An X-ray pulsar/starlight Doppler deeply-integrated navigation method is proposed in this paper. A starlight Doppler measurement-aided phase propagation model, which can remove the orbital effect within the recorded photon Time Of Arrivals (TOAs), is derived, and guarantees that the pulse phase can be extracted from the converted photon TOAs using computationally efficient methods. Some simulations are performed by a hardware-in-loop system to verify the performance of the integrated pulse phase estimation method as well as of the integrated navigation method. The integrated pulse phase estimation method could achieve an estimation performance similar to the existing method for orbiting vehicles at the cost of much less computational complexity, is capable of handling the signals of millisecond pulsars, and is applicable to various vehicles. In addition, the proposed integrated navigation method could provide reliable positioning results for various vehicles.

A pulse phase estimation of an X-ray pulsar with the aid of vehicle orbital dynamics is proposed. The original continue-time X-ray pulsar signal model is modified to be a term of vehicle position and velocity varying with time, and a modified definition of pulse time of arrival is given. The modified signal model is further linearized around the predicted position and velocity of the vehicle to the second order. The initial phase and the coefficients of the extended signal model can be estimated by maximum likelihood estimator. Some simulations are performed to verify the method and show the method has robustness to the initial error within initial state of the vehicle and is capable of handling the phase-estimation problem for pulsars with low fluxes.