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The aim of this study is to estimate reliable velocities along with their realistic uncertainties based on a robust time series analysis including analysis of deterministic and stochastic (noise) models. In the deterministic model analysis part, we use a complete station motion model comprised of jump effects, linear and nonlinear trend, periodic components, and post-seismic deformation model. This part also consists of jump detection, outlier detection, and statistical significance of jumps. We perform the deterministic model analysis in an iterative process to elevate its efficiency. In the noise analysis part, first, we remove the spatial correlation of observations using the weighted stacking method based on the common mode error (CME) parameter. Next, a combination of white and flicker noises is used to determine the stochastic model. This time series analysis is applied for 11-year time series of 25 permanent GNSS stations from 2006 to 2016 in the northwest network of Iran. We reveal that there is a nonlinear trend in some stations, although most stations have a linear trend. In addition, we found that a combination of logarithmic and exponential functions is the most appropriate post-seismic deformation model in our study region. The result of the noise analysis shows that the spatial filtering reduces the norm of post-fit residual vector by 19.34%, 17.51%, and 12.44% on average for the east, north, and up components, respectively. Furthermore, the uncertainties obtained from the combination of white and flicker noises at the east, north, and up components are 5.0, 4.8, and 4.4 times greater than those of the white noise model, respectively. The results indicate that the stations move horizontally with an average velocity of 36.0 ± 0.3 mm/yr in the azimuth of 52.66° NE which is compatible with velocities obtained from MIDAS. We obtained the vertical velocity of most stations in the range of -5 to 5 mm/yr. However, in three stations of GGSH, ORYH, and BNAB, which are in the proximity of Lake Urmia, the vertical velocities are estimated to be -80.9 mm/yr, -50.6 mm/yr, and -11.4 mm/yr, respectively. Moreover, we found that these three stations possess large periodic signal amplitudes in all three coordinate components as well as a nonlinear trend in the up component.
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