Zonotope Shadow and Reflection Matching: A Novel GNSS Reflection-Based Framework for Enhanced Positioning Accuracy in Urban Areas

Abstract: In urban areas, signal reception conditions are often poor due to reflections from buildings, resulting in inaccurate global navigation satellite system (GNSS)-based positioning. Various 3D-mapping-aided (3DMA) GNSS techniques, including shadow matching, have been proposed to address this issue. However, conventional shadow matching estimates positions in a discretized manner. The accuracy of this approach is limited by the resolution of the grid points representing the candidate receiver positions, making it difficult to achieve robust urban positioning and to ensure that the position estimate satisfies user-specified protection levels or safety bounds. To overcome these limitations, zonotope shadow matching (ZSM) has been proposed, which utilizes a set-based position estimate rather than grid-based estimates. ZSM calculates the GNSS shadow--an area on the ground where the line-of-sight (LOS) is blocked and only non-line-of-sight (NLOS) signals can be received--to estimate the receiver's position set. ZSM distinguishes between LOS and NLOS satellites, determining that the receiver is inside the GNSS shadow if the satellite is NLOS and outside if the satellite is LOS. However, relying solely on GNSS shadows limits the ability to sufficiently reduce the size of the receiver position set and to precisely estimate the receiver's location. To address this, we propose zonotope shadow and reflection matching (ZSRM) to enhance positioning accuracy in urban areas. The proposed ZSRM technique is validated through field tests using GNSS signals collected in an urban environment. Consequently, the RMS horizontal position error of ZSRM improved by 10.0% to 53.6% compared with ZSM, while the RMS cross-street and along-street position bounds improved by 18.0% to 50.1% and 30.7% to 59.3%, respectively.