基于可观测度分析的稳定姿态滤波器

Stable Extended Kalman Filter for Attitude Determination Based on Observability Analysis

提出一种适用于惯性/天文组合航天飞行器的稳定姿态滤波器,可以在不降低系统可观测度的前提下解决滤波计算中的奇异问题。对于奇异问题的传统解决方案是删除观测方程的一行,通过对比删除前后系统可观测度的变化,证明此解决方案会导致系统可观测度下降,并指出如何选择最优删除方案以使系统可观测度下降最小。根据对传统解决方案的分析结果,提出了不降低系统可观测度的投影算法。理论分析和仿真试验证明,应用了投影算法的姿态滤波器更为稳定,估计效率更高。

This article presents a stable extended Kalman filter algorithm for spacecraft attitude determination by means of angular rate and vector observation. The filter using the proposed algorithm can solve the singularity in the filtering computation without any loss of system observability degree. The traditional singularity-solving method is to delete a line from the measurement equation. By comparing the system observability degree after and before the line deleting,it is proved that the traditional method tends to decrease the system observability degree. This article also proposes a method to choose the optimal deleting line to reduce the obser-vability degree loss to a minimum. The proposed projection algorithm gives a general solution to the singularity problem without observability degree loss. Theoretical analysis and numerical simulation show that an attitude filter using the projection algorithm provides more stable performance and higher estimation efficiency than one using the traditional method.