A New Method to Model the Ionosphere across Local by ihd16607

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									Advanced Ionospheric Modeling

              Peter Kolb
           Trimble Terrasat

         GPSNet User Seminar
            May 30, 2006
 Outline

• Origin and phenomenology of the ionosphere
• Effect of the ionosphere on GPS signals
• Effect of the ionosphere on network solutions
• Formulation of the ionospheric model
• Model results
  – State of the ionosphere
  – Ambiguity resolution
• Summary
The origin of the ionosphere
                     schematic, not to scale




     Ionization of
      molecules
Electron density as function of altitude
 A typical output of the International Reference Ionosphere
(combination of measurement and sophisticated modeling)
  D. Bilitza, International Reference Ionosphere 2000, Radio Science 2 (26) 2000
                http://nssdc.gsfc.nasa.gov/space/model/ionos/iri.html



                                                                Strongly
                                                                peaked at
                                                                a particular
                                                                altitude




  Integrated value: Vertical TEC (VTEC)
      The origin of the ionosphere
• Gravity keeps gas molecules in the vicinity of
  earth's surface, forming the atmosphere
• Radiation from the sun ionizes a small fraction
  of the gases, forming a dispersive medium, the
  ionosphere
• Ionosphere experiences disturbances
  depending on
  –   solar activity (11 year solar cycle)
  –   geomagnetic disturbances, solar winds
  –   geographic location of the sun relative to earth
  –   air currents (winds) in the upper layers of the
      atmosphere
                                                     11 year solar cycle,
                                                     observed number of sunspots




http://science.nasa.gov/ssl/pad/solar/sunspots.htm
             11 year solar cycle,
             predicted number of sunspots


                                                         rough
                                                         times
                                                         are
                                                         coming
                                                         up soon
                                                         again




http://science.nasa.gov/ssl/pad/solar/sunspots.htm   http://sidc.oma.be
A global VTEC map, calm ionosphere
           ESA Ionospheric Monitoring Facility
        http://nng.esoc.esa.de/gps/ionmon.html




  Vertical Total Electron Content on a global map,
  as derived from GPS base station observations
A global VTEC map, active ionosphere
   Center for Orbit Determination in Europe (CODE)
       http://www.aiub.unibe.ch/ionosphere

    Geographic latitude (degrees)     CODE’S GLOBAL IONOSPHERE MAPS FOR DAY 280,2005
   -60    -30    0     30     60




                                                                                    14:00
                                                                                    06:00
                                                                                    02:00
                                                                                    08:00
                                                                                    18:00
                                                                                    22:00
                                                                                    24:00
                                                                                    20:00
                                                                                    16:00
                                                                                    10:00
                                                                                    00:00
                                                                                    04:00
                                                                                    12:00
                                    -180 -135   -90   -45      0     45      90     135    180
                                                  Geographic longitude (degrees)

                                     0     10     20      30    40    50       60     70
                                                           TEC (TECU)
Complex dynamical behavior also on
small scales
      DLR Institute for Communications and Navigation
N. Jagowski, S. Schlüter, A. Jungstand, http://www.kn.nz.dlr.de


                70
       Latitude (degrees)




                                                                  30
                    60




                                                                             20
                                                                           -2)
          50




                                                                    TEC (m
                                                                  10
                40




                                                                  0
                   -20      -10    0       10      20   30   40
                                  Longitude (degrees)


Vertical Total Electron Content over Europe Oct. 7 2005 ,
     as derived from GPS base station observations.
         Effects of charged gas on radio signals
                                      schematic, not to scale
Sender                                           Receiver
                        charged gas

         Phase signal




         Code signal
Effects of ionosphere on GPS signals
 • Between satellite and rover
   – the number of phase cycles decreases (phase
     velocity increases)
   – the number of code chips increases (code velocity
     decreases)
   – by the same amount if expressed in units of length

 • Magnitude of the effect is
   – proportional to the density of electrons integrated
     over the path of signal propagation (total electron
     content - TEC)
   – proportional to the square of the carrier wavelength
     (dispersive medium): Great tool for multi-frequency
     signals
A case study: BLVA-network




              49.2 km


                        74.9 km
           Electron density, ionospheric layer, pierce points
           and mapping function

Electron
density
(cm-3)
 Enhancement of 'seen'
 electron density along the
 propagation path:
 mapping function m
IRI -
2001                 φ
                         λ
Modeling gradients of the ionosphere
Taylor expansion of Ionospheric effect across
the network projection to the ionosphere



Gradients




            φ
                λ
Modeling gradients of the ionosphere
Taylor expansion of Ionospheric effect across
the network projection to the ionosphere



Gradients




            φ
                λ
Piercepoint geometry
and dynamical evolution
pierce point coordinates in geocentric coordinates
            during a period of 6 hours
   Latitude (degrees)




                                                 20 minutes
                                                 between
                                                 frames
                           Longitude (degrees)
Piercepoint geometry
and dynamcial evolution
 pierce point coordinates in solar centered coordinates
             throughout the course of a day




                                                     http://www.aiub.unibe.ch/ionosphere
                                                        TEC values obtained from CODE
     Latitude (degrees)




                               Longitude (degrees)
                2 frequency phase measurement
                and state variables
                             ionospheric      multipath                measurement
distance traveled
                           phase advance     contribution             and model error
    by signal


              wavelength x         tropospheric               clock offset,
           (phase + int. amb.)         delay                user and satellite




           using                           and forming difference for




          measurement                        state variables
                                                                                   model error
                                     (Ambiguity, Multipath, Ionosphere)          + system noise
    Kalman filter – part 1:
    Observation equation


Observation,                              measurements
measurement                               from N stations


State
vector         N ambiguities   N multipaths     3 parameters
                N stations      N stations      1 ionosphere



Design
matrix

                                  mapping relative distance to
                                  function reference piercepoint
           Kalman filter – part 2:
           Time update

         estimated state for next epoch             state of current epoch
State
vector


Time
update                                                                        Motion of
matrix                                                                        reference
                                                                              point


                                          Parameters of the calculation
System
                                          Same set of parameters applied
noise                                     for all networks around the globe
                  Components of the state vector



          ambiguity (meters)                   multipath (centimeters)                     ionosphere parameters
6.0                                       5                                          2.5
                                         1.0
                                          4
5.8                                                                                  2.0
                                          3
5.6                                      0.5
                                          2                                          1.5
                                          1                                          1.0
5.4
                                          0
                                         0.0
5.2                                      -1                                          0.5

5.0                                      -2                                            0
                                        -0.5
                                         -3                      Japan, day 1
4.8                                                              Japan, day 2           -0.5
                                          -4
                                        -1.0                     (shifted by 4 minutes)
 12:30                                    6000
                                    15:00 12:30   8000   10000                      16000
                                                                  12000 14000 15:00 12:30                               15:00

          differences between                       correlated
                                                     uncorrelated                              activity of ionosphere
         ambiguities are constant                           days
                                                   between stations                              about to decline

                               Use double differences together with code measurement
                               and tropo model to resolve the ambiguity (FAMCAR)
Ionospheric state parameters
from the bavarian sub network
                                                CODE TEC Map (schematic)




                           Latitude (degrees)




                                                                             Observation data: BLVA Day 068, 2002
         local time (h)                                Longitude (degrees)




          local time (h)                                  local time (h)
Ionospheric state parameters
from a Japanese network
                                                CODE TEC Map (schematic)




                           Latitude (degrees)




                                                                             Observation data: GSI Day 019, 2002
         local time (h)                                Longitude (degrees)




          local time (h)                                  local time (h)
Contributions of first
and second order correction terms
Typical orders of magnitude for first and second order derivatives

linear terms      O(aλ ) ~ O(aϕ ) ~ 1 x 10-6 = 1 mm / km

second order      O(aλλ ) ~ O(aλϕ ) ~ O(aϕϕ ) ~ 1 x 10-12 m-1


Network with extensions    O(Δλ) ~ O(Δϕ) ~ 100 km

The corrections of the individual terms to the Ionospheric value is thus


linear terms      O(aλ Δλ) ~ O(aϕ Δϕ) ~ 10 cm

second order      O(1/2 aλλ Δλ2) ~ O(aλϕ Δλ Δϕ) ~ O(1/2 aϕϕ Δϕ2) ~ 1 cm

 Depending on your application, higher order terms need
 to be taken care of, or can be neglected
Application of the model in neworking
software, ambiguity resolution
                       Tracked satellites and fixed satellites                                 Number of unfixed satellites
                       10                                                                 10
                                                                                                                   Zeroth order
number of satellites




                                                                   number of satellites
                        8                                                                  8

                        6                                                                  6
                                                                                                                   homogene
                        4                                                                  4

                        2                                                                  2
                                            Zeroth order
                        9:00      12:00      15:00         18:00                           9:00      12:00         15:00      18:00

                       10                                                                 10




                                                                   number of satellites
number of satellites




                                                                                                                     First order
                        8                                                                  8

                        6                                                                  6

                        4                                                                  4

                        2                                                                  2
                                               First order
                         9:00      12:00     15:00         18:00                           9:00       12:00        15:00      18:00
                                                local time                                            local time
     Resolving ambiguities
     with different orders of approximation
     Japanese network (GSI):                         homogeneous Iono:      96.68 %
     7 stations                                      first order Iono:      97.73 %
     70 km x 60 km                                   second order:          97.58 %

     Swiss network (Swisstopo): homogeneous Iono:                           98.11 %
     29 stations                first order Iono:                           98.52 %
     310 km x 210 km            second order:                               98.57 %

     German network (ASCOS):                         homogeneous Iono:      98.03 %
     28 stations                                     first order Iono:      99.29 %
     250 km x 350 km                                 second order:          99.29 %
                     3 .5
unfixed percentage




                       3

                     2 .5                                                ho mo ge ne o us Io no
                       2
                                                                         f irs t o rde r Io no
                     1.5

                        1                                                s e co nd o rder

                     0 .5

                       0                                             (smaller is better)
                            Japa n   S wissto po   A SC OS   B LVA
Summary

   Model ionospheric phase advance in terms of
   Taylor series to the desired order across local
   area network


   Extract ionospheric parameters, multipath and
   doubly differenced ambiguities by means of a
   Kalman filter


   Obtain increased fixing performance and
   reliability for small to intermediate network sizes
   together with a physical picture of the evolution
   of the ionosphere
EXTRAS
              Mapping function on the curved surface
                                                                                          schematic, not to scale
             Some trigonometry
             leads to
                                                                3.5
                          1
             m=




                                           mapping function m
                                       2
                     ⎛ RE          ⎞                             3

                     ⎜ R + h cos ϕ ⎟
                  1− ⎜             ⎟
                     ⎝ E           ⎠                            2.5



                  ϕ'
                                                                 2


                                                                1.5
h
         ϕ                                                       1

                                                                      0   10   20   30   40   50   60   70   80   90
    RE                                                                              elevation angle
Illustration of PP Dynamics




                                  PP
                        RS

                                       RE

                              RE +h
http://sidc.oma.be




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