A condition number-based observability analysis method and its application in autonomous navigation system

The observability analysis of the autonomous navigation system is complicated due to nonlinearities of state equation and measurement equation. Firstly, the rationality of the condition number in the definition of observability degree of linear system is analyzed. Then, the observability matrix of a nonlinear system is deduced by utilizing the Lie derivative, and a measure method of observability for nonlinear system is derived based on the condition number. The method is applied to the autonomous navigation system of Earth-Moon transfer orbit. The observability under two measurement models, the line-of-sight vectors to the Earth and the Moon, are investigated in detail. Furthermore, the observability degree is used to determine the information-sharing factors dynamically, and combined with the extended Kalman filter to establish an information fusion autonomous navigation algorithm. Simulation results demonstrate the validity of the method of observability analysis. Numerical results show that the estimation accuracy of the orbit parameters meets the requirements for the Earth-Moon transfer orbit.