A Multi-Player Potential Game Approach for Sensor Network Localization with Noisy Measurements

TL;DR

This paper models sensor network localization as a multi-player potential game, analyzing the existence and uniqueness of Nash equilibria under noisy and noiseless conditions, and quantifying localization errors.

Contribution

It introduces a novel game-theoretic framework for sensor network localization, establishing conditions for equilibrium existence and quantifying errors due to noise.

Findings

Nash equilibrium exists and is unique in noiseless case

Equilibrium remains unique with small measurement errors

Equilibrium provides an approximate solution with quantifiable errors

Abstract

Sensor network localization (SNL) is a challenging problem due to its inherent non-convexity and the effects of noise in inter-node ranging measurements and anchor node position. We formulate a non-convex SNL problem as a multi-player non-convex potential game and investigate the existence and uniqueness of a Nash equilibrium (NE) in both the ideal setting without measurement noise and the practical setting with measurement noise. We first show that the NE exists and is unique in the noiseless case, and corresponds to the precise network localization. Then, we study the SNL for the case with errors affecting the anchor node position and the inter-node distance measurements. Specifically, we establish that in case these errors are sufficiently small, the NE exists and is unique. It is shown that the NE is an approximate solution to the SNL problem, and that the position errors can be quantified accordingly. Based on these findings, we apply the results to case studies involving only inter-node distance measurement errors and only anchor position information inaccuracies.