TrackFit: Uncertainty Quantification, Optimal Filtering and Interpolation of Tracks for Time-Resolved Lagrangian Particle Tracking

Advanced Lagrangian Particle Tracking methods (such as the STB algorithm (Schanz et al. 2016)) are a very useful tool for uncovering properties of flow. As a measurement technique, the results of such methods are perturbed by different sources of errors and noise. This work addresses the problem of optimal filtering of particle tracks as well as estimating uncertainties of derived quantities such as location, velocity and acceleration of observed particles. The behavior and performance of this new filtering method (“TrackFit”), first introduced at Gesemann et al. (2016) is analyzed and compared to the Savitzky–Golay filter (Savitzky and Golay (1964)) which is commonly used for these purposes. The optimal choice of parameters of this filtering method as well as the uncertainty quantification of the reconstructed tracks can be extracted from a spectral analysis of the recorded raw particle tracking data. This is in contrast to a Savitzky–Golay filter where the choice of parameters might often be driven by experience and gut feeling. Estimating the power spectral density (PSD) of the particle trajectory signals for the purpose of optimal filtering parameter selection represents a challenge due to possibly short trajectory signals. In the following work we will present a method for PSD estimation that is applicable in this scenario. In addition, we show that regardless of the choice of Savitzky–Golay filter parameters, the resulting filter will not approximate the ideal noise reduction filter well unlike the “TrackFit” described in this work.