Abstract: 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.

一种基于频率细分的X射线脉冲星周期估计方法

[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).