重构X射线脉冲星信号的纯数值模拟新算法

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。

A new numerical simulation algorithm for the reconstruction of X-ray pulsar signal

For navigation using X-ray pulsars, both technique investigation and simulation relay on the X-ray pulsar signal, which is recorded as TOA(time of arrival) by detectors. Because of the unknown pulse phase of detected data, generating photon TOAs of X-ray pulsars is necessary for simulation of algorithms. Based on the fact that the arrival of photons possess nonhomogeneous poisson random process, the modle of the signal of X-ray pulsars is built, and the epoch folding algorithm for pulse profile construction is presented. Two existed simulation algorithm are presented. A new numerical simulation algorithm for the reconstruction of photon TOAs is derivated from distributive function and its inverse function. To avoid approximating in the two algorithms, the derivated algorithm employs the pulse profile fitted by piecewise linear function. The signal of pulsar PSR B0531 21 is simulated, and chi-square goodness-of-fit-test is ultilized to demonstrate that the simulated TOAs follow the poisson distribution. Comparison is implemented among the new and the existed two algorithems, which indicates that the new algorihem is excellent in phonton counts and error of pulse profile. Observed pulse profiles approaches to the standard template profile as observation time increses, which demonstrates that the simulation algorithm is feasible, and the X-ray pulsar signal can be reconstructed effectively.