Maximum Likelihood Estimator, FFT Estimator and Cramér-Rao bounds of the laser Doppler frequency: The effect of a particle trajectory through the measurement volume

This paper addresses the problem of estimating the Doppler frequency in Laser Doppler Velocimetry (LDV) systems by taking into account the effect of the particle trajectory via the measurement volume. The dependency of the burst length on the Cramér-Rao lower bound (CRLB) and the Doppler frequency estimation is investigated by employing the 2D model of the Doppler Burst Signal with the Gaussian envelope. The Maximum Likelihood Estimator (MLE) equations are solved for estimates of the Doppler frequency for LDV systems operating in one particle scattering mode. The numerical examples show the performance of the MLE and FFT with various parameter configurations compared with the derived CRLB. The numerical results confirm the validity of the analysis in terms of the relative effect of the particle trajectory, relative measurement time, size of the volume and signal-to-noise ratio on the accuracy of the estimation.