Mixed-Integer Moving Horizon Estimation for Terrain-Aided Navigation Using Hybrid Zonotopes

Andrew F. Thompson, Joshua A. Robbins, Matthew E. Boler, and Herschel C. Pangborn

Peer Reviewed

Abstract:	Terrain-aided navigation uses topological features to localize a vehicle when other sensors, such as GPS, are unavailable. An aircraft can use a pair of altimeters to make local elevation measurements and compare these readings to a terrain map. Conventional methods of achieving this include Kalman filters and particle filters. The former can be prone to errors due to linearization and multi-modal distributions, and the latter can suffer from sampling limitations. This paper proposes a moving horizon estimation method that leverages the hybrid zonotope set representation and a structure-exploiting mixed-integer solver to perform computationally-efficient and accurate state estimation. Numerical results demonstrate the efficacy of the proposed methods using terrain data from central Pennsylvania and a notional trajectory. Index Terms—moving horizon estimation, terrain-aided navigation, hybrid zonotope
Published in:	2025 IEEE/ION Position, Location and Navigation Symposium (PLANS) April 28 - 1, 2025 Salt Lake Marriott Downtown at City Creek Salt Lake City, UT
Pages:	815 - 820
Cite this article:	Thompson, Andrew F., Robbins, Joshua A., Boler, Matthew E., Pangborn, Herschel C., "Mixed-Integer Moving Horizon Estimation for Terrain-Aided Navigation Using Hybrid Zonotopes," 2025 IEEE/ION Position, Location and Navigation Symposium (PLANS), Salt Lake City, UT, April 2025, pp. 815-820.
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