The Research On Timing Model Of The Pulsar Navigation In The Theory Of General Relativity

A pulsar is a natural body with high pressure, high temperature, high density, and highelectromagnetic field. Its most notable feature is rotating fast, and can emit pulses periodically,so it can be used as the reference frame for time keeping and autonomous navigation, and it isan important research area at present.Timing model is the theoretical basis in the pulsar navigation system. The high precisiontiming model is very important while the high precision navigation is considered. As the pulsaris very distant from us, the timing model should be at least discussed at the space-time scales ofthe solar system. Because the general theory of relativity has changed the traditional cognitionof the space-time, the relativistic issues are the keys to establish the timing model. Generally,the relativistic issues in the pulsar navigation can be summarized into two aspects, one is thescale conversion of the space-time, and the other is transformation of the pulse TOA. Aiming atthese relativistic issues in the timing model, the relativistic effects in the spherically symmetricgravitational filed and axially symmetric gravitational filed are derived, timing models forsingle pulsar and binary pulsar are gained, meanwhile, the error sources of the pulsar navigationare analyzed and the relativistic references of the space-time are discussed.In this thesis, the development of theory and application at home and abroad in the area ofthe pulsar timing and navigation are summarized. The relativistic issues in pulsar navigation areintroduced briefly. The post-Newtonian approximation theory and the multi-referenceapproximation system are introduced, equations for the light propagation, signal deflection andthe periastron precession in spherically symmetric metric field and Reissner-Nordstr m metricfield are derived, and equations for the light propagation and signal deflection in Kerr metricfield are derived. For single pulsar, the TOA equation in1PN metric field is derived, based onthis equation, the1PN timing model for navigation is given, and differences between two kindsof observation models are compared. The2PN timing model is derived while the angularmomentum and quadruple moment of the celestial body is considered. Taking into account thenear-Earth spacecraft, the preliminary models for navigation based on the Geocenter is derived.The pulsar distribution, rotation and other properties of the binary pulsar is analyzed based onthe ATNF database. The timing model for binary pulsar is derived in the Newtonian mechanicsbase on the BT model, and the parameters fitting method for BT model is improved, the timingmodel for binary pulsar navigation is derived in the Newtonian mechanics, and thepost-Newtonian correction formula is gained, the post-Newtonian orbit perturbation for binarypulsar due to the rotation of the pulsar and companion star is given. Depended on the derivation of the timing models, the error sources for pulsar navigationare analyzed. First, the error sources in single pulsar navigation are studied. The main errorsources in the single pulsar navigation include the errors of the position of pulsar and theassumed position of celestial bodies, the errors of planetary ephemeris, and so on. Thedifferences of gravitational delay for various orbits are compared, the gravitational delay by thequadruple moment and angular momentum are analyzed, and the gravitational bending by theplanetaries of solar system is calculated. Second, the errors in binary pulsar timing model arestudied, which include the time error due to the orbital elements, the gravitational delay due tothe companion star, the post-Newtonian correction of orbital elements, the correction of theorbital elements due to the perturbation of the rotation of the pulsar and companion star.At last, the relativistic space-time reference system is introduced, which includes thedefinition and realization of the relativistic celestial reference system and conversions betweenthem. The1PN conversion expression between BCRS and GCRS is derived; the TOAtransformation expressions for different types of onboard clocks are derived. The issuesconcerning the TOA transformation are preliminary discussed.The main innovations of the paper are:1. Considering the gravitational bending effect of the signal propagation, the1PN TOAequation is derived. The mistakes in the some reference literatures are revised, the2PN TOAequation is derived when the angular momentum and the quadruple moment of celestial body istaken into account. Considering the needs of the near-Earth spacecraft, the preliminary modelsfor navigation based on the Geocenter is derived.2. The BT timing model for binary pulsar system is improved, and the timing model forbinary pulsar navigation is derived in Newtonian mechanics, and the post-Newtonian correctionformula is gained.3. The error sources in the pulsar navigation are analyzed by numerical simulation in thegeneral theory of relativity.4. The conversion method for the TOA of the onboard clock in different kinds of orbits isgiven.