# A SLR Pre-Processing Algorithm Based on Satellite Signature Effect
## 4 Results and Discussion  
The clipping method is applied for the observation data provided by Changchun station. Figure 8 shows the main data processing of the clipping method for LAGEOS-1 observation points for January 2021.  
Figure 8A presents the distribution of range residual accepted by Poisson filter and rejection of 2.5 \(\times\) RMS. It is obviously seen the density distribution of fit residual is not homogeneous. The leading-edge density for a fixed bin is variable but the mean value of the long-term range residual is stable, which is in agreement with the previous theoretical results. Figure 8B is the histogram of the preliminary processed range residual distribution. Due to the application of the Poisson filter in the clipping method, larger numbers of ranging data are maintained, which increase from 108,864 to 140,534, and the tail of residual distribution is almost preserved, which is closer to the simulated distribution. Figure 8C demonstrates the distribution of the selected range signals lay between the reference point and clipping point. The result shows the distribution of fit residuals proceeded by the more centralized clipping method, while both the unstable leading edge and distorted tail of observation data were dramatically reduced.  
Figure 8: The diagram of the clipping method. (**A**), the distribution of range residual accepted by Poisson filter and rejection of 2.5 \(\times\) RMS. (**B**), the histogram of the preliminary processed range residual distribution. (**C**), the distribution of the selected range signals lay between the reference point and clipping point.  
Figure 7: The flow chart of the clipping method.  
Table 1 shows the average statistical results of LAGEOS-1 produced by these two different SLR data pre-processing methods. Compared to a normal point algorithm, the property of observation data is obviously improved. The RMS per NP of LAGEOS-1 obtained by the clipping method is reduced from 62.90 \(\pm\) 9.9 mm to 56.07 \(\pm\) 4.69 mm, and the stability of RMS is improved by 53%. Meanwhile, the stability of skewness and Kurtosis for LAGEOS-1 are also improved in different degrees.  
In order to verify the validity and applicability, we analyze the LAGEOS-1 observation data of different months with these two pre-processing methods. The calculated results of RMS, skewness, and kurtosis per normal point are illustrated in Figure 9. It is seen that the RMS per normal point (NP) obtained by the clipping method has decreased significantly and become more concentrated, while the skewness and kurtosis are also obviously reduced. Compared to the normal point algorithm, LAGEOS-1 observation data processed by the clipping method has higher precision and better stability and reliability, which indicates that the clipping method can not only eliminate the long-term but also reduce the short-term satellite signature effect from raw ranging data files.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Normal Point Algorithm** & **Clipping Method** \\ \hline RMS per NP & 62.90 \(\pm\) 9.9 mm & 56.07 \(\pm\) 4.69 mm \\ \hline Skewness per NP & 0.2 \(\pm\) 0.10 & 0.11 \(\pm\) 0.08 \\ \hline Kurtosis per NP & 2.27 \(\pm\) 0.13 & 2.26 \(\pm\) 0.09 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The average statistical results of LAGEOS-1 observation points for January 2021 with different SLR data pre-processing method.  
Figure 9: RMS, kurtosis, skewness per normal point for LAGEOS-1 obtained by the different pre-processing algorithms.