On the Uniqueness of Solutions in GPS Source Localization: Distance and Squared-Distance Minimization under Limited Measurements in Two and Three Dimensions

TL;DR

This paper investigates the conditions under which source localization solutions are unique in GPS, analyzing distance and squared-distance minimization problems in 2D and 3D with limited measurements.

Contribution

It provides new insights into the uniqueness of solutions in GPS localization problems, especially with fewer than three measurements, in both two and three dimensions.

Findings

Uniqueness conditions for source solutions in GPS localization.

Analysis of solutions with fewer than three measurements.

Comparison of distance and squared-distance minimization approaches.

Abstract

The source localization problem, fundamental to applications like GPS, is typically approached as a minimization problem in the presence of various types of noise. Ensuring the uniqueness of solutions in GPS technology is vital for the reliability and accuracy of applications, from everyday navigation to critical military operations. In this paper, we examine two key minimization problems: one focused on distance error and the other on squared distance error. We explore these problems in both three-dimensional space, the standard scenario, and in two-dimensional space as a simplified case. Furthermore, we discuss the number of possible source solutions when the number of measurements is fewer than three.