Implementation and impact of second-order ionospheric term in GPS

1. Implementation and impact of second-order ionospheric term in GPS Manuel Hernández-Pajares, J.Miguel Juan, Jaume Sanz, Raul Orus Res. Gr. Astron. Geomatics, gAGE/UPC, Barcelona, Spain

2. Introduction (1 of 2) • The first order ionospheric term (I1) is the main contribution of the GNSS ionospheric refraction (99.9%). • I1 can be removed when considering the carrier phase or the code ionospheric free combinations of dual frequency measurements (Lc and Pc). • However, because of the increasing demand for precise GPS positioning, the study of the impact of the second-order ionospheric term (I2) –up to few cm in range- has become relevant.

3. Introduction (2 of 2) • I2(defined as Lc correction) can be approximated as proportional to the magnetic field projection along the receiver-transmitter direction, and to the slant total electron content (STEC). • The goal of this work is to show how I2 affects to receiver positions and other parameters, complementing and clarifying the conclusions obtained by previous authors (see for instance Kedar et al. [2003] and Fritsche et al. [2005]). • Finally a simple and accurate I2 correction procedure is proposed.

4. I2 effect on Subdaily Differential Positioning Before studying the I2 impact on global geodetic estimation, its effect on a subdaily differential positioning scenario is analyzed, because of: • The subdaily relative variations of the I2 corrections are larger than for longer (daily or seasonal) periods. 2) The differential positioning model is simpler than a global model, allowing to better understand the I2 vs. parameters relationships. 3) In this way it will be easier to show that the I2 effect conclusions are different from the ones reported by previous authors: In particular, on coordinates, it depends on the differential effect, and is smaller (instead of southward displacement from previous works).

5. Subdaily Differential Experiment • This computation has been performed twice: with and without correcting the I2 effect, the effect is obtained from its difference. • The reference receiver clock has been taken as the reference clock and its coordinates have been strongly constrained. • Precise IGS orbits have been used, considering them fixed. • The satellite clocks have been estimated (most part of the regional orbit corrections are similar, captured by sat. clocks). • Finally, the tropospheric delays in the regional network have been slightly constrained to previously computed PPP values. • 6 consecutive days under solar maximum conditions (days 65-70, 2001, Solar.Max., CAYA, MANA, AOML & JAMA -ref.- IGS receivers).

6. I2 effects on subdaily differential estimation Coordinates (north shift of AOML): Small efect (up to ~1mm) and NO significant dependence on I2 at reference stat. The small observed effect depend on the relative I2 value, regarding to the reference station (I2-I2ref). Satellite clock effect: significant (up to +2cm) and dependent on I2 at reference station Carrier phase bias effect: significant (up to +4cm) and dependent on I2 Coordinates: A negative I2-I2ref produces an increase of range, and a corresponding increase of north (instead of southward) and up component, up to 1mm, in a northern hemisphere station.

7. I2 effect on Global Estimation • The global estimations have been derived from I2 pseudomeasurements taken as observations in an straightforward way suitable for extending the computations. • Among receiver positions and satellite clocks, satellite orbits are also estimated. • The distribution of receivers is a key point in the I2 effect on the geodetic estimations (dependence on I2 differences): A worldwide distribution of receivers as close as possible to a uniform one has been selected. • We are going to focus on the main points of the global study, taking in mind the above summarized results in differential scenario.

8. Mean I2 effect on receiver positions (21 months, 2002 -03) Results are not equivalent to those obtained by previous authors: Among I2 processing complete for all the geodetic parameters, more realistic magnetic field model (see below) and more homogeneous distribution of receivers are some of the hints to explain this. Receiver position effect: Confirming previous results with differential scenario, the dependence on the difference of I2 values wrt neighbour receivers, producing long term effects at mm level and few tenths of mm for daily repeatibility effect.

9. Subdaily residual I2 effect on satellite orbits and clocks (averaged on year 2003) BIAS STD.DEV. NORTH EAST RADIAL CLOCKS Confirming importance of I2 effect on satellite clocks and orbits (up to 1 cm and several mm, latitudinal signatures)

10. I2 effect on Satellite Orbit estimation The overall I2 effect (orbit displacement + dynamical integration) produces a general southward averaged displacement of the orbits of several millimeters. It is correlated with the Global Electron Content (GEC, VTEC integrated along the overall Ionosphere, computations from 2002.3 to 2004). Such displacements are in agreement with the geocenter estimated by Fritsche et al. [2005].

11. A simple and accurate approach to compute and apply the I2 correction: STEC & B terms DCB-corrected smoothed pseudorange (PROPOSED) Aligned ionospheric carrier phase (TRUTH) IONEX-map-derived STEC The Slant Total Electron Content, STEC, can be computed in a simple and accurate-enough way, from geometry-free combination of pseudoranges (PI≡P4), after removing previously estimated interfrequency bias values (quite stable on time). This approach is not affected by the single-layer accuracy limitations in VTEC IONEX format. The Magnetic Field term, B, is computed by using a more realistic model than the dipolar one: the International Geomagnetic Reference model (IGRM), reducing the error up to 60%.

12. Conclusions (1 of 2) • The second order ionospheric effect (I2) and its impact over the GNSS parameter deviations have been presented and discussed in a quantitative and qualitative way. • The I2 effect is mainly captured by the satellite-dependent parameters (orbits and clocks). • The effect on the receiver-dependent parameters is clearly small because they are only affected by the differential value of the I2 effect. • The most affected parameter is the satellite clock, which can show deviations greater than 1 cm (comparable with the accuracy of the Final IGS products). • Satellite positions are affected by a global southward displacement of the orbits of several millimeters, related to the ionization degree of the ionosphere (overall effect of the order of the final IGS orbit accuracy).

13. Conclusions (2 of 2) • The I2 impact on receiver positions (differential dependence) is usually smaller than 1 mm (high latitude receivers would be shifted northwards while the low latitude ones would be moved southwards). • A new way of computing the I2 effect (easier and more accurate) has been presented, improving the correction up to 60%. • The authors of this work think that I2 effect should be taken into account in routinely GNSS geodetic computations because: (1) the contribution of the I2 effect is not negligible (several centimeters in range), (2), the algorithms presented in this work are easy to implement. And (3) the I2 effect on satellites clocks and orbits is significant and should be taken into account to improve its accuracy. THANK YOU! Many more details can be found in: Hernández-Pajares, M., J.M.Juan, J.Sanz and R.Orús, Second-order ionospheric term in GPS: Implementation and impact on geodetic estimates, JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, B08417, doi:10.1029/2006JB004707, 2007

14. References • Afraimovich, E. L., E. I. Astafyeva, and I. V. Zhivetiev (2006), Solar activity and global electron content, Dokl. Earth Sci., 6, 921–924, doi:10.1134/S1028334X06060195. • Bassiri, S., and G. Hajj (1993), High-order ionospheric effects on the global positioning system observables and means of modeling them, Manuscr. Geod., 18, 280– 289. • Fritsche, M., R. Dietrich, C. Kno¨ fel, A. Ru¨ lke, S. Vey, M. Rothacher, and P. Steigenberger (2005), Impact of higher-order ionospheric terms on GPS estimates, Geophys. Res. Lett., 32, L23311, doi:10.1029/2005GL024342. • Hernández-Pajares, M. (2004), Ionosphere IGS WG position paper, paper presented at the IGS Technical Meeting, Bern, Switzerland. • Hernández-Pajares, M., J.M.Juan, J.Sanz and R.Orús, Second-order ionospheric term in GPS: Implementation and impact on geodetic estimates, JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, B08417, doi:10.1029/2006JB004707, 2007 • Kedar, S., G. A. Hajj, B. D. Wilson, and M. B. Heflin (2003), The effect of the second order GPS ionospheric correction on receiver positions, Geophys. Res. Lett., 30(16), 1829, doi:10.1029/2003GL017639. • Klobuchar, J. A. (1978), Ionospheric Effects on Satellite Navigation and Air Traffic Control Systems, AGARD Lect. Ser., vol. 93, Advisory Group for Aerospace Res. and Dev., North Atlantic Treaty Org., Brussels. • Lanyi, G. E., and T. Roth (1988), A comparison of mapped and measured total ionospheric electron content using global positioning system and beacon satellite observations, Radio Sci., 23(4), 483– 492. • Mannucci, A. J., B. D. Wilson, D. N. Yuan, C. H. Ho, U. J. Lindquister, and T. F. Runge (1998), A global mapping technique for GPS-derived ionospheric total electron content measurements, Radio Sci., 33, 565– 582. • Steigenberger, P., M. Rothacher, R. Dietrich, M. Fritsche, A. Rulke, and S. Vey (2006), Reprocessing of a global GPS network, J. Geophys. Res., 111, B05402, doi:10.1029/2005JB003747. • Tsyganenko, N. A. (2003), A set of FORTRAN subroutines for computations of the geomagnetic field in the Earth’s magnetosphere (Geopack), Univ. Space Res. Assoc., Columbia, Md. • Zumberge, J. F., M. B. Heflin, D. C. Jefferson, M. M. Watkins, and F. H. Webb (1997), Precise point positioning for the efficient and robust analysis of GPS data from large networks, J. Geophys. Res., 102, 5005– 5017.

15. BACKUP SLIDES

16. Goals • To characterize the main errors in different geodetic parameters when I2 is neglected. • To show an efficient procedure of second order iono correction (I2). Layout • Introduction • I2 effect on Subdaily Differential Positioning • I2 effect on Global Estimation • A simple and accurate approach to correct I2. • Conclusions

17. I2 effect on Satellite Orbit estimation • As I2 is proportional to the magnetic field (B) projection along the receiver-transmitter direction, the range from northern fiducials stations is shortened (-) compared with the southern ones (+). • This produce a northwardshifting of the satellite positions (specially on daylight high-latitude observations). • The dynamical integration produces a general southward averaged displacement of the orbits, correlated with the Global Electron Content (GEC, VTEC integrated along the overall Ionosphere, computations from 2002.3 to 2004).

18. Daily I2 effect on receiver positions (21 months, 2002 -03) Receiver position effect: Although the shift of the coordinates can reach up to more than one millimeter (see previous slides), the corresponding effect on coordinates repeatibility is smaller, with typical Standard Deviations of few tenths of millimeter.

19. A simple and accurate approach to compute and apply the I2 correction: Magnetic field term The Magnetic Field term, B, is computed by using a more realistic model than the dipolar one: the International Geomagnetic Reference model (IGRM), reducing the error up to 60% regarding the previously used dipolar model (this is specially evident at the Atlantic South Anomaly -see relative error of dipolar model at left hand plot, and comparison of I2 corrections in Ascension Island, ASC1, at right hand plot-).