Modeling of Colored Noise in Long-term GNSS Coordinate Series and its Impact

Objectives: The presence of colored noise in Global Navigation Satellite System (GNSS) coordinate time series data holds significant value for the analysis of GNSS coordinate models, particularly in velocity analysis. In previous studies, researchers have focused on modeling colored noise in the short to medium-term coordinate series of 10-15 years, paying less attention to the variation of long-term accumulation of coordinate series on colored noise modeling. Methods: Therefore, we investigated 78 coordinate series from 26 International GNSS Service (IGS) stations in California over a period of nearly 30 years. We compared eight commonly used noise models by utilizing the maximum likelihood estimation method to estimate the parameters of noise models and the Akaike Information Criterion is applied to select the optimal model among the alternative models. Results: The results indicate that among the selected IGS reference stations, 61.5% of the series exhibit WN+PL+RWN (White Noise + Power-law Noise + Random Walk Noise) as the optimal model in the N direction, while this proportion is 57.7% and 42.3% in the U direction and E direction, respectively. Then the velocity uncertainty (standard deviation) estimation is performed between the optimal model and the control model WN+PL (White Noise + Power-law Noise). We found that the average velocity uncertainty of the preferred model is 5.2 times higher than the control model in the N direction, 5.0 times higher in the E direction, and 4.0 times higher in the U direction. Conclusions: the research in this paper demonstrates the following: the choice of noise models has a significant impact on the estimation of velocity uncertainty parameters, the results vary apparently when different noise models are used. In order to accurately and objectively represent the uncertainty of velocity estimates, it is advisable to carry out meticulous analysis of colored noise modeling in practical applications. Additionally, most of GNSS coordinate series with a duration of over 16 years have the potential to detect RWN, and models without RWN tend to significantly overestimate velocity uncertainty. Hence, the impact of RWN in long-term GNSS coordinate series data cannot be disregarded.