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In the traditional compressed sensing algorithms, the precision of the time delay estimation is closely related to the number of atoms in the dictionary. The bigger the atom number, the smaller the atomic interval becomes, thus the higher the accuracy of the time delay estimation will be. However, the bigger atom number leads to a higher calculation load. Considering the limited calculation capacity of on-board computer, in order to fast obtain high-accuracy time delay estimation value of the integrated pulsar profile of pulsar in the X-ray pulsar-based navigation, we propose a time delay estimation method based on two-level compression sensing. Compressed sensing mainly includes three parts:the dictionary, the measurement matrix, and the recovery algorithm. Among them, the dictionary size is one of the most important factors that affect the estimation accuracy of the compressed sensing. Aiming to solve the problem of the greater computational load with the increase of the atom number in the dictionary of compressed sensing while improving the accuracy of estimation, we combine the rough estimation with the precision estimation as a two-level dictionary. In the first level, the global phase estimation of the low-dimensional integrated pulsar profile is carried out by making use of the feature of the large atomic interval and the small atomic amount of the rough estimation dictionary. Specifically, first, construct a coarse estimation dictionary according to the low-dimensional standard pulsar profile. Then make dimension reduction sampling on the low-dimensional integrated pulsar profile by the rough estimation measurement matrix based on low-dimensional Hadamard matrix. Finally, use an orthogonal matching pursuit method to obtain the predictive estimation of delay value. In the second level, by taking advantage of the small atomic intervals and numbers of the precise estimation dictionary which are suitable for local estimation, the exact time delay estimation of the high dimensional integrated pulsar profile is performed. Specifically, the original position is first corrected by using the predictive estimation of time delay value, that is, shifting the initial high-dimensional integrated pulsar profile as the input signal of the second level. Then the precise estimation dictionary is constructed according to the partial signal of the length of the high dimension standard pulse profile, using the precise estimation measurement matrix sampling on high-dimensional integrated pulsar profile to obtain measurement value. Finally, the optimal matching position is obtained through the recovery algorithm, which is then combined with the predictive estimation of delay value to calculate the prcis time delay estimation value. Theoretical analysis and experimental results show that the quantity of data in the two level dictionary is two orders of magnitude smaller than in the traditional dictionary. The proposed method reduces the computational complexity greatly compared with traditional compression sensing method in the same time delay estimation accuracy. Therefore, this method has the advantages of high precision and small calculation load.
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Keywords:
- time delay estimation /
- compressed sensing /
- X-ray pulsar /
- two level dictionary
[1] Hanson J E 1996 Ph. D. Dissertation (Stanford: Stanford University)
[2] Sheikh S I 2005 Ph. D. Dissertation (Maryland: University of Maryland)
[3] Liu J, Wu J, Xiong L, Fang J C, Liu G 2017 Chin. J. Electron 6 1325
[4] Taylor J H 1992 Philos. T. R. Soc. A 341 117
[5] Tran N D, Renaux A, Boyer R, Marcos S 2014 IEEE Trans. Aeros. Elec. Sys. 50 786
[6] Kang Z W, He X, Liu J 2016 Optik 127 5050
[7] Zhang H, Xu L P, Xie Q, Luo N 2011 Acta Phys. Sin. 60 049701 (in Chinese) [张华, 许录平, 谢强, 罗楠 2011 60 049701]
[8] Fang H Y, Liu B, Li X P, Sun H F, Xue M F, Shen L R, Zhu J P 2016 Acta Phys. Sin. 65 119701 (in Chinese) [方海燕, 刘兵, 李小平, 孙海峰, 薛梦凡, 沈利荣, 朱金鹏 2016 65 119701]
[9] Liu J, Fang J C, Wu J, Kang Z W, Ning X L 2014 IET Radar Sonar Navig 8 1154
[10] Emadzadeh A A, Speyer J L 2011 IEEE Trans. Aeros. Elec. Sys. 47 2317
[11] Emadzadeh A A, Speyer J L 2010 IEEE Trans. Sig. Proc. 58 4484
[12] Li J X, Ke X Z 2010 Acta Astronom. Sin. 51 263 (in Chinese) [李建勋, 柯熙政 2010 天文学报 51 263]
[13] Do T T, Gan L, Nguyen N H, Tran T D 2012 IEEE Trans. Sig. Proc. 60 139
[14] Su Z, Xu L P, Gan W 2011 Sci. Sin.: Phys. Mech. Astron. 41 681 (in Chinese) [苏哲, 许录平, 甘伟 2011 中国科学: 物理学 力学 天文学 41 681]
[15] Li S L, Liu K, Xiao L L 2014 Optik 125 1875
[16] Shen L R, Li X P, Sun H F, Fang H Y, Xue M F 2016 Optik 127 4379
[17] Golshan A R, Sheikh S I 2007 Annual Meeting of Institute of Navigation Cambrige, MA, USA, April 23-25, 2007 p413
[18] Shi G, Lin J, Chen X Y, Qi F, Liu D H, Zhang L 2008 IEEE Trans. Sig. Proc. 55 379
[19] Tropp J A, Gilbert A C 2007 IEEE Trans. Sig. Proc. 53 4655
[20] RXTE https://heasarc nasa gov/docs/archive html [2017-5-24]
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[1] Hanson J E 1996 Ph. D. Dissertation (Stanford: Stanford University)
[2] Sheikh S I 2005 Ph. D. Dissertation (Maryland: University of Maryland)
[3] Liu J, Wu J, Xiong L, Fang J C, Liu G 2017 Chin. J. Electron 6 1325
[4] Taylor J H 1992 Philos. T. R. Soc. A 341 117
[5] Tran N D, Renaux A, Boyer R, Marcos S 2014 IEEE Trans. Aeros. Elec. Sys. 50 786
[6] Kang Z W, He X, Liu J 2016 Optik 127 5050
[7] Zhang H, Xu L P, Xie Q, Luo N 2011 Acta Phys. Sin. 60 049701 (in Chinese) [张华, 许录平, 谢强, 罗楠 2011 60 049701]
[8] Fang H Y, Liu B, Li X P, Sun H F, Xue M F, Shen L R, Zhu J P 2016 Acta Phys. Sin. 65 119701 (in Chinese) [方海燕, 刘兵, 李小平, 孙海峰, 薛梦凡, 沈利荣, 朱金鹏 2016 65 119701]
[9] Liu J, Fang J C, Wu J, Kang Z W, Ning X L 2014 IET Radar Sonar Navig 8 1154
[10] Emadzadeh A A, Speyer J L 2011 IEEE Trans. Aeros. Elec. Sys. 47 2317
[11] Emadzadeh A A, Speyer J L 2010 IEEE Trans. Sig. Proc. 58 4484
[12] Li J X, Ke X Z 2010 Acta Astronom. Sin. 51 263 (in Chinese) [李建勋, 柯熙政 2010 天文学报 51 263]
[13] Do T T, Gan L, Nguyen N H, Tran T D 2012 IEEE Trans. Sig. Proc. 60 139
[14] Su Z, Xu L P, Gan W 2011 Sci. Sin.: Phys. Mech. Astron. 41 681 (in Chinese) [苏哲, 许录平, 甘伟 2011 中国科学: 物理学 力学 天文学 41 681]
[15] Li S L, Liu K, Xiao L L 2014 Optik 125 1875
[16] Shen L R, Li X P, Sun H F, Fang H Y, Xue M F 2016 Optik 127 4379
[17] Golshan A R, Sheikh S I 2007 Annual Meeting of Institute of Navigation Cambrige, MA, USA, April 23-25, 2007 p413
[18] Shi G, Lin J, Chen X Y, Qi F, Liu D H, Zhang L 2008 IEEE Trans. Sig. Proc. 55 379
[19] Tropp J A, Gilbert A C 2007 IEEE Trans. Sig. Proc. 53 4655
[20] RXTE https://heasarc nasa gov/docs/archive html [2017-5-24]
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