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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_at_uwm.edu.pl
IGS AC Workshop Miami Beach, June 2-6, 2008
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Outline

• Research objectives
• ARMA method
• RTK positioning model
• Experiment design
• Test results and analysis
• Conclusion

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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)

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Methodology ARMA prediction of real-valued time
series
Let yt for t 1, 2, . , n be an equidistant
stationary stochastic time series and yt1 be
the prediction at time t1. The
autoregressive-moving average process ARMA(p,q)
is defined by the formula 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
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Methodology ARMA prediction of real-valued time
series
The ARMA forecast L steps ahead
- the part of the operator containing only
nonnegative powers of B
10 previous days of the TEC values were taken
for the prediction computation
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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., Popinski 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
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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
• Ionospheric conditions with max Kp4o and sum of
  Kp 22

http//igscb.jpl.nasa.gov
Test network area
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Methodology Positioning Adjustment Model
Sequential Generalized Least Squares (GLS)

• All parameters in the mathematical model are
  considered pseudo-observations with a priori
  information (s 0 ?)

• Two characteristic groups of interest

- instantaneous parameters (e.g., DD ionospheric
delays)- accumulated parameters (e.g., DD
ambiguities)

• Flexibility, easy implementation of
• stochastic constraints
• fixed constraints
• weighted parameters

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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 gt
  4 required for validation

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Experiment

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

25 km
67 km
50 km
Map www.asg-pl.pl
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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 applied (1-2 hour
  forecast)
• Time-to-fix was analyzed
• Ambiguity resolution success rate was analyzed
• Ambiguity validation failure ratio was analyzed
• True reference coordinates derived using
  Bernese software
• IGS predicted orbits and clocks used (ultra-rapid)

25 km
67 km
50 km
Map www.asg-pl.pl
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Test results
DD Ionospheric correction residuals, KATO-TARG
baseline 25 km
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Test results
DD Ionospheric correction residuals, KATO-WODZ
baseline 50 km
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Test results
DD Ionospheric correction residuals, KATO-KRAW
baseline 67 km
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Test results
Kinematic position residuals (NEU), KATO-TARG
baseline 25 km
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Test results
Kinematic position residuals (NEU), KATO-WODZ
baseline 50 km
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Test results
Kinematic position residuals (NEU), KATO-KRAW
baseline 67 km
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Test results
Kinematic position residuals (NEU),
multi-baseline 25, 50 and 67 km
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Test results and analysis
Ambiguity resolution statistics
minimum 3 epochs (15 seconds) required for
validation
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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

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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