# Cross-Domain Fusion Constellation Design of Communication, Navigation and Remote Sensing
## 3 Constellation Optimization Design  
### Resource Coverage  
Based on Section 2.2, we have obtained a comprehensive basic constellation. The basic constellation is the result of multidisciplinary collaborative design optimization. In the process of optimization, it is necessary to take into account the needs of each sub-functional area, and adopt the method of combining requirements, so there must be redundancy. This is mainly embodied in the number of satellites and their sensors. However, this constellation is relatively redundant, so it will be optimized here through reverse fusion optimization. Because of the high orbit density in space, the LEO mega constellation has the advantage of increasing the weight of satellites covering the ground. We hereby give the following definition.  
**Definition 1**.: _Point a in an area \(A\), if it is covered by at least \(k\) satellites with a certain type of payload resource \(r_{j}\) at time \(t\), then point at that time \(t\) is said to be \(k\)-covered by resource \(j\). If all points in area \(A\) are \(k\)-covered by resource \(j\), then area \(A\) is said to be \(k\)-covered by resource \(j\)._  
The multiple resource coverages of ultra-dense LEO constellations is a waste of resources, which greatly increases the cost of building CDFC as infrastructure. Therefore, it is possible to optimize the payload deployment according to the requirements. For example, in the case shown in Figure 2, the coverage area has two times of coverage to meet the demand, so the payloads of satellites 2 and 4 can be optimized and deleted. For communication and remote sensing payloads, first, consider the k-covered by the payloads. Here, we directly give a sufficient condition [16] for \(k\)-covered, as follows in Lemma 1.  
**Lemma 1**.: _A target area is \(k\)-covered by resource \(j\), when the following conditions are met: 1 If two satellites have an intersection; 2 if all intersections are at least \(k\)-covered. The coordinates of the intersection point are:_  
\[\left(\begin{array}{c}x\\ y\\ z\end{array}\right)=\left(\begin{array}{c}\frac{(y_{2}-y_{1})R_{e}(R_{e}+h) \cos\varrho}{x_{1}y_{2}-x_{2}y_{1}}\\ \frac{(x_{1}-z_{2})R_{e}(R_{e}+h)\cos\varrho}{x_{1}y_{2}-x_{2}y_{1}}\\ 0\end{array}\right)+\lambda\left(\begin{array}{c}y_{1}z_{2}-y_{2}z_{1}\\ z_{1}x_{2}-z_{2}x_{1}\\ x_{1}y_{2}-x_{2}y_{1}\end{array}\right). \tag{13}\]  
Through this method, the satellite coverage can be converted into the coverage of intersection points, and the multiple coverages of payload resources in each functional area can be solved.  
The construction of low orbit mega-constellations has led to more and more satellites. If these constellations are all built, the number of satellites is actually excessive, and the resource coverage is a more multi-layer redundant coverage. Through the satellite function reconstruction and mission planning of the CDFC, the satellites can work together over the same area or between different coverage areas, and unnecessary satellites can be deleted. Therefore, the deployment of satellites and payloads can be optimized through resource coverage to achieve the optimization of CDFC.