Global Positioning System Reference
In-Depth Information
−
Φ
K
k
p
k
p
k,
0
p
k,b
p
k,
0
p
k,b
p
k,
0
p
k,b
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
= Θ
− Θ
= ρ
− Θ
= ρ
+ λ
=−λ
N
k
K
k
+
I
k,
Φ
−
T
k
p
k,
Φ
cdt
P
+
cd
t
k
−
−
− δ
(7.210)
N
k
t
P
I
k,
Φ
−
T
k
p
k,
¯
= λ∆
+
cd
t
k
−
cd
−
− δ
Φ
N
k
is present because
K
k
only approximates
N
k
. The mean discrepancy
µ
k
of all satellites observed at the site and epoch
t
is
Th
e term
∆
S
p
=
1
1
S
p
k
(t)
µ
k
(t)
=
(7.211)
w
here
S
denotes the number of satellites. This mean discrepancy is driven primarily
by
the receiver clock error. The carrier phase correction at epoch
t
is
[29
k,
0
−
Φ
K
k
− µ
k
p
k
p
k,
0
− Θ
p
k,b
− µ
k
= ρ
p
p
k,b
+ λ
∆Φ
= ρ
(7.212)
Lin
—
0.0
——
Nor
*PgE
Th
e second part of this equation follows by substituting (7.209) for the carrier phase
ra
nge. The phase correction (7.212) is transmitted to the moving receiver
m
. The
ro
ver's carrier phase
m
is corrected by adding the carrier phase correction, which
w
as computed at receiver
k
,
Φ
p
m
Φ
p
k
p
m
= Φ
+ ∆Φ
(7.213)
Le
t us consider the single-difference observable (5.12) in the form
[29
p
k
p
k
N
km
−
I
km,
Φ
+
T
km
+ δ
p
km,
p
m
p
m
Φ
− Φ
= ρ
− ρ
+ λ
c(d
t
k
−
d
t
m
)
+
(7.214)
Φ
p
k
and substituted into (7.214). After rearrange-
Equation (7.212) can be solved for
Φ
ment, one obtains
+ λ
N
km
+
K
k
−
p
m
I
km,
Φ
+
T
km
+ δ
p
km,
− Φ
p
m
=−ρ
c(d
t
k
−
d
t
m
)
+ µ
k
+
(7.215)
The left side of this equation is equal to the negative of the corrected carrier phase
Φ
p
m
. The differencing equation (7.215) between two satellites gives an expression that
corresponds to the double-difference observable
N
pq
km
K
k
qp
m
p
m
q
m
Φ
≡ Φ
− Φ
K
k
I
pq
T
pq
km
d
pq
km,
(7.216)
q
m
p
m
= ρ
− ρ
+ λ
+
−
+
km,
Φ
+
+
The position of station
m
can now be computed at site
m
using the corrected obser-
vation
p
m
to at least four satellites and forming three equations like (7.216). These
equations differ from their conventional double-difference form by the fact that the
modified ambiguity
Φ
