Laser Doppler Data Processing

Techniques - (Inter-)Arrival-Time Weighting

(Inter-)Arrival-Time Weighting uses an estimate of the instantaneous data rate to obtain the weighting factor $w_i$ corresponding to the velocity sample $u_i$. The instantaneous data rate, in turn, is estimated from the interval between the particle arrival time $t_i$ and the arrival of the preceding particle $t_{i-1}$.

This weighting scheme has been found to be robust against even varying correlations between the instantaneous data rate and the velocity. The expression of the weighting factor above is suited for the weighted mean and the weighted variance estimators. However, correlation and spectral estimates suffer from a inherent correlation between the inter-arrival times and the lag time of the correlation function. This issue can be solved using the Forward-Backward (Inter-)Arrival-Time Weighting.

However, the efficiency of this weighting method depends on the reduced data rate, which is the number of samples per integral timescale (also called the data density). To get the statistical bias suppressed sufficiently, data densities in the order of about ten samples per integral timescale are necessary. Typical data densities of a few samples per integral timescale are definitely not sufficient. This has led to reservations against using this weighting scheme in the community. Transit-Time Weighting should be preferred. Only if adequate transit times are not available, arrival-time weighting can be used instead, keeping in mind that this weighting scheme is efficient only at high enough data densities.

original paper:

• Barnett D O and Bentley H T III (1974): Statistical Biasing of Individual Realization Laser Velocimeters. Proc. 2nd Int. Workshop on Laser Velocimetry, Purdue University, Lafayette, IN, USA, 428-444

review papers:

• Fuchs W, Albrecht H, Nobach H, Tropea C and Graham L J W (1992): Simulation and Experimental Verification of Statistical Bias in Laser Doppler Anemometry including Non-Homogeneous Particle Density. Proc. 6th Int. Symp. on Appl. of Laser Techn. to Fluid Mech., Lisbon, Portugal, paper 8.2
• Fuchs W, Nobach H and Tropea C (1994): Laser Doppler Anemometry Data Simulation: Application to Investigate the Accuracy of Statistical Estimators. AIAA Journal 32, 9, 1883-1889

overview and comparison:

• Damaschke N, Kühn V, Nobach H (2018): A Fair Review of Non-parametric Bias-free Autocorrelation and Spectral Methods for Randomly Sampled Data in Laser Doppler Velocimetry. Digital Signal Processing, 76, 22-33