Measure of observability for single-output systems and its application

For single-output nonlinear systems, a definition of observability index is given by using condition number, which is used to measure the degree of observability. The Restricted Three-Body system is then studied, the observability degree based on the observation of each element of position variable is given along a reference trajectory, corresponding results and the analysis method itself can help select observables for navigation of spacecraft in complex environments.