# Cross-Domain Fusion Constellation Design of Communication, Navigation and Remote Sensing
## 2 Cross-Domain Fusion Constellation Design Method
### Basic Constellation Design
#### 2.2.4 Constellation Fusion Based on Collaborative Optimization  
Based on the MDO method of collaborative optimization (CO), the basic constellation of navigation, communication, remote sensing and other functional domains can be constructed into a comprehensive constellation. In this paper, CO is divided into general parameters and special parameters for optimization [14]. The multidisciplinary optimization structure of hierarchical collaborative optimization is shown in Figure 1. General design variables are shared by subproblems of each functional domain, and participate in the design optimization process of each subproblem. Special parameters are optimized only in their respective functional areas. As the integrated CDFC spans the fields of communication, navigation and remote sensing, this paper adopts a unified method based on cost measurement to measure the system parameters uniformly. In the synthesis, the cost of CDFC mainly considers the number of satellites and the composition of a single satellite's cost. The cost of a single satellite mainly considers the cost of the basic platform and payloads of the satellite [18]. \[C_{\text{cost}}=\sum_{i=1}^{N_{\text{start}}}C_{i}^{\text{s}at}{=\sum_{i=1}^{N_{ \text{start}}}{(C_{platform}+\sum_{j=1}C_{payload})}}. \tag{11}\]  
In (11), \(C_{platform}\) and \(C_{payload}\) are the costs of satellite platforms and payloads, respectively. One satellite and one platform are presumed, but the number of payloads will be determined later according to the optimized payload deployment. Due to the limitation of satellite volume and power consumption, the configuration that no more than three payloads in a satellite are set. The optimization model established is as follows. The existing objective functions of each domain in Figure 1, namely \(minCost\), \(g1\), \(g2\) and \(g3\), are not repeated. \[ \begin{array}{c}\sum_{j=1}^{N_{1}}{(X_{j}-{X^{\prime}}_{1,j})^{2}}+\sum_{j=1 }^{N_{2}}{(X_{j}-{X^{\prime}}_{2,j})^{2}}\\ +\sum_{j=1}^{N_{3}}{(X_{j}-{X^{\prime}}_{3,j})^{2}}+\sum_{j=1}^{N_{4}}{(X_{j}-{ X^{\prime}}_{4,j})^{2}}\leq\varepsilon.\end{array}  \tag{12}\]  
The constraint in (12) mean that the left side of the inequality should be as close to zero as possible. In the experiment of this paper, after several tests, the convergence effect is better when the value of Algorithm 1 is 0.001. If there are other functional domain designs, they can also be represented by and participate in the constellation design. This method does not limit the number of subjects involved in CO. This paper only focuses on the design optimization of the most common communication, navigation and remote sensing domains. The satellite of the cross-domain fusion constellation must be a software-defined satellite capable of carrying different loads, or even an intelligent satellite capable of autonomous mission planning. Only in this way can the functions of satellites be redefined and realized according to the mission requirements, which is the basis and key of cross-domain fusion constellation. This kind of satellite allows the space-based system to maximize the use of resources in space and time through mission planning and function reconstruction within the entire constellation system, avoiding the shortcoming that traditional constellations can only work in a specific space orbit. Figure 1: Structure diagram of multidisciplinary collaborative design for CDFC. Combining the design structure of Figure 1 with the design of various disciplines, the MDRCO algorithm is shown in Algorithm 1. According to the design requirements of the three functional domain constellations input, under the common domain shared design goal, the initial design variables are gradually optimized and converged, and the initial fusion constellation is finally output.