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A symplectic moving horizon estimation algorithm with its application to the Earth—Moon L2 libration point navigation

A symplectic moving horizon estimation algorithm with its application to the Earth—Moon L2... Abstract Accurate state estimations are perquisites of autonomous navigation and orbit maintenance missions. The extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are the most commonly used method. However, the EKF results in poor estimation performance for systems are with high nonlinearity. As for the UKF, irregular sampling instants are required. In addition, both the EKF and the UKF cannot treat constraints. In this paper, a symplectic moving horizon estimation algorithm, where constraints can be considered, for nonlinear systems are developed. The estimation problem to be solved at each sampling instant is seen as a nonlinear constrained optimal control problem. The original nonlinear problem is transferred into a series of linear-quadratic problems and solved iteratively. A symplectic method based on the variational principle is proposed to solve such linear-quadratic problems, where the solution domain is divided into sub-intervals, and state, costate, and parametric variables are locally interpolated with linear approximation. The optimality conditions result in a linear complementarity problem which can be solved by the Lemke’s method easily. The developed symplectic moving horizon estimation method is applied to the Earth-Moon L2 libration point navigation. And numerical simulations demonstrate that though more time-consuming, the proposed method results in better estimation performance than the EKF and the UKF. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Astrodynamics Springer Journals

A symplectic moving horizon estimation algorithm with its application to the Earth—Moon L2 libration point navigation

Astrodynamics , Volume 3 (2): 17 – Jun 1, 2019

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Publisher
Springer Journals
Copyright
2019 Tsinghua University Press
ISSN
2522-008X
eISSN
2522-0098
DOI
10.1007/s42064-018-0041-x
Publisher site
See Article on Publisher Site

Abstract

Abstract Accurate state estimations are perquisites of autonomous navigation and orbit maintenance missions. The extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are the most commonly used method. However, the EKF results in poor estimation performance for systems are with high nonlinearity. As for the UKF, irregular sampling instants are required. In addition, both the EKF and the UKF cannot treat constraints. In this paper, a symplectic moving horizon estimation algorithm, where constraints can be considered, for nonlinear systems are developed. The estimation problem to be solved at each sampling instant is seen as a nonlinear constrained optimal control problem. The original nonlinear problem is transferred into a series of linear-quadratic problems and solved iteratively. A symplectic method based on the variational principle is proposed to solve such linear-quadratic problems, where the solution domain is divided into sub-intervals, and state, costate, and parametric variables are locally interpolated with linear approximation. The optimality conditions result in a linear complementarity problem which can be solved by the Lemke’s method easily. The developed symplectic moving horizon estimation method is applied to the Earth-Moon L2 libration point navigation. And numerical simulations demonstrate that though more time-consuming, the proposed method results in better estimation performance than the EKF and the UKF.

Journal

AstrodynamicsSpringer Journals

Published: Jun 1, 2019

References