Robust Source Positioning Method With Accurate and Simplified Worst-Case Approximation

Abstract

Worst-case robust approximation was proven to be efficient in alleviating the non-line-of-sight (NLOS) influence for source positioning. However, the existing time-difference-of-arrival (TDOA)-based worst-case solutions still have two issues: 1) Inaccurate objective transformations are introduced in some algorithms, which reduce the accuracy; 2) A method with higher accuracy is computationally intensive. This study proposes an accurate and simplified worst-case approximation method to tackle the troubles. Precisely, we first prove that the nonconvex worst-case objective is piecewise monotone to the NLOS bias. We further use monotonicity to derive an accurate and convex expression of the worst-case objective. Then, we propose simplified transformations to redefine the worst-case approximation problem with fewer constraints. Besides, we prove the effectiveness of the simplified transformations. Simulations and experiments demonstrate that the proposed method with moderate computation exhibits better performance than the state-of-the-art worst-case approximation algorithms.