the last part of the thesis, a novel tracking filter is proposed to reduce the complexity associated with tracking maneuvering objects in a wireless network. The tracking filter is based on a classical Kalman filter, but uses additional information, supplied by the tracked node, to aid in the tracking process. One drawback associated with this type of approach to tracking is the possibility of an unstable filter. We argue that the implementation can be made robust using very simple alterations. Further, we argue that the classical mean-squared-error performance measure is not fully appropriate for delay sensitive applications, and introduce a novel performance measure called the time margin measure, suitable for evaluation of tracking algorithms that operate under latency constraints. We discuss the merits of our proposed tracking filter, with respect to this new performance measure, as compared to a classical Kalman implementation.

Denna post skapades 2006-09-12. Senast ändrad 2008-04-09.

CPL Pubid: 12085