The Relationship of Time Span and Missing Data on the Noise Model Estimation of GNSS Time Series

Accurate noise model identification for GNSS time series is crucial for obtaining a reliable GNSS velocity field and its uncertainty for various studies in geodynamics and geodesy. Here, by comprehensively considering time span and missing data effect on the noise model of GNSS time series, we used four combined noise models to analyze the duration of the time series (ranging from 2 to 24 years) and the data gap (between 2% and 30%) effects on noise model selection and velocity estimation at 72 GNSS stations spanning from 1992 to 2022 in global region together with simulated data. Our results show that the selected noise model have better convergence when GNSS time series is getting longer. With longer time series, the GNSS velocity uncertainty estimation with different data gaps is more homogenous to a certain order of magnitude. When the GNSS time series length is less than 8 years, it shows that the flicker noise and random walk noise and white noise (FNRWWN), flicker noise and white noise (FNWN), and power law noise and white noise (PLWN) models are wrongly estimated as a Gauss-Markov and white noise (GGMWN) model, which can affect the accuracy of GNSS velocity estimated from GNSS time series. When the GNSS time series length is more than 12 years, the RW noise components are most likely to be detected. As the duration increases, the impact of RW on velocity uncertainty decreases. Finally, we show that the selection of the stochastic noise model and velocity estimation are reliable for a time series with a minimum duration of 12 years.

Automated summary

Accurate identification of noise models for GNSS time series is crucial for reliable GNSS velocity field and uncertainty estimation in geodynamics and geodesy. By considering time span and missing data effects, we analyzed the impact of duration and data gaps on noise model selection and velocity estimation using four combined noise models. Results show that longer time series improve the convergence of selected noise models and homogenize the velocity uncertainty estimation. However, inaccurate estimation of noise models can occur for shorter time series, affecting the accuracy of GNSS velocity estimation. Finally, a minimum time series duration of 12 years is recommended for reliable selection of noise models and velocity estimation.