Objectives  At present, the numerical simulation of X-ray pulsar radiation signals is essential for the research on pulsar navigation. It can generate observation signals of any quantity and quality according to the demand. It is thus more cost-effective, maneuverable, and flexible than physical simulation, with great significance for the performance evaluation of pulsar navigation.

  Methods  The development of simulation technologies of X-ray pulsar radiation signals is reviewed, and the current numerical simulation methods of X-ray pulsar signals based on the non-homogeneous Poisson process are analyzed. Then, a numerical simulation method combining the homogeneous Poisson process with classical probability is utilized, and the specific process of numerical simulation is discussed in detail.

  Results  With the flux density functions of the Crab and B1509 pulsars, the time of arrival (TOA) of the signals of the two X-ray pulsars is numerically simulated in different observation periods. Then, the pulse profiles of the two pulsars are folded through Pearson chi-square statistics. The experiments show that for a certain pulsar, a longer observation time means more bins used in the process of pulse profile folding and a generated pulse profile closer to the profile template. For different pulsars, a sharper pulse profile and a smaller pulse half-width indicate a more accurate pulse profile generated over the same observation time. As a result, the X-ray pulsar radiation signals simulated by this method can fold according to certain periods for the generation of pulse profiles, and the results are generally consistent with the existing space observation results. This proves that the proposed simulation method is feasible.

  Conclusions  Compared with the simulation method based on the non-homogeneous Poisson process, the proposed method saves the effort of solving the integral of the flux density function and the inversion of the integral function, thereby greatly simplifying the calculation process of numerical simulation. It is suitable for the simulation of pulsar radiation signals with any flux density.