Uncertainty Quantification in Volumetric Particle Tracking Velocimetry (PTV)

Volumetric PTV resolves 3D flow structures by tracking the motion of tracer particles seeded in a fluid. Recent advances in 3D PTV through iterative particle reconstruction methods like STB have shown increased reconstruction accuracy even for higher seeding densities. However, predicting the uncertainty in such a measurement is challenging due to the underdetermined system of equations associated with the inverse reconstruction problem, coupled with various factors affecting the calibration and tracking process. Here, we quantify the uncertainty in a particle based volumetric reconstruction and subsequently in a 3D PTV measurement. The reconstructed particle position uncertainty is a combination of the uncertainties in the volumetric calibration coefficients and the particle image position estimation. The LSQ fit uncertainty in the mapping function coefficients contributes to the calibration uncertainty. The uncertainty due to the mismatch between the projected and actual particle image locations is also considered. Finally, an uncertainty propagation through the 3D reconstruction equation gives the 3D position uncertainty, which directly affects the uncertainty in a 3D tracking process. The proposed methodology is tested for synthetic uniform flow and vortex ring cases.