Extension of EGNOS Ionospheric Correction Coverage Area
Anna SWIATEK, Iwona STANISLAWSKA, Zbigniew ZBYSZYNSKI, and Beata DZIAK-JANKOWSKA
Space Research Centre, Polish Academy of Sciences, Warszawa, Poland e-mail: [email protected]
A b s t r a c t
Ionosphere coverage is likely to be a driver for the EGNOS cover-age area. Hence, a study considering a dedicated ionosphere algorithm to improve the ionosphere coverage area has been conducted. The logic of the study is the following: the accuracy of the GPS signal depends mainly on the total electron content (TEC). At two close points, TEC changes in time in a very similar way; these are region dependent vari-ables. This correlation decreases with growing distance between the ob-servation points and is anisotropic. Based on TEC variogram analysis, the specific algorithm has been developed. This specific algorithm is pre-sented and discussed.
Key words: GNSS, EGNOS, ionospheric coorections.
1. INTRODUCTION European Geostationary Navigation Overlay System (EGNOS) corrections are distributed over Europe. Their usefulness and adequacy for real condi-tions is not unified within the whole area. The existing infrastructure saves the correction accuracy for a limited area only. At the periphery, the propri-ety of EGNOS corrections is questionable. There is a need to extend the area of applicability of proper correction. The prepared investigations showed that using a statistical method of semivariogram calculations it is possible to extend the ionospheric corrections with satisfying accuracy.
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Statistical averages of maps of medians yield values of a considered pa-rameter at a given point within the studied area. These parameters signifi-cantly differ from the actual measurement. Therefore, such a map can contain significantly inadequate amounts of information. More information can be found on a map constructed on data collected in real time.
Practically every kind of mapping is imperfect and can generate signifi-cant errors, especially within areas inadequately covered by data. Sometimes this can lead to numerical instability in the mapping procedure and to big discrepancies in certain places between the result obtained from the map and the actual value.
If the variability of measured parameters, such as ionospheric character-istics or total electron content (TEC), for instance, is a result of deterministic physical processes, then it should show predictable regularities. Such expec-tations find their expression in the constructed maps. One can say that the map is correctly constructed if the graphic image of a function has been elaborated and it facilitates the definition of values at evenly distributed grid points, or that a function that describes isolines, lines of the constant value of the dependent variable (z) projected onto the surface of two independent var-iables x and y is being formulated. Data used are either a finite number of values of the dependent variable (zi) at given points (xi, yi) or the mathemati-cal expressions binding z, x, and y. The methods used for data description are the so-called weighing techniques, finite differences or equipotential points. As a mapping result we thus obtain not a real map, but an intentional image resulting from the adopted principles of interpretation, as the form of the function z(x, y) is unknown. What is known are only its values at identifica-tion points, i.e., where measurement of a given parameter has been made. Between these points the function values must be interpolated.
We are using some statistical information based on the geostatic kriging method with the variogram determined for particular circumstances. It re-quires extraction of some regular features, the so-called local drifts (short-range deterministic variation). The NeQuick_2_0_1 model (Radicella 2009) has been applied. The NeQuick_2_0_1 model does not describe stormy con-ditions and any specific phenomena, as scintilations for instance. It gives the “averaged” behavior of TEC which is its advantage when used in the pre-sented statistical elaborations. So, the NeQuick model is used to extract the regular part of instantaneous TEC values.
GPS NeQuick2_0_1TEC = TEC TEC .Δ −
2. MODELING THE VARIOGRAM Kriging as a statistical method based on the characteristic variability demon-strated by the variogram, i.e., a function that summarizes the differentiation
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of a given parameter value depending on a distance between different meas-urements. It contains magnitude and spatial scale variability. The value at a studied point situated between measurement points is interpolated by giv-ing it appropriate weight. This weight depends on a distance (d) between a measurement and the requested point and on the degree of correlation with variations measured nearby; it is determined by the variogram. The precision of the estimated variogram depends on the size of data sample and its spatial distribution. If the variogram or semivariogram is anisotropic, we can intro-duce, for instance, the scaling factor (SF) into the distance, as it has been done for COST 251 instantaneous mapping model PLES (PL for Poland, ES for Spain). The anisotropy of a variogram means that it is systematically dif-ferent depending on concerned geographical azimuths, as it is in the case of geographically described ionospheric or plasmaspheric parameters, as well as on parameters depending upon the magnetic field, such as almost all mag-netospheric and solar wind parameters. In the ionospheric case, the scaling factor SF is introduced before the interpolation procedure is applied. SF is taken as the ratio of the length of the E-W and S-N axes of the correlation el-lipse. It results from the placement of a fixed value of the correlation coeffi-cient along the directions defined by the mutual situation of individual data. This coefficient is different in different map areas, and it also changes with variation in geophysical activity.
Let us assume that there is no information about any regularity in varia-bility of the parameter, so the available measurements can be treated as ran-dom variables. It can therefore be assumed that these are regionalized variables dependent on the location of the observation point. Frequently, the values of characteristics observed at points not far from one another are mu-tually correlated, but as their separation increases this correlation decreases. Statistical description is based on the publication (Webster and Oliver 2001).
Information on the variability of a given parameter u over a distance d between measurement points is described by the quantity γ, known as the semivariance at lag d. The “semi” refers to the fact that it is half of a vari-ance: it is half the variance of a difference in this instance; the variance per point when the points are considered in pairs. So γ as a function of d is the semivariogram, usually termed simply the variogram. It is determined by se-lecting successive pairs of values at locations i and i + d:
( )2
1
1( ) ,2
N
u i i di
d u uN
γ′
+=
= −′∑
where N' is the number of such pairs of values selected. In this indirect manner, the variogram characterizes the autocorrelation
between observations:
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( )2( ) 1 ( ) ,u ud dγ σ ρ= −
where σ2 is the variance, and ρ is the correlation coefficient. An instantaneous experimental variogram based on ΔTEC data obtained
from GPS and NeQuick model from a given moment in time (± 1 hour) col-lected under similar geophysical conditions in a selected area provides a variogram. Slant differences are reconstructed to the vertical data. This variogram is anisotropic, so that a set of relations is determined for regions defined by the correlation distance within the central EGNOS area with the directions preliminarily established for about 60°.
The variogram provides a set of equations in which weights may be evaluated in association with the individual N data points. It allows to deter-mine points from the outside of EGNOS area with higher accuracy.
3. DATA USED EGNOS, as an augmentation system helps to improve the navigation posi-tion from about 5 meters to less than 2 metres. It provides information con-taining errors in the position measurements and informs the users about disruptions of satellite signal. The system consists of three segments: Rang-ing and Integrity Monitoring Stations (RIMS) which observe and collect GNSS signal and send it to the Master Control Centres (MCC) which deter-mine the accuracy of GPS and GLONASS signals and determine the position inaccuracies due to disturbances in the ionosphere. Then the computed cor-rections are Up-Linked to the geostationary satellites, which then transmit it for reception by GPS users with an EGNOS enabled receiver.
The EGNOS signal is encoded according to the Radio Technical Com-mission for Aeronautics (RTCA) in DO-229D document (RTCA 2006).
Thanks to ESA service called EGNOS Message Server (EMS), all EGNOS messages are stored and accessible free-of-charge, using standard means (specifically, the FTP protocol). EMS stores the augmentation mes-sages broadcasted by EGNOS in hourly text files. The EGNOS messages can be used in other applications.
In the project the data for further analysis was taken from EMS and de-coded to the simpler form containing only the most important information.
For our purpose, the EGNOS messages nos. 18 and 26 are used. The first of them contains the ionospheric grid point marks – the encoded position of grid point for which the ionospheric corrections are sent. The grid points are located in different degree-distance according to the latitude. For the mid-latitude it is 5 degrees and for high-latitude it is from 10 to 30 degrees. Mes-sage no. 26 contains the ionospheric delay corrections together with their er-rors. The data is presented in increments of 0.125 of unit.
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The output file contains the information about the time of correction, grid point co-ordinates and value of ionospheric delay together with its error and TEC value.
The ionospheric delay and TEC combines the simple dependence:
2
40.3 TEC ,Idf
=
where Id is the ionospheric delay, f is the frequency of signal, and TEC is the total electron content.
Correlation distance has been obtained from the variogram calculations. Its maximum value applied for the procedure is determined by the worst cas-es anticipated for high stormy conditions during October 2003 and Novem-ber 2004. For comparison, 27 full days (24 hours) of EGNOS messages randomly chosen from years 2006-2010 were taken. Half of these selected days are disturbed, half quiet. The full list is presented in Table 1. Also, an additional condition has been taken into account: the EGNOS messages should be complete, especially for the regions close to the east border. This drastically decreases the potential files disturbed conditions.
Table 1 The list of selected quiet and disturbed days
Quiet days Disturbed days
Date DOY Ap Date DOY Ap 22 May 2007 142 13 14 Apr 2006 104 65
9 Oct 2007 282 1 14 Dec 2006 348 47 10 Oct 2007 283 1 15 Dec 2006 349 94 12 Sep 2008 225 1 23 May 2007 143 34 13 Sep 2008 226 0 29 Feb 2008 060 31 23 Jul 2009 204 7 1 Mar 2008 061 22
31 Aug 2009 243 5 22 Jul 2009 203 24 5 Jan 2010 005 1 30 Aug 2009 242 20 6 Jan 2010 006 1 5 Apr 2010 095 55 7 Jan 2010 007 0 6 Apr 2010 096 44 8 Jan 2010 008 1 29 May 2010 149 28 9 Jan 2010 009 1 30 May 2010 150 21
10 Jan 2010 010 3 14 May 2010 134 3 15 May 2010 135 2
Explanations: DOY – Day of Year number, Ap index – measure of the general level of geomagnetic activity over the globe for a given day.
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Variogram calculations were provided for different magnetic/ionospheric conditions separately. Quiet conditions have been considered for geomagnet-ic index Ap ≤ 15 and disturbed for Ap > 15 (Stanislawska et al. 2004). Cor-relation distance determined from the semivariogram for quiet conditions is about 1250 km. For estimation at extremely disturbed conditions, events on 28 October 2003 and 8 November 2004 have been taken into account
Fig. 1. An example of variogram for quiet conditions: (a) linear presentation, and (b) logarithmic. Crosses are averaged data, lines – fitted data, yellow − full data set, red – filtrated data set, and green crosses – data created artificially by the procedure. Colour version of this figure is available in electronic edition only.
(a)
(b)
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(Trichtchenko et al. 2007). Correlation distance for these events decreased to about 800 km. Usually, much more probable results may be obtained while eliminating extreme cases concerning spatial distribution of data and their reliability. Particularly, in this case variations greater than double averaged values have been eliminated. For such selected data set for quiet as well as for disturbed conditions, the correlation distance is decreased to about 750 km including the most disturbed cases as of October 2003 and Novem-ber 2004. Even for such extreme conditions, the distance is not expected to decrease drastically comparing to the averaged situation.
The variogram is calculated on the basis of instantaneous data as shown at the presented example in Fig. 1.
Global IGS maps generated post factum were taken for comparison (IGS products, final and rapid ionospheric TEC grid, ftp://cddis.gsfc.nasa.gov/ pub/gps/product/ionex/). It has to be noted that IGS maps are global and are constructed on more reach database but they with 2- or 11-day time delay, while the idea of EGNOS maps extension is the case of instantaneous crea-tion.
4. DESCRIPTION OF THE PROCEDURE FOR THE EXTENSION OF INFORMATION TO THE EAST OF THE EGNOS AREA
The procedure is based on the mapping data from the EGNOS nodes de-scribed in the previous section and calculated variogram. PLES mapping model has been applied (Stanislawska et al. 2000, Stanislawska and Roth-kaehl 2002). It is based on a kriging instantaneous mapping procedure. The model has been improved according to the variogram interpretation (Stanislawska et al. 2002).
The above-mentioned issue contains the proof that according to the pro-cedure it is possible to recreate values deleted from the data set with suffi-cient accuracy. If the data situated at the border, which was deleted from the input, is recreated according to the procedure with required accuracy, we may conclude that based on the full data set (including earlier deleted val-ues) we may extend the area for a certain distance with the same accuracy. During the next step, the full data set has been taken to construct additional points at the East within the correlation distance determined by the instanta-neous variogram.
All the values from the EGNOS nodes available in the considered mo-ment are used for statistical analysis and to construct the instant variogram. It allows to create additional values within the EGNOS area but also at the border of the area and outside. Proper results can be obtained at a distance from the edge-most nodes where the variance reaches its maximum. In our case, it is about 750 km. Such an approach ensures a continuity of original and recreated data values.
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5. ACCURACY AND RELIABILITY OF THE RESULTS The comparisons were carried out for ∆TEC values at the east border of EGNOS area synthesized from EGNOS messages and IGS global maps val-ues. The RMS error has been calculated for quiet and disturbed conditions separately.
Quality of the procedure is checked in the algorithm when for instanta-neous variogram construction of X number of rows of the easternmost nodes is excluded. X is determined by the correlation distance. In this case, X means 2 rows. The correctness of applied procedure is shown by comparison how the excluded nodes can be recreated. Figures 2-5 present the examples of maps created by means of the elaborated procedure. They are presented together with IGS and EGNOS models maps.
Fig. 2. 5 January 2010 (quiet conditions): left − IGS TEC data, right − EGNOS TEC data. Colour version of this figure is available in electronic edition only.
Fig. 3. 14 April 2006 (disturbed conditions): left − IGS TEC data, right − EGNOS TEC data. Colour version of this figure is available in electronic edition only.
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Fig. 4. 5 January 2010 (disturbed conditions): left – NeQuick model (background for variogram calculation), right − TEC deviations (EGNOS-NeQuick). Colour version of this figure is available in electronic edition only.
Fig. 5. 14 April 2006 (disturbed conditions): left − NeQuick model (background for variogram calculation), right − TEC deviations (EGNOS-NeQuick). Colour version of this figure is available in electronic edition only.
In Table 2, the root mean square error (RMS) difference is presented, where VCURR are data recreated according to the current procedure, EGNOS are the data from the EGNOS nodes, and IGS the data from the IGS maps. The last are available every 2 hours, so they are linearly interpolated for the EGNOS messages moment.
Table 2 RMS difference between current procedure VCURR, EGNOS data (EGNOS),
and IGS (data from the global IGS maps) in TEC units
The results do not depend on time of the day and time of the season. The dependence is shown for magnetic activity. However, the accuracy achieved suggests that except of very high activity as of October 2003 and November 2004, for every moment the EGNOS maps can be extended for 2 rows to the east within the accuracy of the measurement.
The method reproduces 2 rows of EGNOS nodes within the accuracy greater than the accuracy of the “measurement”, in our case, the accuracy of EGNOS and IGS grid values. Local variability of TEC and random errors of measured parameters are much greater than those created by the TEC’s semivariograms (intersection of the variogram with the vertical axis).
6. CONCLUSIONS The presented method allows extending EGNOS area for about 750 km to the east and west during magnetically quiet as well as disturbed conditions with the accuracy below the accuracy of the measurement, also during ex-tremely high geomagnetic disturbances. However, current procedure is pre-pared for the 2 rows extension to the east.
Including data from one of the nearest RIMS site (piers points of the vis-ible GPS satellites) to the procedure allows increasing the accuracy in near-real-time (before the next sequence of the EGNOS information).
Additionally including data from the outside of the EGNOS area to the procedure might makes it possible to construct the higher-accuracy maps.
The procedure has been optimized for application in instant moment af-ter EGNOS message arrived; the results for additional 2 rows at the east from the instantaneous EGNOS nodes appeared 2 min after every message. Thus, the procedure can be used to every EGNOS message in near-real time. Practically it means that it yields a value in every node distant for 2 rows from the edge-most data existent in the current EGNOS message.
Acknowledgmen t s . The work has been partly supported by FP7 pro-ject: EGNOS Extension to Eastern Europe (EEGS), Grant agreement No. 247698.
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Received 20 November 2012 Accepted 5 February 2013
