Studies on spatio-temporal filtering of GNSS-derived coordinates

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Studiesonspatio-temporalfilteringofGNSS-derivedcoordinates.

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JanuszBogusz

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Maciej Gruszczyński, Janusz Bogusz, Anna Kłos, Mariusz Figurski

Military University of Technology, Warsaw, Poland

[email protected]

Studies on spatio-temporal filtering of GNSS-derived coordinates

MOTIVATION

DATA

FILTRATION

METHODS

CONCLUSIONS CME IN NS AND

PPP TIME SERIES

COMPARISION OF STACKING AND FILTERING

METHODS

AUTHORS AND

REFERENCES

MAX. SIZE OF

CME SPATIAL

UNIFORMITY

Maciej Gruszczyński is supported by the EGU Young Scientist’s Travel Award. This research is financed by the Faculty of Civil Engineering.

Studies on spatio-temporal filtering of GNSS-derived coordinates | Vienna 12 – 17 April 2015


Studies on maximum size of CME spatial uniformity

This researche was undertaken in order to determine how large the area can be to keep

the CME values homogeneous. Three different research methods were used, but the

results should be discussed together.

simulation of stochastic part

of GNSS cordinate time series

dividing network into ring-shaped

areas with increasing distances

studies on spatial correlation in GNSS

permanent network



Motivation

The vast majority of measurements using the Global Positioning

System necessitate the existence of thousands of permanently operating

stations that form the regional and global networks of reference stations.

GNSS measurements are used to precisely estimate the station’s positions

and their velocities, and also for ionosphere and troposphere studies.

Permanent GNSS observarions are needed to implement the kinematic

reference frames in geodesy and interpret changes of dynamic character.

GNSS time series that are obtained in the standard processing

contain both signal and noise. Detrended and demeaned residual position

time series are considered as noise and they are the subject of this

researches. Spatial correlation in regional network is caused by common

mode errors which are caused by the sum of many systematic errors.

1/2



Three-level common mode error sources

① The mismodelling of: satellite orbits, the Earth

Orientation Parameters (EOP) or satellite antenna

phase centre corrections.

② The unmodelling of large-scale atmospheric

and hydrospheric effects, as well as small scale crust

deformations.

③ Systematic errors caused by used software

and computing strategies.

2/2



Data

The linear trend and seasonal components were first removed from the XYZ geocentric time series

using least squares estimation (LSE). Secondly, the outliers and offsets were removed with median

absolute deviation criterion, assumed to be optimal for GPS derived coordinates and STARS algorithm

respectively. Then, the LSE model was restored and the transformation into North-East-Up (NEU)

components (figure) was completed. The LSE was performed again for NEU components, having

subtracted the trend and seasonal changes. The time series obtained in this way will be referred to as

the "unfiltered" time series.

Figure ← Analysis is conducted on the basis of

topocentric components, which use stations antenna

location as the center of the coordinate system.



Comparision of stacking and spatial filtering results

The extraction of CME for the set of n permanent stations with time series of daily 1 to i epochs were

applied using four approaches:

1. introduced in 1997 by Wdowinski et al. non weighted stacking method,

2. introduced in 2002 by Nikolaidis weighted stacking method,

where the weights (𝜎𝑗,𝑡𝑖2 ) are the inverse of squared RMS individual station position (this information are

stored in the SINEX files),

1/4

CME1 𝑡𝑖 = 𝑋 𝑗, 𝑡𝑖𝑛𝑗=1

𝑛

CME2 𝑡𝑖 =

𝑋 𝑗, 𝑡𝑖𝜎𝑗,𝑡𝑖2

𝑛

𝑗=1

1𝜎𝑗,𝑡𝑖2

𝑛

𝑗=1



Comparision of stacking and spatial filtering results

The extraction of CME for the set of n permanent stations with time series of daily 1 to i epochs were

applied using four approaches:

3. introduced in 2011 by Tian and Shen ,

4. previously undesribed introduced by authors weighted stacking method,

where the weights (𝑙𝑗) are the distances from network barycentre to j-th station.

2/4

CME3 𝑗, 𝑡𝑖 =

𝑋 𝑘, 𝑡𝑖 ∙ 𝑟 𝑗, 𝑘

𝜎𝑘,𝑡𝑖2

𝑛

𝑘=1

𝑟 𝑗, 𝑘

𝜎𝑘,𝑡𝑖2

𝑛

𝑘=1

CME4 𝑡𝑖 =

𝑋 𝑗, 𝑡𝑖𝑙𝑗

𝑛

𝑗=1

1𝑙𝑗

𝑛

𝑗=1



The reduction of the time series standard deviation

through stacking and filtering approaches 1st method (Wdowinski et al., 1997) 2nd method (Nikolaidis, 2002)

3rd method (Tian and Shen, 2011) 4th method (Authors)

3/4



Decrease in the Pearson correlation coefficient

through stacking and filtering approaches

Figures ← Pearson’s correlation coefficients

estimated for each pair of stations and

computed for each component separately

(unfiltered data presented in red) in relation to

the distance between them.

Correlations computed for filtered time series

presented in four different colours are changing

with time interval of 3 sec to visualize

differences between results obtained by using 4

described methods.

4/4














described methods.

4/4














described methods.

4/4














described methods.

4/4



NS and PPP solutions comparision in terms of CME

distribution

Propulsion Laboratory (JPL) uses

GIPSY-OASIS II software and

provides different positioning

methodology products - Precise

Point Positioning (PPP). In

selected two sets of time series

observational epochs correspond

one with the other. The only

difference is positioning

methodology and used software.

In order to conduct this study, we took 136 statons located in and near to Europe.

Permanent measurements from these stations were processed independently by two

research centers. Military University of Technology EPN Local Analysis Centre (MUT LAC)

provides network solutions time series processed using Bernese 5.0 software. Jet

1/4

OPEN VIEW


Maciej Gruszczyński, Janusz Bogusz, Anna Kłos, Mariusz Figurski OPENED VIEW



Spatial correlations in NS and PPP processed time

series

2/4




(unfiltered data) in relation to the distance

between them. Mean correlation curves derived

using a weighted moving avarage are imposed

on the charts.

• Left chart shows correlation ceofficients

and red mean curves computed for time series

provided by JPL processed in GIPSY-OASIS II

software using precise point positioning,

• Right chart shows correlation ceofficients

and green mean curves computed for time

series provided by MUT LAC processed in

Bernese 5.0 software using network solution.



CME extraction was applied for set of 23 stations (PPP

and NS processed time series) that form 800 km extent

network.

The common mode error was computed as the daily

weighted mean of the unfiltered data from a set of

permanent stations using 2nd method (Nikolaidis, 2002).

The lower value of the standard deviation indicates a

higher precision of time series (lower scatter).

3/4

OPEN VIEW

OPEN VIEW

OPEN VIEW

Standard deviation of PPP and NS processed time

series

Figures → Blue and orange bars show standard

deviation of unfiltered time series processed using

network solution and precise point positioning

respectively.

Brown (PPP) and light blue (NS) lines present

present relative reduction in percent of standard

deviation through the stacking approach.

OPEN VIEW

Figure ↓ The analysed network consisted of 23 permanent

stations which time series were processed by 2 analisys

centres.











For two chosen stations located at 240 km and 270 km from barycentre of network, noise

amplitudes were computed for the North, East and Up components twice: before

performing the filtration and after stacking. The following table presents the amplitudes of

the power-law noise model computed using Hector software (Bos et al., 2012).

Station name and location

Noise amplitudes in millimeters

Network Solution (MUT LAC, Bernese 5.0)

Precise Point Positioning (JPL, GIPSY-OASIS II)

Unfiltered Stacked Unfiltered Stacked

N E U N E U N E U N E U

HOBU Hohenbuenstorf,

Germany

0.8 1.0 3.1 0.2 0.2 2.5 1.5 1.2 4.4 0.7 0.4 3.2

WTZR Wettzell, Germany

1.1 0.9 3.7 0.6 0.3 2.7 1.0 1.3 4.2 0.6 0.4 3.4

Noise amplitudes of PPP and NS processed time

series

4/4



Studies on maximum size of CME spatial uniformity

This researche was undertaken in order to determine how large the area can be to keep

the CME values homogeneous. Three different research methods were used, but the

results should be discussed together. Please open one of the three views listed below in

order to see the research results. simulation of stochastic part

of GNSS cordinate time series

dividing network into ring-shaped

areas with increasing distances

OPEN VIEW

OPEN VIEW

studies on spatial correlation in GNSS

permanent network

OPEN VIEW



Division of the network into ring-shaped areas

according to distance

Then we selected 88 stations with no gaps in the time series

between November 2001 and April 2007 (5.5 years). The radius

of ring-shaped subnetwork was extended from 241 km to 3071

km to obtain 17 subnetworks always consisting of 5 permanent

stations. Each time CME was calculated on the basis of one of

these 17 subnetworks and filtered out from the „core” stations

time series. Reluts are shown beside.

Figures ↓ The changes in standard deviation

derived from the unfiltered (dashed line) and

regionally filtered „core” station’s time series

through the stacking approach (solid line), for

17 ring-shaped subnetwork configurations.

OPEN VIEW

OPEN VIEW

OPEN VIEW

Figure ← The analysed network consisted of 88 permanent stations unevenly distributed all over Europe and adjacent areas. Stations are divided into 17 ring-shaped subnetworks. Three „core” station are located near to the contre of rings (network barycentre).

OPEN VIEW

OPENED VIEW



subnetwork signature/

mean radius

station name

distance from

barycentre

LEIJ 54

“core” DRES 78

POTS 88

PTBB 195

GOPE 222

sn1 HOBU 239 240 WTZR 272

WTZZ 272

WROC 283

BOR1 286

sn2 KLOP 339 351 OBE2 408

KARL 437

EUSK 451

WSRT 463

sn3 TITZ 464 466 MOPI 468

BORK 485

KOSG 502

PFAN 510

sn4 GRAZ 533 530 JOZE 551

BOGI 554

LAMA 573

BZRG 580

sn5 DLFT 598 595 BRUS 612

PENC 615

DOUR 616

ONSA 650

sn6 ZIMM 662 654 ZIMJ 662

SPT0 681

UZHL 736

UNFE 759

sn7 MEDI 793 782 SULP 795

TORI 827

BRAS 843

SHEE 851

sn8 PRAT 869 876 HERS 888

RIGA 929

UNPG 943

STAS 950

sn9 HRM1 991 1015 MAR6 1 034

ABEB 1 155

METZ 1 188

METS 1 188

sn10 GLSV 1 226 1219 TLSE 1 242

MATE 1 248

MAT1 1 248

BUCU 1 251

sn11 SOFI 1 271 1277 ORID 1 304

LLIV 1 313

TRDS 1 320

VAAS 1 366

sn12 BELL 1 420 1402 SVTL 1 430

VIL0 1 472

POLV 1 527

EBRE 1 534

sn13 MALL 1 562 1560 JOEN 1 574

MOBN 1 601

NOT1 1 643

TUBI 1 735

sn14 YEBE 1 743 1743 VILL 1 798

MADR 1 798

KIRU 1 859

KIR0 1 862

sn15 TROM 2 033 1966 TRO1 2 033

ALME 2 044

CASC 2 256

SFER 2 266

sn16 VARS 2 278 2340 REYZ 2 448

REYK 2 448

RABT 2 526

NYA1 3 041

sn17 NYAL 3 041 3071 KULU 3 182

MAS1 3 567

OPENED VIEW









Simulation of stochastic part of GNSS cordinate time

series

Time series were simulated using both the flicker noise model and the white noise model.

Pearson correlation coefficient was computed between 88 pairs of time series for each

model separately. Number of samples in time series are equal to the number of epochs in

5.5 years daily time series (more than 2000 samples).

In the further part of the research stacking (2nd method - Nikolaidis, 2002) was applied for

time series obtained using flicker noise model. For this data, correlation coefficients were

also calculated.

OPEN VIEW

OPENED VIEW





Studies on spatial correlation in GNSS permanent

network

Pearson correlation coefficient between each pair in the

considered GNSS network was computed. For this

research 197 stations distributed at all over Europe and

adjacent areas processed by JPL were taken. The

correlation coefficient was calculated only in case of at least

one year of common time-range.

OPEN VIEW

OPEN VIEW

OPEN VIEW

Figure ← Stations taken to the

spatial correlation analysis.

OPEN VIEW Figures → The correlation coefficients for each

pair of stations (unfiltered data) in the network

in relation to the distance between them. Mean

correlation curves derived using a weighted

moving avarage are imposed on the charts.

OPENED VIEW











Conclusions

• Differences between horizontal and vertical components can be seen (larger

correlation and scatter of Up component).

• The positive effect of CME extraction from stochastic part of time series should be

confirmed by the reduction in its standard deviation (higher stability). But more important

is deterioration of spatial correlation in GNSS permanent networks noticed through the

filtering/stacking approach. The most reliable method should extract only commmon

signals in time series, which prove the existence of uniform systematic errors (CME) in

the network.

• It was confirmed that between any simulated, more than 5 years long, daily sampled

time series affected only by white noise, correlation ceofficients are not greater than 0.05.

Higher values of this coefficient indicate the existence not only random signals in

permanent GNSS networks.

• Time series provided by JPL (PPP) were characterized by higher scatter and grater

correlation between different stations than MUT LAC (network solution) products.



Authors and references

Maciej Gruszczyński He graduated from the Military University of Technology in 2014 with a thesis entitled "Spatio-temporal filtering of the GPS-derived coordinate time series for determination of a common mode error in ASG-EUPOS regional network". Now he is a PhD student on the Faculty of Civil Engineering and Geodesy and works here under the direction of Prof. Janusz Bogusz. In his PhD research he concentrates on GNSS derived time series analysis and deals especially with spatial correlation in permanent station networks.

Janusz Bogusz He graduated from Warsaw University of Technology in 1995. His master thesis concerned navigation using GPS system. In 2000 he made the PhD. related to geodynamics, the tides of the atmosphere in particular. Habilitation thesis (2012) concerned applicability of short-time GPS solutions to the studies of residual dynamic deformational changes in tidal frequencies. Presently he works as the associate professor on the Faculty of Civil Engineering and Geodesy Military University of Technology, Warsaw.

Anna Kłos In 2012 she graduated the Military University of Technology on the Faculty of Civil Engineering and Geodesy with the M. Sc. Degree. Her Master thesis dealt with evaluation of short-term stability of permanent stations of ASG-EUPOS network stations. Now she is a PhD student on the Faculty of Civil Engineering and Geodesy at the Military University of Technology. She deals with time series analysis under the supervision of Prof. Janusz Bogusz.

Mariusz Figurski Vice-Rector. Development of the Military University of Technology. He is a specialist in processing of GNSS observations. He was responsible for establishing geodetic control networks in Poland (WSSG, POLREF, EUREF-POL, EUVN) using GPS. For scientific achievements he was awarded a Silver Cross of Merit by Polish President in 2007.

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Studies on spatio-temporal filtering of GNSS-derived coordinates