Second-differenced Pulsar Measurement Based on Phase and Doppler Frequency Shift for Binary Pulsar Navigation

Fewer isolated pulsars are available for X-ray pulsar navigation, and they are unevenly distributed spatially. In contrast, the number of available binary pulsar for navigation is promising. However, the challenges of using binary pulsars as navigation pulsars is significant time-varying systematic errors. Therefore, to develop a measurement model suitable for both binary pulsars and isolated pulsars, while effectively mitigating timevarying systematic errors, achieving significant navigation accuracy, we propose a second-differenced measurement model based on the phase and Doppler frequency shift of binary pulsars. To linearize the measurement model and reduce the impact of distance on systematic errors, we developed a first-differenced measurement model based on phase difference and Doppler frequency shift. To further suppress time-varying systematic errors, we propose a second-differenced measurement model, which is the difference between the first-differenced measurement model at the neighboring filtering time. For deep space spacecraft, time-varying systematic errors are of significant magnitude but change slowly over the filtering period. Therefore, the second-differenced measurement model effectively mitigates the majority of these errors. In addition, to address the issue of increased random errors caused by the seconddifferenced model, we derived a differential noise covariance matrix that can effectively suppress random errors within the traditional Extended Kalman Filter (EKF) framework. The simulation results demonstrate that the proposed method can simultaneously utilize binary pulsars and isolated pulsars for navigation. It effectively suppresses the impact of time-varying systematic errors, including pulsar direction error and linearization error, leading to improved navigation accuracy.