## 3 Experimental Analysis
### Biases in Carrier Phase Geometry-Free and Ionosphere-Free Combination  
As discussed in Section 2, the carrier phase GFIF combination removes the frequency-independent terms and also the first-order ionospheric error. Only the ambiguity, measurement noises, and hardware delays remain in the combination. In order to examine the variation of observation noises, the ambiguity term is removed through averaging the GFIF combination observations. Figure 10 shows the GFIF carrier phase combinations of BDS GEO satellites C01, C03, and C04 at the stations GMSD and CUT0, as well as those of C06, C09, and C14 at CUT0. The two stations GMSD (30.56\({}^{\circ}\) N, 131.02\({}^{\circ}\) E) and CUT0 (32.00\({}^{\circ}\) S, 115.89\({}^{\circ}\) E) are located in the northern and southern hemispheres, respectively. Shown in each panel is the time series of GFIF (black) and elevation (red) over a two-day period. Figure 9: The multipath combinations of BDS satellites (**a**) C09 (ICSO) and (**b**) C14 (MEO); after the elevation-dependent correction model is applied. It is interesting to note that the GFIF combination variation with satellite elevation at the GMSD station has a trend opposite to that at the CUT0 stations. In Figure 10a, the GFIF combination at GMSD station decreases with respect to elevation but it is an increase trend at CUT0 station in Figure 10b. To verify whether the opposite trends of GFIF variation are hemisphere-dependent, GFIF combinations of more stations are examined. In the northern hemisphere, the stations GMSD, JFNG, and F783 have similar GFIF variation trend, decreasing with elevation. The only exception is the C01 at station F714. In the southern hemisphere, the GFIF variation trend at stations CUT0, F711, and F721 are similar to each other too, increasing with elevation, while that of C01 at station F713 is exceptional. The GFIF carrier phase combination series of JOG2 or NNOR station is not examined as no triple-frequency BDS observables are available at either station. In addition, the GFIF time series of BDS IGSC satellites show significant diurnal periodicity, but no obvious trend with respect to elevation (see satellites C06 and C09 in Figure 10c); neither do those of BDS MEO satellites (see satellite C14 in Figure 10c). The above results indicate that the variation of GFIF combination is not elevation-dependent. The plausible variation trends with respect to elevation in Figure 10a,b substantially reflect the diurnal periodicity in GFIF, since the elevation of each GEO satellite shows clear diurnal periodicity. Similarly, the GFIF combinations at stations F783 (14.52\({}^{\circ}\) N, 121.02\({}^{\circ}\) E) and GMSD (30.56\({}^{\circ}\) N, 131.02\({}^{\circ}\) E) are selected to conduct the between-station-differencing. Here, the station F783 is employed instead of CUT0, since the stations F783 and GMSD, both located at the northern hemisphere, have longer time of common view for the BDS IGSO satellites. As shown in Figure 11, the variation amplitude of GFIF combinations for GEO and IGSO satellites are reduced from \(\sim\)2.0 cm to \(\sim\)1.0 cm after the differencing, and the standard deviations also decrease significantly, from \(\sim\)1.0 cm to \(<\)0.4 cm. The same holds for IGSO satellite C06, whose standard deviation decreases from 1.4 cm to 1.0 cm after the single differencing between two stations. The results in Figure 11 show that the trends contained in the GFIF combination of GEO and IGSO satellites can be, to a great extent, reduced through the single differencing between two stations. It should be noted that the two GNSS stations are distantly separated and their observation conditions are different and independent of each other. The common trends appearing in the GFIF combinations of the two stations should be attributed to the commonly observed satellite, unlikely from the stations.