Wireless Sensor Networks Localization with Isomap

This paper studies the problem of determining the sensors' locations in wireless sensor networks. To alleviate the influence of the noise and the inaccurate measurement in the complicated environment, rather than estimating the pairwise Euclidean distance between sensors, we use the geodesic distance to measure the dissimilarity between sensors, and employ the isomap algorithm to determine the relative locations of sensors. Given sufficient anchors, the relative locations can be aligned to absolute locations by using coordinate transformation. The coordinate transformation matrix can be obtained by minimizing the sum of squares of the errors between the true locations of the anchors and their transformed locations. Since isomap is parameter-sensitive, we also present an adaptive parameter selection procedure based on the locations of anchors. Simulation results show that the isomap algorithm achieves smaller average location error with little quantity of anchors.