Wireless sensor networks (WSN) are widely used in numerous aspects. Least-square localization method of source localization based on energy measurements is focused on due to the tradeoff between performance and computation in underwater wireless sensor networks (UWSN). Firstly, several least-square methods of source localization are reviewed and the performances are compared. Secondly, in terms of one step weighted least-square localization (OS-LS) method a new weighted factor is derived to simplify the operation. Finally, a novel least-square method based on energy measurements is proposed in underwater wireless sensor networks (UWSN). Compared to the existing acoustic source localization methods, this proposed method reduces the computation of Data Fusion Center (DFC) on the premise of ensuring the localization accuracy. Numerous simulation results show that weighted least-square (WLS) method of localization outperforms least-square (LS) localization and the new direct least-square (D-LS) method operates with less computation than the maximum likelihood (ML) and other least-square methods. Furthermore, the direct WLS with correction technique (DC-WLS) method improves the localization accuracy by exploiting the correlation of variables compared to the one without correction technique.
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