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A localization problem in wireless sensor and ad hoc networks can be solved using measured distances and/or directions between neighboring nodes as constraints. With the internode constraints only the relative localization problem can be solved, as for more specific absolute positions a set of prelocalized nodes, called anchors, is needed. In this paper, a new approach for designing and evaluating a distributed anchor-free localization algorithm is presented. It uses only direction constraints relative to the nodepsilas coordinate system as their orientations are assumed to be unknown. The algorithm is based on division of a network into clusters. After the initial clusters are localized, by stitching them together the whole network can be localized. Using the graph rigidity theory we define new structures and their relationships, so the algorithm can provide relative locations to maximum number of nodes for a given number of constraints. The algorithm performance is evaluated through simulations and the obtained results are similar to the centralized version of algorithm. Additional analysis showed that the performance is not dependant on the path and order used for cluster stitching. By comparing the performance to the Cramer Rao bound it is revealed that the error induced by the algorithm correspond to the 30% - 50% of the total localization error.
Date of Conference: June 30 2008-July 2 2008