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

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. © 2019, Editorial Department of Control Theory & Applications. All right reserved.