## 4 The Digital-Twin-Based Detection and Protection Framework
### The Detection and Protection Method in the Framework
#### 4.3.3 GH Detection and Protection Method  
Based on the GH generation mechanism proposed in Section 3.3, we design and implement a GH detection algorithm for the satellite network based on the Walker constellation and the routing mechanism based on link delay, as shown in Algorithm 2. After the satellite network generates routing tables, the ground station analyzes the adjacency of satellite nodes in the satellite network topology and the digital twin data \(Pos_{DT}\) and \(RT_{DT}\) to detect whether there is an SDC error that can trigger a GH. The proposed algorithm proposed is as follows:  
Step 1. (Line 1,13) Based on the data structure shown in Equation (5), for the digital twin routing table \(RT_{DT}^{i}\) of satellite \(i\), the algorithm firstly judges whether it contains all the satellite nodes except itself. If the condition is satisfied, the algorithm jumps to Step 2 to further judge whether the next hop is reachable. If the condition is not satisfied, this means that satellite \(i\) cannot find the next hop to some nodes, and there is a GH node in the satellite network.  
Step 2. (Line 2-3) For each piece of data \(<DEST,\ NEXT>\) in \(RT_{DT}^{i}\), the algorithm judges whether satellite \(i\) and \(NEXT\) are in the same orbit. If the condition is satisfied, jump to Step 3; if the condition is not satisfied, jump to Step 4.  
Step 3. (Line 4-6) If the two satellites are in the same orbit, the algorithm further judges whether satellite \(i\) and \(NEXT\) are adjacent. If the condition is satisfied, this means that satellite \(i\) can send packets to the next hop, and this piece of data will not cause a GH node, and the system can continue to the next piece of data. If the condition is not satisfied, this means that the next hop cannot be reached and there is a GH node in the satellite network.  
Step 4. (Line 7, 11) If the two satellites are not in the same orbit, the algorithm further judges whether satellites \(i\) and \(NEXT\) are in adjacent orbits and adjacent to each other. If the condition is satisfied, jump to Step 5 to further judge whether it is in the link disconnected area. If the condition is not satisfied, this means that the next hop cannot be reached and a GH node exists in the network.  
Step 5. (Line 8-10) The algorithm judges whether \(LAT^{i}\ or\ LAT^{j}\) is bigger than the polar region boundary latitude. If the condition is satisfied, this means that the next hop cannot be reached and a GH node exists in the network. If the condition is not satisfied, this means that satellite \(i\) can send packets to the next hop, and this piece of data will not cause a GH node.
```
Input: \(Pos_{DT},\,{LSA}_{DT}\) and \(RT_{DT}\) Output: if_Grayhole_exist Start
1. if\(\forall(ID_{orb}^{i}\parallel ID_{sat}^{i})\) in \(RT.DEST\):
2. For each piece of data \(<DEST,\ NEXT>\) in \(RT_{DT}\)
3. if \(ID_{orb}^{i}=NEXT.ID_{orb}\):
4. if \(\text{abs}(ID_{sat}^{i}-NEXT.ID_{sat})=1\) or \(\text{abs}(ID_{sat}^{i}-NEXT.ID_{sat})\)= \(M-1\):
5. Not GH item, continue
6. else: GH exists, break
7. elif \(\text{abs}(ID_{orb}^{i}-NEXT.ID_{orb})=1\) and \(ID_{sat}^{i}=NEXT.ID_{sat}\):
8. if \(LAT^{i}\ or\ LAT^{j}\geq\text{Polar region boundary latitude}\):
9. GH exists, break
10. else: Not GH item, continue
11. else: GH exists, break
12. Detect the next piece of data
13. else: GH exists, break
14. return if_Grayhole_exist End
```  
**Algorithm 2** GH detection algorithm  
After completing the GH detection process, if a routing table that can lead to GH is found, the ground station will use the satellite network routing information base \(RIB_{DT}\) to generate the correct routing table for the satellite and upload the routing table to the satellite. If there are no routing tables that can lead to a GH, no additional operation is required for the ground station and satellite network.