# An Evaluation of Optimization Algorithms for the Optimal Selection of GNSS Satellite Subsets
## 4 GNSS Data  
The 24 h GNSS data were obtained from the BIGF (British Isles continuous GNSS Facility) station located on the roof of the Nottingham Geospatial Institute building (Figure 7). The GNSS station is equipped with a Leica AR25.R4 choke ring antenna with strong multi \begin{table}
\begin{tabular}{c c c c c} \hline
**Algorithm** & **Notation** & **Meaning** & **Value** & **References** \\ \hline \multirow{4}{*}{ABC} & \multirow{2}{*}{D} & The problem dimensions, indicating the & & \\  & & satellite constellation size & & \\ \cline{2-5}  & maxIter & The maximum number of iterations & 100 & [26, 28, 61, 62] \\ \cline{2-5}  & pSize & The population size & 100 & [22, 26, 45, 63] \\ \cline{2-5}  & limit & The abandonment limit & D \(\times\) pSize & [64] \\ \hline \multirow{4}{*}{ACO} & maxIter & The maximum number of iterations & 100 & \\ \cline{2-5}  & pSize & The population size & 100 & \\ \cline{2-5}  & \(\rho\) & The evaporation rate & 0.5 & \\ \cline{2-5}  & \(\alpha\) & The relative importance of the trail & 1 & \\ \cline{2-5}  & \(\beta\) & The relative importance of the visibility & 0 & \\ \cline{2-5}  & \(\mathcal{Q}\) & The quantity of trails laid by ants & 100 & \\ \hline \multirow{4}{*}{GA} & maxIter & The maximum number of iterations & 100 & \\ \cline{2-5}  & pSize & The population size & 100 & \\ \cline{2-5}  & Pc & The probability of crossover & 0.8 & \\ \cline{2-5}  & Pm & The probability of mutation & 12 & \\ \hline \multirow{4}{*}{PSO} & maxIter & The maximum number of iterations & 100 & \\ \cline{2-5}  & pSize & The population size & 100 & \\ \cline{2-5}  & Wmax & The initial weights & 0.9 & \\ \cline{2-5}  & Wmin & The final weights & 0.4 & \\ \cline{2-5}  & C1 & The personal acceleration coefficient & 2 & \\ \cline{2-5}  & C2 & The social acceleration coefficient & 2 & \\ \hline \multirow{4}{*}{SA} & maxIter & The maximum number of iterations & 1000 & \\ \cline{2-5}  & pSize & The population size & 1 & \\ \cline{2-5}  & T0 & The initial temperature & 2000 & \\ \cline{1-1} \cline{2-5}  & Tf & The final temperature & 0.01 & \\ \cline{1-1} \cline{2-5}  & \(\alpha\) & The cooling factor & 0.975 & \\ \hline \end{tabular}
\end{table} 
Table 1: The parameter values of the five optimization algorithms. path rejection installed on the pillar of the control point (NGB2) and a Leica GR10 receiver with the capacity to record multi-GNSS signals (GPS, Galileo, GLONASS). On 20 September 2021, GNSS data were collected with a 30 s sampling rate and zero-degree elevation mask. A total of 18-31 satellites were recorded, including 7-13 GPS, 4-10 GLONASS, and 5-10 Galileo satellites (Figure 8). To choose the satellites based on the CNR-WGDOP, using Equation (1), it was necessary to extract (i) satellite pseudorandom noise (PRN), (ii) the satellite observation time, (iii) elevation angles, (iv) azimuth angles, and (v) the CNR values. The raw satellite data (range observations and navigation data) were introduced into the RTK-LIB (version demo5 b34d) software to define the elevation and azimuth of each satellite, extract the required remaining information (satellite PRN, observation time, and CNR), and save the information in a file, as shown in Figure 9.  
The MATLAB (R2022b) software was used to perform the optimal satellite selection by applying the TM and optimization algorithms. The satellite selection was carried out every five minutes. For the examined 24 h GNSS record, the number of GPS satellites ranged from 8 to 13, while the total number of GNSS satellites (GPS, GLONASS, and Galileo) ranged between 18 and 31. In Figure 10, the number of all possible combinations for a sole GPS constellation and for a multi-GNSS constellation are depicted. The graphs illustrate the potential combinations for a number of given trackable satellites. It is evident that the possible satellite  
Figure 8: Number of available GNSS satellites at NGB2 GNSS station for a 24 h period on 20 September 2021.