光学学报, 2011, 31 (10): 1012001, 网络出版: 2011-09-20   

车载激光多普勒测速仪参数估计的Cramer-Rao下限

Cramer-Rao Lower Bound for Parameter Estimation of Mobile Laser Doppler Velocimeter
作者单位
国防科学技术大学光电科学与工程学院, 湖南 长沙 410073
摘要
考虑到加速度和高斯型包络对激光多普勒测速仪的影响,在引入加速度分量的基础上,研究了高斯包络型多普勒信号的参数估计。根据数理统计的理论,分析了多普勒圆频率及其一阶变化率估计方差的Cramer-Rao下限(CRLB),给出了参数估计方差的CRLB计算公式,并讨论了各参数带修正的功率谱估计。理论分析及仿真结果表明:参数估计方差的CRLB与观测数据长度、信噪比和高斯包络的宽度有关,增加观测数据长度和提高信噪比可以减小参数估计方差的CRLB;当观测数据一定时,加速度越大,高斯包络的宽度就越窄,参数估计方差的CRLB越大;当信噪比增加到6 dB时,运用带修正的功率谱估计算法得到的多普勒圆频率及其一阶变化率估计值的方差收敛于相应的CRLB。所得参数估计方差的CRLB与此前其他研究者得出的结论是相互协调的。
Abstract
Considering the influence of acceleration and the Gaussian envelope on laser Doppler velocimeter (LDV), the parameters estimation of Doppler signal with Gaussian envelope is investigated based on introducing the acceleration. According to the theory of mathematics statistics, the Cramer-Rao lower bounds (CRLB) of Doppler circular frequency and its first order rate of change are analyzed, formulas of CRLB are given, and the power spectrum estimation with adjustment is discussed. The theoretical analysis and simulation results show that the CRLB of the variance of estimated parameters are related to the observation data, signal-to-noise ratio (SNR), the width of Gaussian envelope, and it can be decreased by increasing the length of observation data and improving the SNR. When the length of observation data is fixed, the larger the acceleration is, the narrower the Gaussian envelope is, and the CRLB of Doppler circular frequency and its first order rate are also larger. The gap between the variances of the measuring results and the CRLB narrows when the SNR of the signal is improved, almost eliminates when the SNR is higher than 6 dB. The acquired result is in harmony with those acquired by other researchers.
参考文献

[1] D. B. Brayton, H. T. Kalb, F. L. Crosswy. Two-component dual-scatter laser Doppler velocimeter with frequency burst signal readout [J]. Appl. Opt., 1973, 12(6): 1145~1156

[2] René Shov Hansen, Christian Pedersen. All semiconductor laser Doppler anemometer at 1.55 μm [J]. Opt. Express, 2008, 16(22): 18288~18295

[3] D. C. Rife, R. R. Boorstyn. Single-tone parameter estimation from discrete-time observations [J]. IEEE Trans. Inform. Theory, 1974, 20(5): 591~598

[4] 齐国清. 离散实正弦信号参数估计的Cramer Rao方差下限[J]. 数据采集与处理, 2003, 18(2): 151~155

    Qi Guoqing. Cramer Rao bounds of real sinusoid parameter estimation from discrete-time observations [J]. J. Data Acquisition & Processing, 2003, 18(2): 151~155

[5] Richard Bamler. Doppler frequency estimation and the Cramer-Rao bound [J]. IEEE Trans. Geosci. Remote Sensing, 1991, 29(3): 385~390

[6] 沈熊. 激光多普勒测速技术及应用[M]. 北京:清华大学出版社,2004. 37~39

    Shen Xiong. Laser Doppler Velocimetry and Its Application [M]. Beijing: Tsinghua University Press, 2004. 37~39

[7] 孙渝生. 激光多普勒测量技术及其应用[M].上海:上海科学技术文献出版社,1995. 142

    Sun Yusheng. The Technology and Application of Laser Doppler Measurement [M]. Shanghai: Shanghai Scientific and Technological Literature Publishing House, 1995. 142

[8] 王纪强, 张春熹, 马宗峰 等. 激光多普勒测速参数估计的Cramer-Rao下限[J]. 中国激光, 2008, 35(9): 1419~1422

    Wang Jiqiang, Zhang Chunxi, Ma Zongfeng et al.. Cramer-Rao lower bounds of parameter estimation from laser doppler velocimetry [J]. Chinese J. Lasers, 2008, 35(9): 1419~1422

[9] 殳伟群. 激光多普勒测速频率估计的Cramer-Rao下限[J]. 计量学报, 2003, 24(1): 36~39

    Shu Weiqun. The Cramer-Rao bound for frequency estimation from LDA measurements [J]. Acta Metrologica Sinica, 2003, 24(1): 36~39

[10] 周健, 龙兴武. 用于车载自主惯导系统的激光多普勒测速仪[J]. 中国激光, 2010, 37(5): 1316~1321

    Zhou Jian, Long Xingwu. Laser Doppler velocimeter for vehicle inertial navigation system [J]. Chinese J. Lasers, 2010, 37(5): 1316~1321

[11] 周健, 龙兴武. 多点分层差动激光多普勒自身测速仪的研究[J]. 中国激光, 2010, 37(7): 1837~1844

    Zhou Jian, Long Xingwu. Research on multipoint layer-type laser Doppler self-velocimeter [J]. Chinese J. Lasers, 2010, 37(7): 1837~1844

[12] 贺岩, 尚建华,刘丹 等. 用于水下声光通信的外差式激光多普勒振动计[J]. 中国激光, 2009, 36(1): 189~194

    He Yan, Shang Jianhua, Liu Dan et al.. Heterodyne laser Doppler vibrometer for underwater acousto-optic communication [J]. Chinese J. Lasers, 2009, 36(1): 189~194

周健, 魏国, 龙兴武. 车载激光多普勒测速仪参数估计的Cramer-Rao下限[J]. 光学学报, 2011, 31(10): 1012001. Zhou Jian, Wei Guo, Long Xingwu. Cramer-Rao Lower Bound for Parameter Estimation of Mobile Laser Doppler Velocimeter[J]. Acta Optica Sinica, 2011, 31(10): 1012001.

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