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In this paper, energy-based localization methods for source localization in sensor networks are examined. The focus is on least-squares-based approaches due to a good tradeoff between performance and complexity. A suite of methods are developed and compared. First, two previously proposed methods (quadratic elimination and one step) are shown to yield the same location estimate for a source. Next, it is shown that, as the errors which perturb the least-squares equations are nonidentically distributed, it is more appropriate to consider weighted least-squares methods, which are observed to yield significant performance gains over the unweighted methods. Finally, a new weighted direct least-squares formulation is presented and shown to outperform the previous methods with much less computational complexity. Unlike the quadratic elimination method, the weighted direct least-squares method is amenable to a correction technique which incorporates the dependence of unknown parameters leading to further performance gains. For a sufficiently large number of samples, simulations show that the weighted direct solution with correction (WDC) can be more accurate with significantly less computational complexity than the maximum-likelihood estimator and approaches Cramer-Rao bound (CRB). Furthermore, it is shown that WDC attains CRB for the case of a white source.
Date of Publication: Jan. 2008