Rigorous calculation of ionospheric effects on GPS Earth-Satellite paths using a precise path determination method

Strangeways, H.J.; Ioannides, Rigas

doi:10.1556/ageod.37.2002.2-3.17

Cited by 30 publications

(18 citation statements)

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“…The correction of the secondorder ionospheric term will contribute to a better longrange baseline ambiguity resolution (Strangeways and Ioannides 2002) and may contribute to an accuracy improvement in real-time-kinematic (RTK) positioning (Rizos 2002). dh ¼ Hdz; R 0 ¼ ðR À h 0 Þ=H; S 0 ¼ ðS À h 0 Þ=H; Z S R n I e ðhÞ ¼ expð0:5ÞHN 0…”

Section: Resultsmentioning

confidence: 99%

Mitigation of higher order ionospheric effects on GNSS users in Europe

Hoque

Jakowski

2007

GPS Solut

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Current dual-frequency GPS measurements can only eliminate the first-order ionospheric term and may cause a higher-order range bias of several centimeters. This research investigates the second-order ionospheric effect for GNSS users in Europe. In comparison to previous studies, the electron density profiles of the ionosphere/ plasmasphere are modeled as the sum of three Chapman layers describing electron densities of the ionospheric F 2 , F 1 and E layers and a superposed exponential decay function describing the plasmasphere. The International Geomagnetic Reference Field model is used to calculate the geomagnetic field vectors at numerous points along the incoming ray paths. Based on extended simulation studies, we derive a correction formula to compute the average value of the longitudinal component of the earth's magnetic field along the line-of-sight as a function of geographic latitude and longitude, and geometrical parameters such as elevation and azimuth angles. Using our correction formula in conjunction with the total electron content (TEC) along the line-of-sight, the second-order ionospheric term can be corrected to the millimeter level for a vertical TEC level of 10 18 electrons/m 2 .

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Section: Resultsmentioning

confidence: 99%

Mitigation of higher order ionospheric effects on GNSS users in Europe

Hoque

Jakowski

2007

GPS Solut

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“…Figure 17 shows an example of such variation, at Arecibo (Morton et al 2009b). Strangeways and Ioannides (2002) point out that ''since this term is everywhere weighted by the local electron density, the major contribution to the integral will occur where the electron density is greatest, which will be Surv Geophys (2011) 32:197-253 227 around the F layer peak''. This would be expected to be between *250 and 550 km, reducing the effect of the variability somewhat.…”

Section: Integration At a Point: The Thin Shell Modelmentioning

confidence: 99%

“…They also provide plots showing the geographical distribution of the error, which is generally largest close to the geomagnetic equator. Strangeways and Ioannides (2002) performed ray-tracing calculations. They investigated the height at which Bcosh would equal the average value, but found that due to azimuth changes an average value could still underestimate the effect.…”

Section: Integration At a Point: The Thin Shell Modelmentioning

confidence: 99%

A Review of Higher Order Ionospheric Refraction Effects on Dual Frequency GPS

et al. 2010

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Higher order ionospheric effects are increasingly relevant as precision requirements on GPS data and products increase. The refractive index of the ionosphere is affected by its electron content and the magnetic field of the Earth, so the carrier phase of the GPS L1 and L2 signals is advanced and the modulated code delayed. Due to system design the polarisation is unaffected. Most of the effect is removed by expanding the refractive index as a series and eliminating the first term with a linear combination of the two signals. However, the higher order terms remain. Furthermore, transiting gradients in refractive index at a non-perpendicular angle causes signal bending. In addition to the initial geometric bending term, another term allows for the difference that the curvature makes in electron content along each signal. Varying approximations have been made for practical implementation, mainly to avoid the need for a vertical profile of electron density. The magnetic field may be modelled as a tilted co-centric dipole, or using more realistic models such as the International Geomagnetic Reference Field. The largest effect is from the second term in the expansion of the refractive index. Up to several cm on L2, it particularly affects z-translation, and satellite orbits and clocks in a global network of GPS stations. The third term is at the level of the errors in modelling the second order term, while the bending terms appear to be absorbed by tropospheric parameters. Modelling improvements are possible, and three frequency transmissions will allow new possibilities.

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“…Before this, we note that for frequencies of 1 GHz and higher, the traditional technique has been validated against the results of the direct ray tracing by many authors, including ourselves (e.g., Strangeways and Ioannides 2002;Gherm et al 2006;Hoque and Jakowski 2008;Kashcheyev et al 2012). This gives validity to its use in validating the results of calculations employing the alternative technique developed here.…”

Section: Traditional Techniquementioning

confidence: 90%

“…The spherically symmetric case was considered by many authors (see, e.g., Strangeways and Ioannides 2002;Hoque and Jakowski 2008;Petrie et al 2011). In the present consideration, however, this is only the zero-order term, which already takes into account all the ionospheric effects of the spherically symmetric ionosphere, whereas the higher-order corrections take account of the effects due to the horizontal (here angular) gradients of the electron density in the ionosphere.…”

Section: Solution To the Ray Pathsmentioning

confidence: 95%

On the determination of the effect of horizontal ionospheric gradients on ranging errors in GNSS positioning

Danilogorskaya

Zernov

Gherm

et al. 2016

J Geod

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An alternative approach to the traditionally employed method is proposed for treating the ionospheric range errors in transionospheric propagation such as for GNSS positioning or satellite-borne SAR. It enables the effects due to horizontal gradients of electron density (as well as vertical gradients) in the ionosphere to be explicitly accounted for. By contrast with many previous treatments, where the expansion of the solution for the phase advance is represented as the series in the inverse frequency powers and the main term of the expansion corresponds to the true line-of-sight distance from the transmitter to the receiver, in the alternative technique the zero-order term is the rigorous solution for a spherically layered ionosphere with any given vertical electron density profile. The first-order term represents the effects due to the horizontal gradients of the electron density of the ionosphere, and the second-order correction appears to be negligibly small for any reasonable parameters of the path of propagation and its geometry for VHF/UHF frequencies. Additionally, an "effective" spherically symmetric model of the ionosphere has been introduced, which accounts for the major contribution of the horizontal gradients of the ionosphere and provides very high accuracy in calculations of the phase advance.

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Rigorous calculation of ionospheric effects on GPS Earth-Satellite paths using a precise path determination method

Cited by 30 publications

References 0 publications

Mitigation of higher order ionospheric effects on GNSS users in Europe

Mitigation of higher order ionospheric effects on GNSS users in Europe

A Review of Higher Order Ionospheric Refraction Effects on Dual Frequency GPS

On the determination of the effect of horizontal ionospheric gradients on ranging errors in GNSS positioning

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