Estimating particles velocity from laser measurements: maximumlikelihood and Cramer-Rao bounds |
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| Authors: | Besson O. Galtier F. |
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| Affiliation: | Dept. of Avionics & Syst., Ecole Nat. Superieure d'Ingenieurs de Constr. Aeronaut., Toulouse; |
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| Abstract: | 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{-2α2·fd2t2 }cos{2πfdt}, where the Doppler frequency fd is related to the aircraft speed. This paper is concerned with the most precise estimation of the parameters A and fd in the model considered. Cramer-Rao bounds (CRBs) on the accuracy of estimates of A and fd are derived, and closed-formed expressions are given. Approximated formulas provide quantitative insights into the influence of α and fd. 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 α, and the frequency fd on the estimation performance is emphasized. Finally, an application to real data is presented |
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