基于可观测性分析,研究了不同观测模型下的深空自主导航算法。从非线性系统的可观测性分析出发,利用微分几何理论求解出系统的可观测矩阵,并给出了系统的可观测度定义和状态变量的可观测度分析方法;将其应用于深空自主导航系统,分析了不同观测模型下导航系统以及轨道参数的可观测度,并将其作为观测模型的选取准则;根据可观测性分析结果,结合非线性扩展卡尔曼滤波,建立了不同观测模型对应的自主导航算法。最后,以深度撞击任务的实际飞行数据对文中的自主导航算法进行数值仿真,验证了导航系统可观测度与系统状态估计精度之间的关系,结果表明本文提出的可观测性分析方法是可行的。
In this paper,the autonomous navigation approaches for different observation models are studied based on observability analysis.Based on the observability analysis of the nonlinear system,the observability matrix is derived from the theory of differential geometry.Then,a method for measuring the observability index of the system is derived,and the analytical method of the observability index for state variable is given.The principle is applied in the autonomous navigation system for deep space.The observability indexes of navigation system corresponding to different observation models are studied,and the observability indexes of the orbital elements are investigated.The result of the observability analysis is used as a selection criterion of the observation model used in the navigation system.And then,the navigation approaches under different observation models are established by utilizing the extended Kalman filter.Finally,the autonomous navigation approach presented in the paper is validated by the practical data of a deep impact mission.The relation between the observability index of the navigation system and the estimation accuracy of orbit elements is verified,and the method of observability analysis is demonstrated to be feasible.