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

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.