Global Positioning System Reference
In-Depth Information
In most commercial GPS receivers only the L1 frequency is available. The
ionospheric data collected from subframe 4 can be used to reduce the ionospheric
effect; this is often referred to as the single-frequency ionospheric model. Using
this model one can reduce the user root mean square (rms) position error caused
by ionospheric effect at least by 50 percent.
(
7
)
The ionospheric model is
(
3
,
7
)
5
.
0
∗
10
−
9
(AMP)
1
−
x
2
2
+
x
4
24
T
∗
+
if
|
x
|
<
1
.
57
T
iono
=
(
sec
)
!
10
−
9
)
T
∗
(
5
.
0
∗
if
|
x
|≥
1
.
57
(
5
.
9
)
where
T
iono
is the addition delay time and
3
α
n
φ
m
if
AMP
≥
0
AMP
=
(
sec
)
(5.10)
n
=
0
!
AMP
=
0 f
AMP <
0
2
π(t
−
50
,
400
)
PER
x
=
(
radians
)
(5.11)
3
β
n
φ
m
if
PER
≥
72
,
000
PER
=
(
sec
)
(5.12)
n
=
0
!
PER
=
72
,
000
if
PER <
72
,
000
ξ
]
3
T
=
1
.
0
+
16
.
0[0
.
53
−
(5.13)
where
α
n
and
β
n
with (
n
0, 1, 2, 3) are the ionospheric data obtained from the
satellite and
ξ
is the elevation angle between the user and satellite.
Other equations that must be solved are
=
φ
m
=
φ
i
+
0
.
064 cos
(λ
i
−
1
.
617
)(
semicircles
)
(5.14)
ψ
cos
A
cos
φ
i
λ
i
=
l
u
+
(
semicircle
)
(5.15)
L
u
+
ψ
cos
A
if
|
φ
i
|≤
0
.
416
φ
i
=
+
0
.
416
if
φ
i
>
+
0
.
416
(
semicircle
)
(5.16)
!
−
0
.
416
if
φ
i
<
−
0
.
401
0
.
00137
ξ
=
+
0
.
11
+
ψ
0
.
022
(
semicircle
)
(5.17)
10
4
λ
i
t
=
4
.
32
∗
+
GP S
time
(
sec
)
(5.18)
where 0
≤
t<
86
,
400; therefore, if
t
≥
86
,
400 seconds, subtract 86,400 seconds;
if
t<
0 seconds, add 86,400 seconds.
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