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Timing equation in X-ray pulsar autonomous navigation

Zhou Qing-Yong Ji Jian-Feng Ren Hong-Fei

Timing equation in X-ray pulsar autonomous navigation

Zhou Qing-Yong, Ji Jian-Feng, Ren Hong-Fei
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  • The timing equation is the basic theory of dealing with the observable data of pulsar. The pulse timing model is studied; the transformation equation of pulsar photon time of arrival in 1PN approximation is derived, the existing transformation equations are compared and analyzed; the transformation of the proper time from the spacecraft to TCB is also obtained. The process dealing with the observable data of RXTE is achieved by software, the pulsar period is estimated and pulse profile is replicated, the validity of timing equation is approved. The result of software is compared with that of Heasoft, the reason of difference between them is analyzed. Finally, the effects of the planet ephemeris error and the pulsar ephemeris error on data processing are achieved.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 41004013, 41174025, 41204020).
    [1]

    Sheikh S I 2005 Ph. D. Dissertation (USA: University of Maryland)

    [2]

    Ren H F 2011 Ph. D. Dissertation (Zhengzhou: PLA information engineering university) (in Chinese) [任红飞 2011 博士学位论文(郑州:解放军信息工程大学)]

    [3]

    Ren H F, Wei Z Q, Zhai Z H, Wu F M 2012 Acta Geodaetica et Cartographica Sin. 41 41 (in Chinese) [任红飞, 魏子卿, 翟振和, 吴富梅 2012 测绘学报 41 41]

    [4]

    Zhao M, Huang T Y 2009 Science in China (G) 39 1671 (in Chinese) [赵铭, 黄天衣 2009 中国科学:物理学力学天文学 39 1671]

    [5]

    Backer D C, Helling R W 1986 Ann. Rev. Astron Astrophy 24 537

    [6]

    Lorimer D R, Kramer M 2005 Handbook of Pulsar Astronomy (London: Cambridge University Press)

    [7]

    Helling R W 1986 The astronomical Journal 91 650

    [8]

    Murry C A 1983 Vectorial Astrometry (London: Tsechno House of Adam Hilger)

    [9]

    Edwards R T, Hobbs G B, Manchester R N 2006 Mon. Not. R. Astron. Soc. 372 1574

    [10]

    Sheikh S I, Hellings R W, Matzner R A 2007 ION 63rd Annual Meeting, Cambridge, MA, April 23-25, 2007, P432

    [11]

    Shuai P, Li M, Chen Z L, Huang Z 2009 the principle and method the X-ray pulsar-Based navigation system (Beijing: China Astronautic Publishing House) (in Chinese) [帅平, 李明, 陈绍龙, 黄震 2009 X射线脉冲星导航系统原理与方法 (北京:中国宇航出版社)]

    [12]

    Fei B J, Sun W J, Pan G T, Ji C X 2010 Chin. J. Space. Sci. 30 85 (in Chinese) [费保俊, 孙维瑾, 潘高田, 季诚响 2010 空间科学学报 30 85]

    [13]

    Liu J Q, Xu C M 1989 Acta Astronomica Sinica 30 323 [刘甲求, 须重明 1989 天文学报 30 323]

    [14]

    Blanford R, Teukolsky S A 1976 The Astrophysical Journal 205 580

    [15]

    Su Z, Xu L P, Wang T 2011 Acta Phys. Sin. 60 119701 (in Chinese) [苏哲, 许录平, 王婷 2011 物理学报 60 119701]

    [16]

    Zhou Q Y, Ji J F, Wang T 2013 Acta Phys. Sin. 62 019701 (in Chinese) [周庆勇, 姬剑锋, 任红飞 2013 物理学报 60 119701]

    [17]

    Dennies D M, Petit G 2004 IERS Conventions (2003) http: //www.iers.org/iers/publications/tn/tn32/ [2012-08-11]

    [18]

    Liu L, Hou X Y 2012 The orbital mechanics of deep space probe (Beijing: Publishing House of Electronics Industry) (in Chinese) [刘林, 候锡云 2012 深空探测器轨道力学(北京:电子工业出版社)]

    [19]

    Li Z B 2011 Ph. D. Dissertation (Beijing: Chinese Academy of Sciences) (in Chinese) [李志兵 2011 博士学位论文(北京:中国科学院研究生院)]

    [20]

    Lyne A G, Jordan C A, Roberts M E http: //www.jb.man.ac.uk/ ~pulsar/crab.html[2012/09/31]

    [21]

    Lyne A G, Pritchard R S, Graham-Smith F 1993 MNRAS 265 1003

    [22]

    Ray P S, Wood K S, Wolff M N 2002 American Astronomical Society Meeting 201 Dec 2002

  • [1]

    Sheikh S I 2005 Ph. D. Dissertation (USA: University of Maryland)

    [2]

    Ren H F 2011 Ph. D. Dissertation (Zhengzhou: PLA information engineering university) (in Chinese) [任红飞 2011 博士学位论文(郑州:解放军信息工程大学)]

    [3]

    Ren H F, Wei Z Q, Zhai Z H, Wu F M 2012 Acta Geodaetica et Cartographica Sin. 41 41 (in Chinese) [任红飞, 魏子卿, 翟振和, 吴富梅 2012 测绘学报 41 41]

    [4]

    Zhao M, Huang T Y 2009 Science in China (G) 39 1671 (in Chinese) [赵铭, 黄天衣 2009 中国科学:物理学力学天文学 39 1671]

    [5]

    Backer D C, Helling R W 1986 Ann. Rev. Astron Astrophy 24 537

    [6]

    Lorimer D R, Kramer M 2005 Handbook of Pulsar Astronomy (London: Cambridge University Press)

    [7]

    Helling R W 1986 The astronomical Journal 91 650

    [8]

    Murry C A 1983 Vectorial Astrometry (London: Tsechno House of Adam Hilger)

    [9]

    Edwards R T, Hobbs G B, Manchester R N 2006 Mon. Not. R. Astron. Soc. 372 1574

    [10]

    Sheikh S I, Hellings R W, Matzner R A 2007 ION 63rd Annual Meeting, Cambridge, MA, April 23-25, 2007, P432

    [11]

    Shuai P, Li M, Chen Z L, Huang Z 2009 the principle and method the X-ray pulsar-Based navigation system (Beijing: China Astronautic Publishing House) (in Chinese) [帅平, 李明, 陈绍龙, 黄震 2009 X射线脉冲星导航系统原理与方法 (北京:中国宇航出版社)]

    [12]

    Fei B J, Sun W J, Pan G T, Ji C X 2010 Chin. J. Space. Sci. 30 85 (in Chinese) [费保俊, 孙维瑾, 潘高田, 季诚响 2010 空间科学学报 30 85]

    [13]

    Liu J Q, Xu C M 1989 Acta Astronomica Sinica 30 323 [刘甲求, 须重明 1989 天文学报 30 323]

    [14]

    Blanford R, Teukolsky S A 1976 The Astrophysical Journal 205 580

    [15]

    Su Z, Xu L P, Wang T 2011 Acta Phys. Sin. 60 119701 (in Chinese) [苏哲, 许录平, 王婷 2011 物理学报 60 119701]

    [16]

    Zhou Q Y, Ji J F, Wang T 2013 Acta Phys. Sin. 62 019701 (in Chinese) [周庆勇, 姬剑锋, 任红飞 2013 物理学报 60 119701]

    [17]

    Dennies D M, Petit G 2004 IERS Conventions (2003) http: //www.iers.org/iers/publications/tn/tn32/ [2012-08-11]

    [18]

    Liu L, Hou X Y 2012 The orbital mechanics of deep space probe (Beijing: Publishing House of Electronics Industry) (in Chinese) [刘林, 候锡云 2012 深空探测器轨道力学(北京:电子工业出版社)]

    [19]

    Li Z B 2011 Ph. D. Dissertation (Beijing: Chinese Academy of Sciences) (in Chinese) [李志兵 2011 博士学位论文(北京:中国科学院研究生院)]

    [20]

    Lyne A G, Jordan C A, Roberts M E http: //www.jb.man.ac.uk/ ~pulsar/crab.html[2012/09/31]

    [21]

    Lyne A G, Pritchard R S, Graham-Smith F 1993 MNRAS 265 1003

    [22]

    Ray P S, Wood K S, Wolff M N 2002 American Astronomical Society Meeting 201 Dec 2002

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  • Citation:
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Publishing process
  • Received Date:  15 November 2012
  • Accepted Date:  11 March 2013
  • Published Online:  05 July 2013

Timing equation in X-ray pulsar autonomous navigation

  • 1. State Key Laboratory of Geo-information engineering, Xi'an 710054, China;Xi'an Research Institute of Surveying and Mapping, Xi'an 710054
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 41004013, 41174025, 41204020).

Abstract: The timing equation is the basic theory of dealing with the observable data of pulsar. The pulse timing model is studied; the transformation equation of pulsar photon time of arrival in 1PN approximation is derived, the existing transformation equations are compared and analyzed; the transformation of the proper time from the spacecraft to TCB is also obtained. The process dealing with the observable data of RXTE is achieved by software, the pulsar period is estimated and pulse profile is replicated, the validity of timing equation is approved. The result of software is compared with that of Heasoft, the reason of difference between them is analyzed. Finally, the effects of the planet ephemeris error and the pulsar ephemeris error on data processing are achieved.

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