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

Yi Lu, Ossi Kaltiokallio, Mike Koivisto, Jukka Talvitie, Elena Simona Lohan, Henk Wymeersch, Mikko Valkama

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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 ( M ulti- U ser Po sitioning, S ynchronization and A nchor State C 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.

Original languageEnglish
Pages (from-to)10949-10964
Number of pages16
JournalIEEE Transactions on Vehicular Technology
Issue number8
Publication statusPublished - Aug 2023
Publication typeA1 Journal article-refereed


  • 5G mobile communication
  • Anchor uncertainty
  • Clocks
  • Estimation
  • extended Kalman filter
  • joint synchronization and tracking
  • Location awareness
  • millimeter wave networks
  • multi-user positioning and tracking
  • orientation estimation
  • situational awareness
  • Synchronization
  • Uncertainty
  • Uplink

Publication forum classification

  • Publication forum level 3

ASJC Scopus subject areas

  • Automotive Engineering
  • Aerospace Engineering
  • Electrical and Electronic Engineering
  • Applied Mathematics


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