Digital Signal Processing Reference
In-Depth Information
N
, the ambiguity of the carrier phase; and
", other residuals.
One can easily obtain the following equations from Eqs. (
4.1
) and (
4.2
):
d
ion
;1;j
d
ion
;2;j
P
4
D
P
1;j
P
2;j
C
DCB
i
D
C
DCB
j
(4.3)
d
ion
;1;j
d
ion
;2;j
b
1;j
b
2;j
N
1;j
N
2;j
(4.4)
L
4
D
L
i
1;j
L
i
2;j
D
where
DCB
i
D
d
i
1
d
i
2
, and
DCB
j
D
d
1,
j
d
2,
j
stand for differential code biases of
the satellites and differential code biases of the receivers, respectively. Since the
pseudorange observations
P
4
have larger noise, the carrier phases are used to smooth
the pseudorange (Liu et al.
1998
). Smoothed
P
4,
sm
observations can be expressed as
follows:
P
4;sm
D
!
t
P
4
.t /
C
.1
!
t
/ P
4;prd
.t /
.t >1/
(4.5)
where
t
stands for the epoch number, !
t
is the weight factor related with epoch
t
and
P
4;prd
.t /
D
P
4;sm
.t
1/
C
ŒL
4
.t /
L
4
.t
1/
.t>1/
(4.6)
when
t
is equal to 1, which means the first epoch of one observation arc,
P
4,
sm
is equal to
P
4
. Cycle slips and gross errors in the carrier phase observations
should be removed before using the carrier phase observations to smooth the pseu-
dorange observations. Here both dual-frequency pseudorange code observations
(Melbourne-Wubeena combination) and ionospheric residual observations are used
to detect cycle slips and gross errors.
Only the first order of ionospheric refraction is considered while estimating the
ionosphere delay in GPS processing, due to the minor effect of the higher orders.
The ionosphere delay can be expressed as follows:
40:3
f
2
d
ion
D
STEC
(4.7)
where
f
stands for the frequency of the carrier, and
STEC
stands for the slant total
electron content along the path of the signal (see Fig.
4.1
). Substituting Eqs. (
4.7
)
into (
4.3
), and replacing
P
4
by smoothed
P
4,
sm
, we get:
P
4;sm
D
40:3
1
f
1
2
STEC
C
DCB
i
1
f
2
2
C
DCB
j
(4.8)
After smoothing, more reliable DCB estimate values can be extracted from GPS
data and then the STEC can be determined.
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