Bounds for estimation of particle´s velocity from laser measurements

The problem of estimating the speed of a particle of air passing through the region of interference fringes generated by two coherent laser beams is addressed. The signal detected is of the form A.exp{-2α².f_d²t² }cos(2πf_dt)-where the Doppler frequency f_d is related to particle´s velocity. This paper is concerned with the best accurate estimation of the parameters A and f_d in the model considered. Cramer-Rao bounds on the accuracy of estimates of A and f_d are derived and closed-formed expressions are given. Approximate formulas provide quantitative insights into the influence of α and f_d. Additionally, a maximum likelihood estimator is presented. Numerical examples illustrate the performance of the MLE and compare it with the CRB. The influence of the SNR, the sample size, the optical parameter α and the frequency f _d on the estimation performance are emphasized