Global Positioning System Reference
In-Depth Information
radio wave; therefore, the magnitude of the ionospheric delay depends on the signal
frequency. The advantage is that an elimination of the major part of the ionospheric
refraction through a linear combination of dual-frequency observables is possible. However,
inhomogeneous plasma distribution and anisotropy cause higher order nonlinear effects
which are not removed in this linear approach. Mainly the second and third order
ionospheric terms (in the expansion of the refractive index) and errors due to bending of the
signal remain uncorrected. They can be several tens of centimeters of range error at low
elevation angles and during high solar activity conditions.
Brunner & Gu (1991) were pioneers to compute higher order ionospheric effects and
developing correction for them. Since then higher order ionospheric effects have been
studied by different authors during last decades, e.g., Bassiri & Hajj (1993), Jakowski et al.
(1994), Strangeways & Ioannides (2002), Kedar et al. (2003), Fritsche et al. (2005), Hawarey et
al. (2005), Hoque & Jakowski (2006, 2007, 2008, 2010b), Hernández-Pajares et al. (2007), Kim
& Tinin (2007, 2011), Datta-Barua et al. (2008), Morton et al. (2009), Moore & Morton (2011).
The above literature review shows that higher order ionospheric terms are less than 1% of
the first order term at GNSS frequencies. Hernández-Pajares et al. (2007) found sub-
millimeter level shifting in receiver positions along southward direction for low latitude
receivers and northward direction for high latitude receivers due to the second order term
correction. Fritsche et al. (2005) found centimeter level correction in GPS satellite positions
considering higher order ionospheric terms. Elizabeth et al. (2010) investigated the impacts
of the bending terms described by Hoque & Jakowski (2008) on a Global Positioning System
(GPS) network of ground receivers. They found the bending correction for the dual-
frequency linear GPS L1-L2 combination to exceed the 3 mm level in the equatorial region.
Kim & Tinin (2011) found that the systematic residual ionospheric errors can be significantly
reduced (under certain ionospheric conditions) through triple frequency combinations. All
these studies were conducted to compute higher order ionospheric effects on GNSS signals
for ground-based reception. Recently Hoque & Jakowski (2010b, 2011) investigated the
ionospheric impact on GPS occultation signals received onboard Low Earth Orbiting (LEO)
CHAMP (CHAllenging Minisatellite Payload) satellite.
In this chapter, the first and higher order ionospheric propagation effects on GNSS signals
are described and their estimates are given at different level of ionospheric ionization.
Multi-frequency ionosphere-free and geometry-free solutions are studied and residual terms
in the ionosphere-free solutions are computed. Different correction approaches are
discussed for the second and third order terms, and ray path bending correction.
Additionally, we have proposed new approaches for correcting straight line of sight (LoS)
propagation assumption error, i.e., ray path bending error for ground based GNSS
positioning. We have modelled the excess path length of the signal in addition to the LoS
path length and the total electron content (TEC) difference between a curved and LoS paths
as functions of signal frequency, ionospheric parameters such as TEC and TEC derivative
with respect to the elevation angle. We have found that using the TEC derivative in addition
to the TEC information we can improve the existing correction results.
2. Ionospheric propagation effects
Quantitatively, the propagation of a radio wave through the ionospheric plasma is
described by the refractive index of the ionosphere (Appleton-Hartree formula). At high
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