激光多普勒测速参数估计的Cramer-Rao下限

Cramer-Rao Lower Bounds of Parameter Estimation from Laser Doppler Velocimetry

针对固体运动目标高速度、高加速度的特点,研究了高斯白噪声背景下激光多普勒测速回波信号的参数估计问题。通过计算参数矢量的费希尔(Fisher)信息矩阵,分析了实回波信号的多普勒频率和频率变化率估计方差的克拉末-雷奥(Cramer-Rao)下限(CRLB),推导了采样点数较大时回波信号参数方差估计的CRLB计算公式,讨论了各参数的最大似然估计(MLE)。指出回波信号参数估计方差的CRLB与采样点数、信噪比及初相有关,采样点数较大时,实信号参数估计方差的CRLB为对应复信号的2倍。在不同的采样点数和信噪比下仿真表明,提高回波信号的信噪比和增加采样点数可以减小各参数估计方差的CRLB,结果与理论分析吻合。

Aiming at the high-speed and high-acceleration features of solid moving targets, the parameter estimation of laser Doppler velocimetry echo signal under white Gaussian noise were investigated. By computing the Fisher information metrix of parameter vectors, Cramer Rao low hounds （CRLBs） of the real echo signal Doppler frequency and frequency rate were analyzed, formulas of the CRLBs were derived when the length of sample data was large, and the maximum likelihood estimator （MLE） was discussed. The CRLBs of the variance of estimated parameter of the real echo signal are affected by the length of sample data, signal to noise ratio （SNR）, and the initial phase. When the length of sample data is large, the CRLBs of the variance of estimated parameter are twice of the corresponding complex signal. The simulations under conditions of different lengths of sample data and different SNR indicate that increasing the length of sample data and SNR can minish CRLBs of the variance of estimated parameter, and the results fit well with theoretical analysis.