Analysis of weighted centroid-based localization scheme for wireless sensor networks

Weighted centroid-based schemes provide a cost-effective alternative to locate sensors in a Wireless Sensor Network (WSN). In this paper, we describe mathematical characteristics of weighted centroid localization in a WSN. We provide an expression to compute the distance between the weighted and unweighted centroids of a set of points. We present algorithms to compute the weighted centroid in an iterative and non-iterative manner. We provide expressions for the distance between weighted centroids during successive iterations. The analytical framework presented in this paper is general and may incorporate any criterion for assigning weights to locations of anchors involved in the computation of location of a sensor using the weighted centroid. Simulations are carried out to evaluate the performance of weighted centroid localization where weights are assigned using proximities based on the distance and the received signal power. We observed that the normalized error for weights assigned using the received signal power based proximity is less than the weights assigned using distance based proximity.