Improved Time of Arrival measurement model for non-convex optimization with noisy data

TL;DR

This paper proposes a novel method to improve Time of Arrival measurements in noisy environments by transforming local minima into saddle points through dimensionality increase, enhancing optimization robustness.

Contribution

It introduces a new approach that reduces the risk of local minima in non-convex TDOA optimization by increasing the problem's dimensions to transform minima into saddle points.

Findings

Enhanced accuracy in noisy TDOA measurements

Reduced likelihood of local minima trapping in optimization

Improved robustness of the measurement model

Abstract

The quadratic system provided by the Time of Arrival technique can be solved analytical or by optimization algorithms. In real environments the measurements are always corrupted by noise. This measurement noise effects the analytical solution more than non-linear optimization algorithms. On the other hand it is also true that local optimization tends to find the local minimum, instead of the global minimum. This article presents an approach how this risk can be significantly reduced in noisy environments. The main idea of our approach is to transform the local minimum to a saddle point, by increasing the number of dimensions.