# A Fast Indoor/Outdoor Transition Detection Algorithm Based on Machine Learning
## 2 Materials and Methods
### Feature Extraction
#### 2.4.1 Visible Satellite Geometry Topology  
The satellite azimuth is based on the standard of the direct north direction (about the geomagnetic South Pole). The satellite antenna points to the east or west to adjust an angle, which reflects the position of the satellite in space. Its value ranges from 0 to 360\({}^{\circ}\). Figure 5 shows the cumulative probability of the number of visible satellites azimuth using different smartphones in the range of 90 and 180\({}^{\circ}\) in a week. In outdoor scenarios, within the range of 90\({}^{\circ}\), the ratio of the number of the satellite is mainly concentrated in the range from 0.4 to 0.6. Meanwhile, within the range of 180\({}^{\circ}\), the ratio of the number of the satellite is mainly concentrated in the range from 0.6 to 0.8. However, in indoor scenarios, the ratio of the number of satellite start from 0 due to there is no signal. Furthermore, the ratio of the number of the satellite is mainly concentrated in the range from 0.8 to 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Category** & **Features** & **Description** \\ \hline \multirow{5}{*}{**Category**} & \multirow{5}{*}{**Visible satellite geometry**} & \multirow{5}{*}{Az\_dtb\_vector} & A 36-dimensional vector **d** represents the azimuth distribution of the satellite \\ \cline{3-4}  & & & Az\_dtb\_proportion & Satellite azimuth distribution proportion \\ \cline{3-4}  & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \hline \multirow{5}{*}{**Category**} & \multirow{5}{*}{**DoP for positioning satellite satellite satellite**} & \multirow{5}{*}{PDoP, HDoP, VDoP satellites vary**} & The number of satellites change ratio from time t\({}_{2}\) to time t\({}_{1}\) \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \hline \multirow{5}{*}{**Category**} & \multirow{5}{*}{**Visible satellite CNR**} & \multirow{5}{*}{\(\mathrm{P(hold)}_{h-t}\)} & Satellite CNR in collection \(\mathrm{G_{u}}\) hold ratio from time t\({}_{2}\) to time t\({}_{1}\) \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \hline \multirow{5}{*}{**Category**} & \multirow{5}{*}{**Collection G**} & GS\_Num & The number of satellites at the current time \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \hline \multirow{5}{*}{**Category**} & \multirow{5}{*}{**Collection G**} & CS\_Num, & The number of satellites in \(\mathrm{G_{p}}\) under different sliding window lengths \(k\) \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \hline \multirow{5}{*}{**Category**} & \multirow{5}{*}{**Collection S**u} & PDoP\_mean, HDoP\_mean, & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \cline{3-4}  & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The list of considered features for our classifiers. We deeply analyzed and compared the distribution of satellite azimuth in complex indoor and outdoor scenarios. In deep indoors, it is difficult to receive the visible satellite signal because the reinforced concrete and the wall structure block the satellite signal. In shallow indoors, through satellite signals may penetrate the glass curtain wall and window, the azimuth range of observable satellites is limited due to limited exposure to the sky. In semi-outdoors, although blocked by tall buildings and overpass, the scope of the exposed sky is larger than that in shallow indoors, the satellite signal can still be detected after reflecting by the multi-path effect. In the open outdoors, the visual satellite is dispersed in the sky with a strong signal.