The effect of a particle trajectory through the measurement volume on the accuracy of the laser Doppler frequency estimation

The minimum achievable uncertainty of the Doppler frequency estimation of any unbiased estimator is given by the Cramér-Rao lower bound (CRLB). In this paper, we consider the effect of the particle trajectory via the measurement volume on the CRLB by employing the 2D model of the Gaussian envelope of the Doppler Burst Signal (DBS). The simulation results confirmed the theoretical predictions in terms of the relative effect of the particle trajectory, the measurement time, the size of the volume and SNR on the accuracy of the Doppler frequency estimation. The obtained analytical expression for the CRLB could be applied in engineering applications, e.g. requiring the estimation of the uncertainty of cross flow particle velocity with a known mean flow velocity component.