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

TL;DR

The paper tackles the challenge of accurate GNSS positioning in urban environments by moving from grid-based shadow matching to a set-based approach that also leverages GNSS reflections. It introduces ZSRM, which represents buildings and city geometry with constrained zonotopes and computes both shadows and reflections to progressively shrink the 2D receiver position set. Field tests in an urban corridor show that ZSRM can substantially reduce RMS horizontal error and cross-/along-street bounds relative to ZSM, albeit with higher processing time and reliance on robust signal classification. The work demonstrates the practical value of jointly exploiting shadows and reflections for urban GNSS and outlines avenues for robustness enhancements and multi-signal integration.

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.

Figures (18)

• Figure 1: Illustration of GNSS signal reception conditions: LOS-only, NLOS-only, and LOS + NLOS.
• Figure 2: (a) In the grid-based approach, each red grid point represents a candidate receiver position. (b) In the set-based approach, the magenta region represents the entire set of candidate receiver positions.
• Figure 3: Comparison of key differences between the existing ZSM and the proposed ZSRM methods. Subfigures (a)--(c) illustrate ZSM, while subfigures (d)--(f) illustrate ZSRM.
• Figure 4: Examples of set operations (convex hull, Minkowski sum, and intersection) with 2D constrained zonotopes. The orange and blue 2D constrained zonotopes represent $Z_1$ and $Z_2$, respectively, while the black 2D constrained zonotopes are the results of the set operations between them (adapted from Althoff24:CORA).
• Figure 5: GNSS shadow extraction method in the existing ZSM. The shadow direction is shown with thick black arrows, the shadow volume in blue, and the GNSS shadow in black. The ground plane, shown in yellow, is fundamentally 2D but is illustrated with added thickness for visual clarity (adapted from Fig. 2 in Bhamidipati22:Set).