*4.2. Constellation Visibility*

The average number of visible satellites, the average PDOP value, and the satellite elevation distribution of the three tracking networks were analyzed with numerical comparison and statistical study. The number of visible satellites and their statistical property is shown in Figures 4 and 5, respectively.

**Figure 4.** The average number of visible satellites of GPS, GLONASS, and GPS+GLONASS in the high (red), middle (green), and low (blue) latitude networks.

From Figure 5, during the 8 days test period, both constellations have the largest average number of visible satellites in the high latitude network among the three networks. The average visible number of GPS in high latitude regions is significantly larger than in the middle and low latitude regions. The average number of visible satellites of GLONASS in the high and the middle latitude regions is similar but significantly larger than that of the low latitude region.

From the statistical point of view, the GLONASS visible satellites have the smallest standard deviation in the high and middle latitude networks. The percentages of most observed 9 and 8 GLONASS satellites in the high latitude network are 52.37% and 27.63%, respectively. The percentages of most observed 9 and 8 GLONASS satellites in the middle latitude network are 34.20% and 33.64%, respectively. However, the number of GLONASS visible satellites reduces significantly, and the standard deviation increases significantly in the low latitude network. Moreover, the standard deviation of GPS+GLONASS is relatively larger than GPS or GLONASS, and the average number of visible satellites is also larger than those of GPS and GLONASS. The probability of observing satellites less than 12

in three networks of combined GPS and GLONASS is almost zeros, indicating that the combined constellations provide more than 12 visible satellites in most cases.

**Figure 5.** The histogram of visible satellites in the high (red), middle (green), and low (blue) latitude networks. The position of the dashed line and the value x− indicate the average number of visible satellites. The σ<sup>2</sup> represents the variance of the visible satellites' distribution. Please note that the horizontal axis of GPS and GLONASS visible satellites differs from that of GPS+GLONASS.

The histogram of the elevation distribution related to GLONASS, GPS, and GLONASS+GPS is also presented in Figure 6 to further evaluate the quality of the observed satellites.

From Figure 6, GLONASS has a much better elevation distribution than GPS in the high latitude network. The most observed GLONASS satellites' elevation angles in the high latitude network are between 13–33 degrees, while those of GPS are between 6–26 degrees, which are obviously lower than that of GLONASS. In addition, the mean elevation angle of GLONASS is 35.01◦, which is 3.97◦ higher than that of GPS. In the middle latitude network, the elevation angle distribution and average elevation angle between GPS and GLONASS have inconspicuous disparity. In the low latitude network, the percentage peak of GLONASS corresponds to an obviously lower elevation angle than GPS. The elevation distribution of GPS+GLONASS lies between GPS and GLONASS.

The PDOP of GPS, GLONASS, and GPS+GLONASS during the testing period is illustrated in Figure 7.

**Figure 6.** The histogram of elevation distribution of the high (red), middle (green), and low (blue) latitude networks, the position of the dashed line and the value x− indicate the mean elevation.

**Figure 7.** The PDOP of GPS, GLONASS, and GPS+GLONASS in the high (red), middle (green), and low (blue) latitude networks (The GLONASS PDOP for the low latitude network exceed the coordinate threshold, and the small picture in the upper right corner with the rose thread shows the full view of the PDOP).

Figure 7 shows that the PDOP values of GPS are less than 3.0 in all three regions, and the most stable PDOP values appear in middle latitude regions, indicating that the observation geometry of GPS in that region is the best among the three regions. Moreover, the PDOP values of GPS exist daily period in all three regions. GLONASS has the most stable PDOP in high latitude regions, which is more stable than GPS in the same region. However, the PDOP values of GLONASS increase obviously as the latitude decreases. In addition, the PDOP values of GLONASS at low latitude regions show some abnormally large values, up to 92.68, as shown in the upper right corner of the subfigure for low latitude GLONASS PDOP. The PDOP values of GPS+GLONASS exhibit better performance than both GLONASS and GPS stand-alone systems. Although some periods exist in high latitude regions where the PDOP of GPS is up to 2.80, the PDOP values of GPS+GLONASS are quite stable and less than 1.55. Although the PDOP of GPS is up to 2.75 in some periods in low latitudes and the PDOP of GLONASS is very large at certain epochs, the PDOP of GPS+GLONASS remains stable and below 1.44. The combined GPS and GLONASS constellations have the most obvious improvement in observation geometry at low latitudes.
