# 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
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
•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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