Geolocation with FDOA Measurements via Polynomial Systems and RANSAC

TL;DR

This paper introduces a novel geolocation algorithm using polynomial systems and RANSAC for FDOA measurements, leveraging numerical algebraic geometry to improve accuracy and provide measurement bounds.

Contribution

It develops a new polynomial system-based approach for geolocation with FDOA data, integrating RANSAC and establishing measurement bounds for unique solutions.

Findings

Effective geolocation with FDOA using polynomial equations

Integration of RANSAC improves robustness to noise

Provides bounds on measurements for unique solutions

Abstract

The problem of geolocation of a transmitter via time difference of arrival (TDOA) and frequency difference of arrival (FDOA) is given as a system of polynomial equations. This allows for the use of homotopy continuation-based methods from numerical algebraic geometry. A novel geolocation algorithm employs numerical algebraic geometry techniques in conjunction with the random sample consensus (RANSAC) method. This is all developed and demonstrated in the setting of only FDOA measurements, without loss of generality. Additionally, the problem formulation as polynomial systems immediately provides lower bounds on the number of receivers or measurements required for the solution set to consist of only isolated points.