Localization in Sensor Networks using Message Passing Algorithm

We describe a powerful and different approach to solve the localization problem of sensor networks with a very few anchor nodes (we define anchor nodes as those sensors that are equipped with GPS receivers so that they are fully aware of their location). The triangulation procedure (employed usually to solve this problem) fails when we don’t have the anchor nodes lying close to each other, since it requires for any sensor node, at least three anchor nodes in its neighborhood to find its exact position estimate. Our algorithm finds out the position estimates of these sensor nodes. The sensor nodes then act as anchor nodes (for the sensor nodes whose positions are still unknown) increasing the number of anchor nodes in the network, making it possible to carry out the triangulation procedure. The algorithm is based upon the two dimensional distance matrix computed for all the nodes present in the network and a simple message passing scheme. The network is converted into a graph (a dense graph if the number of nodes is large) and subsequently random spanning trees are generated from it. Working on the spanning trees is beneficial since we avoid getting caught in the cyclic nature of the graph. The algorithm takes into account the random nature of the different spanning trees selected. The message is then passed on these spanning trees one by one, their order selected at random. The message propagates from the root of the tree to the succeeding levels/generations. The algorithm then updates the position of the current node by minimizing a two dimensional equation based on distance matrix and the information contained in the message. We further use a cross validation procedure to verify our estimates.