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

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6dB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。

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.