On the Statistical Model of Source Localization based on Range Difference Measurements

TL;DR

This paper develops a statistical model for source localization using range difference measurements with three non-aligned receivers, employing algebraic and geometric techniques to analyze feasible measurement sets.

Contribution

It extends previous noiseless localization models to a statistical framework, utilizing algebraic statistics and information geometry for analysis.

Findings

Characterization of feasible measurement sets as semialgebraic varieties

Application of algebraic statistics and information geometry techniques

Insights into the statistical properties of range difference localization

Abstract

In this work we study the statistical model of source localization based on Range Difference measurements. We investigate the case of planar localization of a source using a minimal configuration of three non aligned receivers. Our analysis is based on a previous work of the same authors concerning the localization in a noiseless scenario. As the set of feasible measurements is a semialgebraic variety, this investigation makes use of techniques from Algebraic Statistics and Information Geometry.