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

• 6 consecutive days under solar maximum conditions
  (days 65-70, 2001, Solar.Max., CAYA, MANA, AOML
  JAMA -ref.- IGS receivers).

• 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
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
(PIP4), 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, doi10.1029/2006JB004707, 2007
14
References

• Afraimovich, E. L., E. I. Astafyeva, and I. V.
  Zhivetiev (2006), Solar activity and global
  electron content, Dokl. Earth Sci., 6, 921924,
  doi10.1134/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, doi10.1029/2005GL024342.
• 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, doi10.1029/2006JB004707, 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,
  doi10.1029/2003GL017639.
• 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, doi10.1029/2005JB003747.
• Tsyganenko, N. A. (2003), A set of FORTRAN
  subroutines for computations of the geomagnetic
  field in the Earths 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 northward shifting 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-).