Global Positioning System Reference
In-Depth Information
n
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
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P k,I − Φ
k,I i
1
n
p
k
p
=
(6.116)
i
= 1
Th e summation goes over the n epochs in the arc. Perhaps one might adopt an
ele vation dependent weighting scheme in (6.116) to take into account the decrease of
m easurement accuracy with elevation angle. The computed offset is added to (6.115)
wh ich can then be modeled as
= 1
− α f I k, 1 ,P (t)
p
k,I (t)
p
k
d p
Φ
− ∆
+
d k
(6.117)
ov er the arc. The term d p is the residual interfrequency satellite delay, which is
es sentially an estimate of T GD , and d k is a residual interfrequency receiver delay. As
wi th the broadcast ionospheric model, we also relate the slant and vertical ionospheric
de lays by the mapping function F(
[La
[22
β
) such that
I k, 1 ,P (
λ
,ϕ,t)
=
F(
β
)I k, 1 ,P (
λ IP IP ,t)
(6.118)
Lin
8 ——
Sho
PgE
On e could use the simple mapping function of Table 6.3 or one that is based on a
re alistic electron density profile model, such as the extended slab density model by
Co ster et al. (1992). The symbols ϕ IP and
λ IP denote the latitude and longitude of the
io nospheric pierce point, whereas
and ϕ identify the receiver location. Since the
io nospheric disturbances follow the motion of the sun (the maximum disturbances
oc cur around 14:00 local time) and tend to follow geomagnetic field lines, it is ad-
va ntageous to parameterize the model for the vertical ionospheric delay I k, 1 ,P in a
so lar-fixed coordinate system whose third axis coincides with the geomagnetic pole
ra ther the geographic pole. One might model I k, 1 ,P by a spherical harmonic series
an d estimate the spherical harmonic coefficients for global ionospheric models. The
Ka lman filter implementation of Mannucci et al. (1998) divides the surface of the
ea rth into tiles (triangles) and estimates the vertical TEC for the vertices. Only obser-
va tions that fall within the triangle are used to estimate the TEC at the vertices of that
tri angle. They assume that the TEC varies linearly within the triangle. Because the
in strumental biases d p and d k are geometry-independent, but the ionospheric delay
de pends on the azimuth and elevation of the satellite, the biases and the ionospheric
ef fect are estimable. The biases are fairly stable and need to be estimated less often
th an the rapidly varying ionospheric parameters. See Sardón et al. (1994) for addi-
tio nal details on the parameterization of TEC and satellite and receiver biases.
λ
[22
 
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