Node localisation in wireless ad hoc networks using Time Difference Of Arrival

Wireless ad hoc networks often require a method for estimating their nodes' locations. Typically this is achieved by the use of pair-wise measurements between nodes and their neighbours, where a number of nodes already accurately know their location and the remaining nodes must calculate theirs using these known locations. Often, a linear least squares solution, or a maximum likelihood estimate (MLE) is used to generate the unknown node locations, making use of range estimates derived from either received power, or time of arrival measurements between the nodes. In this paper we investigate the efficacy of using time difference of arrival (TDOA) measurements for the accurate localisation of the transmitting nodes over long ranges. We compare two traditional techniques; spherical intersection and spherical interpolation for small numbers of measurement probes with known locations and noisy propagation conditions, and introduce novel optimisation techniques that significantly improve their performance.