Novel Algorithm for X-Ray Pulsar Navigation Against Doppler Effects

In this paper, a new method for novel X-ray pulsar navigation is proposed to overcome the Doppler effects from the motion of a deep space explorer. An analysis was undertaken of the dynamic orbit model of the interplanetary trajectory cruise phase. During a pulsar signal observation period, the deep space explorer can be considered to be at a constant acceleration motion. A Doppler compensation method is proposed based on this analysis. The method demonstrates great advantages in terms of low computational cost. However, there is an evident bias due to the Doppler compensation in the pulse time-of-arrival (TOA). Moreover, the pulse TOA bias and the velocity estimation error of the deep space explorer are correlated, resulting in a decline in Kalman filter performance. To deal with this problem, we constructed a TOA measurement bias model with respect to the state estimation error, and we developed an extended Kalman filter (EKF) with correlated measurement bias and state estimation error. Results from simulations suggest that the proposed navigation method is feasible, accurate, and effective. The proposed navigation method based on EKF with correlated measurement bias and state estimation error proves to be more accurate than a traditional EKF-based method.