Abstract:
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 the previous studies, the researchers 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, USA, over a period of nearly 30 years. We employed the maximum likelihood estimation method to estimate the parameters of noise models, comparing eight commonly-used models including white noise (WN), flicker noise, power-law noise (PL), random walk noise (RWN), and generalized Gauss-Markov noise. And 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, 42.3% of the series exhibit WN+PL+RWN as the optimal model in the east (E) direction, while this proportion is 61.5% and 57.7% in the north (N) direction and up (U) direction, respectively. Then the velocity uncertainty (standard deviation) estimation is performed between the optimal model and the control model of WN+PL. We find that the average velocity uncertainty of the preferred model is 5.0 times higher than the control model in the E direction, 5.2 times higher in the N direction, and 4.0 times higher in the U direction.
Conclusions This paper demonstrates that the choice of noise models has a significant impact on the estimation of velocity uncertainty parameters, and 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 the models without RWN tend to significantly overestimate velocity uncertainty. Hence, the impact of RWN in long-term GNSS coordinate series data cannot be disregarded.
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