## 3 Velocity Estimation Using Least Squares Analysis and Statistical Testing
\begin{table}
\begin{tabular}{c c} \hline \hline
**Test Statistic** & **Critical Region** \\ \hline \(T=\frac{\text{b}_{\text{m}}-\text{b}_{\text{d}}}{\text{s}\sqrt{\text{q}_{ \text{d}}}}\) & \(T<-1.96\) or T \(>1.96\) \\ \hline b\({}_{\text{d}}\) = daily velocity; b\({}_{\text{m}}\) = monthly (or four-monthly) velocity; s = unit variance from LSE; q\({}_{\text{i}}\) = element of the cofactor matrix. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Notation and formulation for the Student’s t-test from multi-regression analysis. Figure 4: Vertical velocities of continuous, monthly, and four monthly data with their standard errors. Velocity estimation was further degraded when antenna set up errors were introduced to GPS baseline components. Secondly, the success rate of the vertical component showed about 85% improvement over the study of [PERSON] and [PERSON] (2019). Figure 5: Test statistics concerning the components distributed to latitude. Extending the observation session from 8-10 h to 24 h significantly improved the vertical deformation rates estimated. The velocity estimation for the north and east components was also improved by about 25-40%. Comparisons can also be made between monthly and four-monthly results. Antenna set-up biased results of four-monthly solutions gave about 8% coarser results than the antenna set-up biased one-monthly results. One other detail that we noticed in Figure 5 was that the north component had three blue solid circles, which means some of the estimated velocities significantly differed from the truth without taking into consideration antenna set-up errors. These were the stations ALIC, ONSA, and NRIL. The same applies to the up component in that the velocity estimated at the station UFPR significantly differed from the truth. At this stage, we referred to the site specific information released by the IGS (Figure 6) and some geological reports to interpret this unexpected positioning differences. The top left figure illustrates the environment of the station ALIC. The station was installed on a bedrock, which is the standard for monitoring the tectonic motion. Multipath level and cycle slip level were very low. However it is noted in the figure that the station was surrounded by trees. The fact that the velocity estimated at ALIC significantly differed from the truth might be ascribed to signal attenuation due to tree leaves, and this deteriorates the positioning [30]. The top right figure of Figure 6 gives the environment of ONSA. ONSA was established on a bedrock. However it was placed at a space laboratory in which data were collected from other geodetic instrumentation such as VLBI antennas, gravimeter, and tide-gauges. Note the radome of a huge radio-telescope behind the GPS antenna in the figure. The reason that the estimated velocity at this station significantly differed from the truth might be ascribed to the multipath environment at the vicinity of the GNSS antenna given MP1 and MP2 multipath levels were about 0.80 for the station. In the log file of the station was reported various events in regard to the low data quality, multipath  
Figure 6: Site specific impressions on the IGS stations ALIC, ONSA, NRIL, and UFPR [29]. reduction, and equipment repairs between the years 2012 and 2016, which corresponds to our data analysis period here. In the middle part of Figure 6 is represented the multipath quality of the station NRIL. NRIL was located on top of the roof of the seismology building as stated in the log file released by the IGS. [PERSON], et al. [31] states the station is in a tectonically stable place. The tectonic interaction between Pamir and Tien Shan was examined taking NRIL as one of the stable Eurasian reference stations in the GNSS analysis [32]. However, the multipath environment on the roof as well as shaking of the building might have degraded the positioning quality, given MP1 0.48 and MP2 0.49 multipath levels were comparatively higher. Unfortunately, a picture giving the site description of the GNSS station NRIL was not available on the internet.