UKF稳定性研究及其在相对导航中的应用

讨论了UKF应用于状态方程为线性,测量方程为非线性对象时的稳定性问题。文中给出了一个UKF保持稳定的充分条件,指出适当增加过程噪声和测量噪声方差阵的设置值,有利于保证UKF的稳定性。本文还将UKF应用于航天器相对导航滤波器设计,通过数学仿真和理论分析证实了文中有关UKF稳定性结论的正确性。本文所得到的结论为将UKF应用于实际工程,特别是航天器相对导航滤波器设计,提供了理论参考。

Stability Analysis of UKF and Its Application in Relative Navigation

In this paper, the authors analyse the stochastic stability of the UKF for nonlinear stochastic discrete-time system with linear transition function. It is shown that the estimation error remains bounded if the system satisfies the sufficient conditions, and adjusting the covariance matrixes of system noise and measurement noise could improve the performance of stochastic stability. At last, the UKF is applied to the design of relative navigation filter. The numerical simulation of the designed filter verifies these results of stochastic stability. The results of this paper are valuable theory reference for application of UKF in practice, especially in relative navigation.