An iteratively Reweighted Least Square algorithm for RSS-based sensor network localization

Abstract

In this article, we give a new algorithm for localization based on RSS measurement. There are many measurement methods for localizing the unknown nodes in a sensor network. RSS is the most popular one due to its simple and cheap hardware requirement. However, accurate algorithm based on RSS is needed to obtain the positions of unknown nodes. Recent algorithms such as MDS(Multi-Dimensional Scaling)-MAP, PDM (Proximity Distance Matrix) cannot give accurate results based on RSS as the RSS signals always have large variations. Besides, recent algorithms on sensor network localization ignore the received signal strength (RSS) and thus get a disappointing accuracy. This is because they are mostly focused on the difference between the estimated distance and the real distance. This paper introduces a target function — signal-based maximum likelihood (SML), which uses the maximum likelihood based on the directly measured RSS signal. Inspired by the SMACOF (Scaling by Majorizing A COmplicated Function) algorithm, an iteration surrogate algorithm named IRLS (Iteratively Reweighted Least Square) is introduced to solve the SML. From the simulation results, the IRLS algorithm can give accurate results for RSS positioning. When compared with other popular algorithms such as MDS-MAP, PDM, and SMACOF, the error (distance between the estimated position and the actual position) calculated by IRLS is less than all the other algorithms. In anisotropic network, IRLS also has good performance.