Graphic method for observability and observable states analysis of inertial navigation systems

DOI编号  10.7641/CTA.2019.80441
2020,37(1):98-106

 作者 单位 E-mail 刘鹏 中北大学 pengliu@nuc.edu.cn 任一峰 中北大学 renyifeng@nuc.edu.cn 张亚 东南大学 吴常铖 南京航空航天大学

本文研究平台式惯性导航系统在静基座与动基座下的可观测性与可观测状态确定问题. 主要利用组合图论中的二分图与线性结构化系统中的动态图. 这种基于图论的方法, 不仅能够分析平台式惯性导航系统的可观测性, 而且可以用来确定具体的可观测状态. 针对静基座的情形, 利用二分图的匹配理论来分析可观测状态, 得到的可观测状态与已有的利用代数分析方法得到的相同. 对于动基座的情形, 通过建立分段定常系统分析方法与动态图的Menger-type linking分析方法之间的联系, 从图论的角度得出系统在机动运动下仍是不可观测的. 由于Menger-type linking分析可观测状态相对困难, 进一步引入广义二分图来分析动基座时不同运动状态下系统的可观测状态. 最后, 分别针对静基座和动基座时的惯性导航系统给出其可观测性与可观测状态的分析结果, 实例结果表明本文图论分析方法的简洁性和正确性.

This paper investigates the observability of platform inertial navigation systems under the stationary base and maneuver base, respectively. The main research methods are matching theory of bipartite graph and structural observability of linear system. This graphic approach not only can analyze the observability, but also can determine the observable states. For the stationary base case, the observable states associated with the left matching nodes of the bipartite graph. These results are consistent with the algebraic method. For the maneuver base case, we establish the relations between Menger-type linking and piece-wise constant system. It is difficult to obtain the observable states with Menger-type linking, so we present the extended bipartite graph for analyzing the observable states under different motions. At the same time, compared with the existing algebraic methods, we demonstrates the conciseness and correctness of our conclusion through two examples.