# Reduction of Satellite Signature Effect in High-Accuracy Satellite Laser Ranging to Etalon
## 3 Pre-Processing Algorithm with a Center of Mass Corrections Filter  
A normal point algorithm is a universal method applied in the pro-processing of SLR raw observation data [13]. It eliminates the noise point by a Poisson statistical filter and polynomial filter. Specifically, the first step involves fitting a trend function to the raw range or the residuals from a predicted orbit in order to remove all signatures from the orbit, and then analyzing the distribution of the trend-removed data. In order for a trend function to be fitted iteratively, some level of screening must be performed. Letts criterion method recommends an iterated 2.5 \(\times\) rms rejection criterion for signal photon detection SLR systems and an iterated 3 \(\times\) rms rejection criterion for multi-photon level detection systems. A fitting residual is the deviation of each observation point from the fitting function, which is approximately equal to the random error of the observation point. It Is noteworthy that If these data have a symmetrical distribution about the peak, using the 2.5 \(\times\) rms rejection criterion should be acceptable. However, if the data have a skew distribution, then the arithmetic mean will be biased away from the peak, and the amount of bias will probably depend on the level of final screening applied. The 2.5 \(\times\) RMS screening may not be appropriate for skew distributions of observational data. We simulate the echo signals returned by Etalon from all directions and extract the effective echo signals using the normal point algorithm. The relationship between the center of mass corrections and the incident angles is illustrated in Figure 5.  
Figure 4: Distribution of the returned signals from Etalon at different incident angles. The orange curve corresponds to the simulated echo signal based on the retroreflector uneven distribution model. Figure 5: Variation of the center of mass corrections with incident angles. Even though the normal point algorithm is used to process the raw data from Etalon, the center of mass corrections at different incident angles are not stable. The center of mass corrections will increase when the incident beam is irradiated to an area densely covered by the reflectors, and vice versa. The calibrated results reveal a mean value of 572.5 mm for Etalon's center of mass corrections, which is almost identical to the value offered by the ILRS [14]. As a result of the different orientations of the satellites, the range of the Etalon center of mass corrections has shifted by 28 mm, from 558.8 mm to 586.8 mm. Additionally, we calibrated the root mean square roughness (RMS) of the center of mass corrections for various incident angles. There is a high RMS of 6.7 mm, as demonstrated by the results. The data presented here support the notion that variations in the center of mass corrections for Etalon are responsible for additional range bias in the measurements. In order to eliminate the range bias introduced by the variable effect in the center of mass corrections, we analyze the relationship between the acceptable level for normal point formation and the RMS of center of mass corrections. The 2.5 \(\times\) RMS noise filtering is modified as:  
\[\mathrm{p(x)}=\left\{ \begin{matrix}\mathrm{P_{FR}(x)}\;,&\mathrm{if}-2.5\times \sigma\leq x\leq r\\ 0\;,&\mathrm{else}\end{matrix} \right., \tag{5}\]  
where r is the set limit to clip the full-rate observation data. The range residuals are selected and clipped from \(-2.5\times\) RMS to r to form and calibrate the center of mass corrections. The RMS of the center of mass corrections is the result of 2594 reflected signals for the incident directions equally distributed around Etalon. We quantify the association between clipping location and mean square error (RMS) of center of mass, shown in Figure 5.  
Figure 6 illustrates that the clipping location has a significant impact on the RMS of the center of mass corrections. With the increasing of r, the mean RMS of center of mass corrections gradually decreases, then rises, and finally settles.