A fair review of non-parametric bias-free autocorrelation and spectral methods for randomly sampled data in laser Doppler velocimetry

This paper presents a comparison of currently available methods for non-parametric and bias-free estimation of the autocorrelation function and power spectral density from randomly sampled data. The primary motivation is the processing of velocity data obtained using laser Doppler techniques in turbulent flows. However, the methods are applicable to various other cases of random sampling, including those with small deviations from the ideal Poisson process. Whilst these methods have been compared in the literature before, a fair comparison of their relative performance requires that they be tested under identical conditions. This includes identical use of special processing options and identical processing parameters. This has not been achieved in the literature to date. An example application on publicly available laser Doppler data shows agreement between the results obtained with the different methods. Under this fair comparison, the methods converge in terms of their systematic and random errors, indicating that they are comparably efficient at using the available information content of the randomly sampled signal. The results also identify that the available methods are interchangeable and indicate a possible replacement for the current best-practice procedure in the laser Doppler community.