Analysis of a frequency estimator for a class of laser signals with time-varying amplitude

The authors address the problem of estimating a particle's velocity in the vicinity of an aircraft by means of a laser velocimeter. A model for the signal generated by a particle of air passing through a probe volume consisting of equidistant bright and dark fringes is given. From this model, a frequency estimator based on the phase of the correlation sequence of the signal is proposed. A theoretical analysis of the frequency estimator is presented. In particular, a formula for the variance of the estimate is derived under the assumption of small estimation errors. Numerical examples confirm the validity of the analysis. It is reported that this estimator, although simpler than the maximum likelihood approach, comes close to the Cramer-Rao bound. Finally, the effectiveness of the proposed algorithm is demonstrated on real data.