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When GNSS receivers capable of collecting dual-frequency data are available, it is possible to eliminate the first-order ionospheric effect in the data processing through the ionosphere-free linear combination. However, the second-and third-order ionospheric effects still remain. The first-, second-and third-order ionospheric effects are directly proportional to the total electron content (TEC), although the second-and third-order effects are influenced, respectively, by the geomagnetic field and the maximum electron density. In recent years, the international scientific community has given more attention to these kinds of effects and some works have shown that for high precision GNSS positioning these effects have to be taken into consideration. We present a software tool called RIN-EX_HO that was developed to correct GPS observables for second-and third-order ionosphere effects. RINEX_HO requires as input a RINEX observation file, then computes the second-and third-order ionospheric effects, and applies the corrections to the original GPS observables, creating a corrected RINEX file. The mathematical models implemented to compute these effects are presented, as well as the transformations involving the earth's magnetic field. The use of TEC from global ionospheric maps and TEC calculated from raw pseudorange measurements or pseudoranges smoothed by phase is also investigated.

At equatorial latitudes, ionospheric scintillation is the major limitation in achieving high-accuracy GNSS positioning. This is because scintillation affects the tracking ability of GNSS receivers causing losses of lock and degradation on code pseudorange and carrier phase measurements, thus degrading accuracy. During strong ionospheric scintillation, such effects are more severe and GNSS users cannot rely on the integrity, reliability and availability required for safety-critical applications. In this paper, we propose a novel approach able to greatly reduce these effects of scintillation on Precise Point Positioning (PPP). Our new approach consists of three steps: a) a new functional model that corrects the effects of range errors in the observables; b) a new stochastic model that uses these corrections to generate more accurate positioning; and c) a new strategy to attenuate the effects of losses of lock and consequent ambiguities re-initializations that are caused by the need to re-initialize the tracking. We demonstrate the effectiveness of our method in an experiment using a 30-day static dataset affected by different levels of scintillation in the Brazilian south-eastern region. Even with limitations imposed by data gaps, our results demonstrate improvements of up to 80% in the positioning accuracy. We show that, in the best cases, our method can completely negate the effects of ionospheric scintillation and can recover the original PPP accuracy that would have existed without any scintillation. The significance of this work lies in the improvement it offers in the integrity, reliability and availability of GNSS services and applications.

GPS and GLONASS are currently the Global Navigation Satellite Systems (GNSS) with full operational capacity. The integration of GPS, GLONASS and future GNSS constellations can provide better accuracy and more reliability in geodetic positioning, in particular for kinematic Precise Point Positioning (PPP), where the satellite geometry is considered a limiting factor to achieve centimeter accuracy. The satellite geometry can change suddenly in kinematic positioning in urban areas or under conditions of strong atmospheric effects such as for instance ionospheric scintillation that may degrade satellite signal quality, causing cycle slips and even loss of lock. Scintillation is caused by small scale irregularities in the ionosphere and is characterized by rapid changes in amplitude and phase of the signal, which are more severe in equatorial and high latitudes geomagnetic regions. In this work, geodetic positioning through the PPP method was evaluated with integrated GPS and GLONASS data collected in the equatorial region under varied scintillation conditions. The GNSS data were processed in kinematic PPP mode and the analyses show accuracy improvements of up to 60% under conditions of strong scintillation when using multi-constellation data instead of GPS data alone. The concepts and analyses related to the ionospheric scintillation effects, the mathematical model involved in PPP with GPS and GLONASS data integration as well as accuracy assessment with data collected under ionospheric scintillation effects are presented.

As GPS is modernizing, there are currently fourteen satellites transmitting L2C civil code and seven satellites transmitting L5 signal. While the GPS observables are subject to several sources of errors, the ionosphere is one of the largest error sources affecting GPS signals. Small irregularities in the electrons density along the GPS radio signal propagation path cause ionospheric scintillation that is characterized by rapid fluctuations in the signal amplitude and phase. The ionospheric scintillation effects are stronger in equatorial and high-latitude geomagnetic latitude regions and occur mainly due to equatorial anomaly and solar storms. Several researchers have analyzed the L2C signal quality since becoming available in December, 2005. We analyze the performance of L2C using GPS data from stations in the equatorial region of Brazil, which is subject of weak, moderate and strong ionospheric scintillation conditions. The GPS data were collected by Septentrio PolaRxS-PRO receivers as part of the CIGALA/CALIBRA network. The analysis was performed as a function of scintillations indexes S4 and Phi60, lock time (time interval in seconds that the carrier phase is tracked continuously without cycle slips), multipath RMS and position variation of precise point positioning solutions. The analysis shows that L2C code solutions are less affected by multipath effects than that of P2 when data are collected under weak ionospheric scintillation effects. In terms of analysis of positions, the kinematic PPP results using L2C instead P2 codes show accuracy improvements up to 33 % in periods of weak or strong ionospheric scintillation. When combining phase and code collected under weak scintillation effects, the results by applying L2C against P2 provide improvement in accuracy up to 59 %. However, for data under strong scintillation effects, the use of L2C for PPP with code and phase does not provide improvements in the positioning accuracy.

[1] A method of determining spectral parameters p (slope of the phase PSD) and T (phase PSD at 1 Hz) and hence tracking error variance in a GPS receiver PLL from just amplitude and phase scintillation indices and an estimated value of the Fresnel frequency has been previously presented. Here this method is validated using 50 Hz GPS phase and amplitude data from high latitude receivers in northern Norway and Svalbard. This has been done both using (1) a Fresnel frequency estimated using the amplitude PSD (in order to check the accuracy of the method) and (2) a constant assumed value of Fresnel frequency for the data set, convenient for the situation when contemporaneous phase PSDs are not available. Both of the spectral parameters ( p, T ) calculated using this method are in quite good agreement with those obtained by direct measurements of the phase spectrum as are tracking jitter variances determined for GPS receiver PLLs using these values. For the Svalbard data set, a significant difference in the scintillation level observed on the paths from different satellites received simultaneously was noted. Then, it is shown that the accuracy of relative GPS positioning can be improved by use of the tracking jitter variance in weighting the measurements from each satellite used in the positioning estimation. This has significant advantages for scintillation mitigation, particularly since the method can be accomplished utilizing only time domain measurements thus obviating the need for the phase PSDs in order to extract the spectral parameters required for tracking jitter determination.

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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