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Separate estimation of laser micro-Doppler parameters based on maximum likelihood schemes

Guo Li-Ren Hu Yi-Hua Wang Yun-Peng Xu Shi-Long

Separate estimation of laser micro-Doppler parameters based on maximum likelihood schemes

Guo Li-Ren, Hu Yi-Hua, Wang Yun-Peng, Xu Shi-Long
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  • Laser micro-Doppler (MD) effect is capable of obtaining obvious modulation in weak vibration detection. It helps to estimate target micro-motion parameters with high precision, which may extend the application field of MD to subtle identification and recognition. In laser detection, the multiple scattering points in the field of view will generate the single-channel multi-component (SCMC) signal. Moreover, the micro-Doppler features of each component will be overlapped in the time-frequency domain because of the similar micro-motion parameters. The overlapped SCMC signal makes the estimation of the MD parameters a very difficult problem, and there has been no good method so far. In this paper, a separate parameter estimator based on the maximum likelihood framework is proposed to deal with this underdetermined problem. First, the detailed period scanning method is presented to improve the estimation accuracy of micro-motion frequency from the singular value ratio (SVR) spectrum. Further, the amplitude ratio information of each component is extracted from the SVR spectrum. Then, the closed-form expressions of the maximum likelihood estimation (MLE) for the remaining micro-motion parameters are derived, where the mean likelihood estimation is used to approximate to the performance of MLE. The high nonlinearity and multi-peak distribution shape of the likelihood function (LF) in laser MD signal will lead to incorrect estimation result. To this end, a new LF based on the energy spectrum characteristics is designed. The new LF acts as a smoothing filter to the probability density function, through which the ideal PDF distribution form that has only one smooth peak is obtained. With this modification, the requirements for the initialization are reduced and the robustness in low SNR situation is increased. The Markov chain Monte Carlo sampling is employed to implement the MLE. The Gibbs method is chosen to solve the multi-dimensional parametric problems, and the detailed process is listed. In the end, the simulation results prove the feasibility and high efficiency of the proposed method. The accuracy of parameter estimation reaches the Cramer-Rao boundary. The inverse Radon transform is used as a comparison with the experiment, and the results show the precise estimation advantage of the presented method.
      Corresponding author: Hu Yi-Hua, skl_hyh@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61271353).
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    Chen V C 2006 IEEE Trans. Aerosp. Electron. Syst. 42 2

    [2]

    Jiang Y 2014 Ph. D. Dissertation (Xi'an: Xidian University) (in Chinese) [姜悦 2014 博士学位论文 (西安: 西安电子科技大学)]

    [3]

    Yang J, Liu C, Wang Y 2015 IEEE Trans. Geosci. Remote Sens. 53 920

    [4]

    Chen V C 2011 The Micro-Doppler Effect in Radar (Fitchburg: Artech House) pp15-17

    [5]

    Wang T, Tong C M, Li X M 2015 Acta Phys. Sin. 64 058401 (in Chinese) [王童, 童创明, 李西敏 2015 物理学报 64 058401]

    [6]

    Hong L, Dai F, Wang X 2016 IEEE Geosci. Remote Sens. Lett. 13 1349

    [7]

    Zhu H, Zhang S N, Zhao H C 2014 Acta Phys. Sin. 63 058401 (in Chinese) [朱航, 张淑宁, 赵惠昌 2014 物理学报 63 058401]

    [8]

    Simeunovic M, Popovic-Bugarin V, Djurovic I 2017 IEEE Trans. Aerosp. Electron. Syst. 53 1273

    [9]

    Tan R, Lim H S, Smits A B 2016 IEEE Region 10 Conference, TENCON, 2016 p730

    [10]

    Chen G F 2014 Ph. D. Dissertation (Xian: Xidian University) (in Chinese) [陈广锋 2014 博士学位论文 (西安: 西安电子科技大学)]

    [11]

    Zhao M M, Zhang Q, Luo Y 2017 IEEE Geosci. Remote Sens. Lett. 14 174

    [12]

    Yang Q, Deng B, Wang H 2014 EURASIP J. Wirel. Comm. 1 61

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    Huo K, You P, Jiang W D 2010 Jounal of Electronics Information Technology 32 355(in Chinese) [霍凯, 游鹏, 姜卫东 2010 电子与信息学报 32 355]

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    Deng D H, Zhang Q, Luo Y 2013 Acta Electronica Sinica 41 2339(in Chinese) [邓冬虎, 张群, 罗迎 2013 电子学报 41 2339]

    [15]

    Zhu H, Zhang S N, Zhao H C 2015 Digital Signal Process. 40 224

    [16]

    Sun Z G, Chen J, Cao X 2016 J.Syst. Engin. Electron. 10 1973

    [17]

    Zhang S N, Zhao H C, Xiong G, Guo C Y 2014 Acta Phys. Sin. 63 158401 (in Chinese) [张淑宁, 赵惠昌, 熊刚, 郭长勇 2014 物理学报 63 158401]

    [18]

    Sharafinezhad S R, Alizadeh H, Eshghi M 2014 Elect. Eng. 22nd Iranian Conference on IEEE Iran, 2014 p1673

    [19]

    Wang Y, Wu X, Li W 2016 Neurocomputing 171 48

    [20]

    Yuan B, Chen Z, Xu S 2014 IEEE Trans. Geosci. Remote Sens. 52 1285

    [21]

    Setlur P, Fauzia A, Moeness A 2011 IET Signal Proc. 5 194

    [22]

    Ye Z F 2009 Statistical Signal Processing (Hefei: China University of Science and Technology Press) pp241-246 (in Chinese) [叶中付 2009 统计信号处理(合肥: 中国科学技术大学出版社) 第241-246页]

    [23]

    Guo L R, Hu Y H, Wang Y P 2016 Proceedings of the SPIE, Photonics Asia Beijng, China, October 11-14, 2016 p21

    [24]

    Hu Y, Guo L, Dong X 2016 Ubiquitous Positioning, Indoor Navigation and Location Based Services (UPINLBS) Fourth Int. Conf. IEEE Shanghai, China, November 2-4, 2016 p264

    [25]

    Hou Z F, Yang J, Zhang X 2011 Journal Wuhan University of Technology 1 142 (in Chinese) [侯者非, 杨杰, 张雪 2011 武汉理工大学学报 1 142]

    [26]

    Kay S M 2006 Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall PTR: Upper Saddle River) pp142-150

    [27]

    Li j, Zhao Y J, Li D H 2014 Acta Phys. Sin. 63 130701 (in Chinese) [李晶, 赵拥军, 李冬海 2014 物理学报 63 130701]

    [28]

    Guo L R, Hu Y H, Wang Y P 2017 Infrared and Laser Engineering 46 17 (in Chinese) [郭力仁, 胡以华, 王云鹏 2017 红外与激光工程 46 17]

  • [1]

    Chen V C 2006 IEEE Trans. Aerosp. Electron. Syst. 42 2

    [2]

    Jiang Y 2014 Ph. D. Dissertation (Xi'an: Xidian University) (in Chinese) [姜悦 2014 博士学位论文 (西安: 西安电子科技大学)]

    [3]

    Yang J, Liu C, Wang Y 2015 IEEE Trans. Geosci. Remote Sens. 53 920

    [4]

    Chen V C 2011 The Micro-Doppler Effect in Radar (Fitchburg: Artech House) pp15-17

    [5]

    Wang T, Tong C M, Li X M 2015 Acta Phys. Sin. 64 058401 (in Chinese) [王童, 童创明, 李西敏 2015 物理学报 64 058401]

    [6]

    Hong L, Dai F, Wang X 2016 IEEE Geosci. Remote Sens. Lett. 13 1349

    [7]

    Zhu H, Zhang S N, Zhao H C 2014 Acta Phys. Sin. 63 058401 (in Chinese) [朱航, 张淑宁, 赵惠昌 2014 物理学报 63 058401]

    [8]

    Simeunovic M, Popovic-Bugarin V, Djurovic I 2017 IEEE Trans. Aerosp. Electron. Syst. 53 1273

    [9]

    Tan R, Lim H S, Smits A B 2016 IEEE Region 10 Conference, TENCON, 2016 p730

    [10]

    Chen G F 2014 Ph. D. Dissertation (Xian: Xidian University) (in Chinese) [陈广锋 2014 博士学位论文 (西安: 西安电子科技大学)]

    [11]

    Zhao M M, Zhang Q, Luo Y 2017 IEEE Geosci. Remote Sens. Lett. 14 174

    [12]

    Yang Q, Deng B, Wang H 2014 EURASIP J. Wirel. Comm. 1 61

    [13]

    Huo K, You P, Jiang W D 2010 Jounal of Electronics Information Technology 32 355(in Chinese) [霍凯, 游鹏, 姜卫东 2010 电子与信息学报 32 355]

    [14]

    Deng D H, Zhang Q, Luo Y 2013 Acta Electronica Sinica 41 2339(in Chinese) [邓冬虎, 张群, 罗迎 2013 电子学报 41 2339]

    [15]

    Zhu H, Zhang S N, Zhao H C 2015 Digital Signal Process. 40 224

    [16]

    Sun Z G, Chen J, Cao X 2016 J.Syst. Engin. Electron. 10 1973

    [17]

    Zhang S N, Zhao H C, Xiong G, Guo C Y 2014 Acta Phys. Sin. 63 158401 (in Chinese) [张淑宁, 赵惠昌, 熊刚, 郭长勇 2014 物理学报 63 158401]

    [18]

    Sharafinezhad S R, Alizadeh H, Eshghi M 2014 Elect. Eng. 22nd Iranian Conference on IEEE Iran, 2014 p1673

    [19]

    Wang Y, Wu X, Li W 2016 Neurocomputing 171 48

    [20]

    Yuan B, Chen Z, Xu S 2014 IEEE Trans. Geosci. Remote Sens. 52 1285

    [21]

    Setlur P, Fauzia A, Moeness A 2011 IET Signal Proc. 5 194

    [22]

    Ye Z F 2009 Statistical Signal Processing (Hefei: China University of Science and Technology Press) pp241-246 (in Chinese) [叶中付 2009 统计信号处理(合肥: 中国科学技术大学出版社) 第241-246页]

    [23]

    Guo L R, Hu Y H, Wang Y P 2016 Proceedings of the SPIE, Photonics Asia Beijng, China, October 11-14, 2016 p21

    [24]

    Hu Y, Guo L, Dong X 2016 Ubiquitous Positioning, Indoor Navigation and Location Based Services (UPINLBS) Fourth Int. Conf. IEEE Shanghai, China, November 2-4, 2016 p264

    [25]

    Hou Z F, Yang J, Zhang X 2011 Journal Wuhan University of Technology 1 142 (in Chinese) [侯者非, 杨杰, 张雪 2011 武汉理工大学学报 1 142]

    [26]

    Kay S M 2006 Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice Hall PTR: Upper Saddle River) pp142-150

    [27]

    Li j, Zhao Y J, Li D H 2014 Acta Phys. Sin. 63 130701 (in Chinese) [李晶, 赵拥军, 李冬海 2014 物理学报 63 130701]

    [28]

    Guo L R, Hu Y H, Wang Y P 2017 Infrared and Laser Engineering 46 17 (in Chinese) [郭力仁, 胡以华, 王云鹏 2017 红外与激光工程 46 17]

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  • Citation:
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Publishing process
  • Received Date:  12 December 2017
  • Accepted Date:  23 January 2018
  • Published Online:  05 June 2018

Separate estimation of laser micro-Doppler parameters based on maximum likelihood schemes

    Corresponding author: Hu Yi-Hua, skl_hyh@163.com
  • 1. State Key Laboratory of Pulsed Power Laser Technology, College of Electronic Engineering, National University of Defense Technology, Hefei 230037, China;
  • 2. Anhui Province Key Laboratory of Electronic Restriction Technology, College of Electronic Engineering, National University of Defense Technology, Hefei 230037, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 61271353).

Abstract: Laser micro-Doppler (MD) effect is capable of obtaining obvious modulation in weak vibration detection. It helps to estimate target micro-motion parameters with high precision, which may extend the application field of MD to subtle identification and recognition. In laser detection, the multiple scattering points in the field of view will generate the single-channel multi-component (SCMC) signal. Moreover, the micro-Doppler features of each component will be overlapped in the time-frequency domain because of the similar micro-motion parameters. The overlapped SCMC signal makes the estimation of the MD parameters a very difficult problem, and there has been no good method so far. In this paper, a separate parameter estimator based on the maximum likelihood framework is proposed to deal with this underdetermined problem. First, the detailed period scanning method is presented to improve the estimation accuracy of micro-motion frequency from the singular value ratio (SVR) spectrum. Further, the amplitude ratio information of each component is extracted from the SVR spectrum. Then, the closed-form expressions of the maximum likelihood estimation (MLE) for the remaining micro-motion parameters are derived, where the mean likelihood estimation is used to approximate to the performance of MLE. The high nonlinearity and multi-peak distribution shape of the likelihood function (LF) in laser MD signal will lead to incorrect estimation result. To this end, a new LF based on the energy spectrum characteristics is designed. The new LF acts as a smoothing filter to the probability density function, through which the ideal PDF distribution form that has only one smooth peak is obtained. With this modification, the requirements for the initialization are reduced and the robustness in low SNR situation is increased. The Markov chain Monte Carlo sampling is employed to implement the MLE. The Gibbs method is chosen to solve the multi-dimensional parametric problems, and the detailed process is listed. In the end, the simulation results prove the feasibility and high efficiency of the proposed method. The accuracy of parameter estimation reaches the Cramer-Rao boundary. The inverse Radon transform is used as a comparison with the experiment, and the results show the precise estimation advantage of the presented method.

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