1. Troposphere delay stochastic modelling in precise real-time GNSS applications
Tomasz Hadaś1, Norman Teferle2, Wenwu Ding2, Kamil Kaźmierski1, Nicolas Hadjidemetriou2, Jarosław Bosy1
Institute of Geodesy and Geoinformatics
Wroclaw University of Environmental and Life Sciences
2) Geophysics Laboratory University of Luxembourg
8-10 February 2016, Reykjavik, Iceland

2. ZTD stochastic modelling in RT:
Introduction
ZTD stochastic modelling in RT
Verification
Presentation plan
Plan prezentacji
Introduction:
real-time ZTD WUELS
motivation
ZTD stochastic modelling in RT:
towards optimum stochastic modelling
‚climatological’ tropopshere delay variability
NWM predicted change
Verification:
test network and scenarios
‚climatological’ results
NWM prediction results
8-10 February 2016, Reykjavik, Iceland
2/16

3. Commercial RTK networks in Poland
Plan prezentacji
Introduction
ZTD stochastic modelling in RT
Verification
real-time ZTD WUELS
motivation
Commercial RTK networks in Poland
ASG-EUPOS:
102 in Poland + 23 foreign:
- 125 GPS / 73 GLO / 39 GAL
- permanent service since 2009
- GPS RTN (+GLO at some areas)
Leica SmartNet:
now: 135 stationsin Poland
- GPS, GLO, GAL, BDS, QZSS
- operational + developments
- GNSS RTN
TPI Net PRO:
136 in Poland
- GPS, GLO, GAL
- operational
- GNSS RTN
Trimble VRS Net:
now: 56 in Poland
- GPS, GLO, GAL, 1 BDS
- under development?
- GNSS RTN
4 commercial RTK/RTN networks (2 still under developments) with > 370 stations
WUELS cooperates with ASG-EUPOS and Leica SmartNet:
hourly RINEX files from both network, including foreign stations
1Hz data streams from ~100 Leica SmartNet stations
hopefully soon 1Hz data streams from ASG-EUPOS and +30 from Leica SmartNet
8-10 February 2016, Reykjavik, Iceland
3/16

4. GNSS-WARP software based real-time service:
Plan prezentacji
Introduction
ZTD stochastic modelling in RT
Verification
real-time ZTD WUELS
motivation
WUELS real-time ZTD service development (1)
GNSS-WARP software based real-time service:
BNC used as RTCM decoder of IGS RTS streams
performance: >10stations / 1 (currently: 147 stations / 60 sec.)
strategy: GPS PPP, static, coordinates estimated, VMF, IGS03, IERS 2010 models
8-10 February 2016, Reykjavik, Iceland
4/16

5. WUELS real-time ZTD service development (2)
Plan prezentacji
Introduction
ZTD stochastic modelling in RT
Verification
real-time ZTD WUELS
motivation
WUELS real-time ZTD service development (2)
8-10 February 2016, Reykjavik, Iceland
5/16

6. WUELS real-time ZTD service validation
Plan prezentacji
Introduction
ZTD stochastic modelling in RT
Verification
real-time ZTD WUELS
motivation
WUELS real-time ZTD service validation
Validation:
simulated RT (sp3 and CLK stored with BNC), RINEX files for 10 stations, one week, comparison with EPN final ZTD (1 hour interval)
The best solutions among various stations were obtained with different random walk step setting: 2mm/hour to 5mm/hour. The results were slightly biased: -4 mm to +7 mm (note: DD vs PPP solution) and the standard deviations varies from 7 mm to 12 mm.
Problem: how to set up the optimum random walk for station (location / time dependent)?
8-10 February 2016, Reykjavik, Iceland
6/16

7. Stochastic modelling of ZTD in RT PPP (1) – empirical approach
Plan prezentacji
Introduction
ZTD stochastic modelling in RT
Verification
towards optimum stochastic modelling
‚climatological’ tropopshere delay variability
NWM predicted change
Stochastic modelling of ZTD in RT PPP (1) – empirical approach
Problem: how to set up the optimum random walk for station (location / time dependent)?
1. Empirical approach: Test wide spectrum of settings for each station (postprocessing) and select the best one:
Station WROC: real-time ZTD (RndWlk 1 – 10 mm/h) vs final ZTD (DoY , 2013)
8-10 February 2016, Reykjavik, Iceland
7/16

8. 𝑬 𝑺 𝒏 𝜺 =𝜺 𝒏 𝑬 𝒁𝑻𝑫 𝒕+𝜹𝒕 − 𝒁𝑻𝑫 𝒕 =𝜺 𝜹𝒕 𝑬 𝜺 = 𝒁𝑻𝑫 𝒕+𝜹𝒕 −𝒁𝑻𝑫 𝒕 𝜹𝒕
Plan prezentacji
Introduction
ZTD stochastic modelling in RT
Verification
towards optimum stochastic modelling
‚climatological’ tropopshere delay variability
NWM predicted change
Stochastic modelling of ZTD in RT PPP (2) – universal approach
Problem: how to set up the optimum random walk for station (location / time dependent)?
2. Use other sources of global ZTD (NWM) to estimate 𝜺:
Markov process: memory-less stochastic process in which the future value depends only on a present state, not past states (Markov property). Expected translation distance after 𝒏 steps (each 𝜺 long):
𝑬 𝑺 𝒏 𝜺 =𝜺 𝒏
Adopting it for the tropopshere:
𝑬 𝒁𝑻𝑫 𝒕+𝜹𝒕 − 𝒁𝑻𝑫 𝒕 =𝜺 𝜹𝒕
Rearanging to estimate random walk step size (variability):
𝑬 𝜺 = 𝒁𝑻𝑫 𝒕+𝜹𝒕 −𝒁𝑻𝑫 𝒕 𝜹𝒕
Topic:
Optimization of real-time GNSS troposphere delay estimation algorithms
Host:
Felix Norman Teferle, University of Luxembourg, Luxembourg(LU),
Grantee:
Tomasz Hadas, Wroclaw University of Environmental and Life Sciences, Wroclaw (PL)
Period:
January 17 – January 29, 2016
8-10 February 2016, Reykjavik, Iceland
8/16

9. Yearly UNB-VMF1-G ZHD/ZWD variability
Plan prezentacji
Introduction
ZTD stochastic modelling in RT
Verification
towards optimum stochastic modelling
‚climatological’ tropopshere delay variability
NWM predicted change
Yearly UNB-VMF1-G ZHD/ZWD variability
Mean variability of ZHD in 2013, 2014 and 2015
[mm/hour]
Mean variability of ZWD in 2013, 2014 and 2015
[mm/hour]
8-10 February 2016, Reykjavik, Iceland
9/16

10. Monthly UNB-VMF1-G ZHD/ZWD variability
Plan prezentacji
Introduction
ZTD stochastic modelling in RT
Verification
towards optimum stochastic modelling
‚climatological’ tropopshere delay variability
NWM predicted change
Monthly UNB-VMF1-G ZHD/ZWD variability
Mean monthly variability of ZHD in 2013
[mm/hour]
Mean monthly variability of ZWD in 2013
[mm/hour]
8-10 February 2016, Reykjavik, Iceland
10/16

11. Plan prezentacji NWM variability Introduction
ZTD stochastic modelling in RT
Verification
towards optimum stochastic modelling
‚climatological’ tropopshere delay variability
NWM predicted change
NWM variability
8-10 February 2016, Reykjavik, Iceland
11/16

12. Network and scenarios – climatological variability
Plan prezentacji
Introduction
ZTD stochastic modelling in RT
Verification
test network and scenarios
‚climatological’ results
NWM prediction results
Network and scenarios – climatological variability
‚Climatological’ tests:
• IGS station • radiosonde
Processing scenarios (6):
m, y, m*2, y*2, m/2, y/2
y - mean yearly variability
m - 30-day window variability
DATA: 30s. RINEX, IGS03 (BNC ASCII)
ZTD variability: yearly and 30-day window (UNB-VMF1-G)
NMW prediction test: station WROC, WRF NWP model (1 hour interval)
8-10 February 2016, Reykjavik, Iceland
12/16

13. ‚Climatological’ results – overall
Plan prezentacji
Introduction
ZTD stochastic modelling in RT
Verification
test network and scenarios
‚climatological’ results
NWM prediction results
‚Climatological’ results – overall
8-10 February 2016, Reykjavik, Iceland
13/16

14. Plan prezentacji NWM results reinitialization Introduction
ZTD stochastic modelling in RT
Verification
test network and scenarios
‚climatological’ results
NWM prediction results
NWM results
reinitialization
Finally You can see here a solution with constraining based on high-interval NWM prediction, that is represented here with black line. This solution occurred to be better that any previous solution, with an improvement of about 5%. Below You can see 3 representative examples. The first on the left shows the case, when black lines is closer to the red final-solution line, because the NWM based constraining was much tighter than with yearly or 30-day window mean. On the right, opposite situation – during a rapid change in ZTD, the NWM prediction returns loose constraining, and the solution almost reaches the top of the pick.
The middle case shows the period when all real-time solutions failed to represent the truth, no matter what constraining was applied.
8-10 February 2016, Reykjavik, Iceland
14/16

15. Optimum choice of ZTD 𝜺:
Introduction
ZTD stochastic modelling in RT
Verification
Conclusions
Plan prezentacji
Optimum choice of ZTD 𝜺:
based on ‚climatological’ studies – global approach with look-up table, easy to implement;
based on NWM predictions – requires NWM with high temporal resolution, online NWM access and 𝜀 updates;
~10% of improvements (compared to sinlge global 𝜀).
Implementations in software:
consistent weighting scale
check ZTD related definitions
Further research required:
radiosonde / radiometer comparison
another test period (December 2015?)
8-10 February 2016, Reykjavik, Iceland
15/16

16. Introduction
ZTD stochastic modelling in RT
Verification
Thank You!
Troposphere delay stochastic modelling in precise real-time GNSS applications
Tomasz Hadaś1*, Norman Teferle2, Wenwu Ding2, Kamil Kaźmierski1, Nicolas Hadjidemetriou2, Jarosław Bosy1
Institute of Geodesy and Geoinformatics
Wroclaw University of Environmental and Life Sciences
2) Geophysics Laboratory University of Luxembourg
8-10 February 2016, Reykjavik, Iceland