Maximum-likelihood TOA Estimation of X-ray Pulsar Signals on the Basis of Poison Model

The cycle-stationary Poison model for the photon arrival of X-ray pulsars and the estimation of the pulse's time of arrival (TOA) are discussed. Based on this model, the maximum likelihood estimation (MLE) of the TOA, as well as the Cramer-Rao boundary (CRB), are presented, especially the approximate formulation of the likelihood function and the Cramer-Rao boundary are derived for the low-RSN (signal-to-noise ratio) cases. By using the analytical pulse profile, we have made the Monte-Carlo simulation on the TOA estimation of PSR B1821-24, discussed the estimate error for different observation times and signal-to-noise ratios, and presented the corresponding RSN-thresholds. The results show that this method of data analysis can estimate effectively the timing accuracy of X-ray pulsar pulses and help to evaluate the corresponding performances in other applications.