Mobile Localization in Non-Line-of-Sight Using Constrained Square-Root Unscented Kalman Filter

TL;DR

This paper introduces a constrained square-root unscented Kalman filter for mobile localization in NLOS scenarios, improving accuracy and stability by projecting sigma points onto feasible regions defined by TOA measurements.

Contribution

It develops a novel constrained SRUKF that reduces optimization complexity and enhances robustness for NLOS localization using TOA data.

Findings

Achieves lower localization error than existing methods

Demonstrates improved numerical stability and efficiency

Performs robustly under various NLOS conditions

Abstract

Localization and tracking of a mobile node (MN) in non-line-of-sight (NLOS) scenarios, based on time of arrival (TOA) measurements, is considered in this work. To this end, we develop a constrained form of square root unscented Kalman filter (SRUKF), where the sigma points of the unscented transformation are projected onto the feasible region by solving constrained optimization problems. The feasible region is the intersection of several discs formed by the NLOS measurements. We show how we can reduce the size of the optimization problem and formulate it as a convex quadratically constrained quadratic program (QCQP), which depends on the Cholesky factor of the \textit{a posteriori} error covariance matrix of SRUKF. As a result of these modifications, the proposed constrained SRUKF (CSRUKF) is more efficient and has better numerical stability compared to the constrained UKF. Through simulations, we also show that the CSRUKF achieves a smaller localization error compared to other techniques and that its performance is robust under different NLOS conditions.