A weighted Fastmap algorithm for wireless sensor nodes localization

In this paper a weighted Fastmap (WFM) algorithm is proposed in which more than one pair of anchor nodes is used to evaluate the one-dimensional coordinates of the unknown nodes while in the original Fastmap (FM) algorithm only one pair of anchor nodes was employed. However, some nodes might be too far from the anchor nodes thus resulting in a high coordinate estimation error. This motivates the use of the WFM but at a slight increase in the computational complexity. The optimal WFM weights were determined via (constrained) minimization of the mean-squared error (MSE) of the estimated node coordinates. A simplification of the WFM is also introduced, called the averaged FM (AFM), where the complexity is reduced at the expense of the WFM performance. Both the WFM and AFM exhibit improved performance over the original FM algorithm.