Weighted Linear Least Square Localization Algorithms for Received Signal Strength

Localization based on the received signal strength (RSS) is by far the cheapest and simplest option. By constructing the appropriate path-loss model, the RSS information can be converted to the distance estimates which can determine the position of the target node with Linear Least Square (LLS) algorithm. In this paper, the LLS algorithm can be directly applied by subtracting a reference node equation from the remaining ones rather than defining a new variable, which selects the reference node with the maximal RSS among all the RSS measurements. Furthermore, based on the latest research results about the estimates of the squared distance, we investigate the unbiased and linear minimum mean square error (MMSE) estimates of the squared distance, and the covariance matrixes about the two estimates with the proposed LLS algorithm are derived, respectively. Then the weighted LLS localization algorithms are presented by utilizing the covariance matrixes. Simulation results demonstrate that the localization accuracy of the linear MMSE estimate with the proposed LLS algorithm is superior to the unbiased estimate. Moreover, the proposed weighted LLS algorithms outperform the traditional LLS localization algorithms in terms of localization accuracy.