Localization based on received signal strength (RSS) has drawn great interest in the wireless sensor network (WSN). In this paper, we investigate the RSS-based multi-sources localization problem with unknown transmitted power under shadow fading. The log-normal shadowing effect is approximated through Fenton-Wilkinson (F-W) method and maximum likelihood estimation is adopted to optimize the RSS-based multiple sources localization problem. Moreover, we exploit a sparse recovery and weighted average of candidates (SR-WAC) based method to set up an initiation, which can efficiently approach a superior local optimal solution. It is shown from the simulation results that the proposed method has a much higher localization accuracy and outperforms the other
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