重构 X 射线脉冲星信号的纯数值模拟新算法

摘要

基于 X 射线脉冲星的导航技术，无论技术研究还是实验验证，都是以 X 射线脉冲星信号为基础。但是实际的观测数据无法确定其精确值，不便于进行导航算法的分析验证。因此，通过模拟算法重构 X 射线脉冲星信号十分必要。基于泊松分布建立 X 射线脉冲星信号模型，介绍脉冲轮廓的构建方法；介绍了两种纯数值的脉冲星信号模拟算法。针对这两种算法因近似导致信号模拟不精确的问题，提出一种基于精确光子流量函数的纯数值 X 射线脉冲星信号的模拟算法，该算法采用分段线性函数拟合的脉冲轮廓函数，基于分布函数及其反函数导出。模拟算法重构 PSR B0531＋21脉冲星的信号，并利用χ2拟合优度检验验证模拟算法生成的光子到达时间服从泊松分布。将提出的算法与两种已有的算法进行比较，仿真结果表明从光子数目和脉冲轮廓误差来看，提出的算法都优于其他两种算法，更接近实际信号。由新算法重构的脉冲星信号进行历元折叠得到观测脉冲轮廓，并将其与标准脉冲轮廓比较，发现随着观测时间的增长，观测脉冲轮廓趋近于标准脉冲轮廓，验证了模拟算法是有效可行的。%For navigation using X-ray pulsars,both technique investigation and simulation were based on the X-ray pulsar signal.But practically,the observation data was unable to confirm the exact value or the analysis of validation of navigation algorithm.Therefore,it was necessary for simulation algorithms to reconstruct X-ray pulsars.Based on the fact that the arrival of photons possess non-homogeneous poisson random process,the model of the signal of X-ray pulsars was built,and the epoch folding algorithm for pulse profile construction was presented. Two existed simulation algorithms were presented.A new numerical simulation algorithm based on the reconstruction of photon TOAs (time of arrivals)was derivated from distributive function and its inverse function.To avoid approximating in the two algorithms,the derivated algorithm employed the pulse profile fitted by piecewise linear function.The signal of pulsar PSR B0531 +21 was simulated,and chi-square goodness-of-fit-test was utilized to demonstrate that the simulated TOAs complied with the poisson distribution.Comparison was implemented among the new algorithm and the existed two algorithms.Simulation result indicates that the new algorithm is superior to the existed two algorithms in photon counts and pulse profile error.Observed pulse profiles approaches to the standard template profile as observation time increases,which demonstrate that the simulation algorithm is feasible,and the X-ray pulsar signal can be reconstructed effectively.