Estimating particles velocity from laser measurements: maximum likelihood and Cramer-Rao bounds

We address the problem of estimating particles velocity in the vicinity of an aircraft by means of a laser Doppler system. When a particle passes through the region of interference fringes generated by two coherent laser beams, the signal backscattered is of the form Aexp{-2/spl alpha//sup 2//spl middot/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 the aircraft speed. This paper is concerned with the most precise estimation of the parameters A and f/sub d/ in the model considered. Cramer-Rao bounds (CRBs) on the accuracy of estimates of A and f/sub d/ are derived, and closed-formed expressions are given. Approximated formulas provide quantitative insights into the influence of /spl alpha/ and f/sub d/. Additionally, a maximum likelihood estimator (MLE) 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 is emphasized. Finally, an application to real data is presented.