Performance analysis of relative location estimation for multihop wireless sensor networks

In this paper, we present new analytical, simulated, and experimental results on the performance of relative location estimation in multihop wireless sensor networks. With relative location, node locations are estimated based on the collection of peer-to-peer ranges between nodes and their neighbors using a priori knowledge of the location of a small subset of nodes, called reference nodes. This paper establishes that when applying relative location to multihop networks the resulting location accuracy has a fundamental upper bound that is determined by such system parameters as the number of hops and the number of links to the reference nodes. This is in contrast to the case of single-hop or fully connected systems where increasing the node density results in continuously increasing location accuracy. More specifically, in multihop networks for a fixed number of hops, as sensor nodes are added to the network the overall location accuracy improves converging toward a fixed asymptotic value that is determined by the total number of links to the reference nodes, whereas for a fixed number of links to the reference nodes, the location accuracy of a node decreases the greater the number of hops from the reference nodes. Analytical expressions are derived from one-dimensional networks for these fundamental relationships that are also validated in two-dimensional and three-dimensional networks with simulation and UWB measurement results.