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We consider the problem of localizing the source using range, and range-difference measurements. Both the problems are non-convex, and non-smooth, and are challenging to solve. In this article, we develop an iterative algorithm - Source Localization Via an Iterative technique (SOLVIT) to localize the source using all the distinct range-difference measurements, i.e., without choosing a reference sensor. SOLVIT is based on the Majorization Minimization approach - in which a novel upper bound is formulated, and minimized to get a closed-form solution at every iteration. We also solve the source localization problem based on range measurements, and rederive the Standard Fixed Point algorithm using the Majorization Minimization approach. By doing so, we show a less intricate way to prove the convergence of the Standard Fixed Point algorithm. Numerical simulations, and experiments in an anechoic chamber confirm that SOLVIT performs better than existing reference-based, and reference-free methods in terms of source positioning accuracy.
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