Orbit determination using incremental phase and TDOA of X-ray pulsar<FootNote> Project supported by the National Natural Science Foundation of China (No. 61401340), the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2016JM6035), the Fundamental Research Funds for the Central Universities, China (No. JB161303), and the Areospace T.T.&C. Innovation Program (No. 201515A) </FootNote>

Abstract

X-ray pulsars offer stable, periodic X-ray pulse sequences that can be used in spacecraft positioning systems. A method using X-ray pulsars to determine the initial orbit of a satellite is presented in this paper. This method suggests only one detector to be equipped on the satellite and assumes that the detector observes three pulsars in turn. To improve the performance, the use of incremental phase in one observation duration is proposed, and the incremental phase is combined with the time difference of arrival (TDOA). Then, a weighted least squares (WLS) algorithm is formulated to calculate the initial orbit. Numerical simulations are performed to assess the proposed orbit determination method.

Keywords

Orbit determination algorithm / Single X-ray pulsar detector / Phase increment / Two-body motion equations / Weighted least squares method

References

[1] Backer, D.C., Hellings, R.W., 1986. Pulsar timing and general relativity. Ann. Rev. Astron. Astrophys., 24:537–575. http://dx.doi.org/10.1146/annurev.aa.24.090186.002541

[2] Chester, T.J., Butman, S.A., 1981. Navigation Using X-ray Pulsars. The Telecommunications and Data Acquisition Progress Report No. TDA PR 42-63, NASA, p.22–25.

[3] Deutschmann, J.K., Bar-Itzhack, I.Y., 2001. Evaluation of attitude and orbit estimation using actual earth magnetic field data. J. Guid. Contr. Dyn., 24(3):616–623. http://dx.doi.org/10.2514/2.4753

[4] Emadzadeh, A.A., Speyer, J.L., 2011. Relative navigation between two spacecraft using X-ray pulsars. IEEE Trans. Contr. Syst. Technol., 19(5):1021–1035. http://dx.doi.org/10.1109/TCST.2010.2068049

[5] Farahanifar, M., Assadian, N., 2015. Integrated magnetometer—horizon sensor low-Earth orbit determination using UKF. Acta Astronaut., 106:13–23. http://dx.doi.org/10.1016/j.actaastro.2014.10.007

[6] Hinedi, S., 1993. NASA’s next generation all-digital deep space network breadboard receiver. IEEE Trans. Commun., 41(1):246–257. http://dx.doi.org/10.1109/26.212383

[7] Huang, L.W., Liang, B., 2010. Autonomous initial orbit determination of high-Earth-orbit satellites using X-ray pulsars. J. Syst. Simul., 22(S1):258–261 (in Chinese) .

[8] Liu, J., Fang, J.C., Yang, Z.H., et al., 2015. X-ray pulsar/Doppler difference integrated navigation for deep space exploration with unstable solar spectrum. Aerosp. Sci. Technol., 41:144–150. http://dx.doi.org/10.1016/j.ast.2014.11.019

[9] Ma, J., Xu, J., Cao, Z.B., 2005. A method of autonomous orbit determination for satellite using star sensor. Sci. China Ser. G, 48(3):268–281. http://dx.doi.org/10.1360/142004-23

[10] Mao, Y., Chen, J.P., Song, X.Y., 2010. Single X-ray pulsar dynamic orbit determination. J. Geomat. Sci. Technol., 27(4):251–254 (in Chinese).

[11] Psiaki, M.L., 1995. Autonomous orbit and magnetic field determination using magnetometer and star sensor data. J. Guid. Contr. Dyn., 18(3):584–592. http://dx.doi.org/10.2514/3.21427

[12] Qian, Y., Li, C., Jing, W., et al., 2013. Sun-Earth-Moon autonomous orbit determination for quasi-periodic orbit about the translunar libration point and its observability analysis. Aerosp. Sci. Technol., 28(1):289–296. http://dx.doi.org/10.1016/j.ast.2012.11.009

[13] Ray, P.S., Wood, K.S., Wolff, M.T., et al., 2002. Absolute timing of the crab pulsar: X-ray, radio, and optical observations. Bull. Am. Astron. Soc., 34:1298.

[14] Shang, L., Liu, G., Zhang, R., et al., 2013. An information fusion algorithm for integrated autonomous orbit determination of navigation satellites. Acta Astronaut., 85: 33–40. http://dx.doi.org/10.1016/j.actaastro.2012.12.007

[15] Sheikh, S.I., 2005. The Use of Variable Celestial X-ray Sources for Spacecraft Navigation. PhD Thesis, University of Maryland, College Park, USA.

[16] Sheikh, S.I., Hellings, R.W., Matzner, R.A., 2007. High-order pulsar timing for navigation. 63rd Annual Meeting of the Institute of Navigation, p.432–443.

[17] Sheikh, S.I., Hanson, J.E., Graven, P.H., et al., 2011. Spacecraft navigation and timing using X-ray pulsars. Navigation, 58(2):165–186. http://dx.doi.org/10.1002/j.2161-4296.2011.tb01799.x

[18] Taylor, J.H., 1992. Pulsar timing and relativistic gravity. Phil. Trans. Phys. Sci. Eng., 341(1660):117–134.

[19] Visser, P.N.A.M., van den Ijssel, J., 2000. GPS-based precise orbit determination of the very low Earth-orbiting gravity mission GOCE. J. Geod., 74(7):590–602. http://dx.doi.org/10.1007/s001900000119

[20] Wang, Y., Zheng, W., Sun, S., et al., 2013. X-ray pulsar-based navigation system with the errors in the planetary ephemerides for Earth-orbiting satellite. Adv. Space Res., 51(12):2394–2404. http://dx.doi.org/10.1016/j.asr.2013.02.007

[21] Woodfork, D.W., 2005. The Use of X-ray Pulsars for Aiding GPS Satellite Orbit Determination. MS Thesis, Air University, Maxwell Air Force Base, USA.

[22] Xiong, K., Wei, C., Liu, L., 2013. Autonomous navigation for a group of satellites with star sensors and inter-satellite links. Acta Astronaut., 86:10–23. http://dx.doi.org/10.1016/j.actaastro.2012.12.001

[23] Zhang, H., Xu, L., 2011. An improved phase measurement method of integrated pulse profile for pulsar. Sci. China Technol. Sci., 54(9):2263–2270. http://dx.doi.org/10.1007/s11431-011-4524-8

[24] Zhang, H., Xu, L., Shen, Y., et al., 2014. A new maximumlikelihood phase estimation method for X-ray pulsar signals. J. Zhejiang Univ.-Sci. C (Comput. & Electron.), 15(6):458–469. http://dx.doi.org/10.1631/jzus.C1300347

RIGHTS & PERMISSIONS

2016 Zhejiang University and Springer-Verlag Berlin Heidelberg