The navigating method for XNAV (X-ray pulsar-based Navigation) is similar the one of the Differential GPS (DGPS). In order to position and navigate the spacecraft (or satellite), the two Time of Arrival (TOA) from one X-ray pulsar to both the spacecraft and the solar system barycenter are demanded respectively. The difference between the two TOA is generally called the transformation equation of time. But the existent transformation equation of time is not good enough. In this paper, improvements have been made on some current expressions. The time difference between photon arrival at the observation spacecraft and solar system barycenter in XNAV is presented. It is based on the post-Newtonian approximation spacetime theory in GTR and the neglection of celestial bodies spin of the solar system as well as the effect of eccentric orbit. These considerations are reasonable under the condition that the precision of measure time magnitude is in the order of the nanosecond. The transformation of the proper time from observation spacecraft to BCT (Barycentric Coordinate Time) is also obtained. Based on this relation, a proposal is presented that the frequency of clock at spacecraft can be adjusted in the same way as GPS.
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