  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 paper, 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.
