Approximate maximum likelihood estimation in laser velocimetry

In this paper, we study the estimation of signals of the form s(t) = A.exp {− 2α²f²dt²}.cos (2πfdt) which are encountered in the measurement of particles velocity in a flow by means of laser Doppier velocimeters. We derive an Approximate Maximum Likelihood Estimator of the parameters A and fd in the model considered. The algorithm is based upon replacing the first and second-order derivatives of the log-likelihood function by approximated and easy to compute expressions. Numerical examples illustrate the performance of the proposed method and quantify the influence of the sample size, the frequency fd and the parameter a. They show that the estimator is statistically efficient in a wide range of scenarios.