Wenjia Zhang

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.

To suppress the systematic errors of the X-ray pulsar navigation system (XPNAV) based on the phase and Doppler frequency shift, and eliminate singularity phenomena, a double-differenced autonomous navigation method is proposed. By considering the intrinsic spin phase and time propagation delay of the pulsar, the observation pulse phase models on the spacecraft and Mars were established. To linearize the measurement model, a phase-differenced model was developed by subtracting between the two phase models. To suppress the systematic errors in the phase-differenced model, a double-differenced model based on phase and Doppler frequency shift is proposed, which is the difference between the phase-differenced model at the neighbor filtering time. For a deep-space spacecraft, the magnitude of the systematic error is significant but changes slowly over the filtering period. Therefore, the double-differenced model can suppress the majority of systematic errors. In order to solve the problem of correlation between process and measurement noise, an improved extended Kalman filter (IEKF) method is proposed. The simulation results reveal that the proposed method can effectively suppress the impact of systematic errors, including the pulsar direction error and linearization error.

X-ray pulsar-based navigation (XNAV) is an ideal navigation mode for deep spacecraft. In order to overcome the time-varying frequency problem caused by the acceleration of spacecraft in the process of photons TOA data, this paper proposes an improved method called Non-uniform epoch folding (NUEF). Specifically, the paper analyzes the mechanism of the traditional EF method, and then divides the traditional method into two key stages: Density Analysis and Digital Filtering. Draws the conclusion that the key to limit the pulse time delay estimation accuracy of the traditional method is that the mathematical expectation of the photon density sequence obtained in the first stage of EF cannot maintain periodicity in a long observation time interval; Then the solution NUEF is given. NUEF method abandons the characteristic that bins uniformly distribute on time axis in traditional EF methods. This method uses the principle of equal phase interval to determine the position and length of each bin by introducing external velocity information, and theoretically overcomes the problem of time-varying frequency in the long observation interval; The simulation experiment verifies the effectiveness of NUEF method. Specifically, the pulse time delay estimation accuracy of NUEF method is improved compared to traditional EF method. And because of the elimination of the periodic search process, the computational complexity of the NUEF method has also decreased.