A symplectic moving horizon estimation algorithm with its application to the Earth–Moon L2 libration point navigation
moving horizon estimation, symplectic method, quasilinearization, variational principle, L2 libration point, navigation
Accurate state estimations are perquisites of autonomous navigation and orbit maintenancemissions. The extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are themost commonly used method. However, the EKF results in poor estimation performance forsystems 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 symplecticmoving horizon estimation algorithm, where constraints can be considered, for nonlinearsystems are developed. The estimation problem to be solved at each sampling instant isseen as a nonlinear constrained optimal control problem. The original nonlinear problem istransferred into a series of linear-quadratic problems and solved iteratively. A symplecticmethod 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 parametricvariables are locally interpolated with linear approximation. The optimality conditions resultin 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–MoonL2 libration point navigation. And numerical simulations demonstrate that though moretime-consuming, the proposed method results in better estimation performance than theEKF and the UKF.
Tsinghua University Press
Xinwei Wang,Haijun Peng,A symplectic moving horizon estimation algorithm with its application to the Earth—Moon L2 libration point navigation.Astrodyn.2019, 3(2): 137–153.