An analytical framework for centroid-based localization in wireless sensor networks

The centroid of a set of points can be used by a sensor to compute its location provided that each point represents an anchor with a known location. In this paper, we present mathematical characteristics of centroid based localization in a wireless sensor network. We prove that the centroid of a set of points minimizes an objective function, which is the summation of squares of distances from individual points. We provide a mathematical expression for the minimum value of the summation of the objective function. Also, we provide an expression for the distance between the centroids of a set of k and $$(k+1)$$ points. We describe a scheme for localization of sensors using the centroid of locations of anchors. Our scheme excludes locations of anchors that may adversely affect localization of a sensor.