Arithmetic of frequency drift and time delay between pulse profiles in XNAV

The frequency drift and time delay are two measurement variables of XNAV.Here we systematically discuss the computation method and propose some modifications.First,we further divide the bin into smaller time-interval,and presume photons received in each interval comply with binomial distribution.The folding of observed profile on such interval results in more accurate frequency drift.The second,the observe profile can be divided into ideal profile and the bias,and the time-of-arrival(TOA) is time lag between ideal profile and standard profile.We point out that Sala's TOA formula,derived with maximum of correlation function,only hold for ideal profile.The third,we prove that TOA's error caused by the bias of profile is a constant,in case the observe profile doesn't change during measurement.As above,the computation method of TOA is proposed and the precision of TOA can be smaller than the discern time of the detector.