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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。
In view of the characteristics of high speed and high acceleration of solid moving targets, the parameter estimation of laser Doppler velocimetry echo signals under white Gaussian noise is studied. The Cramer-Rao lower bound (CRLB) of Doppler frequency and frequency variance of real echo signals was analyzed by calculating Fisher’s information matrix of parameter vector, When the number of points is large, the CRLB formula of variance estimation of echo signal parameters is discussed, and the Maximum Likelihood Estimation (MLE) of each parameter is discussed. It is pointed out that the CRLB of the estimated variance of the echo signal parameters is related to the number of sampling points, the signal-to-noise ratio and the initial phase. When the number of sampling points is large, the CRLB of the estimated variance of the real signal is 2 times of the corresponding complex signal. Simulations under different sampling points and SNR show that increasing the signal-to-noise ratio of the echo signal and increasing the number of sampling points can reduce the CRLB of the variance of each parameter estimation. The results are in good agreement with the theoretical analysis.