X-ray pulsar-based airborne clock error estimation using Gaussian process

In order to autonomously calibrate the airborne clocks of deep space explorers, this paper proposes an X-ray pulsar-based airborne clock error estimation method. A pulse phase propagation model incorporating the clock error is derived. Given that both the clock noise and the pulsar timing noise are of power-law spectral densities, their combination is modeled as a Fractional Brownian Motion (FBM) with a fractional-order power spectral density. The clock error series is modeled as a Gaussian Process (GP) with a mean function in the form of 2-order polynomial and an FBM-based covariance function. Finally, the clock error and the hyperparameters of GP are fast estimated by an iterated estimation method. The proposed method is validated via the real clock error data of the G05 satellite in the Global Positioning System (GPS) and the real data of pulsars from the Neutron star Interior Composition ExploreR (NICER).