# Distributed Coordination of Space-Ground Multiresources for Remote Sensing Missions
## 4 Distributed Coordinated Resource Scheduling Algorithm Design Based on ADMM
### Algorithm Implementation
For instance, \(V_{o}^{n}=\{o_{n,i}^{k}|1\leq k\leq K,1\leq i\leq|OM_{n}|\}\). \(A_{L}^{n}\), \(A_{O}^{n}\), \(A_{S}^{n}\), and \(A_{VT}^{n}\) represent the set of link arcs, observation arcs, storage arcs, and virtual arcs related to the RSS system \(n\), respectively. ```
0:\((y_{n}^{C})^{*}\),relaxed variable \(\mathbf{y}^{C}\). 0:\(\{\mathbf{x}_{n^{\prime}}^{*},\mathbf{y}_{n^{\prime}}^{*},\mathbf{z}_{n}^{*}\}_{1\leq n\leq N}\). 1:Initialize:\(G_{R}(V_{R},A_{R}),OM_{R}\gets OM_{n}\);
2:while\(OM_{R}\
eq\varnothing\) is true do
3:\(e\leftarrow\arg\max_{i:om_{n,i}\in OM_{R}}z_{n,i}\);
4:if There exists a path \(p_{0}=o_{n,e}^{sk}\to u^{ck}\) in \(G_{R}\) satisfying \(\left\lceil\frac{st_{n,e}}{\tau}\right\rceil\leq sk\leq\left\lceil\frac{st_{n,e }}{\tau}\right\rceil,e\mathbf{k}=\left\lceil\frac{ct_{n,e}}{\tau}\right\rceil\) and the capacity is not less than \(b_{n,e}\)then
5:\(z_{n,e}^{*}\gets 1,\ OM_{R}\gets OM_{R}-\{z_{n,e}\}\);
6:for\(a\in p_{0}\cap(A_{L}^{n}\cup A_{O}^{n})\)do
7:\(y^{*}(a)\gets 1\);
8:for\(a^{\prime}\in A_{R}\cap AC(a)\)do
9:\(y^{*}(a^{\prime})\gets 0,A_{R}\gets A_{R}-\{a^{\prime}\}\);
10:endfor
11:endfor
12:for\(a\in p_{0}\)do
13:\(C(a)\gets C(a)-b_{n,e}\);
14:endfor
15:else
16:\(z_{n,e}^{*}\gets 0,\ OM_{R}\gets OM_{R}-\{z_{n,e}\}\);
17:endif
18: Substitute the recovered variables into problem P5 and solve the problem again;
19:endwhile
```

**Algorithm 3** Recovery of local relaxed variable in RSS system \(n\)

It can be seen from Algorithms 1-3 that the information interchange among different satellite systems is very limited in the whole distributed resource scheduling process. The only information that needs to be exchanged is intersatellite link scheduling variables (i.e., \(\mathbf{y}^{C}\) and \(\hat{\mathbf{y}}_{n}^{C}\)). More specifically, the DRS system receives the local intersatellite link scheduling variables \(\hat{y}_{n}^{C}\) from the RSS systems and feeds back corresponding global intersatellite link scheduling variables \(\mathbf{y}^{C}\) to them. Other local information, such as mission requests and ground-satellite scheduling states of each RSS system, is well-preserved. Therefore, the proposed distributed coordinated resource scheduling algorithm can protect the local privacy information better than the traditional methods [12; 13; 14]. ## 5 Simulations

### Simulation Setup and Results Description

We conducted simulations via STK and MATLAB to evaluate the performance of the proposed distributed coordinated resource scheduling (DCRS) algorithm. A simulation scenario comprising 3 RSS systems and a DRS system is considered. Specifically, each RSS system consists four RSSs and two ground stations. The DRS system has three DRS on the geosynchronous orbit. The RSSs are distributed in sun-synchronous orbits with a height from 619.6 km to 778 km and inclination from 97.8\({}^{\circ}\) to 98.5\({}^{\circ}\). The transmission rate of the links from RSSs to ground stations and DRSs are 50 Mbps. The storage volume of each RSS and DRS is 200 Gbit. The scheduling horizon is 1 day (from 13 May 2022 04:00:00 to 14 May 2022 04:00:00). We randomly generate 50-200 missions for each RSS system. The observation objects are randomly distributed on Earth with uniform distribution. The amount of data required to be acquired follows a uniform distribution from 5 Gbit to 15 Gbit. The earliest start time follows a uniform distribution from 0 to 86,400 s.

To validate the performance of the proposed DCRS algorithm, we consider the following three scheduling schemes for comparison:

1. No Relay Resource Scheduling (NRRS): The DRS system does not provide relay service for the remote sensing missions, i.e., the observed mission data can only be transmitted to the ground through the ground stations of the belonging RSS system. Non-Coordinated Resource Scheduling (NCRS): The remote sensing missions are scheduled in two stages.