Analysis of Phase-Tracking Methods for Low Flux Millisecond Period X-ray Pulsars to Aid Spacecraft Navigation

Kevin D. Anderson, Darryll J. Pines

Peer Reviewed

Abstract:	X-ray pulsars are potential navigational aids for spacecraft due to their periodic, unique, and stable signals. Phase tracking directly exploits the periodic nature of the pulsar signal to determine a spacecraft’s position and velocity. This allows for more frequent estimates than other x-ray pulsar navigation methods with long observations. The initial concept of phase tracking breaks the observation into small blocks where the pulsar signal frequency is assumed constant. A maximum likelihood estimator (MLE) for initial phase and a second-order digital phase-locked loop (DPLL) track the phase at the detector assuming a nonhomogeneous Poisson Process (NHPP) model for the photon events. This method worked well in previous research with the Crab Pulsar and a one second block. For pulsars with lower flux this method breaks down due to the tradeoff between keeping the DPLL block sizes short and the reality that few photons will arrive in each block. Most MSPs have fluxes that are multiple orders of magnitude lower than the Crab. A new technique is investigated that builds on the original phase tracking structure. A parabolic model for phase evolution is generated from previous velocity and acceleration estimates from a third-order DPLL. This removes the constant frequency assumption, allowing for longer blocks. Four MSPs are considered: B1821-24, B1937+21, J0218+4232, and J0437-4715. The MLE performance for each pulsar is compared to the Cramer-Rao bound. The phase-tracking algorithm will be tested on simulated trajectories including constant acceleration and sinusoidal one-dimensional trajectories along the line-of-sight to each pulsar and part of the Cassini mission cruise. The new algorithm tracks all four pulsars. The average position error after 10 hours on the constant acceleration trajectory, when starting in lock, is -5.7 km for J0437-4715 and below 400 m for the other pulsars. The velocity errors are tens of cm/s or less. It is shown that lower noise bandwidth brings improved tracking error with higher sensitivity to dynamical stress.
Published in:	Proceedings of the 2015 International Technical Meeting of The Institute of Navigation January 26 - 28, 2015 Laguna Cliffs Marriott Dana Point, California
Pages:	554 - 565
Cite this article:	Anderson, Kevin D., Pines, Darryll J., "Analysis of Phase-Tracking Methods for Low Flux Millisecond Period X-ray Pulsars to Aid Spacecraft Navigation," Proceedings of the 2015 International Technical Meeting of The Institute of Navigation, Dana Point, California, January 2015, pp. 554-565.
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