## 4 Target Identification Method between Star Trackers
### Maximum Projection Method  
For k frames of \(M\times N\) astronomical images, denote the data samples as \(f(i,j,k)\), where \(i=1,\ldots,M,j=1,\ldots,N,k=1,\ldots,K\). Assume that the set of images satisfies the following conditions:  
The data samples taken from the image sequence are mutually independent Gaussian random variables and the noise can be considered Gaussian white noise.  
If the moving target does not exist, the data sample can be regarded as a temporally stable but spatially unstable data model. This means that all images are spatially registered and there is no motion clutter.  
The maximum projection of \(K\) samples is expressed as follows:  
\[z(i,j)=\max[f(i,j,1)+f(i,j,1),\ldots,f(i,j,K)] \tag{14}\]  
The above equation implies that the 3D data are projected onto the 2D plane. To describe this process, we assume that there are three consecutive frames of images, as shown in Figure 4a-c below, in which the information of the image is the same except for the moving target and some perturbations. After the maximum projection, the motion of the target is connected, as shown in Figure 4d below. Most importantly, in addition to the maximum projection information, we can obtain the time scale corresponding to the maximum value generated at each pixel position, as shown in Figure 4e below. It can be used to estimate the velocity of the target's motion. Figure 5 shows the image after the projection of the maximum value.  
The median frame image obtained during stellar detection is removed from the maximum projection image to remove the stars from the image.  
The maximum projection image after background removal is binarized by adaptive threshold segmentation.  
In addition to the maximum projection frame, it is also possible to obtain the time scale corresponding to the maximum value on each pixel during projection, i.e., the time information of the maximum projection frame \(\text{max}psi(i,j)\). Binarize the maximum projected image. After being separated from the image noise, and then multiplied with the  
Figure 4: Schematic diagram of the maximum projection principle. (**a**) First frame image. (**b**) Second frame image. (**c**) Third frame image. (**d**) The motion of the target is connected after the maximum projection. (**e**) The time labels generated by the maximum projection at the same time.  
Figure 5: Image after maximum projection (Take five frame images projection as an example.).  
time marker information, the time information frame of the maximum projected image can be obtained (as shown in Figure 6). The formula is as follows:  
\[\begin{array}{l}BWz(i,j)\ =\ \left\{\begin{array}{ll}0,&\quad x<\textit{ threshold}\\ 1,&\quad z(i,j)\leq\textit{threshold}\\ \textit{times}(i,j)\ =\ \max posi(i,j)\times BWz(i,j)\end{array}\right.\end{array} \tag{15}\]  
From Figure 7, it can be seen that in the temporal information frame of the maximum projection, the moving targets are connected domains where the information with the same time markers are clustered together, while the stars are connected domains where the different temporal information are clustered together. After stellar removal, the time information and position information of the moving target can be used for target detection.  
Figure 6: Maximum projection image time information frame.  
Figure 7: Motion targets in time information frames. (Five frame images maximum projection).