Lagrangian Particle Tracking: a link between localization error and fraction of missed particles

This paper aims at analysing the behaviour of particle localisation error in 3D Lagrangian Particle Tracking (LPT) techniques, with a particular emphasis on general properties, independent of a specific algorithm. Based on the hypothesis that in LPT algorithms, errors on the image formation models are solely due to random noise, we show/prove the existence of a best achievable root mean square error (RMSE) on particle localisation, that, for a setup at a given seeding density, depends only on the noise level. We provide a procedure to estimate this lower bound, and show that it can only be reached if there are no missed detections; further on, we establish a link between localisation error and fraction of missed particles. We illustrate the consistency of this model on the results of the recent First Challenge on LPT (see ISPIV21 papers by Leclaire et al. and Sciacchitano et al.)