Adaptive two-stage Kalman filter for X-ray pulsar navigation

In order to overcome the impact of pulsar position error on X-ray pulsar navigation results, this paper designs an adaptive two-stage Kalman filter. According to theoretical and numerical analysis, the influence of pulsar position error on navigation system is mainly reflected in the observation equation. Considering that the current common augmented algorithms have problems such as heavy computational burden and ill-conditioned values, this paper adopts a two-stage filtering method. In order to ensure that the new algorithm can effectively handle the navigation problem when the pulsar position error is time-varying, this paper adds an adaptive adjustment factor based on the traditional two-stage filter. The gain matrix of the secondary filter is controlled in real time by the adaptive adjustment factor to enhance the tracking performance of the algorithm. The final simulation results show that the new algorithm can reduce the position error by 18.9% and the velocity error by 24.3% compared with the ordinary two-stage Kalman filter.