X-ray pulsars are potential aids to spacecraft navigation due to the periodicity, uniqueness, and stability of their signals. As the load on the deep space network increases in the future, techniques to navigate with less frequent communication will become desirable. Improved methods of x-ray pulsar-based spacecraft navigation (XNAV) are developed, analyzed, and confirmed over multiple simulated scenarios. A phase-tracking algorithm modeled at the level of individual photon arrivals provides improvements over the current state of the art, and a novel phase maximum likelihood estimator (MLE) is proposed. Relaxing the constant signal frequency assumption with a second-order Taylor polynomial phase model and feedback of frequency and frequency derivative from a third-order digital phase-locked loop is shown to overcome previous phase tracking difficulties due to low flux with millisecond period pulsars (MSPs), which have the best navigation characteristics.

Empirical MLE tests are performed to determine threshold observation times for convergence to the Cramer-Rao Bound. A lower limit is identified due to Poisson statistics and an upper limit due to orbit dynamic stress. For a 1 m^2 detector, one second for the Crab pulsar and 4000 seconds for the lowest flux MSPs are required. An analytical method is presented to predict the necessary threshold observation times for signals with pulse widths under 0.15 cycles.

Simulations are performed for dynamic stress conditions including two heliocentric trajectories, a cislunar trajectory, and three Earth orbits. The Crab pulsar and four MSPs: B1821-24, B1937+21, J0218+4232, and J0437-4715 are investigated. Position errors of 2 to 7 km are shown for most of the MSPs along the interplanetary and cislunar trajectories. B1821-24 tracks on the Earth orbits with 1 – 2 m^2 detectors with 2.5 – 3.5 km error. B1937+21 and J0218+4232 require larger detector areas.

An extended Kalman filter combines multiple pulsar phase tracking range measurements for various observation schedules. Scenarios with one and three detectors are considered. Position error under 3 km is demonstrated for an interplanetary trajectory. Phase tracking shows great promise for deep space navigation and more limited potential in scenarios with greater orbital dynamics.