Abstract
The main objective of this study was to evaluate the performance of a dual-frequency multi-constellation (DFMC) satellite-based augmentation system (SBAS) broadcast from the Japanese Quasi-Zenith Satellite System (QZSS) in the Arctic and high-latitude regions. We installed a global navigation satellite system (GNSS) antenna and receiver on the roof of the Kjemibygningen (chemistry building) at the University of Oslo, Norway, on February 24, 2021, and conducted experiments continuously until March 17, 2021.
We found that the QZSS-based DFMC SBAS achieved a system availability of 84.68% for localizer performance with vertical guidance when the horizontal and vertical alert limits were set to 40 and 50 m, respectively. This result is below the performance of QZSS-based DFMC SBAS in Japan. However, our analysis shows that adding three or more QZSS reference stations in Europe will enable DFMC SBAS from QZSS to reach 100% availability.
1 INTRODUCTION
As Arctic sea ice cover continues to decline, aviation and maritime activities in the Arctic are increasing (Miller & Ruiz, 2014). A recent study reported that this decline in sea ice cover continues as of 2021 (Kacimi & Kwok, 2022), and in a simulation-based study, Overland and Wang (2013) found that the Arctic Ocean is expected to be “ice-free” during some summer periods between 2030 and 2080. This decline in Arctic Ocean sea ice is expected to increase maritime activities, including ocean resource extraction and vessel traffic. Aviation activity is also expected to increase alongside the increase in maritime activities. Because of the poor infrastructure in the Arctic, the global navigation satellite system (GNSS), which operates with augmentation systems such as the satellite-based augmentation system (SBAS) (Walter et al., 2012) and the advanced receiver autonomous integrity monitoring (ARAIM) technology (Blanch et al., 2014), provides an efficient solution for aviation and maritime navigation in Arctic regions.
Reid et al. (2016) used the MATLAB algorithm availability simulation tool (MAAST) to estimate the availability of the different operations enabled by SBAS and ARAIM. They reported that the dual-frequency multi-constellation (DFMC) SBAS enables aircraft precision approach and precise maritime operations. Moreover, DFMC SBAS has been standardized by the International Civil Aviation Organization (ICAO). The current L1 SBAS broadcasts augmentation messages generated by geostationary (GEO) satellites. Figure 1(a). shows the elevation angle of GEO satellites based on the Almanac released on March 1, 2021. As shown in the figure, the augmentation messages broadcast by GEO satellites are not practically available in the polar region over 72 degrees latitude.
Maximum elevation angle during one day for (a) GEO and b) QZSS satellites in quasi-zenith orbit (QZO). An elevation mask of 5 degrees was applied. The green dots and lines represent the locations and trajectories of the GEO and QZSS satellites in QZO. The red dashed lines indicate 72 degrees latitude, and the red dot shows the location of Oslo, Norway.
However, augmentation messages broadcast by satellites in inclined geosynchronous orbit are a viable option for receiving messages at high latitudes. Three satellites of the Japanese quasi-zenith satellite system (QZSS) in the quasi-zenith orbit (QZO) currently have an inclination angle of ~42 degrees; one of these satellites is a GEO satellite. QZO is similar to inclined geosynchronous orbit but has a higher orbit eccentricity, which enables the satellites to stay longer at high elevation angles over Japan (i.e., with their apogee in the northern hemisphere). As shown in Figure 1(b), the maximum elevation angle of QZSS satellites in QZO is between 10 and 45 degrees at high latitudes, so DFMC SBAS could be available in the Arctic using messages broadcast by QZSS.
The main objective of this study was to evaluate the performance of DFMC SBAS broadcast from Japanese QZSS in the Arctic and high-latitude regions. We selected Oslo, Norway (10.72° E, 59.94° N) as our observation site. Because Oslo is located on the other side of the Earth from Japan and the QZSS coverage region, QZSS signals are not always received in Oslo, as shown in Figure 1(b). This makes Oslo a more challenging, and therefore more worthwhile, site for testing DFMC SBAS performance using messages broadcast by QZSS. However, signals broadcast by the European Geostationary Navigation Overlay Service (EGNOS) satellites can be received in Oslo, so augmentation messages broadcast by the QZSS satellites can be received in the region between the blue and red areas shown in Figure 1(b), with the exception of the white area.
2 GENERATION OF DFMC SBAS MESSAGES
The Electronic Navigation Research Institute (ENRI) has developed a prototype DFMC SBAS ground system using the DFMC messages identified in the ICAO Standards and Recommended Practices. These messages are also captured in Appendix A of the DFMC SBAS Minimum Operational Performance Standards (RTCA, 2023). We employed a reference station to monitor the pseudorange of GNSS satellites sampled every 1 second. Our prototype DFMC SBAS message augmented the satellite clock for the pseudorange of ionosphere-free linear-combination GPS L1/L5, Galileo E1/E5a, and QZSS L1/L5 signals. This augmentation message also included information about satellite position correction for GPS, Galileo, and QZSS. The DFMC SBAS message was generated based on 22 reference stations, as shown in Figure 2, and was assumed to be used in the areas around Japan. For this reason, 12 of the 22 reference stations were located at longitudes ranging from 100 to 180 degrees. Of the remaining 10 reference stations, four were located in North and South America, and six were located in Europe, Africa, and India. The augmentation message was broadcast by QZSS02 (PRN 194) and QZSS04 (PRN 195) every 1 second. Details of this prototype message can be found in Kitamura and Sakai (2019).
Locations of reference stations (red dots).
3 OBSERVATION
Figure 3 shows a sky plot of the GPS, Galileo, EGNOS, and QZSS trajectories in Oslo, Norway, on March 1, 2021. As shown in the figure, the GPS and Galileo satellites rose to a ~ 80-degree elevation angle, and 6–11 GPS and 4–9 Galileo satellites were typically visible. The EGNOS satellites were visible in the 8–20-degree range. Based on these satellite trajectories, the L1 SBAS message could be received in Oslo.
Sky plot of the GPS (blue line), Galileo (red line), EGNOS (black dots), and QZSS (green line) satellite trajectories in Oslo, Norway, from 00:00 UT to 23:59 UT on March 1, 2021. The satellite positions were calculated based on the Almanac released on March 1, 2021.
The QZSS satellites appeared at up to a 13-degree elevation angle, and any QZSS satellites above 5 degrees were visible for ~ 15 hours a day. However, because the azimuth angles of QZSS satellites are similar, the visibility of QZSS is important in non-open sky conditions at high latitudes. For example, when an aircraft banks, it may lose line-of-sight to QZSS satellites. In such situations, there is an increased risk of losing the QZSS signal or experiencing a degradation in positioning accuracy.
We installed an antenna and two receivers on the roof and observation room, respectively, of the Kjemibygningen (chemistry building) at the University of Oslo, as shown in Figure 4. We used a JAVAD GrAnt-G3T antenna, which is capable of receiving signals in the L1, L2, and L5 frequency bands. Using the precise point positioning (PPP) technique, we determined the antenna position (10.71701346° E, 59.937564229° N, and 133.8838 m elevation). The DFMC GNSS ranging signals were received by a JAVAD DELTA receiver, and a Furuno prototype DFMC SBAS receiver was used to receive the DFMC SBAS messages. Both types of signals were recorded using a PC. In addition, the GPS, Galileo, GLONASS, and BeiDou signals were recorded using a JAVAD DELTA GNSS receiver at a 1-Hz sampling rate.
(a) Bird’s eye view of the Kjemibygningen (chemistry building) at the University of Oslo. (b) JAVAD GrAnt-G3T antenna. (c) DFMC and GNSS receivers and data recording laptop.
This experiment was conducted continuously from 9:10:17 UT on February 24, 2021, to 19:44:31 UT on March 17, 2021. During this time, we successfully received and recorded the DFMC SBAS messages broadcasted by QZSS using the Furuno prototype DFMC receiver. The only exceptions were on March 2, 12, and 17, 2021, when the laptop encountered problems; the data on those days were therefore not used in this analysis.
The Furuno receiver recorded the DFMC SBAS messages broadcast by QZSS02 and QZSS04. We started receiving the messages when the satellite elevation angle reached 6.9–9.8 degrees, and the recording continued until the elevation angle was 2.1–5.2 degrees. Despite the positive elevation angle of QZSS04, no messages were received from 07:03 to 13:31 on Feb. 26, 2021, because the satellite was down due to regular maintenance. Overall, the message was received for 849,895 epochs, excluding the time the laptop was down. This corresponds to 53% of the total number of epochs during the sampling period (i.e., 1,609,275). As noted above, the QZSS signals could theoretically be received for 15 hours per day; however, in practice, they were received for only ~ 12.7 hours per day because the Furuno receiver only started to record signals when QZSS rose to a 6.9-degree elevation angle. In this paper, we employed the broadcast ephemeris and augmentation message to test the performance of DFMC SBAS in Oslo.
4 RESULTS
In this study, we calculated the DFMC SBAS augmented position solutions as described in the standards (ICAO, 2023; RTCA, 2023). For this calculation, we used the Saastamoinen tropospheric delay model (Saastamoinen, 1972). The horizontal and vertical protection levels (HPL and VPL) were also calculated using the DFMC SBAS augmentation messages, as described in standards (ICAO, 2023; RTCA, 2023). These protection levels were given by:
1
2
where dmajor is the error uncertainty along the semi-major axis of the error ellipse, and dU is the variance of the model distribution that over-bounds the true error distribution along the vertical axis.
As shown in Figure 4, a building to the northeast of the antenna blocked the field of view below approximately 6 degrees. This building not only obstructed the satellite signals but also contributed to multipath propagation. We accordingly detected multipath propagation using the following condition:
3
where ρi,code is the code pseudorange of the signals, and ρi,CSC is the carrier-smoothed pseudorange. Finally, (i) the residual error of the measured pseudorange of signals and (ii) a geometric distance greater than 20 m were both regarded as multipath propagation when calculating point positioning solutions using the least-mean square method.
Figure 5 shows the calculated, unaugmented point positioning solutions. Each point positioning solution is expressed by the east-north-up (ENU) coordinate relative to a reference position, which is obtained from post-processing using the PPP technique. In this study, the vertical component corresponds to the “up” (vertical) component of the ENU coordinate, and all distances were obtained from the point positioning solutions. As shown in Figure 5, the most frequent values obtained for the east, north, and vertical components were 0.40, 0.09, and –1.30 m, respectively, with corresponding standard deviations of 1.33, 1.24, and 2.71 m.
Point positioning solutions for the (a) horizontal and (b) vertical components obtained using the GPS and Galileo satellites without applying the augmentation message. (c) Black, red, and blue histograms show the positioning solutions for the east, north, and vertical components, respectively.
Figure 6 shows the point positioning solutions obtained using the augmented satellites following the same calculations as in Figure 5. As shown in Figures 5(a) and (b), the most frequent values obtained for the east, north, and vertical components using the augmented satellites were –0.18, –0.04, and –1.12 m away from the reference position, respectively, with corresponding standard deviations of 4.26, 2.99, and 4.77 m. We found no significant differences between the positioning solutions calculated using the augmented and unaugmented satellites; however, the standard deviations of the positioning solutions increased with the augmented satellites.
Positioning solutions for the (a) horizontal and (b) vertical components obtained using the GPS and Galileo satellites while applying the augmentation message. (c) Black, red, and blue histograms show the positioning solutions for the east, north, and vertical components, respectively.
Comparing Figures 5 and 6 confirms that the variability in the augmented positioning solution in Figure 6 was noticeably greater than for the unaugmented solution in Figure 5. This variability appears to be due to either the reduction in the number of satellites or some potential issues within the DFMC SBAS message. To distinguish these effects, Figure 7 shows the positioning solution calculated using the same satellites as Figure 6 but without the DFMC SBAS messages. The standard deviations were 11.90, 8.64, and 12.29 meters, respectively, and the positioning solutions were widely distributed. These high standard deviations indicate that the DFMC SBAS message directly contributed to reducing pseudorange errors. Based on these results, the primary cause of the increased variability in the positioning solution was likely the reduction in the number of satellites.
Positioning solutions for the (a) horizontal and (b) vertical components obtained using the GPS and Galileo satellites without the DFMC SBAS augmentation message. The GNSS satellites used for positioning were the same as in Figure 6. (c) Black, red, and blue histograms show the positioning solutions for the east, north, and vertical components, respectively.
Figure 8 shows integrity triangle charts calculated using Equations (1) and (2) with the DFMC SBAS augmentation message. In this study, the protection levels were calculated for all cases with six or more augmented satellites. The horizontal and vertical positioning error did not exceed the horizontal and vertical protection level. Here, we considered the protection level used in LPV; thus, the horizontal and vertical alert limits (HAL and VAL) were set to 40 and 50 m, respectively. System availability, which is the ratio of (i) the number of data points included in the white triangles (“normal operation”) in both the horizontal and vertical integrity triangle charts to (ii) the total number of data points, was 84.68%.
(a) Horizontal and (b) vertical integrity triangle charts. The white, light red, red, and orange areas indicate normal operation, misleading information, hazardous operation, and system unavailability, respectively.
5 DISCUSSION
The calculated system availability in Oslo was lower than that for Japan, presumably because most of the current reference stations were closely aligned with the longitude of Japan. Indeed, the augmentation message was expected to be used in Japan, and the obtained positioning error and protection level were suppressed in the area around Japan. There were only a few reference stations in Europe. The validity of the augmentation message received in Oslo and the reduction in the number of augmented satellites should therefore be evaluated.
To assess how efficiently the augmentation message improved the positioning solutions, we compared r0 - ρ0 to rAug - ρAug. This comparison is shown in Figure 9, where r0, ρ0, rAug, and ρAug are the unaugmented and augmented geodetic distances to satellites, respectively, and ρ0 and ρAug are the unaugmented and augmented carrier-smoothed code pseudoranges in dual frequency, respectively. The receiver clock offset was extracted and estimated using point positioning. Based on this comparison, the distribution of unaugmented data was slightly wider than that of the augmented data, and the augmentation message improved the pseudorange error for 62% of epochs. The augmentation message therefore improved the positioning solutions. Furthermore, augmentation alone is unlikely to cause the wide variation of the positioning solution or to reduce satellite availability, as seen in Figures 6 and 8. The residual error of unaugmented pseudoranges shows no remarkable dependence on elevation angle, while the residual errors for satellites at high elevation angles were reduced by augmentation. This improvement was likely because satellites at higher elevation angles can be tracked by more monitoring stations than satellites at lower elevation angles, allowing for the creation of more effective messages.
Histograms of r0 - ρ0 (blue) and rAug - ρAug (red).
Figures 10(a), (b), and (c) show a histogram of the number of augmented satellites, a time series for the number of observed satellites, and a time series for the number of augmented satellites. In the unaugmented case, which was shown in Figure 5, we employed 12–17 satellites for positioning. On the other hand, only 3–7 satellites (i.e., fewer than half) were augmented most of the time, and only six or more satellites were augmented for 39.57% of the total number of epochs.
(a) Histograms of the number of observed and augmented satellites. (b) Time series of the number of observed GPS (red) and Galileo (blue) satellites. (c) Time series of the number of augmented GPS (red) and Galileo (blue) satellites.
Table 1 shows the number of satellites, the percentage of augmented intervals, and the system availability. As shown in the table, system availability increases with the number of augmented satellites, to the point where the horizontal component availability reached 100% when 12 or more satellites were augmented. This case was also sufficient for LPV. However, only 1.09% of epochs met this condition, which means PPP using the DFMC SBAS message broadcast by QZSS is currently extremely limited in Oslo.
Variation in system availability based on the number of augmented satellites
However, the GPS satellites that do not broadcast the L5 signals will soon be replaced by satellites that will broadcast the L1 and L5 signals. This infrastructure change means that, in the near future, the augmentation message broadcast from QZSS will be used in almost the same conditions at high latitudes around Japan.
We therefore performed two simple simulations based on anticipated future augmented satellites under the following assumptions and conditions:
Case 1
All satellites transmit L1/L5 or E1/E5a signals as of March 1, 2021.
A satellite position is calculated using the Almanac released on March 1, 2021.
A satellite monitored by more than seven reference stations is regarded as an augmented satellite.
Case 2
In addition to the assumptions of Case 1, we set three temporary reference stations in Oslo, Norway (11.10° E, 60.20° N, 206 m), Milano, Italy (8.72° E, 45.63° N, 221 m), and Reykjavik, Iceland (22.61° W, 63.99° N, 50.0 m), as shown by the blue dots in Figure 11.
(a) Locations of the reference stations for the simulation study. The red dots indicate the reference stations used for generating the augmentation message in March 2022, and the blue dots indicate the temporary reference stations used for simulating Case 2. (b) The number of visible satellites, (c) the number of augmented satellites in Cause 1 and (d) Case 2.
The objective of these simulations was to evaluate whether system availability in the Arctic region can reach 100% once new satellites are in place. In Case 1, we assumed a near-certain future availability based on current installations, and in Case 2, we assumed that new infrastructure must be installed. Figure 11(a) shows the locations of the current (red dots) and temporary (blue dots defined in Case 2) reference stations. The three temporary reference stations were located in Oslo, Milano, and Reykjavik to overcome the nonuniform distribution of the original reference stations.
Figure 11(b) shows the estimated number of observed satellites transmitting L1/ L5 or E1/E5a signals. This estimate is the same as the number of the observed satellites on March 1, 2021, including the satellites transmitting only the L1 signal. However, we estimate that 13–23 satellites transmitting L1/L5 or E1/E5a signals will be observed in the near future. Figure 11(c) accordingly shows the estimated number of satellites augmented by the DFMC SBAS messages broadcast by the QZSS satellites for Case 1. In the Case 1, the number of augmented satellites increased compared to those observed in Oslo as shown in Figure 10(c), and six or more satellites were constantly augmented. The protection levels and augmented positioning solutions will always be provided when the QZSS signal is received. However, 12 or more satellites were augmented for only 9.51% of the total number of epochs. Based on these simulation results, system availability will improve in the near future, but its performance in Oslo will remain inferior to its performance in the areas around Japan, even if all GPS and Galileo satellites transmit L1/L5 and E1/E5a signals.
Figure 11(d) shows the estimated number of observable and augmented satellites transmitting L1/L5 or E1/E5a according to Case 2. A comparison of Figures 11(b) and (d) show that the observed satellites were augmented. In the Case 2 simulation, 18 satellites were typically (about 70%) augmented, and 13 satellites were always augmented. System availability was therefore likely to reach 100%. This result means that the augmentation achieved by employing the DFMC SBAS messages broadcast by QZSS satellites will be sufficient for LPV in Oslo if the QZSS satellites are observed.
The results of Case 2 also depend on the number of temporary reference stations. For Case 2, we calculated the number of satellites that will be augmented by employing either one or two temporary reference stations. By setting one temporary reference station in Oslo, nine or more satellites are expected to always be augmented, and the system availability is expected to reach 99.36%. Although this represents a substantial improvement in expected availability, availability reached 100% only a few times. By setting two temporary reference stations in Oslo, Milano, and/or Reykjavík, 13 or more satellites are expected to always be augmented. In this case, 100% system availability can be consistently achieved; however, because of potential redundancy among stations, we estimate that three additional reference stations would be needed to achieve 100% availability. We expect that estimated availability will improve because new Galileo satellites have been planned for launch; however, more discussion of the satellite geometry is needed, as our study only considered the number of satellites.
6 CONCLUSIONS
We evaluated the performance of DFMC SBAS in the Arctic and high-latitude regions using DFMC SBAS messages generated by a prototype message developed by ENRI based on draft standards and then broadcast from QZSS satellites. For this purpose, we installed a GNSS antenna and receiver on the roof of the chemistry building at the University of Oslo, Norway, on February 24, 2021, and conducted experiments continuously until March 17, 2021. We successfully received signals from the GNSS, Galileo, and QZSS satellites during this period. By performing point positioning without broadcasting the augmentation message, the calculated east, north, and up positioning errors with respect to PPP were 0.40, –0.09, and –0.74 m, respectively. The corresponding standard deviations were 1.33, 1.24, and 2.71 m, respectively. We then calculated the position solutions using augmentation messages, and the east, north, and up positioning errors with respect to the PPP were –0.18, –0.04, and –1.12 m, respectively. The corresponding standard deviations were 4.26, 2.99, and 4.77 m, respectively. Although we observed no significant differences between the mean positioning solutions calculated by the augmented and unaugmented satellites, the standard deviations of the positioning solutions obtained by broadcasting the augmentation message were considerably larger than those without broadcasting the augmentation message. We therefore calculated the positioning solution using the same satellites as for the augmented positioning solution; the standard deviations were 11.90, 8.64, and 12.29 m, respectively, and the positioning solutions were widely distributed. These results indicate that the DFMC SBAS message likely had no potential issues and contributed to reducing pseudorange errors.
We additionally calculated the horizontal and vertical integrity triangle charts for the positioning solutions. For this analysis, the HAL and VAL were set to 40 and 50 m, respectively, because we assumed LPV. We found no positioning errors that exceeded the protection levels, but the protection levels frequently exceeded HAL and VAL. System availability, which is the ratio of the number of data included in the white triangle in both the horizontal and vertical integrity triangle charts to the total number of data, was 84.68%. This estimate of system availability in Oslo was less than that calculated in Japan. We discussed and evaluated the validity of the augmentation message and some augmented satellites and found that the residual error of the augmented pseudorange of signals was smaller than that of the unaugmented pseudorange. The augmentation message therefore improved the positioning solutions and was unlikely to be the cause of the wide standard deviations.
Due to the limited distribution of reference stations, half or more of the observed satellites were not augmented. To calculate the positioning solutions, six or more augmented satellites were needed; however, this level of coverage was achieved for only 39.57% of the total number of epochs. System availability increased with the number of the augmented satellites and reached 100% when 13 or more satellites were augmented. We therefore concluded that the reduced number of augmented satellites caused the decrease in system availability. To evaluate whether system availability can be improved in the near future, we conducted two simple simulations. In the first simulation, we assumed that all satellites transmitted L1/L5 or E1/E5a signals (Case 1). In the second simulation, three additional reference stations were set in Europe (Case 2). In Case 1, six or more satellites were augmented in 100% of the QZSS observable interval, and the availability was expected to be greater than 84%. This result indicates that QZSS performance in the Arctic will not change significantly even if all satellites transmit at dual frequency. However, in Case 2, 13 or more satellites were augmented, and system availability was expected to reach 100%. Although we did not consider satellite geometry, we estimate that three or more stations are needed in Europe to effectively use the augmentation message broadcast from the QZSS satellites to the Arctic region. With these improvements, the system can achieve almost the same performance as in Japan.
HOW TO CITE THIS ARTICLE
Takahashi, T., Saito, S., Kitamura, M., & Sakai, T. (2025). Performance evaluation of DFMC SBAS messages broadcast by the Japanese Quasi-Zenith Satellite System (QZSS) and received in Oslo, Norway. NAVIGATION, 72(2). https://doi.org/10.33012/navi.692
ACKNOWLEDGMENTS
T. Takahashi would like to thank Wojciech Miloch and Bjørn Lybekk for their help installing the antenna and receiver. This study was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI, Grant Number JP20K14544.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
REFERENCES
- ↵Blanch, J., Walter, T., Enge, P., Pervan, B., Joerger, M., Khanafseh, S., Burns, J., Alexander, K., Boyero, J. P., Lee, Y., Kropp, V., Milner, C., Macabiau, C., Suard, N., Berz, G., & Rippl, M. (2014). Architectures for advanced RAIM: Offline and online. Proc. of the 27th International Technical Meeting of the Satellite Division of the Institute of Navigation (ION GNSS+ 2014), Tampa, FL, 787–804. https://www.ion.org/publications/abstract.cfm?articleID=12417
- ↵ICAO. (2023). Aeronautical Telecommunications, Annex 10 to the Convention on International Civil Aviation, Volume I, Radio Navigation Aids, Eighth Edition. International Civil Aviation Organization. https://store.icao.int/en/annex-10-aeronautical-telecommunications-volume-i-radio-navigational-aids
- ↵Kacimi, S., & Kwok, R. (2022). Arctic snow depth, ice thickness, and volume from ICESat-2 and CryoSat-2: 2018–2021. Geophysical Research Letters, 49(5). https://doi.org/10.1029/2021GL097448
- ↵Kitamura, M., & Sakai, T. (2019). DFMC SBAS prototype system performance using global monitoring stations of QZSS. Proc. of the 2019 Pacific PNT Meeting, Honolulu, HI, 382–387. https://doi.org/10.33012/2019.16789
- ↵Miller, A. W., & Ruiz, G. M. (2014). Arctic shipping and marine invaders. Nature Climate Change, 4(6), 413–416. https://doi.org/10.1038/nclimate2244
- ↵Overland, J. E., & Wang, M. (2013). When will the summer Arctic be nearly sea ice free? Geophysical Research Letters, 40(10), 2097–2101. https://doi.org/10.1002/grl.50316
- ↵Reid, T., Walter, T., Blanch, J., & Enge, P. (2016). GNSS integrity in the Arctic. NAVIGATION, 63(4), 469–492. https://doi.org/10.1002/navi.169
- ↵RTCA. (2023). DO-401, Minimum Operational Performance Standard for Dual-Frequency Multi-Constellation Satellite-Based Augmentation System Airborne Equipment. RTCA Inc., Washington. https://my.rtca.org/
- ↵Saastamoinen, J. (1972). Atmospheric correction for the troposphere and stratosphere in radio ranging satellites. In S. W. Henriksen, A. Mancini, & B. H. Chovitz (Eds.), The Use of Artificial Satellites for Geodesy, 247–251. American Geophysical Union (AGU). https://doi.org/10.1029/GM015p0247
- ↵Walter, T., Blanch, J., & Enge, P. (2012). L1/L5 SBAS MOPS to support multiple constellations. Proc. of the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2012), Nashville, TN, 1287–1297.
