基于非齐次Poisson过程的脉冲星到达信号的最大似然相位估计

ML Phase Estimate for X-ray Pulsar Signal Based on Nonhomogeneous Poisson Process

摘要: 假设探测器速度恒定且仅考虑信号的一阶多普勒效应，给出了X射线脉冲星光子流到达的非齐次泊松（Nonhomogeneous Poisson）模型。研究了信号的相位即脉冲到达时刻（TOA）估计的最大似然函数法（ML），并推导了理论上的克拉美罗性能限（CRB）。最后，利用解析形式的脉冲轮廓函数，分别对Crab脉冲星和B1821-24脉冲星的相位估计进行了蒙特卡罗（Monte Carlo）仿真，对估计性能进行了分析和比较。研究和仿真实验表明：该分析方法能够有效分析X射线脉冲星的TOA误差估计，评估不同脉冲星的定时精度。

Abstract: The nonhomogeneous Possion model of photons arrival of X-ray pulsar was presented for the case in which the speed of the detector is constant and only the first-order Doppler effect is considered. The Maximum likelihood(ML) method on pulse phase estimation or time of arrival(TOA) was presented. The Cramer-Rao performance limit(CRB) was deduced. The Monte-Carlo simulations of ML for pulsar Crab and B1821-24 were done using their analytic pulse profile, and the performance was analyzed and compared with the theoretical CRB. Simulation results show that the method is an effective analysis tool for calculating TOA or phase accuracy of X-ray pulsar and would help to evaluate the timing precision of different pulsars.