Range errors due to ionospheric and tropospheric effects for signal frequencies above 100 MHz

Hartmann, G. K.; Leitinger, R.

doi:10.1007/bf02520897

Cited by 104 publications

(73 citation statements)

References 25 publications

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“…(6) by replacing the integral N ds with STEC; by taking the B 0 cosθ term out of the integral (assuming that this product is LoS independent); and by approximating the integral N 2 ds based on the shape parameter η, which is quite independent of satellite elevation, and the maximum electron density in the vertical electron density profile (N max ), where all integrals are assumed along LoS between the receiver (rec) and satellite (sat) (Hartmann and Leitinger, 1984):…”

Section: Discussion and Suggestions For Future Workmentioning

confidence: 99%

“…Ion3 term contains the integral of the square of the electron density, N 2 ds (Eq. 6), which can be estimated using the shape parameter η (Hartmann and Leitinger, 1984). This helps to approximate the ionospheric electron density profile in terms of the maximum electron density, N max , and the shape parameter, η, giving ηN max STEC for this integral.…”

Section: Methodsmentioning

confidence: 99%

“…This helps to approximate the ionospheric electron density profile in terms of the maximum electron density, N max , and the shape parameter, η, giving ηN max STEC for this integral. The shape parameter η can be taken as 0.66 which is valid for different satellite elevations and maximum electron densities (Hartmann and Leitinger, 1984). Based on these arguments, Eq.…”

Section: Methodsmentioning

confidence: 99%

“…As shown by Hoque and Jakowski (2007), the ray bending effect on the GNSS signals becomes significant especially at low satellite elevation angles -below 10 • ; thus this cutoff angle is thought to be an appropriate threshold for comparing the positioning results (considering the corrected and uncorrected observations) with negligible contribution by the ray bending effect. More detailed analyses about the impact of ray bending on the GNSS signal propagation and observations have been shown, among other researchers, by Hoque and Jakowski (2008), who provided an empirical formula for the geometric bending of the GPS signals; Hartmann and Leitinger (1984), who considered the geometric bending of the signals in their analysis of the RREs due to the atmosphere; and Petrie et al (2010), who used the International Reference Ionosphere (IRI) 2007 model (Bilitza and Reinish, 2008) to estimate the potential size of the ray bending effect on the estimated GPS parameters and positioning.…”

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confidence: 99%

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Higher order ionospheric effects in GNSS positioning in the European region

et al. 2011

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Abstract. After removal of the Selective Availability in 2000, the ionosphere became the dominant error source for Global Navigation Satellite Systems (GNSS), especially for the high-accuracy (cm-mm) demanding applications like the Precise Point Positioning (PPP) and Real Time Kinematic (RTK) positioning.The common practice of eliminating the ionospheric error, e.g. by the ionosphere free (IF) observable, which is a linear combination of observables on two frequencies such as GPS L1 and L2, accounts for about 99 % of the total ionospheric effect, known as the first order ionospheric effect (Ion1). The remaining 1 % residual range errors (RREs) in the IF observable are due to the higher -second and third, order ionospheric effects, Ion2 and Ion3, respectively. Both terms are related with the electron content along the signal path; moreover Ion2 term is associated with the influence of the geomagnetic field on the ionospheric refractive index and Ion3 with the ray bending effect of the ionosphere, which can cause significant deviation in the ray trajectory (due to strong electron density gradients in the ionosphere) such that the error contribution of Ion3 can exceed that of Ion2 (Kim and Tinin, 2007).The higher order error terms do not cancel out in the (first order) ionospherically corrected observable and as such, when not accounted for, they can degrade the accuracy of GNSS positioning, depending on the level of the solar activity and geomagnetic and ionospheric conditions (Hoque and Jakowski, 2007). Simulation results from early 1990s show that Ion2 and Ion3 would contribute to the ionospheric error budget by less than 1 % of the Ion1 term at GPS frequencies (Datta-Barua et al., 2008). Although the IF observable may provide sufficient accuracy for most GNSS applications, Correspondence to: Z. G. Elmas (isxzge1@nottingham.ac.uk) Ion2 and Ion3 need to be considered for higher accuracy demanding applications especially at times of higher solar activity.This paper investigates the higher order ionospheric effects (Ion2 and Ion3, however excluding the ray bending effects associated with Ion3) in the European region in the GNSS positioning considering the precise point positioning (PPP) method. For this purpose observations from four European stations were considered. These observations were taken in four time intervals corresponding to various geophysical con- (Marques et al., 2011) was used to calculate the magnitudes of Ion2 and Ion3 on the range measurements as well as the total electron content (TEC) observed on each receiver-satellite link. The program also corrects the GPS observation files for Ion2 and Ion3; thereafter it is possible to perform PPP with both the original and corrected GPS observation files to analyze the impact of the higher order ionospheric error terms excluding the ray bending effect which may become significant especially at low elevation angles (Ioannides and Strangeways, 2002) on the estimated station coordinates.

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Section: Discussion and Suggestions For Future Workmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

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Higher order ionospheric effects in GNSS positioning in the European region

et al. 2011

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“…The perturbation theory has also been used in numerous papers (Hartmann and Leitinger 1984;Brunner and Gu 1991;Hajj 1992, 1993;Prokopov and Zanimonska 2005;Gherm et al 2006;Kim and Tinin 2007;Hernandez-Pajares et al 2007;Jakowski 2008, 2011;Moore and Morton 2011;Petrie et al 2011) when employing the GO equations. At transmission frequencies in the GHz band and higher, the squared ratio of the ionospheric electron plasma frequency to the transmission frequency is generally less than 10 −4 , so that this ratio is a physically small parameter of the problem under consideration.…”

Section: Introductionmentioning

confidence: 99%

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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Ionospheric tomography using ADS-B signals

Cushley

Noël

2014

Radio Sci.

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Numerical modeling has demonstrated that Automatic Dependent Surveillance Broadcast (ADS-B) signals can be used to reconstruct two-dimensional (2-D) electron density maps of the ionosphere using techniques for computerized tomography. Ray tracing techniques were used to determine the characteristics of individual waves, including the wave path and the state of polarization at the satellite receiver. The modeled Faraday rotation was computed and converted to total electron content (TEC) along the raypaths. The resulting TEC was used as input for computerized ionospheric tomography (CIT) using algebraic reconstruction technique. This study concentrated on reconstructing mesoscale structures 25-100 km in horizontal extent. The primary scientific interest of this study was to show that ADS-B signals can be used as a new source of data for CIT to image the ionosphere and to obtain a better understanding of magneto-ionic wave propagation.

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Range errors due to ionospheric and tropospheric effects for signal frequencies above 100 MHz

Cited by 104 publications

References 25 publications

Higher order ionospheric effects in GNSS positioning in the European region

Higher order ionospheric effects in GNSS positioning in the European region

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

Ionospheric tomography using ADS-B signals

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