Gaussian Process and PCA-Based Methods for GNSS Data Gap Filling

Abstract GNSS position time series are essential for monitoring crustal deformation but often contain data gaps due to equipment failures, maintenance, and quality control. Accurate gap filling is vital for reliable velocity estimation, noise characterisation, and tectonic interpretation. This study compares three methodologies for gap imputation: a novel hierarchical Gaussian process regression (GPR) approach using composite kernels to capture multiple temporal scales, weighted principal component analysis (WPCA), and expectation-maximisation PCA (EMPCA). Our GPR framework employs physically interpretable kernels to represent distinct processes, including long‑term trends (radial basis functions), short‑term correlations (Matérn), seasonal cycles (periodic), and measurement/coloured noise (i.e., white and flicker), alongside station‑specific noise modelling and parallel processing for efficiency. Evaluation using synthetic gaps and field data from 70 stations on Italy's North Adriatic coasts shows that GPR achieves superior accuracy, significantly reducing reconstruction error for irregular gaps while providing robust uncertainty estimates. PCA-based methods, though faster, introduce more spurious correlations and are less reliable for station-specific signals. Based on these findings, we provide clear guidelines for method selection depending on gap duration, network density, and computational constraints.