## 5 Localization Algorithm Performance
Low-elevation satellites, which typically experience larger multipath errors, do not impact the solution as much as high-elevation satellites due to the elevation-dependent weighting according to (4). Figure 3 shows the number of received code observations for GPS L1 C/A, L2C-L1 C/A combinations, the sum of L2C-L1 C/A and E5a-E1 combinations as well as the sum of all six pseudo-range observations together. Figure 4 quantifies the quality of the satellite geometry with the corresponding _position dilution of precision_ (PDOP). The curves correspond to different stages of algorithm development: single-frequency GPS, multi-frequency GPS, multi-frequency/multi-constellation GNSS without calibrated DCBs and finally multi-frequency/multi-constellation GNSS with calibrated DCBs. The L2C-L1 C/A ionosphere-free combination was chosen for GPS since it is broadcast by more satellites than L5-L1 C/A. So, without information about the magnitude of receiver DCBs, working with L2C-L1 C/A combinations as the only GPS code observation offers the highest satellite availability of all civil multi-frequency GPS signals. Figure 3: Percentage of GNSS measurement epochs in which no more than the indicated number of satellites was available. As Figure 3 demonstrates, data set 1 suffers from reduced satellite visibility compared to set 2 due to the surrounding buildings. For data set 1 (Figure 3a), single-frequency GPS L1 C/A pseudo-ranges from at least four satellites are available more than 90 % of the time, while at least eight satellites are available more than 30 % of the time. A maximum ten satellites are received simultaneously. In the second data set (Figure 3b), these numbers increase to more than 90 %, more than 75 % and a maximum of eleven, respectively. The number of available L2-L1 C/A combinations is on average two lower than for L1 C/A in the first data set and three lower than for L1 C/A in the second data set. Compared to GPS L1 C/A, the sum of available L2C-L1 C/A and E5a-E1 combinations is on average slightly higher in both data sets. This corresponds to the total number of healthy satellites in orbit: 31 for GPS L1 C/A and 33 for L2C-L1 C/A + E5a-E1 (19 GPS + 14 Galileo) [10; 18]. However, the combined processing of GPS and Galileo introduces another unknown (two receiver clock biases instead of one). Therefore, the number of available pseudo-range observations for position determination is still slightly lower for L2C-L1 C/A + E5a-E1 than it is for GPS L1 C/A. The best results occur for joint processing of all six types of pseudo-range observations: even in data set 1 with its urban canyons and tunnel, code observations from ten or more different satellites are available more than 50 % of the time with a maximum of 15. For data set 2, this percentage rises to 80 % with a maximum of 17. This demonstrates the advantages of the approach to work with L5-L1 C/A and E5a-E1 ionosphere-free combinations preferably, but use L2C-L1 C/A and E5b-E1 combinations as well as L1 C/A and E1 single-frequency pseudo-ranges as backup whenever observations on L5/E5a are unavailable. The advantage is more pronounced on GPS than on Galileo since all Galileo satellites broadcast E5a signals while currently only 12 out of 31 GPS satellites broadcast L5 signals [10]. Figure 4 displays how the varying number of simultaneously available pseudo-ranges affects the PDOP. PDOP is calculated from all pseudo-ranges that were used in the EKF's measurement update, i.e., all pseudo-ranges that passed the plausibility check. Single-frequency GPS achieves a PDOP of less than four in approximately 73% of epochs in data set 1 (Figure 4a) and in approximately 97% of epochs in data set 2 (Figure 4b). For L2C-L1 C/A combinations, these numbers drop to 53% and 84%, respectively. The inclusion of E5a-E1 pseudo-ranges reduces the PDOP again, but it is still  
Figure 4: Percentage of GNSS measurement epochs in which PDOP was at least as good as indicated. higher than for single-frequency GPS: A PDOP less than four is achieved in 71%/85% of epochs for the two data sets.