## 3 Data and Methods
### Methods
#### 3.2.3 Correction Methods  
Decorrelation noise primarily arises from the changes in light conditions and surface radiation intensity. Environmental factors, such as radiation intensity, cloud cover, rain, snow, and other natural conditions, induce changes in surface radiation intensity. These changes lead to the absence of image texture features, resulting in decorrelation noise. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Pairs Num.** & **Acquisition Dates of Image Pairs** & **Track Num.** \\ \hline
1 & 2/04/2018-23/04/2018 & 1155 612 \\
2 & 20/04/2019-21/04/2019 & 1155 612 \\
3 & 07/09/2019-21/09/2019 & 1155 612 \\
4 & 23/04/2018-20/04/2019 & 1155 612 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The image data used for error source analysis. Figure 2: Error components of RapidEye images in the E-W and N-S offset fields. R1, R2, and R3 represent satellite numbers. The error with a systematic trend in (**a**) is an orbital error. The collective deviation depicted in (**e**) is attributed to inter-satellite bias. The outlier in (**b,f**) is decorrelation noise. The trend errors perpendicular to the flight direction in (**c,g**) are attitude jitter distortions. The errors enclosed within the red rectangular (**d**) are terrain shadows. Figure (**h**) includes decorrelation noise and terrain shadow. Image texture features are an important basis for extracting surface information from optical images. Inaccurate texture information can reduce the accuracy of the final offset field. Two common methods for removing decorrelated noise are as follows: (1) Setting the SNR threshold to exclude the region with low SNR. Usually, the regions with an SNR lower than 0.9 are masked. (2) Wide regions affected by decorrelation can also be eliminated, such as those caused by clouds, waters, and vegetation. An orbital error is a trending systematic bias that is affected by the accuracy and stability of the satellite orbit. Preliminary ortho-correction and geometric correction can weaken the effect of this error, but they are insufficient to entirely overcome the systematic bias in images acquired at different times. Notably, there is also a clear trending orbital error in the offset results obtained from RapidEye images (Figure 3), which can be removed using the polynomial fitting method [37; 38]. \[D=a_{0}+a_{1}\ x+a_{2}\ y \tag{1}\]  
where \(D\) is the fitted orbit error, \(a_{0}\), \(a_{1}\), and \(a_{2}\) are the unknown parameters, and \(x\), \(y\) are the row and column numbers or coordinates of the deformation matrix. Attitude jitter distortion is a periodic error streak caused by attitude jitter along the satellite's vertical flight direction. It is caused by external forces in space, such as solar activity and star gravity, coupled with the down-sampling of satellite imaging attitudes. The traditional method of \"Mean value elimination\" [22; 39] can eliminate attitude jitter distortion in a convenient and efficient way. However, its applicability varies depending on the imaging principle of various satellites. By analyzing the error source of RapidEye, we found that its attitude jitter distortions have a gradual trend along the vertical flight direction, and the traditional mean value elimination method is not applicable. This type of asymptotic tendency is particularly prominent in the offset field. Figure 3 illustrates the gradual trend observed in attitude jitter distortions along the vertical flight direction of the offset matrix. Based on the above characteristics, we considered consistency along the parallel flight direction when processing n rows offset by the matrix, as shown below:  
\[Y_{i}=P(1)_{i}\ X_{i}+P(2)_{i}\ (i=1,\ldots,\ n) \tag{2}\]  
\[\Delta y=\ |\ Y_{i+1}\ |\ -\ |\ Y_{i}\ | \tag{3}\]  
\[Y_{i}=Y_{i+1}-sign\ \times E(\Delta y) \tag{4}\]  
Figure 3: The characteristic of attitude jitter distortions of RapidEye.