A fast-moving horizon estimation method based on the symplectic pseudospectral algorithm

In this paper, a fast-moving horizon state estimation algorithm for nonlinear continuous systems with measurement noises and model disturbances is developed. The optimization problem required to be solved at each sampling instant is formulated into a backward nonlinear optimal control problem over the finite past. Once prior knowledge of the observed system is available, constraints can be further imposed. The highly efficient and accurate symplectic pseudospectral algorithm is taken as the core solver, which leads to the symplectic pseudospectral moving horizon estimation (SP-MHE) method. The developed SP-MHE is first evaluated by numerical simulations for a hovercraft. Then the developed method is extended to parameter estimation and applied to a chaotic system with an unknown parameter. Simulation results show that the SP-MHE can generate accurate estimations even under large sampling periods or large noise where regular filters fail. In addition, the SP-MHE exhibits excellent online efficiency, suggesting it can be used for scenarios where the sampling period is relatively small.

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