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).

As a new spacecraft autonomous navigation technology, X-ray pulsar-based Navigation (XNAV) is one of the most promising navigation technologies for deep space exploration. The concept of XNAV was proposed in the 1980 s. After decades of development, XNAV gradually moves from theoretical research to space experiments. This paper introduced the space experiments on pulsar navigation completed at home and abroad in recent years, analyzed the signal processing methods, navigation methods and the X-ray detectors used in XNAV space experiments, and summarized the shortcomings of China’s XNAV space experiments in terms of on-orbit calculation and X-ray detectors. Based on the current situation of space experiments and the practical needs of engineering applications, the future development needs of XNAV are discussed.

This article provides a review on X-ray pulsar-based navigation (XNAV). The review starts with the basic concept of XNAV, and briefly introduces the past, present and future projects concerning XNAV. This paper focuses on the advances of the key techniques supporting XNAV, including the navigation pulsar database, the X-ray detection system, and the pulse time of arrival estimation. Moreover, the methods to improve the estimation performance of XNAV are reviewed. Finally, some remarks on the future development of XNAV are provided.

An accurate period is important to recover the pulse profile from a recorded photon event series of an X-ray pulsar and to estimate the pulse time of arrival, which is the measurement of X-ray pulsar navigation. Epoch folding is a classical period estimation method in the time domain; however, its computational complexity grows as the number of trail periods increases. In order to reduce the computational complexity, this paper improves the fast folding algorithm through segment correlation and amplitude accumulation, which is based on the post-order traversal of a binary tree. Compared with epoch folding, the improved fast folding algorithm can achieve a similar accuracy at the cost of a lower computational burden. Compared with the original fast folding algorithm, the improved algorithm can be applied to detectors with a much smaller effective area. The performance of the method is investigated by simulation data and observation data from the Neutron star Interior Composition Explorer (NICER).