Mitigation of ionospheric effects on GNSS · on real time ionospheric corrections. 2. Real time...

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ANNALS OF GEOPHYSICS, VOL. 52, N. 3/4, June/August 2009

Key words ionosphere – mitigation – TEC – GNSS– positioning – radio-occultation

1. Introduction

Space based radio systems like Global Nav-igation Satellite Systems (GNSS) are affectedby the effects of the ionosphere. Nowadays,GNSS are used to measure positions in theframe of many different types of applications.

The obtained position accuracy which rangesfrom a few mm to about a decameter dependson the type of observables (code or phase meas-urements), the positioning mode (absolute ordifferential) or the fact that positions are com-puted in real time or in post-processing. GNSSare not only used for positioning applications.Indeed, GNSS are now recognized tools for at-mospheric studies: for example, GNSS radio-occultation experiments allow reconstructingvertical electron density and temperature pro-files in the atmosphere. The effects of the iono-sphere remain one of the main factors whichlimit the precision of many applications. It istherefore indispensable to improve existingmitigation techniques. The Total Electron Con-tent is the key parameter for the mitigation ofthe ionospheric error. Nevertheless, the way theionosphere influences GNSS data processing

Mitigation of ionospheric effects on GNSS

René Warnant (1), Ulrich Foelsche (2), Marcio Aquino (3), Benoit Bidaine (4), Vadim Gherm (9), Mohammed Mainul Hoque (8), Ivan Kutiev (5), Sandrine Lejeune (1), Juha-Pekka Luntama (6),

Justine Spits (1), Hal J. Strangeways (7), Gilles Wautelet (1), Nikolay Zernov (9) and Norbert Jakowski (8)(1) Royal Meteorological Institute, Brussels, Belgium(2) WegCenter and IGAM, University of Graz, Austria

(3) IESSG, University of Nottingham, UK(4) University of Liège, Belgium

(5) Geophysical Institute, Bulgarian Academy of Sciences (BAS), Sofia, Bulgaria(6) Finnish Meteorological Institute, Helsinki, Finland

(7) School of Electronic and Electrical Engineering, University of Leeds, UK(8) Deutsches Zentrum für Luft- und Raumfahrt (DLR), Neustrelitz, Germany

(9) Department of Radio Physics, University of St. Petersburg, Petrodvorets, Russia

Abstract The effects of the ionosphere remain one of the main factors which limit the precision and the reliability of manyGNSS applications. It is therefore indispensable on the one hand to improve existing mitigation techniques andon the other hand to assess their remaining weaknesses. Mitigation techniques depend on the type of applicationconsidered. Therefore, specific mitigation techniques have to be developed. The paper summarizes work per-formed on this topic in the frame of WP 3.2 «Mitigation techniques» of COST 296.

Mailing address: Dr. René Warnant, Royal Meteorolo-gical Institute, Avenue Circulaire 3, B-1180 Brussels, Bel-gium; e-mail: [email protected]

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R. Warnant, U. Foelsche, M. Aquino, B. Bidaine, V. Gherm, M. M. Hoque, I. Kutiev, S. Lejeune, J. P. Luntama, J. Spits, H. J. Strangeways, G. Wautelet, N. Zernov and N. Jakowski

techniques depends very much on the type ofapplication. Therefore, specific mitigation tech-niques have to be developed. Ionospheric ef-fects are also an important limitation to the re-liability of GNSS applications: when mitigationtechniques fail, the «nominal» precision level isnot reached; in this case, users are not necessar-ily aware about the problem. This is an impor-tant issue for European positioning systemGalileo which is supposed to give certified pre-cision levels to its customers. This is particular-ly true for so-called «Safety of Life» applica-tions like landings of air planes. Therefore, it isalso important to assess remaining weaknessesin mitigation techniques.

The paper reviews work performed in theframe of Work Package 3.2 «Mitigation tech-niques» of COST Action 296 to improve iono-sphere mitigation techniques in the frame ofdifferent applications and to assess their re-maining weaknesses. At the present time, agrowing number of users need results in realtime. Such applications are particularly vulner-able to ionospheric threats. Therefore, we focuson real time ionospheric corrections.

2. Real time ionospheric corrections for Single frequency users usingNeQuick model

Single frequency GNSS receivers constitutethe simplest and most common systems which

need real time mitigation for ionospheric ef-fects.

To this extent they take benefit from quick-run empirical models such as NeQuick chosenin the framework of the European positioningsystem Galileo (Orus et al., 2007). This glob-al model provides monthly median electrondensity profiles for given time, location andsolar flux (Radicella and Leitinger, 2001). It istherefore well suited for Total Electron Con-tent (TEC) computation thanks to electrondensity integration along satellite-to-receiverray paths.

This parameter is indeed needed for the mit-igation of the ionospheric delay affectingGNSS applications and handled for Galileo bythe so-called Single Frequency IonosphericCorrection Algorithm. NeQuick is based onmonthly median maps – known as CCIR maps– of ionosonde parameters. Consequently theGalileo algorithm includes the computation ofan effective ionization level replacing solar fluxin order to adapt the model to actual conditions.

Since the definition of this algorithm, anew version of NeQuick – called v2 from nowon – has been released (Nava et al., 2008). Itinvolves simplifications in the representationof the bottomside as well as a unique formulafor a key parameter of the topside formulationpreviously defined through two equations,each one used for six months of the year. Atthe University of Liège, to compare both ver-sions of the model to actual data, we initially

Table I. Comparison between NeQuick version 1 and 2 and GPS vertical TEC in 2002.

v1 v2 Evolution

TECmeas [TECu] 23.2

TECmod [TECu] 21.7 20.9 -3.7%

Bias [TECu] 1.5 2.3 52.1%

Relative [%] 6.6 10.0

RMS [TECu] 7.0 4.5 -35.3%

Relative [%] 30.0 19.4

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chose one analysis method which allows touncouple NeQuick formulation from its un-derlying data i.e. the CCIR maps, replacingthem by digisonde measurements. Then wecomputed vertical TEC and compared it withGPS TEC.

We performed tests for mid-latitudes(Dourbes Geophysical Observatory in Bel-gium) and high solar activity level (2002) usinghourly data points for the whole year with a77% availability level (Bidaine and Warnant,2007). We obtained the global (yearly) statisticsof table I showing an average underestimationof NeQuick TEC, slightly worse for the secondversion. However we observe a major improve-ment from NeQuick v2 as the Root MeanSquare (RMS) difference decreases by morethan a third.

We attribute this evolution mainly to theunification of the topside parameter formula asthe six-month inversion of the monthly meandifference visible for NeQuick v1 has nearlycompletely disappeared in the second version(fig. 1).

Further investigations highlighted remain-ing weaknesses in the topside and we are cur-rently analysing results for other stations andyears.

The final goal of our study is to try to im-prove the Galileo single frequency algorithmresults among others.

3. Real time ionospheric corrections basedon operational GNSS measurements

3.1. Real time corrections using ground basedmeasurements

The use of ground based observations of thesatellite transmission to perform 2-D ionos-pheric tomography was first proposed inAusten et al. (1988). Continuous visibility andstability of the transmitted signals make GNSSsatellites ideal for this purpose. Ground basedGNSS observation networks provide a continu-ous flow of information that can be used for re-al time monitoring of the characteristics of theionosphere and its dynamic processes. Howev-er, sophisticated data processing techniques areneeded to fully exploit the potential of theGNSS observations. As a return, real timeionospheric monitoring can potentially allowregional mitigation of the ionospheric errors inGNSS applications with a very good accuracyand in real time.

Prerequisites for high resolution real timeionospheric tomography are timely availabilityof the observation data and sufficiently densenetworks of observing stations. At the momentthe large open GNSS networks like IGS (Inter-national GNSS Service), SuomiNet and EPN(EUREF Permanent Network) provide a verygood starting point for ionospheric tomography.

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Fig. 1. Comparison between NeQuick version 1 (left) and 2 (right) and GPS vertical TEC in 2002: monthlystatistics.

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The constraints of these networks are the sparseobservations especially at high latitude regionsand delayed availability of the data. The latterconstraint is not critical for scientific research,but it would be a significant problem in the de-velopment of an operational GNSS error miti-gation service. Regional networks often providedata with less delay and from a denser distribu-tion of stations than global networks. Especial-ly commercial GNSS networks are typically de-signed for real time services to assist satellitenavigation applications. Dense regional GNSSnetworks are also used to provide informationon crustal deformation related to seismic activ-ity (e.g. California and Japan). Use of regionalGNSS networks for ionospheric tomographyhas been demonstrated e.g. by Lee et al. (2007),Ma et al. (2005) and Wen et al. (2008).

FMI (Finnish Meteorological Institute) hasassessed the feasibility of using observationsfrom a regional GNSS network in Finland toperform mesoscale ionospheric tomography inthe Auroral region. The auroral region is chal-lenging due to the complexity of the ionosphere,

especially during geomagnetic storms. The ob-servation system used in this work is the VRS(Virtual Reference Station) network in Finlandoperated by Geotrim Ltd. This network contains86 GNSS ground stations providing two fre-quency GPS and GLONASS observations. Thesampling rate of the observations is 1 Hz and allobservation data is transferred to the central pro-cessing facility in near real time (NRT).

The software used by FMI for ionospherictomography is the MIDAS (Multi-InstrumentData Analysis System) algorithm developedand implemented by the University of Bath(Mitchell and Spencer, 2003). MIDAS is an ex-tension into 3-D of the 2-D tomography algo-rithm originally presented by Fremouw et al.(1992). The MIDAS algorithm is based on alinear least squares inversion that can fit relativeGPS differential phase data to correspondingdata formed from integrations through an or-thogonal basis set of model ionospheres. Elec-tron density and TEC (Total Electron Content)maps retrieved with MIDAS have been used inmany studies (e.g. Meggs et al. (2004) Mate-

Fig. 2. A regional TEC map retrieved from slant GPS observations with the MIDAS algorithm. The colour barshows the TEC values in TECU (1 TECU = 1016 electrons/m2).

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rassi and Mitchell (2005); Meggs et al. (2005);Yin et al. (2004); Yin and Mitchell (2005)).

The research performed at FMI in theframework of the COST 296 action has beenbased on observation data set collected from theGeotrim network in December 2006. Thisproved to be very good test period as at leasttwo geomagnetic storms took place during themonth. The periods of disturbed ionosphere incombination with the very quiet winter days oflow solar activity form a good basis for assess-ing the performance of the tomography algo-rithm.

Figure 2 shows an example of a verticalTEC map at 02:45 UTC during the geomagnet-ic storm on 15 December 2006. The TEC maphas been integrated from a 3-D electron densitymap retrieved from slant GPS observations.These results are very promising as for the firsttime the retrieved maps seem to capture themesoscale features of the ionospheric plasma.However, validation of the high resolution elec-tron density and TEC maps is a challenge as in-dependent reference observations with a similarresolution are not available. The validationplans include intercomparison of the retrievedionospheric characteristics with observationsfrom ground based magnetometer and auroralcamera network (MIRACLE), riometers andionosonde station at Sodankylä GeophysicalObservatory (SGO). The most promising refer-ence for ionospheric tomography is the Ionos-pheric Tomography Chain operated by SGO.This chain provides 2-D electron density plotsin a vertical plane above the chain of five re-ceivers located in Finland and Sweden.

The high resolution 3-D electron densitymaps can be used to estimate the ionosphericrefractivity error for any GNSS receiver withinthe region covered by the retrieved solution e.g.in mobile single frequency GNSS applicationsthe ionospheric correction can be determinedbased on the rough location of the receiver. Thistype of service requires production of ionos-pheric error corrections in real time. This re-quires regional nowcasting of the ionosphericcharacteristics. The main bottle neck at the mo-ment in the development of an operational serv-ice is the coverage of the available observa-tions. Using just one network seriously limits

the coverage of the retrieved electron densitymaps. EUMETNET (The Network of EuropeanMeteorological Services) has set up the E-GVAP (EUMETNET GPS water vapour pro-gramme) project to collect NRT observationsfrom European GNSS stations. The current E-GVAP network covers more than 400 GNSSsites. Collaboration with the E-GVAP projectcould be a potential way for collecting observa-tions for a Europe-wide NRT ionospheric mon-itoring and nowcasting service.

3.2. Real time corrections using ground and space based measurements

The permanent monitoring of the structureand dynamics of the ionosphere is a key to suc-cessfully overcoming problems associated withthe ionospheric impact on GNSS applicationsincluding both regular effects as well as pertur-bation induced signal degradation. DLRNeustrelitz has established a near real timeionospheric data service using three types ofGNSS measurements illustrated in fig. 3.(http://w3swaci.dlr.de).

Dual frequency GPS measurements over theEuropean area are used to derive the integral ofthe electron density (TEC) between the trans-mitting GNSS satellite and the receiver. Consid-ering the increasing availability of dense GPSnetworks and the fact that one receiver maytrack up to more 10 satellites simultaneously, alarge number of measurements can be obtainedby ground based measurements. Before the TECmeasurements can really be used, the hardwarebiases of individual satellite-receiver pairs haveto be removed by calibration procedures basedon Kalman filtering. After calibrating the link-related TEC data the observations are assimilat-ed into an ionospheric model for creating TECmaps. The European TEC maps are updatedevery 5 minutes making them attractive for sin-gle frequency users to correct remaining ionos-pheric errors. The spatial grid resolution is 1x1deg. These data are used to support GPS refer-ence networks or single point positioning. Aspointed out in Section 7 TEC data can also beused to correct higher order effects (Jakowski etal., 2005a,b,c; 2006; 2007).

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In addition to the ground based GPS meas-urements, measurements onboard Low EarthOrbiting (LEO) satellites such as CHAMP andGRACE are also performed.

Whereas GPS radio occultation measure-ments provide up to about 150 vertical electrondensity profiles in anti-velocity direction nearthe orbit plane (Jakowski, 2005a,b), topsidetracking data for satellite positioning are effec-tively be used to monitor the 3D electron densi-ty distribution of the topside ionosphere/plas-masphere near the orbit plane (Heise et al.,2002).

The electron density reconstructions mayreveal strong plasma density enhancements inparticular in the polar region (Jakowski et al.,2007).

Four types of products/services are deliv-ered to different user groups: warning, nowcast,forecast, post analysis.

4. Real time corrections using triple frequency techniques

GNSS dual frequency measurements can beused to reconstruct TEC. Most of the dual fre-quency TEC reconstruction techniques requirethe use of code measurements to resolve phaseambiguities. As a consequence, the precision ofthe reconstructed TEC is affected by code mul-tipath delays and differential satellite and re-ceiver hardware delays (Ciraolo et al., 2007)and is usually limited to 2-3 TEC units at mid-latitudes (Warnant and Pottiaux, 2000).

The cornerstone of our approach relies onthe use of the third frequency available onGlobal Navigation Satellite Systems (GNSS),i.e. Galileo and modernized GPS, for an im-proved TEC reconstruction. As TEC is the keyparameter for the mitigation of ionospheric ef-fects on different space based systems, in par-

Fig. 3. Schematic view on GNSS based monitoring in SWACI: (1) – ground based GPS monitoring; (2) – radiooccultation; (3) – topside reconstruction using GPS navigation data.

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ticular on GNSS, a more precise TEC recon-struction would allow to improve the precisionand the reliability of many GNSS navigationand positioning techniques.

In our approach, TEC is reconstructed basedon undifferentiated triple frequency (L1-L2-L5)GNSS measurements. The basic idea is to formdifferent combinations of triple frequency codeand phase measurements in order to solve am-biguities by successive approximations (Spitsand Warnant, 2008). This is actually done inthree distinct steps.

The objective of the first step is to resolvethe so-called extra-widelane (EWL) ambigui-ties by computing a combination of dual fre-quency (L2/L5) code and phase measurements.Then the objective of the second step is to re-solve the so-called widelane (WL) ambiguitiesby computing a combination of dual frequency(L1/L2) phase measurements.

In the third step, we introduce the valuesof those EWL and WL ambiguities in a sys-tem of two dual frequency (L1/L2 and L2/L5)phase combinations, which allows us to re-trieve the TEC.

In this method, code measurements are onlyused in the first step, so that code multipath delaysand differential satellite and receiver hardware de-lays do not affect the precision of the TEC. Fur-thermore, even if phase delays could affect theprecision of the reconstructed TEC, we can expectan improvement of one order of magnitude in re-gards with the dual frequency technique.

As the third frequency was not yet availableat the beginning of our work, we have developedsoftware to simulate realistic GPS and Galileotriple frequency code and phase measurements.Thanks to this triple frequency simulation soft-ware, we were able to validate our TEC moni-toring technique on the three-step level. As faras the first step is concerned, the comparison ofthe obtained EWL ambiguities with the initialsimulated ones shows that it is possible to re-solve the EWL ambiguities at their correct inte-ger values. The results of the second step showthat as expected we only obtain approximatedvalues of the WL ambiguities. However, it doesnot prevent us from obtaining the correct TECvalues – i.e. the values initially simulated – inthe third step. In conclusion, the method has

been successfully validated on GPS and Galileosimulated data but still requires further valida-tion on real data. We have started to validate ourtechnique on GIOVE-A real data. As far as thefirst step is concerned, the results on real dataare in good agreement with those on simulateddata. Further validation is ongoing.

5. Mitigation techniques in GNSS radio occultation applications

Phase changes (Doppler shift) in signalsfrom GNSS satellites are the basic measure-ments of the Radio Occultation (RO) technique(Kursinski et al., 1997). These are caused by therespective motions of the transmitting and re-ceiving satellites, by the Earth’s ionosphere, andby the neutral atmosphere (the desired quantity).The kinematic Doppler Effect can be determinedand removed via precise knowledge of the satel-lite’s positions and velocities, routinely availablefrom modern precise orbit determination meth-ods. The effect of the ionosphere is frequency-dependent (see Section 7) and can therefore beremoved to a high degree using a linear combi-nation of measurements at two GNSS frequen-cies – a process known as «ionospheric correc-tion» (Vorob’ev and Krasil’nikova 1994).

Higher order ionospheric effects, however,are not removed by this approach (see section7) and ionospheric residual errors are an impor-tant part of the error budget in retrieved atmos-pheric profiles from about 30 km upwards,where the atmospheric signal is already small(Kursinski et al., 1997). Ionospheric residualerrors, in particular systematic ones, are impor-tant for RO-based climate monitoring, since po-tential decadal scale variability of residualionospheric systematic errors could pretendshort-term trends in RO climatologies of thestratosphere (Foelsche et al., 2008). This effectis currently analyzed in detail employing simu-lation studies over more than two solar cycles.

Climatologies of the upper troposphere andlower stratosphere for the period 2001-2008(therewith including phases with high and lowsolar activity) have been built using RO datafrom the German CHAMP satellite (Foelsche etal., 2007). Comparisons to operational analyses

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from the European Centre for Medium-RangeWeather (ECMWF) forecasts show very goodoverall agreement in the domain below about 30km altitude. Differences exceeding 0.5 K cangenerally be attributed to ECMWF deficiencies,as they gradually disappear with improvementsat ECMWF. Above 30 km there is a systematicdifference between CHAMP and ECMWF, thelatter being colder than the former by up to about2 K at 35 km altitude. So far it has not beenpossible to find any relation between these sys-tematic differences and the phase of the solar cy-cle. The situation is more favorable when look-ing at parameters which are closer to the funda-mental measurements. Early results using bend-ing angle data at high altitudes (Rocken et al.,2008) indicate a potential way to use informationcontained in the data to remove ionosphericresidual errors. At altitudes above 60 km, wherethe contribution from the neutral atmosphere isalmost negligible, there is a small but systematicdifference between measurements during dayand night, which is apparently related to the totalelectron content. Differences between nighttimeRO measurements from the COSMIC constella-tion and climatology for the first four months of2007 are on average about -0.4·10-7 rad, whilethose between day-time measurements and cli-matology are larger by a factor of ~3. Initial re-sults based on CHAMP RO data (B. Schreiner,UCAR, Boulder, USA, pers. comm., July 2008)show furthermore, that nighttime differences un-der low and high solar activity are very similar,while daytime differences show a correlationwith solar activity. These results, although pre-liminary, may show a way to correct for residualionospheric errors in the context of climate mon-itoring, where averages over large numbers ofRO profiles are used, without relying on externalinformation about the state of the ionosphere.Correcting daytime measurements by the offsetbetween day and night should than remove themajor part of ionospheric residuals with varia-tions on decadal scale.

6. Mitigation of scintillation effects

The widely used ionospheric scintillationindices S4 and σϕ represent a practical measure

of the intensity of amplitude and phase scintil-lation affecting GNSS receivers. These indiceshowever do not provide sufficient informationregarding the actual tracking errors that degradeGNSS receiver performance when scintillationoccurs. Suitable receiver tracking models, sen-sitive to scintillation (Conker et al., 2003), al-low the computation of the variance of the out-put error of the receiver PLL (Phase LockedLoop) and DLL (Delay Locked Loop), whichexpresses the quality of the range measure-ments used by the receiver to calculate user po-sition. The capability of incorporating phaseand amplitude scintillation effects into the vari-ance of these tracking errors allows the applica-tion of relative weights (based on the inverse ofthese variances) to measurements from differ-ent satellites. This proposed technique gives theleast squares stochastic model used for positioncomputation a more realistic representation, inparticular under a scintillation scenario, wherethe ionospheric irregularities will affect eachsatellite differently. An example of the applica-tion of this technique is shown in fig. 4. Theplots refer to the error in height when a baselineof ~125 km in the Arctic region (average geo-magnetic latitude > 75°N) is processed on anepoch by epoch relative solution based on C1and P2 pseudoranges only, during a 24 hour pe-riod (10 December 2006) of disturbed geomag-netic conditions (Kp � 4). Results show anoverall improvement of about 38% in height ac-curacy. Improvement for other baselines, rang-ing from 1 km to 750 km, under varying geo-magnetic conditions (4 � Kp � 6), varied be-tween 17% and 34% (Aquino et al., 2009).

Detailed comparisons with alternative ap-proaches, such as weighting according to satel-lite elevation angle and by the inverse of thesquare of the standard deviation of thecode/carrier divergence, are presented in(Aquino et al., 2009), where the influence ofmultipath effects on the proposed mitigationapproach is also discussed. Higher levels of S4may relate to multipath, rather than to actualamplitude fades due to the ionosphere (scintil-lation), in particular at low elevation angles.The findings in (Aquino et al., 2009) howeversuggest that with the input of the S4 in the DLLtracking model of (Conker et al., 2003) the pro-

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posed approach provides an effective way toimprove the solution, also mitigating interven-ing multipath effects.

To implement the mitigation of the carrierphase solution with the use of the PLL model of(Conker et al., 2003) it is necessary to access thepower spectral density (PSD) of fluctuations inthe amplitude and carrier phase output, whichwas possible with the use of high rate scintilla-tion data. Experiments were conducted where acarrier phase-based mitigated solution was alsoimplemented and compared with the conven-tional solution. During a period of occurrence ofhigh phase scintillation it was observed thatproblems related to ambiguity resolution can bereduced by the use of the proposed mitigated so-lution. Details of these results are given in

(Aquino et al., 2008 and 2009). For practical fu-ture use of the method in carrier phase position-ing it is envisaged that the strategy proposed in(Aquino et al., 2007) and further developed in(Strangeways, 2008) can be applied, where thescintillation indices can be used (in combinationwith auxiliary high rate phase data) to computethe PLL tracking error variance.

7. Higher order ionospheric influences in dual frequency systems

7.1. Higher order range errors

Whereas the first-order range error in GNSSapplications can be completely eliminated by a

Fig. 4. 24 hours (10 Dec 2006) time series of errors in height for baseline Lyb0/Nya1 when epochwise (1minute) non-mitigated solution (left below) and mitigated solution (right above) are computed based only on C1and P2 pseudoranges.

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linear combination of dual frequency measure-ments at the two frequencies L1 and L2, higherorder terms of the refractive index n given in eq.7.1 cannot be mitigated in a linear approach.

(7.1)

Here f denotes the signal frequency, fp theplasma frequency (fp < 25 MHz), Θ the angle be-tween the Earth’s magnetic field vector and thepropagation vector and fg the gyro frequency.

Several attempts have been made to mitigatesecond order effects (e.g. Brunner and Gu, 1991;Bassiri and Hajj, 1993; Jakowski et al., 1994;Hoque and Jakowski, 2006; 2007) applying dif-ferent approaches. Depending on information onthe ray path geometry, the electron density distri-bution and the shape of the geomagnetic field itis possible to correct the higher order effects withan accuracy of about 1 mm.

Unfortunately, the knowledge of the actualelectron density distribution and the geomagnet-ic field structure is rather poor in operationalGNSS applications. Thus, correction formulastaking into account the ionosphere and geomag-netic field structures could be of practical im-portance. Following this approach, empiricalformulas depending only on ray path geometry(azimuth and elevation) and TEC have been de-veloped to compute higher order effects for se-lected regions with accuracy in the mm level(Hoque and Jakowski, 2006; 2007). TEC can beprovided by real-time ionospheric monitoringservices such as SWACI (see Section 3). Due tothe anisotropy in the refraction index, intro-duced by geomagnetic field dependent terms ineq. 7.1, the second order effect depends on thedirection of the ray path as it is shown in fig. 5.Systematic range errors of this type will not can-cel out in measurement statistics.

The computation made for a receiver posi-tion at 51°N and 10°E, clearly indicates a maxi-mum error in southward direction. Taking intoaccount that the error in the sample shown in fig.5 can reach up to 60 mm, precise applicationsrequire a correction of higher order effects. Ifmore than two frequencies are available asplanned in modernized GPS or GALILEO sys-tems, higher order effects can directly be miti-gated by using more frequency combinations.

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7.2. Determination and correction of higher order terms for GPS/GNSSrangefinding/positioning

7.2.1. Introduction

Although the standard dual frequencymethod is able to correct for the majority of theionosphere induced delay or phase advance, themost accurate positional determination (1 cmaccuracy or better) requires more preciseionospheric correction, taking also into ac-count the effect of the Earth’s geomagneticfield on the refractive index and the curvatureof the ray path. However, it is not possible toobtain a precise analytical solution for propa-gation in an anisotropic media, such as theEarth’s ionosphere, because of the non-separa-ble variables in the resulting equations. Al-though numerical ray-tracing can be employed,the small step size required for cm accuracy isquite computationally intensive. To overcomethis problem, an approximate analytical pertur-bation method valid at L-band has been formu-lated (Gherm et al., 2006) to calculate thegroup delay or phase advance for satellite toEarth paths accurately, conveniently andspeedily. At these frequencies, utilized for GPSand the future Galileo system, this accuracywas found to be about 2mm and comparablewith the best previous numerical techniquesusing high precision ray-tracing (Strangewaysand Ioannides, 2002) but with a vastly smallercomputational burden.

The method has also been validated againstexact analytical calculations for the isotropiccase and by the most precise numerical ray-tracing for the anisotropic case. The methodcan be used to determine the higher order ion-osphere terms due to the geomagnetic field, thesquare of the electron density along the propa-gation path (rather than just the TEC) and thecurvature of the ray path due to refraction inthe ionosphere. Two components of the latterneed to be calculated, one due to the gradientperpendicular to the path direction in the planeof propagation and the other perpendicular tothe path and the plane of propagation.

This enables the phase advance due to re-fraction by horizontal gradients to be evaluated

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as well as by the vertical electron density gra-dient.

By determining all the higher order iono-sphere errors, the RRE (residual range error)for the GPS or other L-band satellite navigationsystems using the dual frequency method canalso be easily determined. By determining thehigher order errors accurately for the condi-tions pertaining to any GPS satellite to receiv-er path, these errors can be subtracted from thetotal phase advance so that only the f -2 depend-ence remains which can be eliminated usingthe dual frequency method. Although somecorrection procedures rely on experimental de-termination of the f -2 and f -3 terms using 3 fre-quencies, these will not always be availableand, furthermore, the f -3 error is very small (~2cm) and with some uncertainty in all the othererrors sources, would be very hard to deter-mine accurately in this way.

7.2.2. Description of the perturbation method

The phase advance including the higher or-der errors terms for ordinary (ο) and extra-ordi-nary (x) modes for a satellite to ground path havebeen determined using perturbation theory in thegeometrical optics equations (Kravtsov andOrlov, 1990) leading to the following formulae:

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Fig. 5. Left panel: Illustration of the effect of the ray path-magnetic field geometry causing an asymmetry in therefraction. Right panel: Second order ionospheric range error (radial distance from 0-60 mm) for the GPS L2frequency assuming a vertical TEC of 100 × 1016 electrons/m2 for a mid-European station as a function of az-imuth at different elevation angles.

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(7.4)

The equations (7.2 to 7.4) have been veri-fied and validated by comparison with the rig-orous solution of the problem for the isotropicspherically layered ionosphere. They have alsobeen validated for the more general case of anarbitrary 3D ionosphere with horizontal ionos-pheric gradients and permeated geomagneticfield (Gherm et al., 2006) by comparison withthe most precise ray-tracing calculations(Strangeways and Ioannides, 2002).

7.2.3. Calculation of the higher order errors on GPS

The program enables the main error due tothe electron density (proportional to f -2) as wellas the higher order terms in f -3 and f -4 to be de-termined (Strangeways et al., 2007a). An RRE(Residual Range Error) will result from applica-tion of the standard dual frequency model due tothe incorrect weighting of these terms (assumedf -2 rather than f -3 or f- -4 dependence) and this canalso be determined. An example of such a calcu-lation for the L1 GPS frequency is given in fig.6. This shows all these errors for a profile with avertical TEC of 72.6 for the extraordinary modedetermined for a GPS satellite to ground (20°latitude) path at zero azimuth to the magneticmeridian. A value of the horizontal electrondensity gradient, normalised to the local elec-tron density, of 0.001/km was employed at allheights. A recent extension to the program per-mits actual horizontal gradients to be deter-mined using the 3D NeQuick ionosphere modeland incorporates the realistic CO2 geomagneticfield model (Strangeways et al., 2007b). Thedistance errors due to the relative contributionsto the phase advance can be seen in the figurefor both the curvature in the plane of propaga-tion and perpendicular to it. The doted line, rep-resenting the higher order term due to the squareof the profile of electron density along the pathis the smallest error term for elevations less than

cos

LXY ds

Lds

Y X r s ds

l h21

21

1

L L

s

10

0 0

0

!

"

dΨ

= +

=

=

] ]^g gh

# #

#

30° for these parameters. The geomagnetic fieldterm is generally the largest of these errorsources at L-band, although not for very low el-evation paths. The direction of the error due tothe magnetic field is reversed if the direction ofthe path is North to South rather than South toNorth or for the other magneto-ionic mode.Consequently, sometimes the geomagnetic fieldinduced and curvature induced errors will addand sometimes cancel each other. The RRE fordual frequency L1/L2 is also plotted taking ac-count of the effect all the higher error termswould have on this determination.

7.2.4. Discussion concerning determination of the higher order errors.

The second order error term involves an inte-gral along the ray path of the product of the elec-tron density and the component of the geomag-netic field in the direction of the wave normal.Some workers find an approximation of this us-ing the TEC multiplied by B at some particularaltitude along the path which takes into accountthe «weighting» of the product with the actual(varying) electron density along the path. This al-titude tends to be higher than the electron densitymaximum and also shows a latitudinal depend-ence. Others use the ionosphere shell approxima-tion and determine the product at the pierce pointat the shell altitude. The latter is less accurate.However, calculation of this term by integrationof this product along the path shows that it cantake two distinct forms which depend on geo-magnetic latitude and path elevation (Gherm etal., 2006). Thus care must be taken using the ap-proximate treatments mentioned above.

The third order error terms exist due toterms in f -4 in the expansion for the refractiveindex which yield corresponding terms in bothphase advance and group delay (of which onlythe first is normally considered) and also due torefraction (curvature) of the ray path. This takesplace both in the plane of propagation and per-pendicular to it. It is important to note that thecurvature term cannot be determined by the ad-ditional length of the refracted path comparedwith the l.o.s. (line of sight path) as the refrac-tion of the path results in propagation in regions

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where the refractive index is different from thatfor the l.o.s path (Strangeways, 2008). For thephase path, this difference in refractive indexresults in a phase advance which is generallyabout double the magnitude of the phase delaycaused by the additional path length but in theopposite direction.

Thus the refraction causes the phase path tobe more advanced than it would be for the l.o.sand the error is of opposite sign to that whichwould be determined on the basis of just thedifference in path length.

7.2.5. Discussion of correction procedures

Employing the standard dual frequencyscheme, the approximate slant TECs for the

paths to the receiver from all the satellites visi-ble at any one time can be determined. Then theelectron density profiles used to determine thehigher order error terms can be normalised tothese TEC values. Profiles can be chosen froman ionosphere model such as IRI for the appro-priate time of day, month, sunspot number etc.The magnitude of the higher order terms foreach satellite to receiver path, using theirknown azimuth and elevation (based on an ap-proximate receiver location) and an assumedgeomagnetic field model, can then be deter-mined. Then the higher order terms for eachpath can be subtracted from the observed valuesof L1 and L2 to determine corrected ranges forall the satellites. For phase this will of coursealso involve resolving the ambiguities. Themost accurate estimate of the second order er-

field effectf-4curvature in propagation planecurvature perp. to planeRRE

field

effe

ct, F

-4 a

nd c

urva

ture

err

ors

in m

etre

s

Elevation in degrees

0,02

0,015

0,01

0,005

0

-0,005

-0,010 10 20 30 40 50 60 70 80 90

Fig. 6. Higher order errors for the GPS L1 frequency due to the f -3 and f -4 terms (including curvature terms) andthe resultant RRE for dual frequency L1/L2.

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ror can be found by integration along the wholepath using the formula given in eq. 7.2. Such acorrection strategy was employed on simulateddata by Nagarajoo et al. (2007) and this errorfound to be reduced by about one order of mag-nitude (e.g from 1.7 cm to 1.7 mm).

The curvature error can also be calculatedusing the perturbation formulae given above(the last term in eq. 7.2 using also eq. 7.3 and7.4). This term depends strongly on the electrondensity gradients at all points along the pathand these then need to be known in both theplane of propagation and in the direction per-pendicular to it. In our program these are givenusing the NeQuick 3D ionosphere model. Sincethe gradients from this model will only be anapproximation to the real case, the percentageerror in predicting this term is larger than forthe second order term. However the curvatureterm is generally about an order of magnitudesmaller than the second order term at GPS fre-quencies, except for low elevations that are un-likely to be used for ground-observed GPSsatellites. Then, the absolute error in determin-ing the curvature term is still likely to be small-er than that in the determination of the secondorder (geomagnetic field) error. Kim and Tinin(2007) have also independently obtained a for-mula for the third order term using perturbationtheory. Their formulation also includes the ef-fect of ionosphere irregularities which the pres-ent authors have treated separately (Gherm etal., 2005).

8. Effects of local structures in the iono-sphere on real time high precision GNSSapplications

Nowadays, Global Navigation SatelliteSystems or GNSS measure positions in realtime with an accuracy ranging from a few me-ters to a few centimeters. The best precisionscan be reached in differential mode usingphase measurements. In differential mode, mo-bile users improve their positioning precisionthanks to so-called «differential corrections»provided by a reference station. For example,the Real Time Kinematic technique (RTK)measures positions in real time with a preci-

sion usually better than a decimeter when thedistance between the reference station and theuser is smaller than 20 km. In practice, theionospheric effects on GNSS radio signals re-main the main factor which limits the precisionand the reliability of differential positioning.As differential applications are based on the as-sumption that the measurements made by thereference station and by the mobile user are af-fected in the same way by the ionospheric ef-fects, these applications are affected by gradi-ents in TEC between the reference station andthe user. For this reason, local variability in theionospheric plasma can be the origin of strongdegradations in positioning precision. GNSSreal time users who undergo degradations intheir applications are not necessarily aware ofthis problem: this is an important limitation tothe reliability of GNSS positions. For this rea-son, we decided to characterize ionosphericvariability which can pose a threat to the RTKpositioning technique.

As already mentioned, small-scale variabil-ity in the TEC is the origin of degraded GNSSpositioning conditions. Therefore, in a firststep, we performed a detailed study of the mainionospheric phenomena which can induce localvariability in TEC. In practice, GNSS carrierphase measurements can be used to monitor lo-cal TEC variability: small-scale ionosphericstructures can be detected by monitoring TEChigh frequency changes at a single station; asionospheric disturbances are moving, we canexpect that such structures will induce TECtemporal variability which can be detected at asingle station (Warnant and Pottiaux, 2000). Weapplied this method (called «one-station»method) to the GPS data collected at the perma-nent (mid-latitude) station of Brussels from1994 to 2006. Two main types of structureshave been observed: Travelling IonosphericDisturbances (TID’s) and «noise-like» struc-tures. We call «noise-like structures», the vari-ability in TEC shown in fig. 7. We analysed themaximum daily Rate of TEC (RoTEC) valuesobserved at Brussels between January 2001 andDecember 2006. We have afterwards groupedthese values according to the seasons: we ob-tained the maximum seasonal RoTEC valueswhich appear in the table II.

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The largest RoTeC detected at Brussels wereobserved during severe geomagnetic storms. Forexample, the storm of the DOY 303/03 (30thOctober 2003) which presented a DST mini-mum index of -383 nT was responsible for thelargest RoTEC gradients observed during theperiod 1994-2006: 9.839 TECU/min. RoTECdue to TID’s are much smaller than RoTEC dueto geomagnetic storms: the analysis of a lot ofTID cases shows that the maximum RoTEC val-ue observed during the occurrence of a TID was

about 1.5 TECU/min. Moreover, the analysis oftable II shows that strong irregularities occureven during solar minimum, for example, duringthe summer 2006, where gradients up to 1.2TECU/min were reached. In addition, let us un-derline that this maximum RoTEC of summer2006 was larger than the maximum RoTEC ofsummer 2001 (solar maximum). This meansthat, even during periods where the probabilityof occurrence of ionospheric irregularities isvery low, large RoTEC can be observed. This is

Table II. Maximum seasonal RoTEC values at Brussels from January 2001 to December 2006 (expressed inTECU/min).

Spring Summer Autumn Winter

2001 6.881 1.122 4.028 9.068

2002 0.745 1.821 1.946 2.211

2003 0.693 0.653 9.839 1.231

2004 1.581 1.152 0.861 1.263

2005 1.234 2.579 0.503 1.276

2006 0.582 1.197 0.805 0.845

Fig. 7. Ionospheric variability at Brussels on 20th November 2003 (satellite 2).

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a very important issue for GNSS users.The one-station method allows to measure

TEC variability in time but GNSS differentialapplications are affected by variability in spacebetween the user and the reference station.Therefore, in a second step, we developed soft-ware which reproduces, as far as possible, posi-tioning conditions experienced by RTK users onthe field (Lejeune and Warnant, 2008). We usedthis software to assess ionospheric effects onRTK for 4 days representative of different «typ-ical» ionospheric conditions: quiet ionosphericactivity (as measured by the one-stationmethod), medium and large amplitude TID’sand noise-like variability due to a severe geo-magnetic storm (20th November 2003). We con-sidered the case of users who have already fixedtheir phase ambiguities to the correct integer.Again, the largest effects were observed duringthe geomagnetic storm of 20th November 2003where the positioning error due to ionospherereached 80 cm. The maximal values of this errorobserved for TID’s were 15 cm and 22 cm, re-spectively for the medium-amplitude TID andthe large-amplitude TID. During quiet days interms of ionospheric variability, the positioningerror due to ionosphere is typically 1-2 cm butreached 5 cm, which is still within the usualRTK accuracy level. We have also studied thecase where ionospheric disturbances occur dur-ing the ambiguity resolution process: as soon asthe ionospheric residual error reaches 10 cm (ahalf wavelength), the ambiguity resolutionprocess can be corrupted and positioning errorsare growing up to several meters. During ourstudy, we also found that there is a relationshipbetween the baseline length and the effects onpositioning: positioning error due to ionosphereincreases with increasing baseline length. In ad-dition, for a given ionospheric disturbance, thepositioning error due to the ionosphere dependsvery much on baseline orientation.

9. Conclusions

The paper reviews work performed in theframe of Work Package 3.2 «Mitigation tech-niques»of COST Action 296 to improve iono-sphere mitigation techniques in the frame of

different applications and to assess their re-maining weaknesses. As the way the iono-sphere influences GNSS data processing tech-niques depends very much on the type of appli-cation, specific mitigation techniques have tobe developed.

At the present time, a growing number ofusers need results in real time. Such applica-tions are particularly vulnerable to ionosphericthreats. Therefore, we put the focus on real timeionospheric corrections. The Galileo SingleFrequency Ionospheric Correction Algorithm isbased on the NeQuick model; remaining weak-nesses in this model have been investigated atthe University of Liege mainly by comparingNeQuick TEC with GPS TEC. Ground andSpace based GNSS observations provide a con-tinuous flow of information that can be used forreal time monitoring of the characteristics ofthe ionosphere and its dynamic processes.Finnish Meteorological Institute has assessedthe feasibility of using observations from a re-gional GNSS network in Finland to performmesoscale ionospheric tomography in the Au-roral region. Deutsches Zentrum für Luft- undRaumfahrt (DLR) Neustrelitz has established anear real time ionospheric data service usingground and Space based GNSS measurements.At the Royal Meteorological Institute of Bel-gium, a new TEC reconstruction technique isbeing developed based on triple frequencyGalileo or (modernized) GPS measurements.The increased accuracy in TEC reconstructionwill allow to improve ionosphere mitigationtechniques used in many applications. The Uni-versity of Graz has investigated ionosphere mit-igation techniques used in the frame of radiooccultation experiments of which the goal is toretrieve neutral atmosphere parameters. TheUniversity of Nottingham has developed a tech-nique allowing to mitigate scintillation effectson GNSS positioning.

Many GNSS applications rely on the dualfrequency correction for the mitigation ofionospheric effects; the remaining influence ofhigher order terms has been investigated atDLR, University of Leeds and University of St.Petersburg.

Local variability in TEC can be the origin ofstrong degradation in high precision real time

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positioning applications. The Royal Meteoro-logical Institute of Belgium and the Geophysi-cal Institute of the Bulgarian Academy of Sci-ences have characterized small-scale structuresin TEC which can pose a threat for these appli-cations.

Acknowledgements

The investigations presented here weremainly carried out and coordinated in the frameof the COST 296 activity «Mitigation of Ionos-pheric Effects on Radio Systems (MIERS)».Work package leaders thank very kindly allcontributors to this very challenging scientifictopic.

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