# A SLR Pre-Processing Algorithm Based on Satellite Signature Effect
## 3 New Clipping Algorithm Based on Satellite Signature Effect  
The long tail and obvious noise points of the return signal can be eliminated effectively by a normal point algorithm, but there remains some distortion at the front and back edge (see Figure 5). We calculate the center of mass (CoM) of the pre-processed echo signal for different incident angles and find that it is not constant or stable when the observation data are processed by normal point algorithm. Figure 5 plots the variation of the CoM of the reflected signal from different incident laser direction. The RMS of mean value is 0.48 mm and the difference between the maximum and minimum can reach up to be 3.79 mm. These results illustrate that a normal point algorithm can reduce the long-term effect of satellite signature on reflected signal but not erase the instability of SLR data distribution introduced by the variation of satellite signature effect for each observation.  
The main factors causing this phenomenon is that the observation arcs for each observation is different and the relative rotation velocity of LAGEOS-1 to the terrestrial station is variable. When the observation period is very short or the relative position of the satellite moves slightly, the waveform for each observation will not change greatly and the center of the fit residuals will not be far from the average value. However, when the observation period is too long or the observation is interrupted by clouds or other shelters, the polynomial fitting in normal point algorithm cannot describe the fluctuation  
Figure 4: The fit residuals distribution of LAGEOS-1.  
Figure 5: The variation of the CoM of the reflected signal processed by normal point algorithm.  
of the reflected waveforms, and the mean value of fit residuals in fixed bin will not be stable anymore.  
In order to further minimize the short-term satellite signature effect and improve the stability of the observation data, a new clipping method is proposed for SLR data processing. First, we use the mean value of the long-term fit residuals distribution instead of the leading edge as the fixed reference point for normal points. This is because the return pulse intensity for each observation in Changchun station is unstable, which makes the identification of the leading edge difficult. So, we rewrite the Equation (10) as:  
\[p^{\prime}(x)=\begin{cases}p_{FR}(x)&-2.5\times\sigma_{p}\leq x\leq r\\ 0&else\end{cases} \tag{11}\]  
where \(r\) is the distance between the clipping location from the reference point. Based on the Equations (9) and (11), the distribution of fit residuals and the corresponding CoM are calculated at different acceptance levels by adjusting the value of \(r\). Figure 6 shows the relationship between clipping location and mean value RMS of CoM. Due to the distortion at the front and back edge of the fit residuals distribution, the curve of mean value RMS presents to be concave. We define the minimum (5.6 mm) in the curve as the clipping location in the new method to reduce the system error introduced by the variation of satellite signature effect for short-time and obtain the best stability of observation data.  
The flow chart of the clipping method is indicated in Figure 7. The new algorithm differs from the conventional SLR data processing in two main respects. First, Poisson filter is used to extract more valid observation data to ensure the reflected waveform to be close to the theoretical result [21]. Second, the normal points are generated based on the range residuals which lay between the fixed reference point and the clipping location. In addition, the rejection by 2.5 \(\times\) RMS is repeated again after clipping the tail data to reduce the noise of the leading edge and makes the results more concentrated and stable.  
Figure 6: The relationship between clipping location and mean value RMS.