Reconstruction of Random Fields Concentrated on an Unknown Curve using Irregularly Sampled Data

Guillaume Perrin (1, 2, 3) , Christian Soize (4)

1 Université Gustave Eiffel
2 RT-UQ - GDR2172 - Quantification d'incertitudes (RT-UQ)
3 COSYS - Département Composants et Systèmes
4 MSME - Laboratoire Modélisation et Simulation Multi-Echelle

In the world of connected automated objects, increasingly rich and structured data are collected daily (positions, environmental variables, etc.). In this work, we are interested in the characterization of the variability of the trajectories of one of these objects (robot, drone, or delivery droid for example) along a particular path from irregularly sampled data in time and space. To do so, we model the position of the considered object by a random field indexed in time, whose distribution we try to estimate (for risk analysis for example). This distribution being by construction concentrated on an {unknown curve}, two phases are proposed for its reconstruction: a phase of identification of this {curve}, by clustering and polynomial smoothing techniques, then a phase of statistical inference of the random field orthogonal to this {curve}, by spectral methods and kernel reconstructions. The efficiency of the proposed approach, both in terms of computation time and reconstruction quality, is illustrated on several numerical applications.

Mots clés: Statistical inference; manifold learning; nonparametric representation; data-driven sampling

Domaines: Mathématiques [math]; Statistiques [stat]

Guillaume Perrin, Christian Soize. Reconstruction of Random Fields Concentrated on an Unknown Curve using Irregularly Sampled Data. Methodology and Computing in Applied Probability, 2024, 26 (1), pp.9. ⟨10.1007/s11009-024-10079-w⟩. ⟨hal-04504936⟩