Pulsar Phase and Doppler Frequency Estimation for XNAV Using On-orbit Epoch Folding

This paper introduces a pulsar phase and Doppler frequency estimation method for X-ray pulsar-based navigation (XNAV) using on-orbit epoch folding. A modified phase propagation model is derived as a term of position of vehicle, taking the orbital motion of the vehicle into account. For a deep space explorer mission, a linearized pulsar phase model is derived, dividing the received phase into a predicted part and an estimated part. A framework called on-orbit epoch folding is provided. The framework consists of removal of vehicle orbital motion effect, search for the period of converted photon time of arrivals (TOAs), and estimation of the initial phase. The removal of vehicle orbital motion effect can convert the original photon TOAs with a time-varying frequency into a photon TOA with a constant frequency. A cost function for the search for the period is derived by describing the empirical profile as a histogram and by maximizing the log-likelihood function of histogram. And the initial phase problem can be well solved by existing algorithms. Simulations have shown that the proposed method is feasible to various vehicles in deep space.