Slajd kinematic by nikeborome

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									  Real-time Kinematic GPS Positioning
Supported by Predicted Ionosphere Model


          P. Wielgosz and A. Krankowski
     University of Warmia and Mazury in Olsztyn, Poland
                 pawel.wielgosz@uwm.edu.pl




                   IGS AC Workshop
               Miami Beach, June 2-6, 2008
                  Outline

   Research objectives

   ARMA method

   RTK positioning model

   Experiment design

   Test results and analysis

   Conclusion
          Research Objectives

   Develop and evaluate methodology and algorithms
    for OTF-RTK positioning technique suitable for
    medium and long ranges 10-100 km

   Test applicability of predicted ionosphere models to
    support medium range OTF-RTK positioning

   Evaluate prediction model based on ARMA method

   Study the impact of the model accuracy on the
    ambiguity resolution (speed and reliability)
    Methodology – ARMA prediction of
         real-valued time series

Let yt for t =1, 2, …. , n be an equidistant stationary stochastic time series and y t+1 be
the prediction at time t+1. The autoregressive-moving average process ARMA(p,q) is
defined by the formula:              p               q
                             yt   i yt i  i  t i
                                    i 1           i 0

where: i are autoregressive coefficients, i are the moving average coefficients,
p and q are the autoregressive and moving average orders, i is a white noise process

After introducing the backshift operator BK the process can be converted to :

                                     B
                              yt         t   B t                 B K yt  yt  k
                                     B
      Methodology – ARMA prediction of
           real-valued time series

                     The ARMA forecast L steps ahead

                        
                                   B   yt
                        yt  L    L  
                                   B   B 

       B  
       L        - the part of the operator containing only nonnegative powers of B
       B 




* 10 previous days of the TEC values were taken for the prediction computation
     Methodology – ARMA prediction of
          real-valued time series

           Our previous studies showed that the TEC
            prediction for 1- to 3 hours ahead yields values
            very close to real, observed TEC (under quiet to
            moderate geomagnetic conditions)
           After 3 hours the quality of the forecast diminishes
            very quickly
           ARMA forecasting method is very simple and does
            not need any a-priori information about the process
            nor additional inputs such as, e.g., solar or
            geomagnetic activity indices


Reference:
  Krankowski A., Kosek W., Baran L.W., Popiński W., 2005, Wavelet analysis and
  forecasting of VTEC obtained with GPS observations over European latitudes, Journal of
  Atmospheric and Solar-Terrestrial Physics, 67 (2005), pp. 1147 – 1156
     Methodology – ARMA prediction of
          real-valued time series

                                      GPS data from
                                       European IGS
                                       stations were used
                                       for TEC calculations
                                      10 previous days of
                                       the TEC values were
                                       taken for the
                                       prediction
                                       computation
                                      Prediction for May
                                       8, 2007
http://igscb.jpl.nasa.gov             Ionospheric
                                       conditions with max
                                       Kp=4o and sum of
               Test network area       Kp = 22+
    Methodology – Positioning
        Adjustment Model
    Sequential Generalized Least Squares (GLS)

   All parameters in the mathematical model are considered
    pseudo-observations with a priori information (σ = 0 ÷ )
         F ( Lb , LbX )  0
              F
                                 BFVF  BX VX  WF  0

   Two characteristic groups of interest:
     Lb - instantaneous parameters (e.g., DD ionospheric delays)
      F
     LX - accumulated parameters (e.g., DD ambiguities)
      b




   Flexibility, easy implementation of:
      stochastic constraints
      fixed constraints
      weighted parameters
      Methodology – Positioning
   MPGPS software was used for all calculations
   Mathematical model uses dual-frequency code and
    phase GPS data
   Unknowns: DD Ionospheric delays, Tropospheric TZD
    per station, DD ambiguities, rover coordinates
    • Tropospheric TZD calculated at the reference stations and
      interpolated to the rover location, tightly constrained in
      GLS
    • DD Ionospheric delays obtained from the ARMA forecast,
      constrained to 10-20 cm in GLS
   Ambiguity resolution: Least square AMBiguity
    Decorrelation Algorithm (LAMBDA)
   Validation: W-test - minimum of 3 observational
    epochs (for 5-second sampling rate) and W-test > 4
    required for validation
                  Experiment

                        •GPS data from ASG-EUPOS and
                        EPN networks
                        •24-hour data set collected on
                        May 8, 2007 with 5-second
                        sampling rate
        25 km
                        •KATO station selected as a
                        simulated user receiver (rover)
                        •Ambiguity resolution was
                67 km   restarted every 5 minutes (288
50 km
                        times)
                        •Maximum 5 minutes (60
                        epochs) for initialization
                        allowed

 Map: www.asg-pl.pl
                  Experiment
                        •3 baselines of different length
                        were processed independently
                        (single baseline mode) and also
                        in a multi-baseline mode (all
                        baselines together)
                        •predicted iono model was
        25 km
                        applied (1-2 hour forecast)
                        •Time-to-fix was analyzed
                        •Ambiguity resolution success
50 km           67 km   rate was analyzed
                        •Ambiguity validation failure
                        ratio was analyzed
                        •”True” reference coordinates
                        derived using Bernese software
                        •IGS predicted orbits and clocks
 Map: www.asg-pl.pl
                        used (ultra-rapid)
                      Test results
                         DD iono correction residuals
      0.12

       0.1

      0.08

      0.06

      0.04

      0.02
[m]




         0

      -0.02

      -0.04

      -0.06

      -0.08

       -0.1

      -0.12
           0   2880   5760          8640           11520   14400   17280
                                  Epoch no.




DD Ionospheric correction residuals, KATO-TARG baseline – 25 km
                       Test results
                         DD iono correction residuals
       0.12

        0.1

       0.08

       0.06

       0.04

       0.02
 [m]




          0

       -0.02

       -0.04

       -0.06

       -0.08

        -0.1

       -0.12
            0   2880   5760          8640          11520   14400   17280
                                  Epoch no.




DD Ionospheric correction residuals, KATO-WODZ baseline – 50 km
                      Test results
                         DD iono correction residuals
      0.12

       0.1

      0.08

      0.06

      0.04

      0.02
[m]




         0

      -0.02

      -0.04

      -0.06

      -0.08

       -0.1

      -0.12
           0   2880   5760          8640           11520   14400   17280
                                  Epoch no.




DD Ionospheric correction residuals, KATO-KRAW baseline – 67 km
                       Test results
       0.25

        0.2

       0.15

        0.1

       0.05
 [m]




          0

       -0.05

        -0.1

       -0.15

        -0.2

       -0.25
            0   2880    5760     8640      11520   14400   17280
                               Epoch no.




Kinematic position residuals (NEU), KATO-TARG baseline – 25 km
                       Test results
       0.25

        0.2

       0.15

        0.1

       0.05
 [m]




          0

       -0.05

        -0.1

       -0.15

        -0.2

       -0.25
            0   2880    5760     8640      11520   14400   17280
                               Epoch no.




Kinematic position residuals (NEU), KATO-WODZ baseline – 50 km
                       Test results
       0.25

        0.2

       0.15

        0.1

       0.05
 [m]




          0

       -0.05

        -0.1

       -0.15

        -0.2

       -0.25
            0   2880    5760     8640      11520   14400   17280
                               Epoch no.




Kinematic position residuals (NEU), KATO-KRAW baseline – 67 km
                        Test results
        0.25

         0.2

        0.15

         0.1

        0.05
  [m]




           0

        -0.05

         -0.1

        -0.15

         -0.2

        -0.25
             0   2880    5760     8640      11520   14400   17280
                                Epoch no.




Kinematic position residuals (NEU), multi-baseline 25, 50 and 67 km
       Test results and analysis
          Ambiguity resolution statistics

                  Ambiguity    Ambiguity      Average
                  resolution   validation   Time-to-fix
                   success      failure       [epochs
                     rate         rate          (s)]
                     [%]           [%]
   KATO-TARG        99.6          0.4       3.1 (15.5)
     25 km
  KATO-WODZ         98.2          1.8       3.5 (17.6)
    50 km
  KATO-KRAW         92.6          1.1       7.4 (36.7)
    67 km
 Multi-baseline     100.0         0.0       3.2 (16.3)



*minimum 3 epochs (15 seconds) required for validation
                     Conclusions

• Cm-level horizontal kinematic position accuracy can be
  achieved using proposed methodology with dual-frequency
  GPS data over distances of tens of km
• When the ionospheric correction accuracy is better that ½
  cycle of L1 signal, fixed solution is possible just after a few
  observational epochs only
• The ionosphere forecast model reduce ~ 40% of the
  ionospheric delay (its accuracy is limited by the base
  model)
• The applicability of the presented forecast model is limited
  to the distances of 25-50 km in a single-baseline mode and
  to 60-70 km in a multi-baseline mode
             Future Developments


• Research on the level of stochastic constraints
  imposed on the ionospheric corrections
   • Too tight constraints cause false fixes

   • Too loose constraints make time-to-fix longer



• Test prediction of more accurate ionospheric (base)
  models
   • Higher accuracy base models will also improve accuracy
     of the prediction, and hence, the predicted TEC level will
     be more beneficial to RTK positioning

								
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