UKF参数估计在三体Lambert问题中的应用

Application of UKF parameter estimation in the three-body Lambert problem

为了快速精确地求解三体Lambert问题,提出了一种新的基于无损卡尔曼滤波(UKF)参数估计的数值求解算法,该算法由初值猜测和精确解求解两部分组成.首先,基于地月系统二体模型,通过简单迭代求解三体Lambert问题的初值.然后,将三体Lambert问题对应的两点边值问题转化为参数估计问题,通过UKF滤波算法求解,可得到收敛的精确解.该算法是基于概率估计理论的,不仅避免了传统数值方法推导相关梯度矩阵的复杂性,而且降低了三体Lambert问题对初值精确度的要求,从而显著降低了三体Lambert问题求解的难度.数值仿真表明,该方法求解效率较高,具有良好的鲁棒性,与微分修正算法、二阶微分修正算法对比具有更大的收敛域.

A new algorithm based on unscented Kalman filter（ UKF） parameter estimation was proposed for the fast and efficient solution of the three-body Lambert problem. The algorithm was divided into two steps,guessing the initial solution and searching the exact solution. The initial solution of the three-body Lambert problem was generated using the two-body model of the Earth-Moon system. Then the two-point boundary value problem corresponding to the original three-body Lambert problem was converted to a parameter estimation problem. Through solving the converted problem using UKF,the converged exact solution was found. The algorithm was based on the theory of probability,so the derivation of the gradient matrixes required by traditional numerical methods was omitted. Moreover,the demand for the accuracy of the initial solutions for the three-body Lambert problem was modified. Therefore,the difficulty of solving the three-body Lambert problem was greatly reduced. Numerical examples indicate that the algorithm is of high efficiency and robustness and obtains a larger convergence domain compared with the differential-correction method and the second order differential-correction method.