Deteriorated integrated profile aided pulse phase and Doppler frequency estimation for XNAV

Accurate estimation of pulse phase and Doppler frequency is crucial in X-ray pulsar-based NAVigation (XNAV). Current XNAV flight experiments commonly rely on the Maximum Likelihood Estimator (MLE) for the estimation of pulse phase and Doppler frequency. Although this method delivers exceptional precision, its computational demands are substantial due to the joint estimation of pulse phase and Doppler frequency. These demands are further exacerbated by the non-convex nature of the likelihood function. In this paper, a Deteriorated Integrated Profile (DIP) aided pulse phase and Doppler frequency estimation method is proposed. This method rapidly estimates pulse phase and Doppler frequency through merely three epoch-folding operations on the photon TOAs. These results constrain the pulse phase and Doppler frequency to a narrow range, which allows for the solution of the MLE problem at a low computational cost. The effectiveness of the proposed method is validated by numerical simulations.