Cramer-Rao lower bounds of parameter estimation from laser doppler velocimetry

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 matrix of parameter vectors, Cramer-Rao low bounds (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.