UKF参数估计在航天器气动辅助变轨问题中的应用

为快速精确地求解气动辅助变轨问题，提出一种基于无损卡尔曼滤波(UKF)参数估计的数值求解方法。首先，针对气动辅助变轨问题，利用极大值原理将其转化为对应的两点边值问题;然后，以协态变量的初值作为估计参数，以末端条件为期望观测值，将该两点边值问题转化为参数估计问题，并应用UKF滤波算法求解。该算法基于估计理论，避免了计算传统数值方法所需要的梯度矩阵，同时克服了猜测协态变量初值的困难，降低了求解气动辅助变轨问题的难度。数值仿真表明，该算法结构简单，求解效率高，具有良好的鲁棒性。

Application of UKF Parameter Estimation in Spacecraft Aeroassisted Orbital Transfer Problem

An algorithm based on the unscented Kalman filter (UKF) parameter estimation is proposed for the fast and efficient solution of the spacecraft aeroassisted orbital transfer problem. Firstly, the problem is converted to a two-point boundary value problem by using the maximum principle. Then the two-point boundary value problem is transformed into a parameter estimation problem which sets the initial values of the costates as the parameters to be estimated and the boundary values as the desired observations, and the converted problem is solved by using UKF. This algorithm is based on the theory of probability, so the derivation of the gradient matrices required by the traditional numerical methods is avoided. Moreover, the difficulty of guessing the initial values of the costates is overcome. Therefore, the difficulty of solving the spacecraft aeroassisted orbital transfer problem is greatly reduced. The numerical simulations indicate that the algorithm is simple, efficient and robust.