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Liu et al. Satell Navig (2021) 2:6 Page 3 of 17

compared with BDS-2 only positioning (Zhang et al. systematic inter-system biases exist between BDS-3
2017, 2018; Xu et al. 2018; Qu et al. 2019). and BDS-2, thereby afecting the achievable accuracy
During the construction of operational BDS-3 constel- for combined BDS-3/BDS-2 single point positioning
lation, several studies examined the data quality of B1C/ and precise point positioning. In such cases, BDS-2 and
B2a/B2b observations of available BDS-3 satellites as of BDS-3 should be considered as two separate systems, and
their writing and the results were similar to those of the additional inter-system bias should be considered (Jiao
experimental satellites (Xie et al. 2018; Wu et al. 2019a; et al. 2019; Song et al. 2020; Zhang et al. 2020b; Zhao
Xu et al. 2019; Yang et al. 2019a). Regarding Real-Time et al. 2020). About combining BDS-3/BDS-2 for precise
Kinematic (RTK) positioning, initial assessments were RTK positioning, previous studies either treated them
presented recently based on the 18 new satellites and directly as two separate constellations and used the clas-
their navigation signals of the BDS-3 primary system. sical loosely combined or intra-system model, i.e., one
Zhang et al. (2019b) evaluated the RTK performance of satellite was selected as the reference satellite for BDS-2
combined BDS-3/BDS-2 solution using dual-frequency and BDS-3, separately, or did not explicitly present
B1I/B3I observations with respect to BDS-2 only solu- their approaches (Hou et al. 2019; Zhang et al. 2019b, c,
tion. It was demonstrated that additional BDS-3 observa- 2020a; Shi et al. 2020). To fully utilize the interoperability
tions could lead to improved RTK positioning accuracy between BDS-3 and BDS-2, the tightly combined double-
in horizontal and vertical directions of the involved base- diferencing (i.e., a single reference satellite was selected
line vectors, with improvement by 1–2 mm for a 20 m for all BDS-3 and BDS-2 satellites) of observations from
baseline and by 1–2 cm for a 10 km baseline, respectively. common frequencies (i.e., the legacy B1I/B3I) should be
Zhang et al. (2019c) indicated that the ambiguity reso- employed. Te benefts of applying such a tightly com-
lution success rate of RTK was improved from 88.5 to bined model have been investigated intensively. Te
91.4% by incorporating BDS-3 observations, whereas the results demonstrated that the tightly combined model
positioning accuracy was comparable. Hou et al. (2019) can improve RTK performance, particularly in chal-
assessed the RTK positioning accuracy of combined lenging observational conditions where only a limited
BDS-3/BDS-2, BDS-3 only, and BDS-2 only solutions number of satellites and single-frequency observations
using their stochastic model. Te results demonstrated were tracked (Odijk et al. 2017; Wu et al. 2017, 2019b).
that the accuracy of RTK positioning was improved by However, users must carefully consider the Diferential
65% by comparing the BDS-2/BDS-3 case with the BDS-2 Inter-System Biases (DISBs) when using this approach,
only case. Shi et al. (2020) further revealed that the addi- even though the frequency of the involved observations
tional BDS-3 observations accelerated the RTK position- from diferent systems is identical. Once the DISBs are
ing convergence for medium-long baseline compared carefully considered, the satellites from diferent Global
with BDS-2 only solution. Zhang et al. (2020a) indicated Navigation Satellite Systems (GNSSs) can be used as if
that RTK positioning was feasible with the BDS-3 pri- they were from a single GNSS constellation (Odijk and
mary system. Te achievable positioning accuracy for Teunissen 2013; Paziewski and Wielgosz 2015). Mi et al.
the involved short baseline was better than 1 cm for both (2020) preliminarily estimated the phase and code DISBs
BDS-3 only and combined BDS-2/BDS-3 solutions. of BDS-3/BDS-2 B1I/B3I signals between two Trimble
Although some initial assessments of BDS-2/BDS-3 Alloy receivers and discovered that they were zero for
RTK were reported, only a few studies analyzed the the same receiver types, as expected. However, whether
BDS-3 only RTK positioning performance because the non-zero DISBs of BDS-3/BDS-2 B1I/B3I signals exist
number of visible BDS-3 satellites was limited at that between diferent receiver types is yet to be elucidated,
time with the BDS-3 primary system (Hou et al. 2019; necessitating further investigations.
Zhang et al. 2020a). Te number of the visible satellites In this study, we evaluated the single-epoch short
were four to six for only a relatively short observation baseline RTK performance of the BDS-3 full constella-
period. With the completion of the BDS-3 full constella- tion as well as its tight combination with the BDS-2 full
tion, the situation has been changed. It is worthwhile to constellation. We frst investigated the characteristics of
carry out a comprehensive performance evaluation of the the phase and code DISBs between BDS-3/BDS-2 B1I/
RTK positioning with the BDS-3 full constellation and its B3I signals. Ten we preliminarily evaluated the RTK
combination with BDS-2 full constellation. positioning performance using single- and dual-fre-
Furthermore, BDS-2 and BDS-3 are two generations quency BDS-3/BDS-2 observations. Both the static and
of BDS operated and maintained by their individual con- kinematic datasets collected in Wuhan were processed
trol systems (Song et al. 2020). Due to various factors, and analyzed to demonstrate the RTK performance of
e.g., diferent quality of time-keeping clocks and difer- tightly combined BDS-3/BDS-2 and BDS-3 only solu-
ent receiver types in the ground monitoring network, tions by ambiguity resolution and positioning accuracy.