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Liu et al. Satell Navig (2021) 2:6 Page 15 of 17

positioning, BDS-3 and BDS-2 can be considered as improvements for the combined BDS-3/BDS-2 solutions
one constellation without additional DISBs. Tere- were mainly due to the larger number of the observed
fore, the tightly combined BDS-3/BDS-2 B1I/B3I satellites. Furthermore, we found that the improvements
observations can be easily processed in precise rela- were signifcant when single-frequency observations
tive positioning. Tese results implied the full inter- were used and the elevation cut-of angle was above 40°,
operability between BDS-3 and BDS-2 B1I/B3I sig- thereby confrming the benefts of the tightly combined
nals for precise relative positioning. BDS-3/BDS-2 solutions in challenging observational
2. BDS-3 only solution delivered an ambiguity resolu- environments. It is noteworthy that the benefts of the
tion performance comparable to that of the BDS-2 tightly combined BDS-3/BDS-2 model are more easily
only solution. Te performance can be much experienced outside the Asia–Pacifc region, as the num-
improved by using a tightly combined BDS-3/BDS-2 ber of visible BDS-3/BDS-2 satellites there decreases dra-
solution. Although reliable single-epoch single-fre- matically in the absence of GEO and IGSO satellites.
quency ambiguity resolution was infeasible for the It is noteworthy that only 29 among 30 BDS-3 satel-
BDS-2 only and BDS-3 only solutions, it was feasi- lites are currently operational. With operation of the
ble for tightly combined BDS-3/BDS-2 solution. Te last BDS-3 GEO satellite, BDS-3 RTK performance in
single-epoch single-frequency BDS-3/BDS-2 tightly the Asia–Pacifc region will be improved. One should
combined solution can correctly fx the ambiguities also note that the above results are derived based on
with success rate of more than 96.9% even at the ele- the experimental data collected in Wuhan. Future tests
vation cut-of angle of 40°, indicating a superior per- should be performed using the data collected from dif-
formance of the tightly combined BDS-3/BDS-2 RTK ferent areas on a global scale. In addition, the existence
in the Asia–Pacifc region. About the dual-frequency of DISBs between BDS-3/BDS-2 B1I/B3I signals should
cases, the ambiguities were successfully resolved with be investigated for more types of commercial GNSS
the rates exceeding 90.6% and 97.8% at the elevation receivers.
cut-of angle of 40° for BDS-3 and tightly combined
BDS-3/BDS-2, respectively.
3. Te positioning accuracy of the BDS-3 only solution Abbreviations
ADOP: Ambiguity dilution of precision; BDS: BeiDou navigation satellite sys-
was obviously better than BDS-2 only solution due to tem; BDS-1: BeiDou demonstration navigation satellite system; BDS-2: BeiDou
better satellite distribution geometry for the current regional navigation satellite system; BDS-3: BeiDou global navigation satellite
BDS-3 full constellation; additionally, it can be sig- system; DISB: Diferential inter-system bias; GNSS: Global navigation satellite
system; Galileo: Galileo navigation satellite system; GPS: Global positioning
nifcantly improved by a tight combination of BDS-3 system; GPST: GPS time; GEO: Geostationary orbit; IGSO: Inclined geostationary
and BDS-2. Our kinematic experiment demonstrated orbit; MEO: Medium earth orbit; MGEX: Multi-GNSS experiment; PDOP: Posi-
that the RMS of three-dimensional position was tion dilution of precision; RMS: Root-mean-square; RTK: Real-time kinematic;
3D: Three-dimensional.
3.29 cm for BDS-2, 2.24 cm for BDS-3, and 1.89 cm
for tightly combined BDS-3/BDS-2. Acknowledgements
4. Because C59 and C60 transmit only B1I/B3I signals The authors would like to acknowledge MGEX for providing the GNSS data
and broadcast ephemerides. Figure 1 was plotted based on RTKLIB developed
but not B1C/B2a signals currently, the ambiguity res- by Tomoji Takasu from Tokyo University of Marine Science and Technology,
olution and positioning performances of BDS-3 B1I and Figs. 3a and 12c were edited using Google Earth. The authors appreciate
and B1I/B3I solutions were much better than those the constructive and valuable comments from the anonymous reviewers.
of BDS-3 B1C and B1C/B2a solutions. Tese results Author contributions
confrmed that the BDS-3 GEO satellites contribute WL and XZ proposed the idea and drafted the article; MW, WW, and WK per-
signifcantly to single-epoch precise relative position- formed the evaluation and assisted in data analysis; WL and ZZ assisted in data
collection; WL and MW assisted in article revision. All authors have read and
ing in the Asia–Pacifc region. approved the fnal manuscript.
Authors’ Information
Additionally, we computed and compared (but not Wanke Liu is currently a professor at Wuhan University. He obtained his B.Sc.,
presented herein) the RTK performance of tightly com- Master, and Ph.D. degrees in Geodesy and Survey Engineering from the School
bined and loosely combined BDS-3/BDS-2 solutions. As of Geodesy and Geomatics of Wuhan University in 2001, 2004, and 2008,
expected, the improvements were marginal (less than respectively. His main research interests include GNSS precise positioning and
multi-sensor integrated positioning.
1.5%) for both the single- and dual-frequency cases,
which is reasonable considering the facts that the aver- Mingkui Wu is currently a lecturer in the China University of Geosciences
age number of observed satellites was about 13.5, and (Wuhan). He obtained his B.Sc., and Master, and Ph.D. degrees in Geodesy and
Survey Engineering from the School of Geodesy and Geomatics of Wuhan
the ambiguity resolution success rates exceeded 95.6% University in 2010, 2012, and 2017, respectively. His main research interests
for the loosely combined model even under an eleva- include multi-GNSS precise positioning and GNSS attitude determination.
tion cut-of angle of 40°. Tese results indicated that the