Bayesian Filtering for Joint Multi-User Positioning, Synchronization and Anchor State Calibration

Abstract

Millimeter (mmWave) positioning can go beyond classical localization, allowing to extract more complete situational awareness in terms of, e.g, clock offsets, antenna orientations or landmark locations. In this article, we formulate an extended Kalman filtering (EKF)-based framework called MU-PoSAC ( <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</u> ulti- <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U</u> ser <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Po</u> sitioning, <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</u> ynchronization and <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</u> nchor State <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</u> alibration), that allows to jointly estimate and track the locations and clock offsets of multiple users together with the unknown locations and orientation offsets of the anchors, building on angle-of-arrival (AoA) and time-of-arrival (ToA) measurements. We provide an extensive set of numerical results in the context of mmWave 5 G New Radio (NR) deployment in an industrial facility with moving robots and other industrial vehicles, incorporating full-scale ray-tracing for accurate propagation modeling as well as actual uplink reference signal based AoA and ToA estimators. Our numerical results show that estimating and tracking the overall system state is feasible, and that a single reference anchor can further enhance the estimation accuracy. In addition, more users are shown to lead to better performance, due to the beneficial coupling of the anchor state. Therefore, our study demonstrates that in order to maximize the estimation performance, it is desirable to have at least one anchor state precisely known, and to have multiple users in the system. Finally, the important practical aspect of Line-of-Sight (LoS) blockage is addressed. It is shown that in the considered industrial use case, the proposed MU-PoSAC framework can offer robustness against intermittent LoS blockage.