Impact of the Pulsar's Direction on CNS/XNAV Integrated Navigation

Celestial navigation system (CNS) and X-ray pulsar-based navigation (XNAV) are two kinds of autonomous navigation methods for spacecraft. Because these two methods are complementary, CNS/XNAV integrated navigation is a feasible solution to improve the navigation accuracy and reliability. However, the pulsar's direction has a great impact on the navigation accuracy of CNS/XNAV integrated navigation because of the existence of measurement errors. In this paper, the analytic expression of the estimation errors of CNS/XNAV integrated navigation is deduced, based on which the impact of the pulsar's direction on the estimation errors is analyzed. A modified observability analysis method on the basis of the unscented Kalman filter is presented and applied to give the quantitative index of the pulsar's direction, whose observability matrix is constructed by the equivalent state transition matrix and measurement matrix. The equivalent state transition matrix is obtained through sigma points, and the equivalent measurement matrix is acquired with the help of the cross-covariance matrix and the predicted covariance matrix. Simulations demonstrate that the position and velocity estimation errors of CNS/XNAV integrated navigation increase exponentially with the angle between the pulsar's direction and the target body's direction. Both the error analysis method and the observability analysis method have been verified as suitable and effective for the analysis of the best choice for a pulsar in the CNS/XNAV integrated navigation system.