Abstract

The ionosphere is the ionized part of the earth’s atmosphere lying between about 50 km and several earth radii (Davies, 1990) whereas the upper part above about 1000 km height up to the plasmapause is usually called the plasmasphere. Solar extreme ultraviolet (EUV) radiation at wave lengths " 130 nm significantly ionizes the earth’s neutral gas. In addition to photoionisation by electromagnetic radiation also energetic particles from the solar wind and cosmic rays contribute to the ionization. The ionized plasma can affect radio wave propagation in various ways modifying characteristic wave parameters such as amplitude, phase or polarization (Budden, 1985; Davies, 1990). The interaction of the radio wave with the ionospheric plasma is one of the main reasons for the limited accuracy and vulnerability in satellite based positioning or time estimation.\r \r A trans-ionospheric radio wave propagating through the plasma experiences a propagation delay / phase advance of the signal causing a travel distance or time larger / smaller than the real one. The reason of the propagation delay can be realized considering the nature of the refractive index which depends on the density of the ionospheric plasma. The refractive index (n ≠ 1) of the ionosphere is not equal to that of free space (n = 1). This causes the propagation speed of radio signals to differ from that in free space. Additionally, spatial gradients in the refractive index cause a curvature of the propagation path. Both effects lead in sum to a delay / phase advance of satellite navigation signals in comparison to a free space propagation.\r \r The variability of the ionospheric impact is much larger compared to that of the troposphere. The ionospheric range error varies from a few meters to many tens of meters at the zenith, whereas the tropospheric range error varies between two to three meters at the zenith (Klobuchar, 1996). The daily variation of the ionospheric range error can be up to one order of magnitude (Klobuchar, 1996). \r \r After removal of the Selective Availability (SA, i.e., dithering of the satellite clock to deny full system accuracy) in 2000, ionosphere becomes the single largest error source for Global Navigation Satellite Systems (GNSS) users, especially for high-accuracy (centimeter - millimeter) applications like the Precise Point Positioning (PPP) and Real Time Kinematic (RTK) positioning. Fortunately, the ionosphere is a dispersive medium with respect to the 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.\r \r 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), Hernandez-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. Hernandez-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.\r \r 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. Document type: Part of book or chapter of book