Global Positioning System Reference
In-Depth Information
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
is again complicated by temporal and spatial variability of the troposphere. The map-
ping function models this dependency. We relate the slant hydrostatic and wet delays,
SHD and SWD, to the respective zenith delays by
SHD
=
ZHD
·
m
h
(ϑ)
(6.19)
SWD
=
ZWD
·
m
wv
(ϑ)
(6.20)
The slant total delay (STD) is
STD
=
ZHD
·
m
h
(ϑ)
+
ZWD
·
m
wv
(ϑ)
(6.21)
The literature contains many models for the mapping functions
m
h
and
m
wv
. The one
in common use is Niell's (1996) function,
[19
#
%
&
(
a
h
a
1
+
1
+
b
h
1
+
c
h
b
1
+
Lin
—
*
1
——
Nor
PgE
1
+
1
+
1
cos
ϑ
−
c
m(ϑ)
=
+
h
[km]
a
a
h
cos
ϑ
+
cos
ϑ
+
b
cos
ϑ
b
h
cos
ϑ
cos
ϑ
+
cos
ϑ
+
+
+
c
c
h
(6.22)
Th
e coefficients for this expression are listed in Table 6.1 (for
m
h
) and Table 6.2
(fo
r
m
wv
) as a function of the latitude
ϕ
of the station. If
ϕ<
15° one should use
th
e tabulated values for
ϕ
[19
=
15°; if
ϕ>
75° then use the values for
ϕ
=
75°; if
15°
75°, linear interpolation applies. Expression (6.22) gives the hydrostatic
m
apping functions if the coefficients of Table 6.1 are used. Before substitution, how-
ev
er, the coefficients
a
,
b
, and
c
must be corrected for periodic terms following the
ge
neral formula
≤
ϕ
≤
a
p
cos
2
DOY
DOY
0
365
.
25
−
a(ϕ,
DOY
)
=˜
a
−
π
(6.23)
TABLE 6.1
Coefficients for Niell's Hydrostatic Mapping Function
b
·
10
3
·
10
3
·
10
3
a
p
·
10
5
b
p
·
10
5
c
p
·
10
5
ϕ
a
˜
c
˜
15
1.2769934
2.9153695
62.610505
0
0
0
30
1.2683230
209152299
62.837393
1.2709626
2.1414979
9.0128400
45
102465397
209288445
63.721774
2.6523662
3.0160779
4.3497037
60
102196049
209022565
63.824265
3.4000452
7.2562722
84.795348
75
102045996
2.9024912
64.258455
4.1202191
11.723375
170.37206
a
h
·
10
5
b
h
·
10
3
c
h
·
10
3
2.53
5.49
1.14
