Kalman filter-based volumetric PTV particle tracking

Volumetric Particle Tracking Velocimetry (3D-PTV) is a non-invasive optical technique that measures fluid flow velocity by tracking the motion of neutrally buoyant tracer particles seeded into the flow. Each particle's images from different cameras are triangulated to find the 3D positions, which are subsequently tracked across frames to estimate the Lagrangian trajectory. This process is especially challenging at higher particle concentrations leading to overlapping particle images and erroneous reconstructions. Shake-The-Box has overcome this issue for time-resolved data by imposing the temporal continuity of tracks using a Wiener filter-based track predictor. However, optimal Wiener filter predictions require stationarity of the track evolution process and knowledge of noise statistics. On the other hand, a Kalman filter's Bayesian approach works on an uncertainty-informed iterative estimation methodology. Taking into consideration the recently proposed comprehensive 3D-PTV uncertainty estimation model we integrate a Kalman filter-based (KF) prediction, in place of the Wiener filter, to update the trajectory at each step. The current framework is tested for a synthetic vortex ring case at different noise levels.