Y. Lu*, O. Kaltiokallio*, M. Koivisto*, J. Talvitie*, E. S. Lohan*, H. Wymeersch†, and
M. Valkama*
* Department of Electrical Engineering, Tampere University, Finland
† Department of Electrical Engineering, Chalmers University of Technology, Sweden
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 (Multi-User Positioning, Synchronization and Anchor State Calibration), 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 5G 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.
IEEE Transactions on Vehicular Technology.
Videos and Demonstrations
The video demonstration shows the estimation and tracking behavior of the proposed MU-PoSAC algorithm, with 1m anchor location uncertainty and 6 degrees orientation offset uncertainty (variable definitions are given in the article).
Specifically, the left top subplot reflects the tracking performance from the top view, showing the horizontal tracking behavior of all the considered dynamic users (represented by cross markers) and static anchors (marked as red circles). The cyan colored dashed curves represent the true trajectories of the users, while the colored solid lines on top of them are the estimated trajectories. The ellipses (rather small in the plot) refer to the estimation uncertainty (2.5 sigma). The green cross markers are the initial user locations.
For better illustration, a zoomed view of anchor 3 is plotted in the left bottom subplot, where the red circle marker represents the ground truth location of the anchor together with the orientation in azimuth domain plotted in black solid line, while the green solid circle dot marker is the estimated anchor location together with the estimated orientation in azimuth domain plotted in red dashed curve. The green dashed ellipse shows the 2.5 sigma posterior uncertainty. The green triangle marker refers to the initial location of the anchor 3.
Moving towards the right, we have the 3D positioning errors as well as the clock offset errors manifested as a function of time. The same colors are used in conjunction with the corresponding colors used in the 2D plot above. On the right top corner, the errors of orientation offsets for all three anchors are given as a function of time.
The results herein are obtained based on the specific realizations in terms of the initial state and measurements. For the performance on average, please refer to the figures plotted in the Results section of the article.