# SOLVIT:A Reference-Free Source Localization Technique using Majorization Minimization

## TL;DR

This paper introduces SOLVIT, an iterative, reference-free source localization algorithm based on Majorization Minimization, which improves accuracy over existing methods by effectively utilizing all range-difference measurements.

## Contribution

The paper presents a novel reference-free localization method using Majorization Minimization, providing a simpler convergence proof and enhanced accuracy.

## Key findings

- SOLVIT outperforms existing methods in accuracy.
- The approach offers a simpler convergence proof for fixed point algorithms.
- Numerical and experimental results validate improved localization performance.

## Abstract

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.