A Direct Phase Estimation Method of X-ray Pulsar Signal Without Epoch Folding

X-ray Pulsar Navigation (XPNAV) is an attractive method for the future deep space autonomous navigation. Currently, techniques for the phase estimation of X-ray pulsar radiation involves maximization of generally non-convex object functions based on average profile from epoch folding method, which results in suppression of useful information and high computation. In this paper, a new maximum likelihood (ML) directly utilizing the measured Time of Arrivals (TOAs) is present. The x-ray pulsar radiation will be traded as a cyclostationary process and the TOAs of the photons in a period will be redefined as a new process, whose probability distribution function is the normalized standard profile of the pulsar. We proved the new process is equivalent to the general used Poisson model. Then, the phase estimation problem is recast as a cyclic shift parameter estimation process under ML estimation, and we also put forwards a parallel ML estimation method to improve the ML solution. Furthermore, numerical simulation results show how the herein described estimator present a higher precision and reduced computation complexity compared with the current estimators.