# Presentation: 390113

## Real-time Kinematic GPS Positioning Supported by Predicted Ionosphere Model

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

*University of Warmia**** ****and**** ****Mazury in Olsztyn, Poland*
*pawel.wielgosz@uwm.edu.pl*

## Research objectives

ARMA method

RTK positioning model

Experiment design

Test results and analysis

Conclusion

- 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)

**Notes:**
Say that we are working on long-range network-RTK, and one of the steps is to test predicted ionosphere models
One of the model tested is ARMA-based TEC forecast developed at UWM

## Methodology – ARMA prediction of real-valued time series

- Let *y**t* for t =1, 2, .... , n be an equidistant stationary stochastic time series and yt+1 be
- the prediction at time t+1. 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* B**K* the process can be converted to :

**Notes:**
In time series analysis, the backshift operator operates on an element of a time series to produce the previous element. 

## 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

**Notes:**
Note that the lag operator (L) can be raised to arbitrary integer powers

## 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

**Notes:**
The TEC prediction in theses studies were tested on IGS-like iono model (quite rough with accuracy 2-4 TECU) and it worked very well up to 3 hours, so basically the forecast accuracy is on the level of, e.g., the original IGS model, so we wanted to try it in medium-range RTK – refer questions to the cited paper

## 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 Kp=4o and sum of Kp = 22+

- Test network area

- http://igscb.jpl.nasa.gov

**Notes:**
We used ~40 stations with separation of several hundreds of km to derive the base model that was used later for the forecast
10 previous days were used, quiet iono period was selected, the most disturbed day in that period was April 28 with sum Kp = 32+ and max Kp was 5- on that day.
For RTK positioning we used prediction of about ~2 hours

## Methodology – Positioning Adjustment Model 

- All parameters in the mathematical model are considered _*pseudo-observations*_ with a priori information (σ = 0 ÷ )

**Sequential Generalized Least Squares (GLS)**

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

- Two characteristic groups of interest:

_*Flexibility*_, easy implementation of:
- stochastic constraints
- fixed constraints
- weighted parameters

**Notes:**
Our regular GLS stuff

## 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

**Notes:**
Our regular MPGPS stuff

## Experiment 

**67 km**

**50 km**

**25 km**

- Map: www.asg-pl.pl

- 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

**Notes:**
Data source and experiment design
Say that on of the stations was located in Krakow – very popular place in Europe among Americans ;)

## Experiment 

**67 km**

**50 km**

**25 km**

- Map: www.asg-pl.pl

- 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)

**Notes:**
Data source and experiment design

## Test results

- DD Ionospheric correction residuals, _KATO-TARG baseline – 25 km_

**Notes:**
On the plot we have difernt DD iono residuals marked with differen coulours (24 hours of data) . The residuals are = reference truth – the prediction
Say: quality of the DD iono corrections derived from predicted model is very good, however the baseline is rather short, the CORRECTIONS remove ~40% on the iono delay. The corrections error is on the ever of a quarter of L1 cycle so OTF-RTK should work very well
 DD iono constraints = 10cm

## Test results

- DD Ionospheric correction residuals, _KATO-WODZ baseline – 50 km_

**Notes:**
Say: quality of the DD iono corrections for longer baseline have worse quality, but still around half of L1 cycle. So OTF RTK still may work by the initialization time may be longer
 DD iono constraints = 15cm

## Test results

- DD Ionospheric correction residuals, _KATO-KRAW baseline – 67 km_

**Notes:**
Say: quality of the DD iono corrections for 67 baseline have even worse quality, around half to 3/4 of L1 cycle. So OTF RTK still may work by the initialization time may be longer and we may expect some validation faliures
 DD iono constraints = 20cm

## Test results

- Kinematic position residuals (NEU), _KATO-TARG baseline – 25 km_

**Notes:**
Position residuals to the truth obtained with Bernese 5.0, NE – blue and green, U – red, (24 hours of data)
Very good accuracy – 2cm horizontal and 7-8 cm vertical
Remember that usually we have 1 epoch fix, but we wait 3 epochs for the validation

## Test results

- Kinematic position residuals (NEU), _KATO-WODZ baseline – 50 km_

**Notes:**
Position residuals to the truth obtained with Bernese 5.0, NE – blue and green, U – red,
similar – 2cm horizontal and 7-8 cm vertical, but we have some wrong fixes here, some of them passed validation – here we plot all the positions, validated and not validated

## Test results

- Kinematic position residuals (NEU), _KATO-KRAW baseline – 67 km_

**Notes:**
Much more wrong fixes, so the methodology hits its limits (remember, we plot here all positions, even not solved – 7.4%)

## Test results

- Kinematic position residuals (NEU), _multi-__baseline __25, 50 and 67__ km_

**Test results**

**Notes:**
? It solved for 100% ambi with 0% validation failure and 3,25 epochs time to fix. 
It works the best

## Test results and analysis

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

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

**Ambiguity resolution statistics**

**Notes:**
Nice statistics – so the forecast may be applied for baselines up to 25-50 km, 67 km is already too long 
The method works quite fast - the distances counted in tens of km

## 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 1⁄2 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

**Notes:**
I to tez jutro.....