Nonparametric estimation of non-stationary velocity fields from 3D particle tracking velocimetry data

Nonparametric estimation of nonstationary velocity fields from 3D particle tracking velocimetry data is considered. The velocities of tracer particles are computed from their positions measured experimentally with random errors by high-speed cameras observing turbulent flows in fluids. Thus captured discrete data is plugged into a smoothing spline estimate which is used to estimate the velocity field at arbitrary points. The estimate is further smoothed over several time frames using the fixed design kernel regression estimate. Consistency of the resulting estimate is investigated. Its performance is validated on the real data obtained by measuring a fluid flow of a liquid in a (rotating) square tank agitated by an oscillating grid.