# Effective Multi-Frame Optical Detection Algorithm for GEO Space Objects
## 3 Methodology
### Candidate Filtration and Supplement: CFS  
After obtaining all the candidate coordinates, an effective post-processing technique based on CFS is deployed to filtrate the true targets and supplement the misdetected target coordinates as the final prediction results. The CFS method is proposed in the light of the principle of moving continuity and trajectory consistency of space objects across the frames. We utilize the fact that the targets move with uniform speed along a straight-line trajectory. The flowchart, as shown in Figure 7, summarizes the overall procedures of the proposed CFS method.  
Figure 6: The framework of PP-YOLOv2.  
Figure 7: Flowchart of the proposed CFS method.  
In the first step, considering all potential straight-line trajectories, we take a search window to group point sets. As shown in Figure 8a, a sample of space objects is captured in all 5 frames within one sequence denoted as \(P^{i},i\in[1,2,3,4,5]\). When all the \(P^{i}\) are registered to a common coordinate system, the distance between any two adjacent points \(P^{i}(x^{i},y^{i})\) and \(P^{i+1}(x^{i+1},y^{i+1})\) is the same. According to the statistics of the training dataset, we obtained the maximum and minimum value of the interval distance as \(R_{\text{max}}\) and \(R_{\text{min}}\). Then, we use the ringlike search window to group point sets of potential trajectories, as shown in Figure 8b. The special search strategy we take to improve efficiency is that the number of elements in each point set is limited to \(N=3\). Only the collinear cases of 3 points from successive or inconsecutive frames are considered, all of which are shown in Figure 8c.  
For the cases in which trajectory dots come from \(N\) successive frames, all the coordinate points of the searching starting frame \(f_{s}\in\{f_{1},f_{2},f_{3}\}\) will be used as the search starting points. Next, we capture all the potential trajectory points of the next frame \(f_{s+1}\) that fall into the search window. Then, the frame \(f_{s+1}\) is set as the starting frame to search potential trajectory points of the frame \(f_{s+2}\) the same way.  
As for the cases of inconsecutive frames, the maximum interval is two frames or three frames. An enumeration method is used to capture the potential trajectories as much as possible. When the maximum interval is 2 frames, the searching starting frame is \(f_{s}\in\{f_{1},f_{2}\}\) and the single-step search window size \(S_{n},n\in[1,2]\) is set to \(\{r,2r\}\) and \(\{2r,r\}\), respectively. When the maximum interval is 3 frames, the searching starting frame are \(f_{s}\in\{f_{1}\}\) and the single-step search window size are set to \(\{r,3r\}\) and \(\{3r,r\}\), respectively.  
Figure 8: The schematic diagrams of three steps in the proposed CFS strategy: (**a**) a schematic view of the line in space-time intersecting image planes in a discrete ordered set of locations; (**b**) the ringlike search window; (**c**) the enumeration of potential candidate targets of sequence-based detection results.  
Then, in step 2, we implement linear fitting to all points sets resulted from step 1 and obtain all linear trajectories across the sequence frames. In step 3, according to the results from linear fittings based on a least-squares technique, we can compute the missed target coordinates and supplement for the final detection results.