Localization in Wireless Sensor Networks: Solvability Improvement Technique Using Priori Information from Sensing Data and Network Properties in Unit Disk Graph Model

Abstract

From the theoretical point of view, network localization can be viewed as finding a unique solution from distances constraint among points. The one of the difficulties is that even if the network is uniquely localizable, it is proven to be an NP-Hard [1]. It is also true that the network graph has to be sufficiently dense [2]. This poses even more challenges to the original problem as we often work on sparse networks. To cope with this, in [3], we introduce priori knowledge to assist the process of finding the unique localization solution. It helps to speed up the searching algorithm; however, the ambiguity still exists among sparse networks. In this paper we try to bring as much priori knowledge as possible to assist or to be used as constraints. Hopefully this will reduce search space and reach the unique solution quickly. In clean environment, this extra info will, by some magnitude, bring the graph closer to the unique answer. We start from integer-coordinate noise-free position and then add sources of priori knowledge. Then we examine the case where assisted data can be noisy. A search is used within the noisy but useful constraint. The justification of using the assisted knowledge is from the practical uses of some networks, e.g. sensor network, where other measurements are available and they are often correlated and can be helpful in determining the positions.