Improved Time of Arrival measurement model for non-convex optimization

TL;DR

This paper proposes a novel approach to improve Time of Arrival measurement by transforming local minima into saddle points through dimensionality increase, reducing convergence issues in non-convex optimization.

Contribution

It introduces a method that transforms local minima into saddle points via dimension lifting, maintaining non-convexity while enhancing optimization reliability.

Findings

Reduced risk of convergence to local minima

Enhanced accuracy in TOA measurements

Maintained non-convex problem structure

Abstract

The quadratic system provided by the Time of Arrival technique can be solved analytically or by optimization algorithms. In practice, a combination of both methods is used. An important problem in quadratic optimization is the possible convergence to a local minimum, instead of the global minimum. This article presents an approach how this risk can be significantly reduced. The main idea of our approach is to transform the local minimum to a saddle point, by increasing the number of dimensions. In contrast to similar methods such as, dimension lifting does our problem remains non-convex.