Generalized Matérn Process for GNSS Coordinate Series Noise Modeling

Abstract

GNSS coordinate series noise modeling is essential for reliable geophysical signal estimation and uncertainty assessment. The generalized Gauss–Markov (GGM) noise model and the Matérn process (MP) noise model are widely used to describe low-frequency spectral flattening in GNSS coordinate series, but they differ in their definition domains, parameterizations and autocovariance function (ACF) structures. These differences may lead to misconceptions, complicate noise model comparison and practical implementation. Building on a systematic review of the theories of GGM and MP, this study proposes a generalized Matérn process (GMP) noise model. By introducing a fractional step size hyperparameter μ into the differencing operator, GMP provides a unified framework that continuously connects the two models: when μ = 1, GMP reduces to GGM; as μ → 0, the spectrum of GMP approaches that of MP. The preferred range of μ is investigated using 420 GNSS coordinate series from 140 global GNSS sites, considering differences in geographical region, coordinate component and length of observations. The results show that the preferred values of μ are robustly concentrated within the interval [0.7, 1]. Large-scale validation is then conducted using 846 GNSS coordinate series from 282 global GNSS sites. The experimental results show that under AIC, BIC and BICtp, the proposed WN + GMP family consistently accounts for a large proportion of the optimal models. These results demonstrate that GMP provides a more general noise model family for GNSS coordinate series noise modeling and can improve the fidelity and flexibility of stochastic noise modeling.