Bias in particle tracking acceleration measurement

Abstract

We investigate sources of systematic error (bias) in acceleration statistics derived from Lagrangian particle tracking data and demonstrate techniques to eliminate or minimise these bias errors introduced during processing. Numerical simulations of particle tracking experiments in isotropic turbulence show that the main sources of bias error arise from noise due to random position errors and selection biases introduced during numerical differentiation. We outline the use of independent measurements and filtering schemes to eliminate these biases. Moreover, we test the validity of our approach in estimating the statistical moments and probability densities of the Lagrangian acceleration. Finally, we apply these techniques to experimental particle tracking data and demonstrate their validity in practice with comparisons to available data from the literature. The general approach, which is not limited to acceleration statistics, can be applied with as few as two cameras and permits a substantial reduction in the position accuracy and sampling rate required to adequately measure the statistics of Lagrangian acceleration.Graphical abstractSources of bias error in Lagrangian Particle Tracking measurements are explored. Methods are presented and validated to correct acceleration statistics for the main sources of systematic errors introduced by random position error and filtering, allowing for a substantial improvement in the effective temporal resolution of particle tracking measurements.