Abstract: Application of unscented Kalman filter (UKF) algorithm in solving two-point boundary value problem (TPBVP) is a key technology in the indirect method of optimization problem solving algorithms,and usually the final solution can only be given through numerical iteration methods.Due to the high sensitivity and strong nonlinear dynamic characteristics of the two-point boundary value problem,the accuracy of the initial value of the numerical iteration is required to be very high,otherwise it is difficult to obtain a convergent solution.In order to reduce the requirements of the initial value accuracy,based on the UKF algorithm,an optimal parameter estimation method is given,which can be used to solve the two-point boundary value problem.This method adopts Gaussian distribution model,which can describe the original nonlinear problem with accuracy of second order or higher,and has a larger convergence range and stronger robustness.The example of spacecraft trajectory optimization verifies the effectiveness and reliability of this algorithm.

Key words: unscented Kalman filter (UKF), parameter estimation, two-point boundary value problem (TPBVP), trajectory optimization, Gaussian distribution, nonlinear

摘要： 两点边值问题求解是最优化问题间接法求解算法中的关键技术,通常只能通过数值迭代方法给出最终解。而由于两点边值问题的高敏度和强非线性动力学特性,对数值迭代初值的精度要求非常高,否则难以得到收敛解。为了降低对初值精度的要求,基于无损卡尔曼滤波算法,给出了一种最优参数估计方法,可用于两点边值问题求解。此方法采用高斯分布模型,可以二阶以上精度描述原非线性问题,具有较大的收敛域和较高的鲁棒性。通过航天飞行器轨迹优化算例,验证了此算法的有效性和可靠性。

关键词: 无损卡尔曼滤波, 参数估计, 两点边值问题, 轨迹优化, 高斯分布, 非线性