Using NeQuick to reconstruct the 3D Electron Density of the Ionosphere

Transcription

1 Using NeQuick to reconstruct the 3D Electron Density of the Ionosphere Benefits and capabilities in single frequency positioning applications Bruno Nava, Sandro Maria Radicella Telecommunications/ICT for Development Laboratory The Abdus Salam International Centre for Theoretical Physics (ICTP) Trieste, Italy Stefano Lagrasta, Fulvio Greco Satellite Systems and Applications Telespazio S.p.A. Rome, Italy Abstract The term ionospheric effect identifies a well known propagation effect, perturbing GNSS signals and ranging observables collected by a navigation receiver. In the case of a single-frequency operating device, the capability of mitigation relies upon the availability of a model for such an effect. This paper aims to demonstrate NeQuick ability of accurately reconstructing the ionospheric behavior at a given date. The ionospheric 3D model is adapted to real situations, starting from experimental input data to determine the solar effective ionization level maps : a crucial input information to properly drive NeQuick operation. Key words: NeQuick, ionosphere modelling and estimation, GNSS I. INTRODUCTION GPS users adopt the ICA/Klobuchar compensation strategy. The advent of Galileo brought to the attention a new approach, much more complex and potentially promising, that is based on the NeQuick ionosphere electron density model. NeQuick was developed at the Aeronomy and Radiopropagation Laboratory of the Abdus Salam International Centre for Theoretical Physics (ICTP, Trieste, Italy) with the collaboration of the Institute for Geophysics, Astrophysics and Meteorology of the University of Graz (Austria) [3], [4], [6], [7]. It is a quick run model particularly designed for transionospheric propagation applications able to reproduce the 3D climatologic behaviour of the ionosphere electron density. In the present work the latest version of the model, the NeQuick, has been used. Its full description, including the complete analytical formulation, can be found in [8]. In the frame of a simulation facility developed for the Italian Space Agency (ASI) and the Air Navigation Services company (ENAV), the International Centre for Theoretical Physics (ICTP) and Telespazio dealt with the problem of reproducing, at a given date, the observed ionospheric electron density. The issue is not simply to implement a realistic ionospheric profile and a delay effect on synthetic (simulated) Navigation observables. More precisely, the purpose is emulating exactly the effect that was observed over a defined time period. As a matter of fact, using the NeQuick model, different ionosphere electron density retrieval techniques have been developed, based on the model adaptation to experimental (GPS derived) data, both in terms of vertical TEC maps [5] and slant TEC measurements [13] data. This paper illustrates how the electron density reconstruction method described in [5] has been applied (for the first time) to a real case for mitigating ionospheric effects in positioning calculations. II. ABOUT IONOSPHERIC EFFECT ON RANGING The ionosphere is a dispersive medium for GNSS signals at L band, being characterized by a refractivity index n that is a function of the specific RF carrier frequency f. The ionospheric effect determines a group propagation delay on ranging signals. Thus a code range measurement, which is the primary observable available internally to a navigation receiver, suffers from an extra-length iono which is due to ionosphere: n( s ) iono 1 ds The integral is intended to be calculated along the geometric path from the receiver to the GNSS satellite that emits the related signal. An explicit formula is available for the value of' n ; in a first order approximation, one has: n( s ) 1 Ne( s ) e f 4 0 m where: N e = electron density [Electrons / m 3 ] m = rest mass of the electron = [Kg]

2 e = charge of the electron = [Coulomb] 0 = vacuum permittivity = [Farad / m] f = carrier frequency [Hz] so that: n( s ) N e( s ) f and thus, with good approximation (up to an accuracy of about 1%, for the L-band GNSS signals), it can be assumed: iono f stec f N ( s ) ds e In the previous formula, stec denotes the slant Total Electron Content (TEC) resulting from the linear integration of N e along the satellite-to-receiver ray-path. The stec is to be provided in units of [Electrons / m ] to fit Eqn. 4; however, for practical manipulation and display of numerical values, it is commonly expressed in TECU (TEC Units), where 1 TECU = [Electrons / m ]. The magnitude of the ionospheric delay effect on GNSS code range measurements is proportional to the stec and becomes more and more significant as far as low geographic latitudes are achieved [9]. III. STANDARD MITIGATION TECHNIQUES The single-frequency receiver applies a feed-forward compensation for the undesired term iono, before attempting the solution of navigation equations. derive explicitly some estimate for stec, based upon the adoption of an ionospheric model. The GPS user applies the so called ICA/Klobuchar compensation model [1], whilst SBAS (EGNOS, WAAS) architecture considers a surface grid model: in both cases, it happens like if the ionospheric effect would occur at an (ideal) thin shell surrounding the Earth at a fixed altitude h m of about 450 [Km]. The intersection of the GNSS signal optical path with the thin shell is named Ionospheric Pierce Point (IPP) ( see Figure 1. ) and it plays a central role for those models. Based upon the ionospheric thin shell approximation, the stec is obtained by a product: stec F( E ) vtec( IPP ) In the previous expression, F=F( E ) is a slant factor coefficient depending on RF propagation path elevation E w.r.t. user receiver local horizon. vtec(ipp) is the Vertical TEC, or integral of free electron density, evaluated along the zenith direction of the already mentioned IPP. Resulting compensation model takes the form: F( E ) vtec f iono GPS ICA/Klobuchar gives interpolation formulae for the (overall) right factor of Eqn. 6 and for slanting factor F(E). Model is based upon 8 parameters (only), broadcast by GPS satellite and applicable to the Earth globe. SBAS compensation technique is much more sophisticated. The EGNOS space segment transmits, as primary element, vtec values applicable at the nodes of a geographic (regional) grid. The user must interpolate acquired grid point values to achieve the vtec amount applicable at the IPP. Then, as it is the case for all thin shell based models, it must convert vtec into required stec by application of a slanting factor F(E). E IPP Navigation Satellite = Receiver Position = Ionospheric Pierce Point (IPP) E 1 = E F(E 1 ) vtec(ipp) = F(E ) vtec(ipp) E 1 E h m Figure. : Inconsistencies forced by thin shell paradigm Figure 1. : The Ionospheric Pierce Point (IPP) at the thin shell However, in order to use Eqn. 4 to this purpose, it needs to The reconstruction of stec by projecting a vtec effect, faithlessly located at the thin shell sphere, through a slanting factor F(E), brings a number of undesired drawbacks, including mathematical inconsistencies. According to Eqn. 5, two

3 different propagation paths occurring through the same IPP and characterized by equal elevation angles E 1 =E appear affected by the same stec, whilst the chance to find out stec 1 stec in real life is quite improbable (see Figure. ). An estimate of the mapping function errors for specific ionospheric conditions can be found in [14]. IV. NEQUICK APPROACH The novelty with NeQuick, compared to standard modeling and mitigation techniques already familiar to GNSS receiver technology, is that it abandons the supposition of a (virtual) thin shell surface, along with necessity of projecting a vertical effect through a slanting function. As such, NeQuick provides a full 3D representation of the electron density N e within the atmosphere. The basic inputs of the NeQuick model function are: point position {x, y, z}, UTC time t (hour of day), month m, and solar flux f10.7 (or, alternatively, sunspot number); the output is the electron concentration N e at the given location and time, being N e = N e ( s, t, m, f10.7), s = s(x, y, z). Note that solar flux f10.7 can be expressed in terms of mean sunspot number R1 according to an empirical relationship: f R1 R1 NeQuick is provided by its authors as a Fortran coded package. In the next future it will be downloadable from ITU-R web site (at present, only the previous version, NeQuick 1, is available at [11] ), along with a number of input data structured as ASCII files (with name extension.asc ). If NeQuick is intended to be used for mitigating or simulating the ionospheric effect in a GNSS receiver, then a numeric integration procedure is to be set up, for summing N e along the RF signal propagation path existing between satellite signal source and user location, as it is required by Eqn. 4. The NeQuick computer package includes specific (example) integration routines to accumulate the electron density along (any) ground-to-satellite ray-path. In the case of Galileo navigation system users, a specific version of the NeQuick model is used and an effective solar flux A z can be reconstructed from an interpolation formula, as a function of the so called Modified Dip-Latitude angle, : 0 a1 a A z a From the point of view of NeQuick, A z plays a role similar to f10.7, being characterized by the same physical units and constituting a sort of real-time estimate for Solar flux f10.7. It has to be underlined that, being A z a NeQuick-derived effective parameter, it is only valid for the model itself. As a matter of fact, the receiver will acquire current estimates for a 0, a 1, a by Galileo satellite Navigation message, whilst is computed internally by the model. In the case of NeQuick and for the purpose of this work, MoDip was obtained by direct interpolation, as a function of the intended point position {x, y, z}, using tabulated values within modip.asc file. One understands that solar activity is a key element of the NeQuick computation process. It has a short-term variability, and is used as tuning element of NeQuick in order to adapt it to a real (actual, experimental) ionospheric behavior. Other aspects of ionosphere modeling evolve as well in the mid or long term. For instance, additional data are archived in other ASCII files, allowing to obtain numerical maps describing the F-peak plasma frequency f 0 F and the propagation factor M(3000)F. 1 The temporal and spatial variations of f 0 F and M(3000)F are described by the Comité Consultatif International des Radiocommunications (CCIR) which computes proper coefficient sets to this aim []. The CCIR parameters feed a harmonics (custom) modeling, consisting first of a Fourier analysis, accounting for the monthly median diurnal variation (thus depending on hour time UT). The coefficients of Fourier expansion are, in turn, to be computed according to a worldwide description, based upon spherical (Legendre) functions, depending upon geographic longitude () and latitude () independent variables. Thus, NeQuick makes also use of the CCIR files distributed by ITU-R; such files are named CCCIRxx.asc, with xx=m+10, m denoting reference month, as a number from 1 to 1. V. PAPER OBJECTIVES The first aim of the article is to describe how a given (real) vtec map can be reconstructed, using the NeQuick model and the concept of the effective ionization level parameter, A z. This is achieved by putting into operation an approach which goes far beyond Galileo interpolation strategy given by Eqn. 8. The key element here, is obtaining an accurate functional description of A z in terms of point coordinates in space, along the propagation path of RF navigation signal. Once that A z = A z (s) values are achievable, a corresponding reconstruction of the 3D ionosphere electron density is allowed by NeQuick, along the same path. Secondly, this paper intends to show that NeQuick operation parameters related to solar activity, when fitted on an assigned vtec map, allow to provide an estimate of stec which can significantly improve the solution of positioning equations performed by a single-frequency navigation receiver. In order to verify NeQuick capability to improve the range delay corrections in single frequency positioning applications, a test case has been defined. For a given time interval, the observables collected by a geo-referenced GPS receiver have been considered and the relevant RINEX files processed to compute its position, using a 1 M(3000)F = MUF(3000) / f0f, where MUF(3000) is the highest frequency that, refracted in the ionosphere, can be received at a distance of 3000 [km].

4 standard positioning algorithm based on ICA/Klobuchar ionospheric compensation model. Over the same time window, NeQuick model has been adopted to compute all the stec values necessary to implement full ionospheric range delay corrections. In particular, for each epoch, the slant TEC values corresponding to the receiver-to-satellite links have been computed using the NeQuick model, driven by D A z grids. The structure of A z grids is very similar to that one of standard vtec maps: each grid is spaced 5 in longitude (),.5 in latitude (), and covers the whole Earth globe (7373 grid points). A z grids are obtained from a complex optimization process, driven by real vtec maps, being stored with a sampling period of 10 [min] and interpolated, both in space and time. This way, electron density N e at given space coordinates accounts for the reconstructed effective solar flux at that point, and that time. It will be shown that the prospected approach enables to gain a significant accuracy in the computation of the PVT solution. VI. ADAPTING NEQUICK TO AN ACCURATE MODELING OF OBSERVED IONOSPHERE We remind that A z is a parameter that can be considered as a proxy for the Solar activity index f10.7, and therefore is intended to be used as a primary input for the NeQuick to be able to accurately reconstruct a (real) stec along any ground-to-satellite link. Emulating the real ionospheric effect that was observed over a defined time window relies upon the possibility of reconstructing the so called effective ionization level A z = A z ( s ), using a custom approach which provides first what we defined A z grids. With a sample interval of 10 [min], 144 A z grids cover a daily period of 4 hours. Each grid stores 7373 = 539 values of A z = A z (,, t ), t being a fixed UT tag. This corresponds to parameter values per day, each computed as result from NLP optimization process; by the way, they could be a proper input to obtain the three interpolation coefficients ( a 0, a 1, a ) to be broadcast by Galileo system, foreseen by Eqn. 8. The active monitoring of ionosphere by International research centers generates data products that can be downloaded from Web sites. In particular, vtec maps are obtainable; a typical case is that one of AIUB Ionex formatted files. Ionex data appear sampled every hours; they are vtec values estimated at the nodes of a spherical coordinate grid which is spaced exactly in the same way intended for A z grids: 5 in longitude,.5 in latitude, covering the whole Earth globe (7373 points). vtec maps are now the input to the optimal determination of A z grid values. To this aim, Ionex data are preliminarily interpolated and re-sampled to obtain additional vtec maps, according to a prescribed sample time of 10 [min]. A single vtec map will originate a (single) A z grid, evaluated at the (fixed) UT = t. The optimization algorithm attempts to determine the effective ionization grid values A z = A z ( m, n ) (m=1,,73, n=1,,73) that, once ingested by NeQuick function N e = N e ( s, t, m, A z ( m, n )), with A z in place of f10.7, allow to best reconstruct the original (input, experimental) vtec map. VII. ACCURACY OF RECONSTRUCTED A Z GRIDS AND NEQUICK MODELING: COMPARING VTEC MAPS A period of high solar activity was selected, within solar cycle 3 ( see Figure 3. ), more precisely: October, 7 th -10 th 00. This interval is also geomagnetically disturbed as indicated by the World Data Center for Geomagnetism, Kyoto. Figure 3. : Solar Cycle #3 Nevertheless, such a period is interesting, as it corresponds to the MIDAN Demo campaign in Middle East (MID) region, a joint initiative of European Commission, ESA, ENAV, and Telespazio, endorsed by the ICAO MID Office. The purpose of MIDAN demonstration was to verify the feasibility of extending SBAS/EGNOS services from the original (ECAC) provision area to the ICAO MID Region. For this reason, essential logistic and technical support was locally provided by the Air Navigation Services Providers/Civil Aviation Administrations of Egypt (NANSC), Bahrein (CAA) and Saudi Arabia (PCA), which hosted three portable RIMS. Static and in-flight measurements were carried out using equipment and aircraft of ENAV, and the support of Telespazio, that performed as well: interconnection of sensor equipment with ESTB, through the Mediterranean Test Bed infrastructure at Fucino Space Centre; provision of uplink to a SBAS GEO payload (Inmarsat IOR); development of data analysis; assistance in presenting results at Fourth Meeting Of The Middle East GNSS Task Force (GNSS TF/4), occurred in Cairo (May 4 th 6 th, 004). For the test dates, RIMS observation data are still available at Telespazio, collected from GPS/SBAS receivers (Novatel Millenium). It seemed a good idea to select the associated

5 ranging measurement data set(s) to assess the validity of presented approach. The AIUB/CODE Ionex format files for the intended period were downloaded 3, and contain global ionosphere maps for DOYs 80,, 83 in 00. To make an example, at UT t = 14:00 of DOY=81, the shape of vtec is shown in Figure 4. On a first trial, the ionospheric effect was compensated according to ICA/Klobuchar model coefficients, which can be retrieved within the public available navigation message Rinex files brdcddd0.0n (with the day of year ddd = 80,,83), a standard IGS product downloadable from NASA CDDIS ftp site 4. After, having reconstructed by NLP the pertinent effective ionization level grids A z = A z (,, t ) every 10 minutes over the whole MIDAN Demo period, NeQuick processing was adopted to implement a feed-forward compensation of the ionospheric effect on code range measurements. Let us consider the case of DOY=81; the ICA/Klobuchar broadcast coefficients reported within Rinex navigation message data file brdc810.0n for such a date are: a 0 = E8 a 1 = E8 a = 1.190E7 a 3 = E8 b 0 = E+5 b 1 = E+4 b =.610E+5 b 3 = E+5 Figure 4. : AIUB/CODE vtec map 14:00) In Figure 6., the resulting (large) 3D positioning error (after ICA/Klobuchar has been applied to compensate for ionospheric effects) is shown; such a 3D error is intended as norm of vector difference between the known, geo-referenced position coordinates of the Cairo RIMS and the outcome of single-frequency positioning algorithm. The processed data slot corresponds to the time period from UT 14:00 onwards (about 3 hours): Figure 6. : 3D error [m], Klobuchar iono model (Cairo RIMS, DOY=81) The same positioning algorithm, using NeQuick ionospheric effect compensation, achieves the results shown in the following Figure 7. Figure 5. : reconstructed vtec map via NeQuick 14:00) The optimization process which drives to the achievement of an effective ionization grid A z = A z (,, t = 14:00) allows to feed NeQuick and reconstruct vtec for the same date and time, obtaining the map shown in Figure 5. VIII. ACCURACY OF RECONSTRUCTED A Z GRIDS AND NEQUICK MODELING: COMPARING POSITIONING SOLUTIONS As already said, for the selected dates, the ranging observables from 3 portable RIMS equipment have been processed, according to a standard single-point positioning algorithm. Figure 7. : 3D error [m], NeQuick iono model (Cairo RIMS, DOY=81) For the sake of a comparison, the positioning equations were also solved without applying any compensation for the ionospheric range error and the results are shown in the following Figure 8. 3 From AIUB site: ftp://ftp.unibe.ch/aiub/code/ 4 ftp://cddis.gsfc.nasa.gov/pub/gps/data/daily/

6 Figure 8. : 3D error [m], no iono mitigation (Cairo RIMS, DOY=81) In order to analyze the model performance at a different geographic location, the observations corresponding to DOY=80 for the RIMS installed at Bahrain have been processed. The results are illustrated in the following Figure 9. and Figure 10. The achieved results demonstrate the concrete possibility of using NeQuick to reproduce real, worldwide ionospheric conditions existing at a defined date, supporting as well a single frequency navigation receiver to achieve a better positioning solution. As a general consideration, NeQuick is especially effective and useful wherever ionosphere has more intense effects and larger perturbing offsets on ranging observables, like it happens at low geographic latitudes. ACKNOWLEDGMENT We take opportunity to thank National Institutions like Italian Space Agency (ASI) and Air Navigation Service Company (ENAV), which funded the Programmes which allowed to accomplish, among other activities, the R&D on NeQuick capability to emulate a defined (real) ionospheric scenario. Figure 9. : 3D error [m], Klobuchar iono model (Bahrain RIMS, DOY=80) Figure 10. : 3D error [m], NeQuick iono model (Bahrain RIMS, DOY=80) CONCLUSIONS The article is based on a sophisticated use of most recent NeQuick algorithm version, adopted to reproduce and mitigate the ionospheric delay on L-band radio-navigation ranging signals. The approach makes use of D worldwide input information on ionospheric status (vtec maps) to estimate D effective ionization level maps that can properly feed NeQuick, which is, in turn a full 3D electron density model. The paper shows first the capability of NeQuick to reconstruct a real vtec map with a high degree of truthfulness, when in challenging ionospheric environmental conditions.then, it demonstrates how the standard single-frequency receiver positioning can be improved, when operating in the same ionospheric situation. Indeed, real data have been processed over a 4-day period, by using the ESTB RIMS observables collected on October 00, during ESA/ENAV MIDAN Demo campaign in Middle East. NeQuick allowed obtaining reliable estimates of stec and a successful compensation for ranging delay iono affecting GPS C/A code measurements, thus significantly mitigating the positioning offset. REFERENCES [1] Klobuchar, J. A.: Ionospheric Effects on GPS. Chap. 1, Pag Global Positioning System: Theory and Applications. Vol 1. Published by the American Institute of Aeronautics and Astronautics, Inc., [] Bilitza, D., Sheikh, N. M., Eyfrig, R.: A global model for the height of the F-peak using M(3000)F values from the CCIR numerical map, Telecomm. J., 46, , [3] Di Giovanni, G., Radicella, S.M.: An Analytical Model of the Electron Density Profile in the Ionosphere, Advances in Space Research, 10, 11, pp. 7-30, [4] Leitinger, R., Radicella, S. M.:, The Evolution of the DGR Approach to Model Electron Density Profiles. Advances in Space Research, 7, 1, pp , 001. [5] Nava, B., P. Coisson, G. Miro Amarante, F. Azpilicueta, S. M. Radicella: A model assisted ionospheric electron density reconstruction method based on VTEC data ingestion. Annals Geophys., 48, , 005. [6] Leitinger, R., Zhang, M., Radicella, S. M.: An improved bottomside for the ionospheric electron density model NeQuick, Annals of Geophysics, Vol. 48, N. 3, 005. [7] Coïsson, P., Radicella, S.M., Leitinger, R., Nava, B.: Topside electron density in IRI and NeQuick: features and limitations, Adv. Space Res., 37. pp , 006. [8] Nava, B., Coïsson, P., Radicella, S. M.: A new version of the NeQuick ionosphere electron density model. Geophysical Research Abstracts, Vol. 9, 007. [9] Gende, M. A., Radicella, S. M., Nava, B., Brunini, C.: Ionospheric Effect in Instantaneous Positioning. ION NTM 003, Anaheim, CA, 003. [10] Radicella, S.M., Nava, B., Coïsson, P.: Ionospheric Models For Gnss Single Frequency Range Delay Corrections. Fisica Della Tierra Pag. 7-39, No. 0, 008. [11] NeQuick 1 software package (Fortran 77 source code) at ITU: [1] ICAO Report of the Fourth Meeting of the Middle East GNSS Task Force (GNSS TF/4) Cairo, 4 6 May 004, Report.pdf [13] Nava, B., S. M. Radicella, R. Leitinger, and P. Coïsson (006), A nearreal-time model-assisted ionosphere electron density retrieval method, Radio Sci., 41, RS6S16, doi:10.109/005rs [14] B. Nava, S.M. Radicella, R. Leitinger, P. Coïsson, "Use or total electron content data to analyze ionosphere electron density gradients", Advances in Space Research, vol. 39 N. 8, , doi: /j.asr , 007