A Pulse Time-Delay Estimation Method for XNAV: Nonuniformly Epoch Folding

X-ray-pulsar-based navigation 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 photon time-of-arrival data, this article proposes an improved method called nonuniform epoch folding (NUEF). Specifically, this article analyzes the mechanism of the traditional epoch folding (EF) method and then divides the traditional method into two key stages: density analysis and digital filtering. This article 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. The NUEF method abandons the characteristic that bins are uniformly distributed 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 the NUEF method. Specifically, the pulse time-delay estimation accuracy of the NUEF method is improved compared to the traditional EF method. Because of the elimination of the periodic search process, the computational complexity of the NUEF method decreases.