Observability Analysis of Synchronous Location and Timing with X-ray Pulsars

In the X-ray pulsars navigation,clock errors are one of the most important factors that influence the navigation and could not be neglected.The clock errors are extended as the state variable based on the observability rank condition of nonlinear system.The system of synchronous location and timing based on X-ray pulsars is proved to be observable,which supplies theoretic proof to the application of navigation based on X-ray pulsars.