Approximate maximum likelihood estimation in laser velocimetry

In this paper, we study the estimation of signals of the form s(t) = A.exp {− 2α
²
f
²
d
t
²
}.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 f
d
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 f
d
and the parameter a. They show that the estimator is statistically efficient in a wide range of scenarios.