TOA-based passive localization of multiple targets with inaccurate receivers based on belief propagation on factor graph

TL;DR

This paper introduces belief propagation algorithms on factor graphs for passive localization of multiple targets using TOA measurements, accounting for receiver position inaccuracies, and demonstrates improved accuracy over traditional methods.

Contribution

It proposes both sample-based and parametric BP algorithms to jointly localize targets and refine receiver positions under uncertain conditions, with theoretical performance bounds.

Findings

Both algorithms outperform conventional methods in simulations.

The algorithms improve receiver position accuracy.

The parametric method offers lower computational complexity.

Abstract

Location awareness is now becoming a vital requirement for many practical applications. In this paper, we consider passive localization of multiple targets with one transmitter and several receivers based on time of arrival (TOA) measurements. Existing studies assume that positions of receivers are perfectly known. However, in practice, receivers' positions might be inaccurate, which leads to localization error of targets. We propose factor graph (FG)-based belief propagation (BP) algorithms to locate the passive targets and improve the position accuracy of receivers simultaneously. Due to the nonlinearity of the likelihood function, messages on the FG cannot be derived in closed form. We propose both sample-based and parametric methods to solve this problem. In the sample-based BP algorithm, particle swarm optimization is employed to reduce the number of particles required to represent messages. In parametric BP algorithm, the nonlinear terms in messages are linearized, which results in closed-form Gaussian message passing on FG. The Bayesian Cramer-Rao bound (BCRB) for passive targets localization with uncertain receivers is derived to evaluate the performance of the proposed algorithms. Simulation results show that both the sample-based and parametric BP algorithms outperform the conventional method and attain the proposed BCRB. Receivers' positions can also be improved via the proposed BP algorithms. Although the parametric BP algorithm performs slightly worse than the sample-based BP method, it could be more attractive in practical applications due to the significantly lower computational complexity.