Optimal Local Map Registration for Wireless Sensor Network Localization Problems

Abstract

In this chapter, we present an optimal local map registration algorithm for constructing global maps from local relative maps for wireless network localization applications. A wireless network is partitioned into sub-networks with overlapping or common nodes that shared by different sub-networks. Local maps are built for each sub-network, which consist of the relative coordinates of nodes in each network. The local maps are then transformed into a global map using a set of affine transforms with each consisting of a rotation, a reflection and a translation for each individual local map. The optimal transform is found by minimizing the discrepancies, in the global map, of the common sensor nodes shared by different local maps. A computationally efficient gradient projection algorithm is developed for finding the optimal transforms. The local map registration approach can solve many of the problems encountered by pairwise map merging based techniques and is able to achieve global optimal performance. More importantly, the technique provides a systematic approach for constructing global maps from local maps. Computer simulations are used to demonstrate the performance and effectiveness of the proposed algorithm.