The Timing Equation in X-Ray Pulsar Autonomous Navigation
The timing equation is the basic theory of dealing with the observable data of pulsar. The pulse timing model is studied; With analyzing the existing conclusions about timing equations, the transformation equation of pulsar photon time of arrive in 1PN ap
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The Timing Equation in X-Ray Pulsar Autonomous Navigation Qingyong Zhou, Jianfeng Ji and Hongfei Ren
Abstract The timing equation is the basic theory of dealing with the observable data of pulsar. The pulse timing model is studied; With analyzing the existing conclusions about timing equations, the transformation equation of pulsar photon time of arrive in 1PN approximation is derived, and the classic transformation equations are compared with; the transformation of the proper time from the spacecraft to TCB is also obtained. Keywords: SSB
Pulse timing model Crab pulsar Time delay of gravity
51.1 Foreword X-ray pulsar, especially millisecond pulsar has strong flux density of radiation and extremely stable rotation frequency [1]. The autonomous navigation of spacecraft is achieved when receiving the signals from at least four pulsars in different direction so the X-ray pulsar autonomous navigation gets the great international
Project supported by the State Key Development Program for the National Natural Science Foundation of China (Grant Nos. 41004013, 41174025, 41204020). Q. Zhou (&) J. Ji H. Ren State Key Laboratory of Geo-information Engineering, Xi’an 710054, China e-mail: [email protected] J. Ji e-mail: [email protected] H. Ren e-mail: [email protected] Q. Zhou J. Ji H. Ren Xi’an Research Institute of Surveying and Mapping, Xi’an 710054, China
J. Sun et al. (eds.), China Satellite Navigation Conference (CSNC) 2013 Proceedings, Lecture Notes in Electrical Engineering 245, DOI: 10.1007/978-3-642-37407-4_51, Ó Springer-Verlag Berlin Heidelberg 2013
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attention. Since July 2004, the DARPA of USA has started to carry out ‘‘X-ray Source-based Navigation for Autonomous Position Determination (XNAV)’’, the other countries had the similar plans [2]. Timing equation is the basic theory of dealing with the observable data of pulsar, whose accuracy has the direct influence on the capacity of the autonomous navigation for spacecraft, and the refinement of pulsar’s parameters in the XNAV [3]. For reaching the accurate solutions of pulsar navigation, the high precision timing equation is need to be established by analyzing all effects which can be modelled in timing data correctly [4]. The accuracy of timing equation improves with the development of the academic level and precision of observational equipments. Their researches of the early scientists mainly focused on the correction of the TOA of photons recorded by the ground-based telescope for getting higher precision observable data [1]. As the upgrade of observation equipment and the development of signal processing technology, the general relativity effects become to be a necessary considered factor, and establishing the timing equation in the relativistic framework is the precondition of high-precision dealing with observable data. For dealing the data of the radio telescope on the Earth and the xray data of satellites in space, some foreign experts analyzed all geometry and relativistic effects in the propagation of pulsar
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