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

• Published in: Methodology and computing in applied probability Vol. 26; no. 1; p. 9
• Main Authors: Perrin, Guillaume, Soize, Christian
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2024; Springer Nature B.V; Springer Verlag
• Subjects: Approximation; Business and Management; Clustering; Economics; Electrical Engineering; Fields (mathematics); Life Sciences; Mathematics; Mathematics and Statistics; Polynomials; Probability distribution; Reconstruction; Risk analysis; Sampled data; Spectral methods; Statistical inference; Statistics; Structured data; 62G07; 60B99; Data-driven sampling; 60G60; Nonparametric representation; Statistical inference; Manifold learning; 62M30; data-driven sampling; nonparametric representation; manifold learning
• ISSN: 1387-5841; 1573-7713
• DOI: 10.1007/s11009-024-10079-w

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.