## 4 Calibration of Differential Code Biases
 \tag{14}\]  
In order to calibrate DCB\({}_{IF,A}\), the DCB between a ionosphere-free linear combination \(\rho_{IF}\) and a single-frequency pseudo-range \(\rho_{\alpha}\), the ionospheric delay for the signal \(\alpha\) needs to be eliminated. This was done with _total electron content_ (TEC) maps provided by the _International GNSS Service_ (IGS) via the _Ionosphere Map Exchange Format_ (IONEX). Input data for DCB calibration was collected with two JAVAD TRIUMPH-LS receivers, both connected to the same roof antenna. In accordance to [4], 24 h data sets with 30 s sampling rate and a minimum elevation of 20\({}^{\circ}\) were used. Data collection was performed on days 151, 153 and 154 of 2018. On day 152, both receivers were shut down and restarted to enable the detection of potential turn-on biases. Figure 2 displays the estimated DCBs between L2C-L1 C/A ionosphere-free combinations and L1 C/A for the six data sets. Every day a total of approximately 12,000 observations was collected with each receiver. Although the DCB estimates are noisy, it is obvious that the DCB is nonzero. No significant variation over time is evident. Also, no turn-on bias can be identified because the curves for _day of year_ (DOY) 151 (Figure 2a,d) are similar to the ones from DOY 153 (Figure 2b,e) and DOY 154 (Figure 2c,f). These findings are supported by the statistical analysis presented in Table 5: All four calibrated DCBs are stable over the examined time span. The standard deviation for a single 24 h set ranges from approximately 0.6 m to approximately 0.8 m while the maximum difference of the means is approximately 0.3 m. For the combination of all six data sets, the standard deviation ranges from approximately 0.7 m to approximately 0.8 m. The means estimated from all six data sets combined reveal the reason why the proposed processing of different types of ionosphere-free combinations together with single-frequency observations for GPS (see Section 2.2) did not work properly: While the DCB of \(-\)1.9 m between L5-L1 C/A and L1 C/A is small enough to still maintain some benefit from the utilization of dual-frequency observations, this is apparently not the case for the DCB of 3.8 m between L2C-L1 C/A and L1 C/A. The combined processing of all three observation types (L1 C/A, L2C-L1 C/A and L5-L1 C/A) amplifies the problem because the DCB between L2C-L1 C/A and L5-L1 C/A is approximately 5.7 m. The problem is less pronounced on Galileo: While the DCBs between E5a-E1 and E1/E5b-E1 and E1/E5a-E1 and E5b-E1 are approximately \(-\)3.0 m/3.3 m/ \(-\)6.3 m respectively, the fact that all Galileo satellites broadcast the same signals results in a high availability of the preferred E5a-E1 ionosphere-free combinations. That is why only very few E5b-E1 combinations and E1 single-frequency pseudo-ranges have to be used as backup. The common-mode error of \(-\)3.0 m on all E5a-E1 ionosphere-free combinations is simply added to the receiver clock bias \(c\delta t^{rec}\) and does not affect positioning performance. With the obtained calibration values for all four types of ionosphere-free combinations, it is possible to use a total of six different types of pseudo-range observations simultaneously: L5-L1 C/A and E5a-E1 as first choice, L2C-L1 C/A and E5b-E1 as second choice, single-frequency L1 C/A and E1 as third choice for GPS and Galileo, respectively. To verify the DCB calibration and provide an impression about the achievable accuracy for the upcoming Section 5, single-epoch solutions were computed from the six collected 24 h data sets, making use of all six different types of pseudo-range observations. This was done in three different ways: once with our self-developed software and the calibrated DCBs, once with our self-developed software but without the calibrated DCBs and once with RTKLIB [17], using similar settings as in the self-developed software (positioning mode: single,  
Figure 2: DCB between L2C-L1 C/A ionosphere-free combinations and L1 C/A.