Methods of Pulse Phase Tracking for X-ray Pulsar Based Spacecraft Navigation using Low Flux Pulsars

In this paper, the method of pulse phase tracking for X-ray pulsar based spacecraft navigation is expanded to accommodate signals arriving from pulsars with lower flux than the Crab Pulsar. Spacecraft position and velocity estimates can be calculated using phase and frequency estimates of an observed pulsar signal. This allows for nearly continuous updates of vehicle motion estimates over short time frames and eliminates the need to time transfer all of the arriving photons to an inertial reference at the solar system barycenter. Previous work in pulse phase tracking uses a maximum likelihood estimator (MLE) for initial phase and a second-order digital phase-locked loop (DPLL) with a one second block size. This technique accurately tracks phase and Doppler frequency using simulated photons modeling the output of the Crab Pulsar. This method breaks down when considering pulsars that have a lower flux. The main difficulty is balancing the need to keep DPLL block sizes short with the fact that very few photons arrive in any given block of the phase tracking algorithm. Most X-ray pulsars have fluxes that are multiple orders of magnitude lower than the Crab Pulsar. Two phase tracking methods for low flux X-ray pulsars are hypothesized and tested. The first involves removing the dynamics from the signal each block using estimates of the detectors velocity and acceleration. This parabolic phase model is used to compute an MLE for initial phase. The output is fed into a third-order DPLL to give estimates for the next block. The second method uses a three parameter MLE that is derived to estimate the phase, frequency, and frequency derivative of a pulsar signal. These estimates are sent to a frequency locked-loop assisted phase locked-loop. Both methods allow for longer blocks which is essential unless the detector area or background rejection is improved. The two methods are validated and compared on their ability to track detectors undergoing constant acceleration along the line-of-sight to a pulsar and to track a portion of the Cassini cruise trajectory using PSR B1821-24 and PSR B1937+21.