Precise Orbit Determination of Global Navigation Satellite System of ...

Chapter 4 Major Error Sources of Satellite Observations
Shorter wavelength radio signals pass through the ionosphere but are affected by it. These shorter wavelengths
are used by satellites for communication and navigation purpose, and the ionosphere affects the signals rather
like the way the atmosphere causes "twinkling" of the stars.
Considerable efforts have, therefore, been concentrated on modeling this ionospheric parameter. Several models
are available including the Chiu model (Chiu, 1975), the Bent model (Bent et al. 1972) that has been used
extensively for satellite tracking, the semi-empirical SLIM model (Anderson et al, 1987) based on theoretically
obtained grid values, and the FAIM model (Anderson et al, 1989) that uses the Chiu formalism together with the
SLIM results. The International Reference Ionosphere (IRI) is probably the most mature of these models, having
undergone more than two decades of scrutiny and improvement.
At present, almost all empirical models of ionospheric parameters are limited to non-auroral, magnetically quiet
conditions. Major efforts are underway to extend ionospheric predictability beyond these limitations. A
promising venue seems to be the inclusion of real-time data from the newly developed automatical recording and
scaling ionosondes.
Following Hofmann-Wellenhof (1992), Klobuchar (1996), Seeber (1993) and Wild (1994), the phase and range
refractive indices can be written as
a
n p = 1+
(4-10)
2
f
n r
a
= 1−
(4-11)
2
f
Then first orders of ionospheric group and phase delays for range and phase observations are proportional to the
integrated number of free electrons along the propagation path and inversely proportional to the square of
transmission frequency and can be written as
∆S = � Ndl
f
ion 40.
3
p 2
34
(4-12)
∆S = − � Ndl
f
ion 40.
3
r (4-13)
2
where f is the carrier frequency and � Ndl is Total Electron Content (TEC), integrated along the path from
ground tracking station to satellite.
From Eq.(4-12) and Eq.(4-13) it can be seen that changes of range and phase caused by the ionospheric
refraction may be restricted to the determination of the total electron content (TEC). TEC itself is dependent on
sunspot activities, seasonal and diurnal variations, the line of sight which includes elevation and azimuth of the
satellite and the position of the observation site.
Usually TEC can be measured using dual frequency observations forming wide-lane linear combination (L4). In
the case of code observations the total electron content is proportional to the difference of the ionospheric
refraction on the two frequencies. Ionospheric error can also be removed by ionosphere-free linear combination
(L3). For single frequency users, some mathematical models, for examples, Klobuchar model (Klobuchar, 1996)
and single-layer model (Wild 1994) may be used.
Following Wild (1994), a simple and widely used mathematic model, single-layer model (SLM) will be
discussed here.
SLM is based on the assumption that all free electrons are concentrated in a spherical layer of infinitesimal
thickness (single layer) at a height H above the earth’s surface. From Eq.(4-12) and Eq.(4-13), ionospheric
correction can be written as
TVEC
S
f z
ion 40.
3
∆ = ±
2 cos ′
where
z′ zenith distance at the intersection P of the actual signal with the single-layer
(4-14)