Abstract: X-ray pulsar-based navigation (XNAV) is a promising autonomous navigation technique for deep space spacecraft. To mitigate the impact of pulsar timing noise in XNAV, this paper proposes a stochastic differential equation (SDE) model for pulsar timing noise. Based on its fractional-order power spectral density (PSD) model, widely adopted in pulsar astronomy, pulsar timing noise is viewed as the output of a fractional-order shaping filter driven by white noise. The fractional-order transfer function of the shaping filter is approximated by a rational transfer function utilizing the Oustaloup approach, and the SDE model of the pulsar timing noise is then derived. Using the SDE model, an improved XNAV method is proposed that estimates pulsar timing noise along with the spacecraft's position and velocity. Experimental results based on simulated data and real data from NICER demonstrate that the derived SDE model performs well at characterizing pulsar timing noise in both the frequency and time domains. Compared with the conventional XNAV method, which does not account for pulsar timing noise, and the state-augmented (SA) approach with the first-order autoregressive (AR) model assumption, the proposed improved XNAV method achieves lower position estimation error. Compared with the SA approach with AR model assumption, the proposed method improved the position estimation accuracy by about 60%.

Key words: Pulsars, X-ray pulsar-based navigation, Pulsar timing noise, Shaping filter, Stochastic differential equation