Constrained Localization: Mapping Wireless Sensor Nodes in Predefined Positions

This paper proposes a novel method for solving localization problems leveraging on node position constraints. This consists in mapping n wireless nodes onto n predefined positions in a map. The problem may be solved by first applying standard localization algorithms to get an initial estimate of the node positions in the area and, successively, mapping each estimated position to the closest admissible point in the map. Results can be improved by applying algorithms that are explicitly designed to manage the available information for the constrained problem. In this study, we propose three algorithms, based on a greedy, multi dimensional scaling, and belief propagation approach, respectively. The algorithms are analyzed and compared by using synthetic data. Results reveal that the belief propagation approach, suitably modified to account for the position constraints, outperforms the other algorithms in all the considered settings.