Intersection of Error Ellipsoids from at Least Two Positioning Sensors for Improved Sensor Fusion

Patrick Henkel, Medeea Horvat, and Luka Sachße

Peer Reviewed

Abstract: Autonomous driving requires a precise and reliable positioning. A sensor fusion of multiple complementary sensors (e.g. Global Navigation Satellite System (GNSS) receivers, inertial sensors, odometry, camera, Lidar, Ultra-Wide Band) is typically performed to achieve the objectives of both high precision and high reliability. A sensor fusion relies on an accurate knowledge of the measurement statistics. For static GNSS receivers, this assumption is typically well justified as multipath errors are only slowly changing with time. Henkel and Sperl (2016) and Henkel et al. (2016) showed that pseudorange multipath errors can be estimated as additional state parameters within the RTK and PPP solution. Unfortunately, an accurate knowledge of the measurement statistics is often not available for kinematic receivers in challenging environments: More specifically, the number of measurement epochs needed to estimate the measurement statistics is in urban environments often much larger than the number of epochs with equal statistics, e.g. a car can pass below a tree within one second, and thereby drive from an area with excellent satellite visibility via a severe multipath environment to another area with very good satellite visibility. This shows the need for a verification and adaption of the GNSS measurement statistics with the help of other sensors. In this paper, we propose a method that checks the consistency of the error ellipsoids from different sensors by searching a common intersection point of all ellipsoids. We provide a general numerical approach as an analytical solution exists only for the intersection of two ellipsoids. The proposed method should be applied as part of the pre-processing to improve the statistics of the measurements from each sensor. We show that the proposed method is numerically very efficient, i.e. it can reduce the number of samples needed to find the intersection by up to two orders of magnitude compared to a brute-force search.
Published in: Proceedings of the 2023 International Technical Meeting of The Institute of Navigation
January 24 - 26, 2023
Hyatt Regency Long Beach
Long Beach, California
Pages: 1110 - 1117
Cite this article: Henkel, Patrick, Horvat, Medeea, Sachße, Luka, "Intersection of Error Ellipsoids from at Least Two Positioning Sensors for Improved Sensor Fusion," Proceedings of the 2023 International Technical Meeting of The Institute of Navigation, Long Beach, California, January 2023, pp. 1110-1117. https://doi.org/10.33012/2023.18641
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