Global Positioning System Reference
In-Depth Information
h
h
()
()
−
6
∫
−
6
∫
∆
S
=
10
d
N
h dh
+
10
d
N
h dh
(7.27)
tropo
d
d
h
=
0
h
=
0
Evaluation of (7.27) using the expressions for
N
d
(
h
) and
N
w
(
h
) in (7.25) and
(7.26) yields
−
6
10
5
[
]
∆
S
=
N
h
+
N
h
(7.28)
tropo
d
,
0
d
ww
,
0
=
d
+
d
dry
wet
To compute the tropospheric correction in (7.28), pressure and temperature
inputs are required, which can be obtained using meteorological sensors. When the
satellite is not at zenith, a mapping function model is needed to determine how much
greater a delay can be anticipated due to the larger path length of the signal through
the troposphere. It is common to refer to the delay for a satellite at zenith as a
verti-
cal delay
or
zenith delay
and the delay for satellites at any other arbitrary elevation
angle as a
slant delay
. Mapping functions that relate slant and vertical delays will be
discussed later in this section.
One accurate method for modeling the troposphere's dry and wet components
at zenith without meteorological sensors was developed at the University of New
Brunswick. In this model [17, 22, 23], referred to as UNB3, the dry and wet compo-
nents are considered functions of height,
h
, in meters above mean sea level and of
five meteorological parameters: pressure,
p
, in millibars, temperature,
T
, in Kelvin,
water vapor pressure,
e
, in millibars, temperature lapse rate, , in K/m, and water
vapor lapse rate, (unitless). Each of the meteorological parameters is calculated by
interpolating values from Tables 7.1 and 7.2. Using pressure as an example, the
average pressure,
p
0
( ), at latitude
75º) is calculated by using the two
values in the
p
0
column of Table 7.1 corresponding to those two values of latitude,
(15º
<
<
i
and
, that are closest to
, as follows:
i
+1
(
)
φφ
φφ
−
[
]
()
()
( )
()
i
p
φ
=
p
φ
+
p
φ
−
p
φ
⋅
0
0
i
0
i
+
1
0
i
(
)
−
i
+
1
i
Similarly, the seasonal variation,
∆
p
(
φ
), is found in the same way from Table 7.2, as
follows:
(
)
φφ
φφ
−
[
]
()
()
( )
()
i
∆
p
φ
=
∆
p
φ
+
∆
p
φ
−
∆
p
φ
⋅
i
i
+
1
i
(
)
−
i
+
1
i
For latitudes less than 15º, simply use the values of parameters in the first row
without interpolation; for latitudes greater than 75º, use the values of parameters in
the last row. Finally, the pressure,
p
, is determined, taking into account the day of
the year,
D
, with the first day being January 1, as follows:
(
)
2
π
DD
−
()
()
min
pp
=
φ
−
∆
p
φ
⋅
cos
0
365 25
.
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