Observability criteria for angles-only relative navigation to a near-earth asteroid

DOI编号  10.7641/CTA.2019.90822
2019,36(12):1979-1987

 作者 单位 E-mail 董天舒 北京空间飞行器总体设计部 d_tian4778@sina.com 王大轶 北京空间飞行器总体设计部 李文博 北京控制工程研究所

针对近地小行星仅测角相对导航系统的非线性可观测性分析问题, 本文基于非线性系统局部弱可观性理论给出了新的可观测性判据. 首先, 通过分析非线性系统李导数的共有属性, 给出了李导数梯度空间的共有子空间. 进一步, 利用该共有子空间和非线性系统局部弱可观性定义给出了新的可观性判据. 经理论证明, 该判据适用于非线性系统任意阶李导数, 并且给出的可观性结论可与高阶可观性矩阵秩判据的结论等价. 与传统的秩判据相比, 该判据具有无需进行高阶李导数运算, 无需进行高维矩阵运算的优点. 因此该判据适合在轨计算, 具有一定的工程价值. 最后仿真结果验证了可观性判据有效性.

Aiming to solve the problem of nonlinear observability analysis for angles-only relative navigation to the near-earth asteroid, a novel observability criterion is presented in this paper by the theory of nonlinear system locally weakly observability. Firstly, a common subspace of Lie derivatives gradients space can be determined from analyzing common features to the system Lie derivatives. Secondly, this paper proposes a novel observability criterion by combining the subspace of Lie derivatives gradients space and the definition of the nonlinear system locally weakly observability. The theory proves that the criterion applies to any orders of Lie derivatives of the nonlinear system, and the observability conclusion given is equivalent to the conclusion of the rank criterion of the higher-order observability matrix. Compared with the traditional rank criterion, this criterion has the advantage of not requiring high-order Lie derivative operations and high-dimensional matrix operations. As a result, this criterion is suitable for on-orbit calculation and has certain engineering value. Finally, the simulation results verify the validity of the novel observability criterion.