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Orbit Determination Using Pulsar Timing Data and Orientation Vector

Published online by Cambridge University Press:  24 October 2018

Hua Zhang ,
Rong Jiao  and
Luping Xu
Hua Zhang*
Affiliation:
(School Aerospace Science and Technology, Xidian University, Xi' an, China710126)
Rong Jiao
Affiliation:
(School of Electronic Engineering, Xi' an Shiyou University, Xi' an, China710165)
Luping Xu
Affiliation:
(School Aerospace Science and Technology, Xidian University, Xi' an, China710126)
*
(E-mail: zhanghua@mail.xidian.edu.cn)
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Abstract

X-ray Pulsar Navigation (XPNAV) uses the Time Difference of Arrival (TDOA) of the pulsar signal between the spacecraft and Solar System Barycentre (SSB) to determine position. In this paper, a novel method to improve the performance of XPNAV via exploiting the pulsar position vector is proposed. First, the field of view of the collimator is utilised to find the pulsar orientation direction. Then, a searching strategy based on the modified Powell method under given coordinate frames is proposed. We also mathematically prove the existence of the extreme value of the searching strategy. Subsequently, an observation model based on the pulsar radiation vector is presented and applied to formulate the observation function together with pulsar time transfer function. Finally, an Adaptive Divided Difference Filter (ADDF) algorithm is introduced to iteratively estimate the position and velocity of the spacecraft. Numerical simulations show that the vector searching method is feasible and the pulsar radiation direction can improve the navigation performance by 75%. The simulation results also show that the ADDF performs better than Unscented Kalman Filtering (UKF) and DDF in position estimation.

Keywords

Pulsar NavigationAdaptive divided difference Kalman filteringInformation Fusion
Type
Research Article
Information
The Journal of Navigation , Volume 72 , Issue 1 , January 2019 , pp. 155 - 175
Copyright
Copyright © The Royal Institute of Navigation 2018 

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References

REFERENCES

Bar-Itzhack, I. Y. and Oshman, Y.. (1985). Attitude Determination from Vector Observations: Quatemion Estimation. IEEE Transactions on Aerospace and Electronic Systems, 1, 128–136.Google Scholar
Battiti, R. (1992). First- and Second-Order Methods for Leaming: Between Steepest Descent and Newton's Method. NEURAL COMPUTATION, 4, 141–166.Google Scholar
Becker, W., Kramer, M., and Sesana, A. (2018). Pulsar Timing and Its Application for Navigation and Gravitational Wave Detection. Space Science Reviews, 214, 30.Google Scholar
Brown, R. G. and Hwang, P. Y. C. (1997). Introduction to random signals and applied Kalman filtering: with MATLAB exercises (4th Edition). John Wiley & Sons, Inc.Google Scholar
Chen, P. T., Speyer, J. L., Bayard, D. S., and Majid, W. A. (2017). Autonomous Navigation Using X-Ray Pulsars and Multirate Processing American Control Conference, 40, 4563–4569.Google Scholar
Deng, X. P., Coles, W., Hobbs, G., Keith, M. J., Manchester, R. N., Shannon, R. M. and Zheng, J. H. (2012). Optimal interpolation and prediction in pulsar timing. Monthly Notices of the Royal Astronomical Society, 424, 244–251.Google Scholar
Dey, A., Sadhu, S. and Ghoshal, T. K. (2015). Adaptive divided difference filter for nonlinear systems with non-additive noise. Proceedings of the 2015 Third International Conference on Computer, Communication, Control and Information Technology, Hooghly, India.Google Scholar
Graven, P., Collins, J., Sheikh, S., Hanson, J., Ray, P. and Wood, K., (2008). XNAV for deep space navigation. 31st Annual AAS Rocky Mountain Guidance and Control Conference, 131, 349–364.Google Scholar
Guo, P., Sun, J., Hu, S. and Xue, J. (2018). Research on navigation of satellite constellation based on an asynchronous observation model using X-ray pulsarAdvances in Space Research, 61, 787–798.Google Scholar
Hanson, J. E. (2006). Principles of X-ray Navigation. SLAC-Report-809.Google Scholar
Huang, Z., Li, M., and Shuai, P. (2009). On time transfer in X-ray pulsar navigation. Science in China, 52, 1413–1419.Google Scholar
Huyer, W. and Neumaier, A. (1999). Global optimization by Multilevel Coordinate Search. Journal of Global optimization, 14, 331–355.Google Scholar
Jiao, R., Xu, L. P., Zhang, H. and Li, C. (2016). Augmentation method ofXPNAV in Mars orbit based on Phobos and Deimos observations. Advances in Space Research, 58, 1864–1878.Google Scholar
Lewis, R. M., Torczon, V. and Trosset, M. W. (2000). Direct search methods: then and now. Journal of Computational and Applied Mathematics, 124, 191–207.Google Scholar
Liu, J., Fang, J. C., Yang, Z. H., Kang, Z. W. and Wu, J. (2015). X-ray pulsar/Doppler difference integrated navigation for deep space exploration with unstable solar spectrum. Aerospace Science & Technology, 41, 144–150.Google Scholar
Liu, J., Ma, J. and Tian, J. (2010). Pulsar/CNS integrated navigation based on federated UKF. Journal ofSystems Engineering and Electronics, 21, 675–681.Google Scholar
Loke, M. H. and Barker, R. D. (1996). Rapid least-squares inversion of apparent resistivity pseudosections by a quasi-Newton method. Geophysical Prospecting, 44, 131–152.Google Scholar
Luo, N., Xu, L. P. and Zhang, H. (2012). Method of autonomous celestial navigation based on UKF and information fusion. Chinese Space Science & Technology, 32, 1–9.Google Scholar
Ma, P., Wang, T., Jiang, F., Mu, J. and Baoyin, H. (2017). Autonomous Navigation of Mars Probes by Single X-ray Pulsar Measurement and Optical Data of Viewing Martian Moons. Journal of Navigation, 70, 18–32.Google Scholar
Mitchell, J. W., Hassouneh, M. A., Wintemitz, M. B., Valdez, J. E., Price, S. R., Semper, S. R., Yu, W. H., Arzoumanian, Z., Ray, P. S., Wood, K. S., Litchford, R. J. and Gendreau, K. C., (2015). SEXTANT-station explorer for X-ray timing and navigation technology, AIAA Guidance, Navigation, and Control Conference MGNC 2015-Held at the AIAA SciTech Forum 2015.Google Scholar
Ning, X., Gui, M., Zhang, J., Fang, J. and Liu, G. (2017). Impact of the Pulsar's Direction on CNS/XNAV Integrated Navigation. IEEE Transactions on Aerospace & Electronic Systems, 53, 3043–3055.Google Scholar
Ning, X., Yang, Y., Gui, M., Wu, W., Fang, J. and Liu, G. (2018). Pulsar navigation using time of arrival (TOA) and time differential TOA (TDTOA). Acta Astronautica, 142, 57–63.Google Scholar
Nørgaard, M., Poulsen, N. K. and Ravn, O. (2000). New developments in state estimation for nonlinear systems. Automatica, 36, 1627–1638.Google Scholar
Powell, M. J. D. (1964). An efficient method for finding the minimum of a function of several variables without calculating derivatives. Computer Journal, 7, 155–162.Google Scholar
Qiao, L., Liu, J., Zheng, G. L. and Zhi, X. (2009). Augmentation of XNAV System to an Ultraviolet Sensor-Based Satellite Navigation System. IEEE Journal of Selected Topics in Signal Processing, 3, 777–785.Google Scholar
Sheikh, S. I. and Pines, D. J. (2006). Recursive Estimation of Spacecraft Position Using X-ray Pulsar Time Arrival Measurements. Navigation, 53, 149–166.Google Scholar
Sheikh, S. I., Golshan, A. R., and Pines, D. J. (2007). Absolute and relative position determination using variable celestial X-ray sources. Advances in the Astronautical Sciences, 128, 855–874.Google Scholar
Sheikh, S. I., Hellings, R. W. and Matzner, R. A. (2007). High-order pulsar timing for navigation. Navigation. Proceedings of the Annual Meeting-Institute of Navigation, Cambridge, MA, United States.Google Scholar
Sheikh, S. I. (2005). The use of variable celestial X-ray sources for spacecraft navigation. University of Maryland, College Park, United States Maryland.Google Scholar
Takahashi, T., Abe, K., Endo, M., Endo, Y., Ezoe, Y, Fukazawa, Y., Hamaya, M., Hirakuri, S., Hong, S., Horii, M., Inoue, H., Isobe, N., Itoh, T., Iyomoto, N., Kamae, T., Kasama, D., Kataoka, J., Kato, H., Kawaharada, M., Kawano, N., Kawashima, K., Kawasoe, S., Kishishita, T., Kitaguchi, T., Kobayashi, Y., Kokubun, M., Jun'ichi, K., Kouda, M., Kubota, A., Kuroda, Y., Madejski, G., Makishima, K., Masukawa, K., Matsumoto, Y., Mitani, T., Miyawaki, R., Mizuno, T., Mori, K., Mori, M., Murashima, M., Murakami, T., Nakazawa, K., Niko, H., Nomachi, M., Okada, Y., Ohno, M., Oonuki, K., Ota, N., Ozawa, H., Sato, G., Shinoda, S., Sugiho, M., Suzuki, M., Taguchi, K., Takahashi, H., Takahashi, I., Shin'ichiro, T., Ken-Ichi, T., Tamura, T., Tanaka, T., Tanihata, C., Tashiro, M., Terada, Y., Shin'ya, T., Uchiyama, Y, Watanabe, S., Yamaoka, K., Yanagida, T. and Yonetoku, D. (2007). Hard X-Ray Detector (HXD) on Board Suzaku. Publications-Astronomical Society of Japan, 59, S35–S51.Google Scholar
Wang, Y. and Zhang, W. (2017). Pulsar phase and Doppler frequency estimation for XNAV using on-orbit epoch folding. IEEE Transactions on Aerospace & Electronic Systems, 52, 2210–2219.Google Scholar
Wang, Y., Zheng, W. and Zhang, D. (2017). X-ray Pulsar/Starlight Doppler Deeply-integrated Navigation Method. Journal of Navigation, 70, 829–846.Google Scholar
Wei, E., Jin, S., Zhang, Q., Liu, J., Li, X., and Yan, W. (2013). Autonomous navigation of Mars probe using X-ray pulsars: Modeling and results. Advances in Space Research, 51, 849–857.Google Scholar
Zhang, H. and Xu, L. (2011). An improved phase measurement method of integrated pulse profile for pulsar. Science China Technological Sciences., 54, 2263–2270.Google Scholar
Zhang, X., Shuai, P., Huang, L., Chen, S. and Xu, L. (2017). Mission Overview and Initial Observation Results of the X-Ray Pulsar Navigation-I Satellite. International Journal of Aerospace Engineering, 2017, 1–7.Google Scholar
Zhang, X. Y., Shuai, P. and Huang, L. W. (2016). Phase tracking for pulsar navigation with Doppler frequency. Acta Astronautica, 129, 179–185.Google Scholar