Investigation of X-ray Pulsar Signal Phase Tracking for Spacecraft Navigation

Abstract

X-ray pulsars are potential aids to spacecraft navigation due to their signal periodicity, uniqueness, and stability. A subset called millisecond period pulsars (MSPs) has the best timing characteristics. Pulse phase tracking is a method that directly exploits a pulsar’s periodic signal to determine spacecraft position. A method is proposed and simulated that overcomes previous difficulties with phase tracking of MSPs due to their low signal flux. The new method relaxes the constant signal frequency assumption used in previous phase tracking formulations by using a phase maximum-likelihood estimator with a second-order Taylor polynomial phase model and feedback of frequency and its first derivative using a third-order digital phase-locked loop. Simulations are performed over a variety of dynamic stress conditions by modeling a heliocentric trajectory of the MSL mission, a cislunar trajectory, and three Earth orbits: the ISS, a GPS satellite, and a DirecTV satellite. The Crab Pulsar and the four MSPs of PSR B1821-24, PSR B1937+21, PSR J0218+4232, and PSR J0437-4715 were investigated. All the pulsars considered, except J0437-4715, which has the lowest signal-to-noise ratio, navigated the MSL and cislunar trajectories with range errors on the order of 2 – 6 km. The B1821-24 signal is trackable on the Earth orbits considered with a detector area of 1 – 2 m^2 with errors on the order of 2.5 – 3.5 km. Pulsars B1937+21 and J0218+4232 required much larger detector areas to be successfully tracked while in the Earth orbits. Phase tracking, and XNAV in general, shows great promise for deep space scenarios such as the simulated MSL and cislunar trajectories. Higher dynamic stress scenarios are more challenging and limit the applicability due to the low flux of the desirable pulsars for navigation. An extended Kalman filter is simulated to combine multiple pulsar phase tracking observations in sequence along the MSL and cislunar trajectories, resulting in position errors under 3 km and 4 km, respectively.