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{-2/spl alpha//sup 2/.f/sub d//sup 2/t/sup 2/}cos(2/spl pi/f/sub d/t)-where the Doppler frequency f/sub d/ is related to particle's velocity. This paper is concerned with the best accurate estimation of the parameters A and f/sub d/ in the model considered. Cramer-Rao bounds on the accuracy of estimates of A and f/sub d/ are derived and closed-formed expressions are given. Approximate formulas provide quantitative insights into the influence of /spl alpha/ and f/sub 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 /spl alpha/ and the frequency f/sub d/ on the estimation performance are emphasized.