IEEE Instrumentation & Measurement - September 2023 - 43

In this study, a new single-frequency PPP-B2b time transfer
was investigated. Two TAI timekeeping laboratories, including
the National Time Service Center of the Chinese Academy
of Sciences (NTSC) and the Telecommunication Laboratories
(TL), external atomic clock IGS station (USUD) and an IGS station
(CUSV) with an internal clock were selected to validate
the accuracy of the PPP-B2b product in SF comparison applications
from zero-baseline CCD and long-baseline time links.
Method
Currently, the PPP-B2b product provides satellite orbit and
satellite clock offset correction of navigation ephemeris for
BDS-3 and GPS users, respectively.
Precise Satellite Orbit
The rough satellite position which is calculated through the
broadcast ephemeris is corrected using the PPP-B2b product
and (1) to obtain the precise satellite position:





 
X
Y
Z
orbit
orbit
orbit





=





X
Y
Z
tion vector; X Y
brdc
brdc
brdc





In (1), X YZorbit orbit orbit  represents the precise satellite posi

T
brdc brdc Zbrdc  indicates the real-time satellite
T
position calculated from the ephemeris; []e eeradial along cross
corresponds to the unit vectors which can be calculated as (2)
in radial, along-track, and cross-track directions, respectively;
and δδ δOO O
 
R AC represents the orbit correction vector
T
from the PPP-B2b product:










eradial =
ecross =
r
r
r
r
×
×
ν
ν
e ee= ×
along cross radial
In (2), r and ν are the satellite position and velocity vectors of
ephemeris.
Precise Satellite Clock
The precise satellite clock offset is obtained by correcting the
satellite clock offset of ephemeris through the PPP-B2b product
and (3):
dt
prec
s
= dt
brdc
s
−
C0
c
In (3), dtprec
s indicates the precise clock offset; dtbrdc
s
(3)
indicates
the satellite clock offset calculated from ephemeris; C0 indicates
the clock correction provided by the PPP-B2b product in
meters; and c indicates the speed of light.
GRAPHIC SF PPP-B2b Model
The biggest challenge for SF PPP is the treatment of ionospheric
delay. Averaging SF pseudorange observations and
carrier phase observations to remove first-order ionospheric
September 2023
PPP Time Transfer
The receiver clock offset can be considered as time difference
between the receiver local time tloc and the GNSS reference
time tref. The GNSS reference time of the two stations through
time transfer is eliminated by the difference, which is written
as (6):
∆= − = − − − = − tloc,2 (6)
t dt dtr
ɶɶ
,, ,
r12 1
(tloc
IEEE Instrumentation & Measurement Magazine
tref loc 2
)(t
,
tref loc,1
t
)
43
(2)
−[e adial along cross ]⋅
r ee





δ
δ
δ
O
O
O
R
A
C





(1)
delays is called GRAPHIC [7]. Meanwhile, combining with
broadcast ionospheric products such as the Beidou global
broadcast ionospheric delay correction model (BDGIM) [8] to
replace IGS ionospheric products [9], constraining the ionospheric
delay in the pseudorange observation equation with
the broadcast ionosphere model, a new SF PPP-B2b time transfer
model was investigated. The ionosphere-free SF PPP-B2b
model can be written as follows:









In (4), pr iono j
s
p µεɶ
r iono j
s
l
IF j
s
rj
s
, =
_, = ⋅ +⋅ + + +
p , + l ,
r
s
rr j
s
2
x cd I Ts
t
= ⋅ +⋅ + + ,,
s
Ion I= + ion
rj
s
,
µ λξ
ζ
r
s
x cd T N
tɶ
s
rr
rj
s
+
r rj
s
, _,
r
ɶ
IF j
s
(4)
_, refers to pseudorange observation corrected using
the differential code bias PPP-B2b product; µr
s denotes the
receiver-to-satellite unit vector; c is the speed of light in vacuum,
x denotes the vector of receiver position increments; dtrɶ
refers to the receiver clock offset in seconds; Irj
s
,
ionospheric delay in meters; Tr
meters; εr iono j
s
prj
s
,
refer to the raw observations minus the computed
values of the carrier phase and pseudorange; λ ɶNrj
,
and lrj
s
,
s
the ambiguity in meters; ξIF j
s
, represents
represents ionospheric-free SF
observation noise; Ions denotes ionospheric delay calculated
from broadcast ephemeris; and ζion denotes broadcast ephemeris
ionospheric measurement noise. Thus, the SF PPP-B2b
time transfer estimated parameter vector X is:
X x dt T I Nλ ɶ
ɶ
= 

s
rr ,, .
rj
s
rj
s


(5)
Process and Strategies
SF PPP using the PPP-B2b product is performed as shown
in Fig. 1. Table 1 lists SF PPP-B2b processing strategies. The
PPP processing process is divided into data preparation, data
preprocessing, error correction, Kalman filtering and estimation.
Navigation ephemeris and the PPP-B2b product are
used to recover precise satellite orbit and clock offset, and
raw observations are also required for PPP calculation. Data
preprocessing consists of gross error, clock slip detection reparation
and cycle slip detection to provide pure raw data for
subsequent high-precision algorithms. Errors are processed
by models, empirical formulas and parameters estimated. The
parameters estimated after Kalman filtering are verified by residual
and the receiver clock offset can be obtained.
s is the tropospheric delay in
_, refers to the pseudorange observation noise;
refers to the
r iono j
s

IEEE Instrumentation & Measurement - September 2023

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