## 4 Case Study
### Capability-Requirement-Satisfaction Assessment  
Table 2 shows the capability structure parameters of a satellite-navigation-and-positioning system of systems, including sub-capability names, bottom indicators, weights, capability requirements, actual levels, and the credibility of the actual levels.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Node** & **Recognition Frame \(\Theta\)** \\ \hline Space-navigation-and-positioning system capability (_SNP_) & (high (_H_), medium (_M_), low (_L_)) \\ Anti-jamming capability (_A_) & (high, low) \\ Anti-compression capability (_AC_) & (high, low) \\ Anti-spoofing capability (_AS_) & (high, low) \\ System survivability (_SS_) & (high, low) \\ Satellite survivability (_SAS_) & (high, low) \\ Ground station survivability (_GSS_) & (high, low) \\ Security and confidentiality (_SC_) & (high, low) \\ Encryption capability (_EC_) & (high, low) \\ Anti-virus capability (_AV_) & (high, low) \\ Navigation and positioning capability (_NP_) & (high, low) \\ Positioning accuracy (_PA_) & (high, low) \\ Speed accuracy (_SA_) & (high, low) \\ Timing accuracy (_TA_) & (high, low) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Identification framework for space navigation and positioning capabilities.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Capability** & **Sub-Capabilities and Indicators** & **Weight** & \begin{tabular}{c} **Ideal** \\ **Value** \\ \end{tabular} & \begin{tabular}{c} **Minimum** \\ **Value** \\ \end{tabular} & \
\begin{tabular}{c} **Actual** \\ **Value** \\ \end{tabular} &
\begin{tabular}{c} **Credibility** \\ \end{tabular} \\ \hline Anti-jamming capability (0.15) & Anti-compresion capability (dBc) & 0.6 & 120 & 50 & 90 & 1 \\ capability (0.15) & Anti-spoofing capability (dBc) & 0.4 & 100 & 40 & 90 & 1 \\ \hline System survivability & Satellite survivability & 0.7 & 100 & 60 & 90 & 0.9 \\ (0.1) & Ground-station survivability & 0.3 & 100 & 60 & 80 & 0.9 \\ \hline Security and confidentiality (0.1) & Encryption capability & 0.5 & 100 & 50 & 70 & 0.9 \\ \hline Navigation and confidentiality (0.1) & Anti-virus capability & 0.5 & 100 & 50 & 80 & 0.9 \\ \hline Navigation and positioning & Positioning accuracy (m) & 0.4 & 5 & 20 & 10 & 0.95 \\ positioning & Speed accuracy (m/s) & 0.3 & 0.1 & 0.5 & 0.2 & 0.95 \\ capability (0.65) & Timing accuracy (ns) & 0.3 & 10 & 100 & 50 & 0.95 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Capability parameters.  
For example, a positioning accuracy with a confidence level of 0.95 means that the horizontal positioning accuracy is less than or equal to 10 m at a confidence level of 0.95.  
Table 3 shows the prior belief distribution of the requirement-satisfaction degree for each index.  
We calculated the belief distribution of the requirement-satisfaction degrees of second-layer capabilities using the method described in Section 3.3.  
Table 4 and Figure 3 show the belief distributions of the requirement-satisfaction degrees for second-layer capabilities.  
Figure 2: Conditional-belief-parameter table for spatial navigation and positioning capabilities.  
Figure 3 shows that the system anti-jamming capability has the highest requirement-satisfaction degree, followed by both system survivability and the navigation-and-positioning capability; the security and confidentiality capability has the lowest requirement-satisfaction degree. In addition, the cognitive uncertainty of the anti-jamming capability is the lowest, and the cognitive uncertainty of the other three capabilities is similar.