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一种基于最优频段的X射线脉冲星累积轮廓时延估计方法

方海燕 刘兵 李小平 孙海峰 薛梦凡 沈利荣 朱金鹏

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一种基于最优频段的X射线脉冲星累积轮廓时延估计方法

方海燕, 刘兵, 李小平, 孙海峰, 薛梦凡, 沈利荣, 朱金鹏

Time delay estimation method of X-ray pulsar observed profile based on the optimal frequency band

Fang Hai-Yan, Liu Bing, Li Xiao-Ping, Sun Hai-Feng, Xue Meng-Fan, Shen Li-Rong, Zhu Jin-Peng
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  • 为提高X射线脉冲星导航中累积脉冲轮廓的时间延迟估计精度, 分析了X射线脉冲星累积脉冲轮廓的频谱特性和现有Taylor快速傅立叶变换时延估计算法的缺陷, 提出了一种基于最优频段的累积轮廓时延估计算法, 并通过建立不同信噪比下时延估计误差与所采用频段之间的关系以确定最优频段. 数值及实测数据实验结果表明: 在短时观测或光子流量较小时, 该算法优于常用的近似最大似然 (FAML)、相关 (CC)、最小二乘 (NLS) 及加权最小二乘 (WNLS) 方法; 在观测时间较长或光子流量较大时, 该算法的估计精度与CC及NLS方法相当, 但其运算量低于NLS, FAML 及WNLS方法. 本文所提算法适用于短时观测脉冲轮廓或低流量脉冲星的高精度时延估计.
    In order to improve the time delay estimation accuracy of the observed profile in the X-ray pulsar based navigation, the spectral characteristics of the observed profile of X-ray pulsar and the drawback of the classical Taylor fast Fourier transform (FFT) time delay estimation method are analyzed. It is found that when estimating the time delay, we can abandon the higher frequency components that are always affected by noise seriously, but only utilize the information about the low frequency part. Based on this idea, by modifying the weigh function of the classical Taylor FFT time delay estimation method, a new time delay estimation algorithm based on the optimal frequency band is proposed, in which the optimal frequency band is determined by establishing the relationship between the selected frequency band and the time delay estimation accuracy under different signal-to-noise ratios (SNRs). Then by using the real data obtained with the proportional counter array, the low-energy (2-60 keV) detection instrument boarded on the Rossi X-ray Timing Explorer satellite, the optimal frequency as a function the SNR of observed profile is given for the PSR B0531+21 (namely the Crab pulsar) through the Monte-Carlo technique. Since the parameters of different pulsars are known, in practical navigation, the optimal frequency in an observation time for a certain pulsar can be estimated in advance by using the simulation data or the obtained real data of the pulsar, which can remarkably alleviate the onboard computational burden. Finally, a series of numerical simulations and experiments using real data of Crab pulsar are designed to evaluate the performance of the proposed time delay estimation algorithm. The main results can be summarized as follows: the proposed estimator outperforms the normally used fast approximate maximum-likelihood (FAML), cross correlation (CC), nonlinear least square (NLS) and weighted nonlinear least-square (WNLS) estimators when the observation time is short or the source flux is small; when the observation time is long or the source flux is large, its estimation accuracy is almost the same as those of CC and NLS estimators and lower than those of the FAML and WNLS estimators, but its computational complexity is smaller than those of NLS, FAML and WNLS estimators. The above results indicate the high estimation accuracy and high computational efficiency of the proposed time delay estimation method, which can be used in the case that the observation time is restricted to be short or the source flux of the usable pulsar is small in X-ray pulsar based navigation.
      通信作者: 方海燕, hyfang@xidian.edu.cn
      Corresponding author: Fang Hai-Yan, hyfang@xidian.edu.cn
    [1]

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    Bei X M, Shuai P, Huang L W, Sun H F, Wu Y J, Zhang Q 2014 Acta Phys. Sin. 63 219701 (in Chinese) [贝晓敏, 帅平, 黄良伟, 孙海峰, 吴耀军, 张倩 2014 物理学报 63 219701]

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    Emadzadeh A A, Speyer J L 2010 IEEE Trans. Sig. Proc. 58 4484

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    [12]

    Zhu J, Ji P Y 2008 Chin. Phys. B 17 356

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    Xue M F, Li X P, Fu L Z, Liu X P, Sun H F, Shen L R 2016 Acta Astron. 118 1

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    Huang L W, Liang B, Zhang T 2013 Sci: China G: Phys. Mech. Astron. 56 848

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    Emadzadeh A A, Golshan A R, Speyer J L 2009 Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference Shanghai, China, December 16-18, 2009 p1488

    [16]

    Li J X, Ke X Z 2011 Chin. Astron. Astr. 35 19

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    Rinauro S, Colonnese S, Scarano G 2013 Signal Process. 93 326

    [18]

    Zhang H, Xu L P 2011 Sci. China: Technol. Sci. 54 2263

    [19]

    Sun H F, Bao W M, Fang H Y, Bao W M 2015 J. Huazhong Univ. Sci. Technol. (Natural Science Edition) 43 121

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    Taylor J H 1992 Philos. T. R. Soc. A 341 117

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    Sun H F, Bao W M, Fang H Y, Li X P 2014 Acta Phys. Sin. 63 069701 (in Chinese) [孙海峰, 包为民, 方海燕, 李小平 2014 物理学报 63 069701]

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    Piersol A G 1981 IEEE Trans. Acoust. Speech Signal Process. ASSP-29 471

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    Ross S M 2007 Introduction to Probability Models (9th Ed) (New York: Elsevier) pp101-110

  • [1]

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

    [2]

    Xue M F, Li X P, Sun H F, Liu B, Fang H Y, Shen L R 2015 Acta Phys. Sin. 64 219701 (in Chinese) [薛梦凡, 李小平, 孙海峰, 刘兵, 方海燕, 沈利荣 2015 物理学报 64 219701]

    [3]

    Shuai P, Li M, Chen S L, Huang Z 2009 Principles and Techniques of X-ray Pulsar Based Navigation System (Beijing: China Astronauic Publishing House) p15 (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) 第15页]

    [4]

    Xue M F, Li X P, Fu L Z, Fang H Y, Sun H F, Shen L R 2015 Sci. China: Inf. Sci. 58 122202

    [5]

    Bernhardt M G, Becker W, Prinz T, Breithuth F M, Walter U 2011 Proceedings of 2 nd International Conference on Space TechnologyAthens, Greece, September 15-17, 2011 p1

    [6]

    Becker W 2009 X-Ray Emission From Pulsars and Neutron Stars, in Neutron Stars and Pulsars (Berlin: Springer) pp91-95

    [7]

    Sala J, Urruela A, Villares X 2004 ARIADNA Study 3 4202

    [8]

    Hanson J E 1996 Ph. D. Dissertation (USA: Stanford University)

    [9]

    Bei X M, Shuai P, Huang L W, Sun H F, Wu Y J, Zhang Q 2014 Acta Phys. Sin. 63 219701 (in Chinese) [贝晓敏, 帅平, 黄良伟, 孙海峰, 吴耀军, 张倩 2014 物理学报 63 219701]

    [10]

    Emadzadeh A A, Speyer J L 2010 IEEE Trans. Sig. Proc. 58 4484

    [11]

    Emadzadeh A A, Speyer J L 2011 Navigation in Space by X-Ray Pulsars (Berlin: Springer) pp24-26

    [12]

    Zhu J, Ji P Y 2008 Chin. Phys. B 17 356

    [13]

    Xue M F, Li X P, Fu L Z, Liu X P, Sun H F, Shen L R 2016 Acta Astron. 118 1

    [14]

    Huang L W, Liang B, Zhang T 2013 Sci: China G: Phys. Mech. Astron. 56 848

    [15]

    Emadzadeh A A, Golshan A R, Speyer J L 2009 Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference Shanghai, China, December 16-18, 2009 p1488

    [16]

    Li J X, Ke X Z 2011 Chin. Astron. Astr. 35 19

    [17]

    Rinauro S, Colonnese S, Scarano G 2013 Signal Process. 93 326

    [18]

    Zhang H, Xu L P 2011 Sci. China: Technol. Sci. 54 2263

    [19]

    Sun H F, Bao W M, Fang H Y, Bao W M 2015 J. Huazhong Univ. Sci. Technol. (Natural Science Edition) 43 121

    [20]

    Taylor J H 1992 Philos. T. R. Soc. A 341 117

    [21]

    Sun H F, Bao W M, Fang H Y, Li X P 2014 Acta Phys. Sin. 63 069701 (in Chinese) [孙海峰, 包为民, 方海燕, 李小平 2014 物理学报 63 069701]

    [22]

    Piersol A G 1981 IEEE Trans. Acoust. Speech Signal Process. ASSP-29 471

    [23]

    Zhao Z, Hou Z Q 1985 Acta Acustica 10 201 (in Chinese) [赵真, 侯自强 1985 声学学报 10 201]

    [24]

    Ross S M 2007 Introduction to Probability Models (9th Ed) (New York: Elsevier) pp101-110

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出版历程
  • 收稿日期:  2015-12-05
  • 修回日期:  2016-03-02
  • 刊出日期:  2016-06-05

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