Global Positioning System Reference
In-Depth Information
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q
km,
GPS
.
N
pq
km,
GPS
.
ξ
=
S
S
+
S
GLO
−
2
D
S
S
+
S
GLO
(7.121)
s
km,
GLO
.
N
rs
km,
1
,
GLO
.
ξ
Ap
plying the covariance propagation (4.34), the covariance matrix of double-dif-
fe
rence ambiguity is
D
T
. Having
Σ
N
it is possible to determine the integer
do
uble-difference ambiguities using a technique such as LAMBDA. The subsequent
co
nstraint solution, in which the integer ambiguities are treated as known quantities,
yi
elds the final estimates for the station coordinates, the
S
GPS
parameters
ξ
Σ
N
=
DC
ξ
q
km,
1
,
GPS
|
N
s
km,
1
,
GLO
|
N
, as well as the final time estimates
d
an
d
S
GLO
parameters
ξ
ˆ
t
km
|
N
.
The variance-covariance propagation step can be avoided by using a parameteri-
za
tion in terms of
[27
p
km,
1
,
GPS
for the base GPS satellite and the GPS double differences
ξ
pq
km,
1
,
GPS
N
pq
ξ
≡
km,
1
,
GPS
. The respective parameters for the GLONASS satellites are
Lin
—
*
2
——
No
PgE
km,
1
,
GLO
r
km,
1
,
GLO
=
N
rs
ξ
km,
1
,
GLO
. A submatrix of the design matrix that reflects
th
is parameterization is shown in Table 7.5. Ambiguity fixing can then be directly ap-
pl
ied to the variance-covariance submatrix of the estimates
ξ
and
ξ
rs
km,
1
,
GLO
.
Having the parameter estimation completed, using single-difference observations
an
d fixing GPS-GPS and GLO-GLO double-difference ambiguities, we can inspect
th
e double difference (GPS and GLO base satellites)
pq
km,
1
,
GPS
and
ξ
pr
km,
1
= ξ
p
km,
1
,
GPS
|
r
km,
1
,
GLO
|
∆ξ
− ξ
N
pr
=
km,
1
+
d
km,
1
,
GLO
−
d
km,
1
,
GPS
[27
N
N
(7.122)
N
pr
km,
1
=
+
DDRB
TABLE 7.5
Submatrix for Alternate Parameterization of
ξ
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Note:
The table shows the case for
S
GPS
=
5 and
S
GLO
=
4.
