## 4 Positioning Performance of GPS/QZSS and BDS/QZSS in the Asia-Pacific Region  
### Availability and PDOP of GPS/QZSS and BDS/QZSS  
Availability mainly describes the number of visible satellites above the mask angles and is the most basic performance measure of a navigation system. The theoretical minimum number of satellites to achieve SFSE DD baseline resolution for a single system is 4 and for multisystem is n + 3, where n is the number of systems. PDOP is another indicator revealing the relative position quality of the constellation-user geometric structure. The more scattered the satellite distribution, the larger the geometric volume of the constellation and the higher the position precision [24]. To evaluate the availability and PDOP of the integrated GPS/QZSS and BDS/QZSS, the GPS, BDS, and QZSS data of a week was collected and calculated. The time interval ranges from 4 February to 2 March 2018, and the sampling frequency is 30 s. Figure 2 shows the number of visible satellites and the PDOP value under the BDS, GPS, BDS/QZSS, and GPS/QZSS cases with mask angles of \(0^{\circ}\), \(10^{\circ}\), \(20^{\circ}\), and \(35^{\circ}\) at the HKLT station in Hong Kong, from day of year (DOY) 54 to 60. Table 2 gives the average number of visible satellites (minimum value) and the mean PDOP displayed in Figure 2. Figure 3 presents availability and PDOP trends with the increasing mask angle from 0 to \(35^{\circ}\). For the single GPS, when the mask angle changes from \(0^{\circ}\) to \(20^{\circ}\), the minimum/mean/maximum number of satellites (NOS) decreases from \(7/10/13\) to \(4/6.9/10\) and the corresponding PDOP increases from \(2.63/1.62/1.1\) to \(20.5/4.25/1.65\); the differences of the mean NOS and PDOP are 3.1 and 2.63, respectively. When the mask angle increases to \(35^{\circ}\), the mean PDOP is 9.39 and the mean NOS is 3.6, which is lower than boundary value of 4. In that case, the single GPS cannot provide constant and accurate position service. For integrated GPS/QZSS, the mean NOS and mean PDOP with mask angles of \(0^{\circ}\), \(20^{\circ}\) and \(35^{\circ}\) are \(13/1.39\), \(9.4/2.69\) and \(5.5/4.92\), respectively. The improvement in NOS and PDOP are \(3/0.23\), \(2.5/2.44\) and \(1.9/4.47\), respectively. This means that even above elevations of \(20^{\circ}\) and \(35^{\circ}\), there are still 2.5 and 1.9 visible QZS, respectively, which could greatly improve the observation conditions and the positioning accuracy of the single GPS. For the single BDS, when the mask angle is less than \(20^{\circ}\), an average of 10.1 BDS satellites can be observed, which is many more satellites than for GPS (6.9). Even when the mask angle is set to \(35^{\circ}\), there are still at least five and an average of seven BDS satellites (high-elevation satellites) in the field of vision, which ensures a full-time BDS positioning in Hong Kong. After augmented by QZSS, the improvement in PDOP is approximately 0.27/0.29/0.47 with a mask angle of \(0^{\circ}/20^{\circ}/35^{\circ}\). QZSS bring about a great improvement in the NOS and PDOP for GPS, which supports the sustainable high accuracy positioning of GPS under difficult conditions. \begin{table}
\begin{tabular}{c|c c c c c c c} \hline \hline
**Mask Angle** & \multicolumn{2}{c}{\(\mathbf{0^{o}}\)} & \multicolumn{2}{c}{\(\mathbf{10^{o}}\)} & \multicolumn{2}{c}{\(\mathbf{20^{o}}\)} & \multicolumn{2}{c}{\(\mathbf{35^{o}}\)} \\ \hline
**SystemIndex** & **NOS/Min** & **PDOP** & **NOS/Min** & **PDOP** & **NOS/Min** & **PDOP** & **NOS/Min** & **PDOP** \\ \hline BDS & **11.4/8** & 2.02 & **10.9/7** & 2.17 & **10.1/7** & 2.40 & **7.0/5** & 3.68 \\ BDS/QZSS & **14.4/11** & 1.75 & **13.8/10** & 1.88 & **12.6/9** & 2.16 & **8.9/6** & 3.21 \\ GPS & **10/7** & 1.62 & **8.8/6** & 1.96 & **6.9/4** & 4.25 & **3.6/1** & 15.92 \\ GPS/QZSS & **13/10** & 1.39 & **11.7/9** & 1.65 & **9.4/6** & 2.69 & **5.5/3** & 11.93 \\ \hline \hline \end{tabular}
\end{table}