Global Positioning System Reference
In-Depth Information
km
t
2
, t
2
− ρ
km
t
1
, t
1
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
pq
km
(t
p
, t
q
)
pq
pq
∆ρ
= ρ
(5.33)
The initial integer ambiguity
N
pq
km
(
1
)
cancels in (5.32). The triple-difference ob-
servable is probably the easiest to deal with because of this cancellation. Often the
triple-difference solution serves as a preprocessor to get good initial positions for the
double-difference solution. The triple differences have the advantage in that cycle
slips are mapped as individual outliers in the computed residuals. Individual outliers
can usually be detected and removed. The resulting cycle slip free observations can
then be used in the double-difference solution.
A delta range is the difference in time of observables at the same station. For
example,
k
t
2
, t
1
−
f
1
c
∆ρ
ϕ
k,
1
(t
2
,t
1
)
p
I
k,
1
,ϕ
(t)
t
p
¯
∆
=
f
1
∆
d
t
k
+
f
1
∆
d
+ ∆
[17
(5.34)
f
1
c
∆
T
k
(t)
p
k,
1
,ϕ
(t)
+
+ ∆δ
+ ∆
ε
1
,ϕ
Lin
—
5.0
——
Lon
PgE
k
t
2
, t
1
= ρ
k
t
2
− ρ
k
t
1
p
p
p
∆ρ
(5.35)
Th
ese delta ranges are a function of the change in topocentric distance between the
sta
tion and the satellite, provided there is no cycle slip between the epochs
t
1
and
t
2
.
Th
ey do not depend on the initial ambiguity because of the differencing over time.
Th
e delta range (5.34) depends on the change of the receiver and satellite clock errors
fro
m epoch
t
1
to epoch
t
2
.
The between-satellite difference (5.4)
[17
f
1
c
ρ
f
1
ϕ
pq
pq
k
(t
p
, t
q
)
N
pq
k
I
pq
c
T
pq
f
1
d
t
pq
k,
1
(t)
=
+
(
1
)
+
+
k,
1
,ϕ
(t)
+
(t)
k
(5.36)
pq
k,
1
,ϕ
(t)
+ δ
+
ε
1
,ϕ
pq
k
(t
p
, t
q
)
p
k
(t
p
)
q
k
(t
q
)
ρ
= ρ
− ρ
(5.37)
does not depend on the receiver clock error but, instead, contains again an integer
ambiguity.
5.
3 INITIAL EVALUATION
5.
3.1 Satellite Clock Corrections
The control segment maintains GPS time to within 1
s of UTC(USNO) according
to the Interface Control Document (ICD-GPS-200C, 2000), but GPS time does not
follow the UTC leap-second jumps. The full second offset is readily available on
the Internet and from various data services, if needed. The user needs GPS time
and not UTC because the observations are time-tagged with GPS time; it is also
µ
