On the Equation of Position Measurement of XNAV

The equation of position measurement of XNAV (X-ray pulsar-based autonomous navigation) reveals the relation between the time of arrival (TOA) of an X-ray photon and the spacecraft position at this moment. In specific dis- cussions of navigation, the TOA is generally replaced by the difference between the TOA and a preset “time reference”, and the spacecraft position is expressed by the position vector in the barycentric system of the solar system. The “time reference” may be the true TOA at the solar-system barycenter (SSB), or an “equivalent TOA” at SSB. As the true TOA at SSB is difficult to obtain, the “equivalent TOA” is more convenient for navigation. The equations of position measurement based on the two kinds of “time reference” are discussed, the equa- tion based on the “equivalent TOA”, which has the time accuracy of 0.1 ns, is given, and the physical meanings of the every term in which are analyzed.