A Method for Estimating X-Ray Pulsar Period and Pulse Time Delay: Applying the Improved Z²_n,bin -test to Complex Profiles

In order to apply the Z² statistic to the estimation of the navigation pulsar period and time delay, and thus further improve the accuracy of X-ray pulsar navigation, this paper proposes a method for estimating the pulsar period and time delay with complex profiles based on the improved Z n , bin 2 -test. Based on the prior information of the amount of photon data in the observation task, this method adaptively determines the optimal harmonic truncation order under different data qualities. In order to solve the problem of the change rate of complex profile signals being too fast, the binned data is rephased according to the principle of equal photon intensity segmentation within the bin, and the optimal number of bins suitable for the PSR B0531+21 pulsar is selected. Through simulation, a quantitative analysis was conducted on factors that affect the performance of the estimation algorithm, such as observation time, detector area, noise interference, etc. Simulation results show that the proposed estimation method has greater advantages when the observation time is short, the detector area is small, and the interference noise is large. In addition, the observation data of the PSR B0531+21 pulsar is processed and analyzed. The period estimation accuracy of the method proposed is 3.6532 ns, which is 39.57% higher than that of the χ²-test method. The method we proposed has the advantages of being suitable for navigation pulsars, strong environmental adaptability, high estimation accuracy, and strong estimation stability, which can further improve the performance of X-ray pulsar navigation.