TY - JOUR T1 - Set-Valued Shadow Matching Using Zonotopes for 3D-Map-Aided GNSS Localization JF - NAVIGATION: Journal of the Institute of Navigation JO - NAVIGATION DO - 10.33012/navi.547 VL - 69 IS - 4 SP - navi.547 AU - Sriramya Bhamidipati AU - Shreyas Kousik, AU - Grace Gao Y1 - 2022/12/21 UR - https://navi.ion.org/content/69/4/navi.547.abstract N2 - Unlike many urban localization methods that return point-valued estimates, a set-valued representation enables robustness by ensuring that a continuum of possible positions obeys safety constraints. One strategy with the potential for set-valued estimation is GNSS-based shadow matching (SM) in which one uses a three-dimensional (3D) map to compute GNSS shadows (where line-of-sight is blocked). However, SM requires a point-valued grid for computational tractability, with accuracy limited by grid resolution. We propose zonotope shadow matching (ZSM) for set-valued 3D-map-aided GNSS localization. ZSM represents buildings and GNSS shadows using constrained zonotopes, a convex polytope representation that enables propagating set-valued estimates using fast vector concatenation operations. Starting from a coarse set-valued position, ZSM refines the estimate depending on the receiver being inside or outside each shadow as judged by received carrier-to-noise density. We demonstrate our algorithm’s performance using simulated experiments on a simple 3D example map and on a dense 3D map of San Francisco. ER -