## 6 Conclusions  
Considering the formal errors of position time series data available, IPCA was proposed in this paper for the spatiotemporal filtering of regional GNSS time series, in which formal errors were employed to construct weight factors. When formal errors were homogeneous, IPCA was reduced to PCA. The proposed IPCA was applied to process the position time series of 25 GNSS stations in the Yunnan Province. After spatiotemporal filtering, the average error of the position time series was reduced. For PCA, the average reductions were 15.84%, 10.86%, and 14.32% for the North, East and Up coordinate components, respectively. For IPCA, the correspondent average reductions were 18.23%, 15.42%, and 18.25%. The improvements of IPCA relative to PCA were 2.39%, 4.56% and 3.93%, respectively, for the three components. Moreover, this improvement was proportional to the standard  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Case 1**} & \multicolumn{3}{c}{**Case 2**} & \multicolumn{3}{c}{**Case 4**} \\ \hline  & \multirow{2}{*}{**PCA**} & \multirow{2}{*}{**IPCA**} & \multicolumn{3}{c}{**Up**} & \multicolumn{3}{c}{**North**} & \multicolumn{3}{c}{**East**} & \multirow{2}{*}{**PCA**} & \multirow{2}{*}{**IPCA**} \\ \cline{4-4} \cline{6-10}  & & & **PCA** & & & & & & \\ \hline \multirow{2}{*}{Group 1} & RMS & 0.69 & 0.68 & 0.69 & 0.68 & 0.61 & 0.60 & 0.82 & 0.80 & 1.99 & 1.93 \\ \cline{2-10}  & Imp & 1.45 & 1.75 & 1.64 & 2.50 & 3.00 & \\ \hline \multirow{2}{*}{Group 2} & RMS & 0.74 & 0.73 & 0.74 & 0.73 & 0.67 & 0.66 & 0.96 & 0.93 & 1.78 & 1.71 \\ \cline{2-10}  & Imp & 1.35 & 1.35 & 1.49 & 3.13 & 3.93 & \\ \hline \multirow{2}{*}{Group 3} & RMS & 0.65 & 0.64 & 0.65 & 0.64 & 0.62 & 0.61 & 0.86 & 0.84 & 0.72 & 0.71 \\ \cline{2-10}  & Imp & 1.54 & 1.54 & 1.61 & 1.23 & 3.2 & 1.39 & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Mean RMS (mm) and relative improvement (%) in each test.  
deviation of the weight factor. Meanwhile, regardless of whether PCA or IPCA was employed, flicker noise was dominant in the extracted CME. To further demonstrate the advantages of IPCA relative to PCA, 500 simulations with four cases were performed and the results showed that regardless of whether local effects existed or not, IPCA outperformed PCA in terms of RMS of extracted CME signals. The mean RMS reduction of the extracted CME ranged from 1.35% to 3.93%. Additionally, analysis of the synthetic time series showed that IPCA was not dependent on the initial signal. Meanwhile, the improvement of IPCA relative to PCA was mainly related to the standard deviation of the weight factor, and somewhat related to the magnitude of formal errors. Overall, the findings from both the real and synthetic time series analysis highlight the necessity of considering formal errors and the effectiveness of the IPCA approach in spatiotemporal filtering.  
This work was predominantly sponsored by the Natural Science Foundation of China (41731069 and 41474017). It was also supported by the Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (No.2017 RCJJ074) and the Shandong Provincial Natural Science Foundation, China (ZR201702210134). We acknowledge the CMONOC for providing raw position time series calculated with GAMIT ([[ftp://ftp.cgps.ac.cn/products/position](ftp://ftp.cgps.ac.cn/products/position)]([ftp://ftp.cgps.ac.cn/products/position](ftp://ftp.cgps.ac.cn/products/position))). All figures were generated using GMT software [34].  
[PERSON] provided the initial idea and concept; and [PERSON] carried out the data analysis and wrote the main manuscript text.  
The authors declare no conflict of interest.