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Liu et al. Satell Navig (2021) 2:6 Page 4 of 17

Furthermore, the benefts of tightly combined BDS-3/ Feasibility of tightly combined BDS-2 and BDS-3
BDS-2 solution with respect to BDS-3 only and BDS-2 B1I/B3I RTK without additional DISBs
only solutions were evaluated. It is noteworthy that Previous studies have demonstrated that the values of
although the navigation signals of the last BDS-3 GEO code and phase DISBs depend on receiver types of the
satellite were not tracked in our tests, it did not afect our involved receivers at both endpoints of a baseline. If the
performance assessment of the BDS-3 full constellation. involved receivers are of the same type and frmware ver-
In this paper, we frst present an overview of the cur- sion, the DISBs are about zero. Otherwise they are gener-
rent BDS-3/BDS-2 constellations. Te existence and ally non-zero. Considering that they are generally stable
characteristics of phase and code DISBs between BDS-3/ in time even if the receivers restart, they can be accurately
BDS-2 B1I/B3I signals are investigated in “Feasibility of calibrated and corrected in advance (Odijk and Teunissen
tightly combined BDS-2 and BDS-3 B1I/B3I RTK with- 2013; Yuan and Zhang 2014; Paziewski and Wielgosz 2015).
out additional DISBs” section. “Performance assessment Mi et al. (2020) estimated the DISBs of BDS-3/BDS-2 B1I/
of tightly combined BDS-2/BDS-3 RTK” presents the B3I signals between two Trimble Alloy receivers. It was dis-
performance assessment of tightly combined BDS-3/ covered that they were in fact absent for the same receiver
BDS-2 RTK using both single- and dual-frequency obser- types. In this section, we focus on estimating and analyzing
vations. Conclusions are given in “Conclusions and dis- the characteristics of code and phase DISBs between over-
cussions” section. lapping frequencies of BDS-3/BDS-2 B1I/B3I signals with
both the same and diferent receiver types. Te feasibility
of tightly combined BDS-3/BDS-2 B1I/B3I RTK without
Current BDS-2/BDS-3 constellations additional DISBs will be investigated and identifed.
BDS-2 has been in full operation with 14 satellites, com-
prising four MEO, fve GEO, and fve IGSO satellites DISB estimation approach
since December 27, 2012. Another three BDS-2 replace- Assume that B1I/B3I observations from n B BDS-2 satel-
ment satellites (two GEO and one IGSO) were launched lites and n ∗ BDS-3 satellites are observed simultaneously
in 2016, 2018, and 2019 (CSNO-TARC 2020). Currently by two receivers at both endpoints of a zero or short base-
(early July 2020), BDS can provide open services with 44 line. Tese two receiver sites are denoted by base station b
operational satellites, including 15 BDS-2 and 29 BDS-3 and rover station r. If BDS-2 and BDS-3 are considered as
satellites (see Table 2). As an example, Fig. 1 demon- two separate systems and only a single BDS-2 satellite ( 1 B )
strates the sky plot and availability of BDS-3 and BDS-2 is selected as the reference satellite for all the BDS-2 and
satellites at the Multi-GNSS EXperiment (MGEX) sta- BDS-3 satellites, then the tightly combined double-difer-
tion WUH2 in Wuhan on June 21, 2020. As shown, all enced observation equation with DISB estimation for short
operational BDS-3/BDS-2 satellites listed in Table 2 were baselines is expressed as (Wu et al. 2017, 2019b):
observed. Note that BDS-3 GEO satellites C59 and C60
 1 B s B 1 B s B 1 B s B 1 B s B
currently transmit only B1I/B3I signals, which means  φ br,f = ρ br + f N br,f + ε br,f

that only 27 among 29 BDS-3 operational satellites trans-  φ 1 B s ∗ = ρ 1 B s ∗ + f (N 1 ∗ s ∗ + δ B∗ ) + ε 1 B s ∗


br,f
mit new B1C/B2a/B2b signals, whereas they all transmit  P br,f = ρ br + e 1 B s B br,f br,f (1)
1 B s B
1 B s B
the legacy B1I/B3I signals. Tis could cause the number  br,f br br,f


B∗
1 B s ∗
1 B s ∗
of visible BDS-3 satellites with B1I/B3I signals difer-  P br,f = ρ 1 B s ∗ + d br,f + e br,f
br
ent from that with B1C/B2a signals in the Asia–Pacifc
region. We will show this in the following analysis. where s B and s ∗ denote BDS-2 and BDS-3 satellites,
respectively, and s B = 2 B , . . . , n B , s ∗ = 1 ∗ ,2 ∗ , . . . , n ∗ ; f is
Table 2 Status of operational BDS-2 and BDS-3 satellites as of July 2020
System Orbit Number PRN Service signals
BDS-2 GEO 5 C01–C05 B1I/B2I/B3I
IGSO 7 C06–C10, C13, C16
MEO 3 C11, C12, C14
BDS-3 GEO 2 C59, C60 B1I/B3I
IGSO 3 C38, C39, C40 B1I/B3I/B1C/B2a/B2b
MEO 24 C19–C30, C32–C37, C41–C46
Total 44