PT  - JOURNAL ARTICLE
AU  - Sriramya Bhamidipati
AU  - Shreyas Kousik,
AU  - Grace Gao
TI  - Set-Valued Shadow Matching Using Zonotopes for 3D-Map-Aided GNSS Localization
AID  - 10.33012/navi.547
DP  - 2022 Dec 21
TA  - NAVIGATION: Journal of the Institute of Navigation
PG  - navi.547
VI  - 69
IP  - 4
4099  - https://navi.ion.org/content/69/4/navi.547.short
4100  - https://navi.ion.org/content/69/4/navi.547.full
SO  - NAVIGATION2022 Dec 21; 69
AB  - 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.