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CLC number: V448; P128.4

On-line Access: 2015-10-08

Received: 2015-02-09

Revision Accepted: 2015-06-19

Crosschecked: 2015-09-09

Cited: 2

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Citations:  Bibtex RefMan EndNote GB/T7714


Li-Rong Shen


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Frontiers of Information Technology & Electronic Engineering  2015 Vol.16 No.10 P.858-870


A novel period estimation method for X-ray pulsars based on frequency subdivision

Author(s):  Li-rong Shen, Xiao-ping Li, Hai-feng Sun, Hai-yan Fang, Meng-fan Xue

Affiliation(s):  School of Aerospace Science and Technology, Xidian University, Xi’an 710071, China

Corresponding email(s):   slr_xidian@163.com, xpli@xidian.edu.cn, sunhaifeng@163.com, hyfang@xidian.edu.cn, xuemf@163.com

Key Words:  Pulsar navigation, Period estimation, Frequency subdivision, Continuous Lomb periodogram

Li-rong Shen, Xiao-ping Li, Hai-feng Sun, Hai-yan Fang, Meng-fan Xue. A novel period estimation method for X-ray pulsars based on frequency subdivision[J]. Frontiers of Information Technology & Electronic Engineering, 2015, 16(10): 858-870.

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author="Li-rong Shen, Xiao-ping Li, Hai-feng Sun, Hai-yan Fang, Meng-fan Xue",
journal="Frontiers of Information Technology & Electronic Engineering",
publisher="Zhejiang University Press & Springer",

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%T A novel period estimation method for X-ray pulsars based on frequency subdivision
%A Li-rong Shen
%A Xiao-ping Li
%A Hai-feng Sun
%A Hai-yan Fang
%A Meng-fan Xue
%J Frontiers of Information Technology & Electronic Engineering
%V 16
%N 10
%P 858-870
%@ 2095-9184
%D 2015
%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1500052

T1 - A novel period estimation method for X-ray pulsars based on frequency subdivision
A1 - Li-rong Shen
A1 - Xiao-ping Li
A1 - Hai-feng Sun
A1 - Hai-yan Fang
A1 - Meng-fan Xue
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 16
IS - 10
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EP - 870
%@ 2095-9184
Y1 - 2015
PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1500052

period estimation of X-ray pulsars plays an important role in X-ray pulsar based navigation (XPNAV). The fast Lomb periodogram is suitable for period estimation of X-ray pulsars, but its performance in terms of frequency resolution is limited by data length and observation time. Longer observation time or oversampling can be employed to improve frequency analysis results, but with greatly increased computational complexity and large amounts of sampling data. This greatly restricts real-time autonomous navigation based on X-ray pulsars. To resolve this issue, a new method based on frequency subdivision and the continuous Lomb periodogram (CLP) is proposed to improve precision of period estimation using short-time observation data. In the proposed method, an initial frequency is first calculated using fast Lomb periodogram. Then frequency subdivision is performed near the initial frequency to obtain frequencies with higher precision. Finally, a refined period is achieved by calculating the CLP in the obtained frequencies. Real data experiments show that when observation time is shorter than 135 s, the proposed method improves period estimation precision by 1–3 orders of magnitude compared with the fast Lomb periodogram and fast Fourier transform (FFT) methods, with only a slight increase in computational complexity. Furthermore, the proposed method performs better than efsearch (a period estimation method of HEAsoft) with lower computational complexity. The proposed method is suitable for estimating periods of X-ray pulsars and obtaining the rotation period of variable stars and other celestial bodies.

This paper attempts to obtain the rotation period of a pulsar by using the so-called 'Continuous Lomb Periodgram (CLP)' method to process the X-ray observation data. This method is valuable and can be used for searching new X-ray pulsars.


创新点:提出频率细分的方法,推导continuous Lomb periodogram (CLP),实现X射线脉冲星非等间隔到达光子序列在细分频率处的频域分析。该方法可以显著减少运算复杂度,同时提高频域分析的频率分辨率,进而提高脉冲星周期估计的精度。
方法:首先,考虑到X射线脉冲星信号是非等间隔到达的光子序列,本文采用专门用于非等间隔数据处理的fast Lomb方法对一段短时观测的脉冲星实测数据进行频域分析,获得一个初始频率作为脉冲星旋转频率的初值。然后,在该初始频率附近以高的频率分辨率做频率细分,获取设定数量的高精度细分频率。最后,对该段短时观测的脉冲星数据在这些细分频率处做CLP分析。在CLP中,峰值位置所对应的频率即为估计出的具有较高精度的脉冲星旋转频率,由该频率就可以确定高精度的脉冲星旋转周期。实测数据分析表明:当观测数据小于135 s时,本文算法的周期估计精度比fast Lomb方法和FFT方法高1到3个数量级,且仅增加了一点计算复杂度。同时,相比于HEAsoft的周期估计方法(efsearch),本文算法具有精度高计算复杂度低的优势。
结论:本文算法解决了fast Lomb方法在周期估计时精度受数据长度和观测时间限制的问题,显著提高了X射线脉冲星周期估计的精度并降低了计算复杂度。同时短时高精度的周期估计有助于提高TOA估计精度及X射线脉冲星导航中实时位置和速度的估计精度。本文算法还可以用于变星及其他天体的周期估计。


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[1]Chester, T.J., Butman, S.A., 1981. Navigation Using X-Ray Pulsers. TDA Progress Report 42-63, p.22-25.

[2]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.

[3]Feng, D.J., Xu, L.P., Zhang, H., et al., 2013. Determination of inter-satellite relative position using X-ray pulsars. J. Zhejiang Univ.-Sci. C (Comput. & Electron.), 14(2):133-142.

[4]Ge, M.Y., 2012. The X-Ray Emission of Pulsar. PhD Thesis, University of Chinese Academy of Sciences, China (in Chinese).

[5]Hanson, J.E., 1996. Principles of X-Ray Navigation. SLAC-Report-809, Stanford University, USA.

[6]Hu, G.S., 2003. Digital Signal Processing: Theory, Methods and Implementation. Tsinghua University Press, China (in Chinese).

[7]Jenkins, J.S., Yoma, N.B., Rojo, P., et al., 2014. Improved signal detection algorithms for unevenly sampled data. Six signals in the radial velocity data for GJ876. Mon. Not. R. Astron. Soc., 441(3):2253-2265.

[8]Kaspi, V.M., Taylor, J.H., Ryba, M.F., 1994. High-precision timing of millisecond pulsars. III: long-term monitoring of PSRs B1855+09 and B1937+21. Astrophys. J., 428(2):713-728.

[9]Laguna, P., Moody, G.B., Mark, R.G., 1998. Power spectral density of unevenly sampled data by least-square analysis: performance and application to heart rate signals. IEEE Trans. Biomed. Eng., 45(6):698-715.

[10]Leahy, D.A., Darbro, W., Elsner, R.F., et al., 1983. On searches for pulsed emission with application to four globular cluster X-ray sources: NGC 1851, 6441, 6624, and 6712. Astrophys. J., 266:160-170.

[11]Li, J.X., Ke, X.Z., 2010. Period estimation method for weak pulsars based on coherent statistic of cyclostationary signal. Acta Phys. Sin., 59(11):8304-8310 (in Chinese).

[12]Li, J.X., Ke, X.Z., Zhao, B.S., 2012. A new time-domain estimation method for period of pulsars. Acta Phys. Sin., 61(6):069701.1-069701.7 (in Chinese).

[13]Liu, J., Ma, J., Tian, J.W., et al., 2012. Pulsar navigation for interplanetary missions using CV model and ASUKF. Aerosp. Sci. Technol., 22(1):19-23.

[14]Liu, J., Fang, J.C., Ning, X.L., et al., 2014. Closed-loop EKF-based pulsar navigation for Mars explorer with Doppler effects. J. Navig., 67(5):776-790.

[15]Lomb, N.R., 1976. Least-squares frequency analysis of unequally spaced data. Astrophys. Space Sci., 39(2):447-462.

[16]Lyne, A.G., Graham-Smith, F., 2006. Pulsar Astronomy. Cambridge University Press, UK.

[17]Manchester, R.N., Taylor, J.H., 1977. Pulsars. W. H. Freeman, San Francisco, USA.

[18]Mao, Y., 2009. Research on X-Ray Pulsar Navigation Algorithms. PhD Thesis, The PLA Information Engineering University, Zhengzhou, China (in Chinese).

[19]Matsakis, D.N., Taylor, J.H., Eubanks, T.M., 1997. A statistic for describing pulsar and clock stabilities. Astron. Astrophys., 326:924-928.

[20]Press, W.H., Rybicki, G.B., 1989. Fast algorithm for spectral analysis of unevenly sampled data. Astrophys. J., 338:227-280.

[21]Scargle, J.D., 1982. Studies in astronomical time series analysis. II: statistical aspects of spectral analysis of unevenly spaced data. Astrophys. J., 263:835-853.

[22]Schulz, M., Stattegger, K., 1997. Spectrum: spectral analysis of unevenly spaced paleoclimatic time series. Comput. Geosci., 23(9):929-945.

[23]Scott, D.M., Finger, M.H., Wilson, C.A., 2003. Characterization of the timing noise of the Crab pulsar. Mon. Not. R. Astron. Soc., 344(2):412-430.

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

[25]Shuai, P., 2009. Principle and Method of the X-Ray Pulsar Navigation System. China Aerospace Press, China (in Chinese).

[26]Stellingwerf, R.F., 1978. Period determination using phase dispersion minimization. Astrophys. J., 224:953-960.

[27]Sun, H.F., Xie, K., Li, X.P., et al., 2013. A simulation technique of X-ray pulsar signals with high timing stability. Acta Phys. Sin., 62(10):109701.1-109701.11 (in Chinese).

[28]Wang, Y.D., Zheng, W., Sun, S.M., et al., 2014. X-ray pulsar-based navigation using time-differenced measurement. Aeros. Sci. Technol., 36:27-35.

[29]Xie, Q., 2012. Study on Signal Identification and Cycle Ambiguity Resolution Technology for X-Ray Pulsar. PhD Thesis, Xidian University, China (in Chinese).

[30]Xiong, Z., Qiao, L., Liu, J.Y., et al., 2012. Geo satellite autonomous navigation using X-ray pulsar navigation and GNSS measurements. Int. J. Innov. Comput. Inform. Contr., 8(5A):2965-2977.

[31]Zhang, C.H., Wang, N., Yuan, J.P., et al., 2012. Timing noise study of four pulsars. Sci. China Phys. Mech. Astron., 55(2):333-338.

[32]Zhang, H., Xu, L.P., Shen, Y.H., et al., 2014. A new maximum-likelihood phase estimation method for X-ray pulsar signals. J. Zhejiang Univ.-Sci. C (Comput. & Electron.), 15(6):458-469.

[33]Zhou, Q.Y., Ji, J.F., Ren, H.F., 2013. Quick search algorithm of X-ray pulsar period based on unevenly spaced timing data. Acta Phys. Sin., 62(1):019701.1-019701.8 (in Chinese).

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