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

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.