Bayesian Estimation of Localization Uncertainty in Joint Particle–Flow Reconstruction

Physics-informed data assimilation (DA) for Lagrangian particle tracking (LPT) reconstructs velocity and pressure fields from particle tracks by balancing the data with prior information from the governing equations. This balance depends on the assumed particle localization uncertainty, whose depth-wise component, σz, is often poorly characterized. Mis-specified uncertainty can cause the reconstruction to overfit to noise or smooth out genuine fluctuations, producing errors that propagate to the pressure field and downstream quantities of interest. We address this problem by reformulating neural-implicit particle advection (NIPA), a DA method for LPT, as a Bayesian inference problem. The resulting framework infers σz together with the latent particle positions and Eulerian flow fields. Measurement-based uncertainty estimates are incorporated as weak priors on σz, and the extension has nearly the same computational cost as the original formulation. The method is evaluated using a synthetic turbulent channel flow, an experimental zero-pressure-gradient turbulent boundary layer, and an experimental fluid-structure interaction case. In the synthetic case, the inferred uncertainty recovers the true uncertainty to within 3% across a sixteen-fold sweep of prior centers. In the experimental cases, the inferred values of σz and reconstructed fields are stable across the same sweep. These results show that depth-wise localization uncertainty can be inferred using DA, reducing the sensitivity of reconstructions to manually prescribed uncertainties.