Realization of ETRS89: Alternatives, future concepts/mkuhar/Zalozba/WG_Brussels_ETRS89-Gu… · Least-squares estimation of transformation parametes 31 defining points used fortheestimationof

Realization of ETRS89:Alternatives, future concepts

Werner GurtnerJ h IhdJohannes IhdeJens Luthardt

EUREF Symposium, Brussels, June 18-20, 2008

AIUBAstronomisches Institut der Universität Bern

ETRS89 Definition

Resolution No 1, Firenze 1990

"recommends that the system to be adopted by EUREF will be coincident with ITRS at the epoch 1989.0 and fixed to the stable part of the Eurasian Plate and will be

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fixed to the stable part of the Eurasian Plate and will be known as European Terrestrial Reference System 89 (ETRS89)"

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"accepts that … for most applications, the coordinates will have no time variation"

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Resolution No 1, Bern 1992

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"recommends that this solution (Bernese solution of EUREF GPS 1989 campaign) be accepted as the current realiastion of the ETRS89 under the name of EUREF89"

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Conclusions from the definition

"fixed to the stable part" implies that the ETRS is rotating "somehow" with the Eurasian plate"no time variation" implies the desire to avoid

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no time variation implies the desire to avoid changes in time of the positions of European stations within the stable part

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The definition does not say anything about the realizations nor the reference epoch of the realizations

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el realizations

The first realization (EUREF89) was based on

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posi The first realization (EUREF89) was based on SLR/VLBI-derived "fiducial stations" given in ITRF89 at epoch 1989.0

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First realization of ETRS89

ITRF892000

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008 1995

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ETRF89 1989 0

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el ETRF89EUREF89

1989.0

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z =z

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Most simple realization based on a ITRFyy

Just fulfilling the requirement "fixed to the stable part":Just fulfilling the requirement fixed to the stable part :

Take a realization of ITRS ITRFyy

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yyDetermine "somehow" rotation pole and rotation rate dr/dt of the Eurasian plate from this solution

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Select a reference epoch for the realizationMove all European reference stations into the reference epoch by their ITRFyy velocities

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el reference epoch by their ITRFyy-velocitiesRotate them by the rotation angle

d /d * ( 1989 0)

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posi r = dr/dt * (tref-1989.0)

into the ETRS89 ETRFyy

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Later Realizations of ETRS89

ITRF89 ~ ITRF2000 ~ ITRF2005 ETRF2005

ETRFyy = f(ITRFyy)

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008 ETRF2000

z2005

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ETRF89

EPN

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el ETRF89 z2005z2000

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z89=z89

z2000

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Remarks to the Most simple realization

Each realization is completely independent from earlier realizations (unless the ITRFyy datum depends on earlier datums)

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008 In the early days the applied rotation was based on plate

motion models

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Changes/uncertainties in the applied rotation rate will become more disturbing with time

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more disturbing with time

Changes/uncertainties related to the datum realizations of subsequent ITRFyy may also lead to significant variations of

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posi subsequent ITRFyy may also lead to significant variations of

positions in the ETRFyy counterpart

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Improvements (1)

Include additional parameters into the ptransformation ITRFyy ETRFyy

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008 E.g., to attenuate effects from changes in the datum

Mainly translations, Zuheir also includes translation rates

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Various ways how to determine such additional parameters

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el parameters

Proposal by Zuheir to base these additional parameters on

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posi the values determined in the "memo", i.e. based on global analysis

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Improvements (2)

R f ll b t li ti ETRF tRefer all subsequent realizations ETRFyy to a reference realization, e.g., ETRF2000, i.e. extract and combine parameters from the memo in a way

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and combine parameters from the memo in a way that they take into account the datum differences to ETRF2000 (actually between ITRFyy and ITRF2000)

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el Remark: The "memo values" are results from the global analysis, they are not specifically

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posi optimized for Europe

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Alternative Realization of ETRS89

ITRF..2005rz ~ (z2005- z1989) / (t2005-1989.0) 2005005 989 005

~ (z2005- z2000) / (t2005-1989.0)~ ...

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008 ETRF2000

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ETRF89

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el ETRF89 z2005z2000

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z89

ITRF2005 European Realization:Determine best-fitting transformation parameters between

ITRF2005 and previous ETRS89 realization, e.g., ETRF2000

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Rigorous Solution

Select a reference realization ETRF00, e.g., ETRF2000Select max number of European stations that

are present in both ETRF2000 and ITRFyy with sufficiently long history

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historylie in the "stable part" of Europe

Move the stations into common reference epoch using

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8-2 Move the stations into common reference epoch using

respective velocities (ETRF2000 and ITRFyy)Determine Helmert transformation parameters between

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pthe two sets of coordinates (least squares adjustment)Introduce the smallest possible number of parameters,

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posi e.g., 3 translations, 3 rotations and r.rates and

Include additional derivatives, if necessary

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Least-squares estimation of transformation parametes

31 defining points used for the estimation of

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for the estimation of transformation parameters between ITRF and ETRF

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i.e . withoutHOFN on Island

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el HOFN on IslandKELY and THU1 on GreenlandNYAL on Spitsbergen

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Transformation parameters from ITRF2005 Ep. 2000.0 to ETRF2000 Ep. 2000.0

Tx mm

Ty mm

Tz mm

D 10-9

Rx mas

Ry mas

Rz mas

sigma0mm

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mm mm mm 10 mas mas mas mm43 ±3

46 ±6

-46 ±3

1.0 ±0.5

0.7 ±0.2

5.8 ±0.1

-8.8 ±0.1

2.5

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δTx mm/y

δTz mm/y

δTz mm/y

δD 10-9/y

δRx mas/y

δRy mas/y

δRz mas/y

sigma0mm/y

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el -0.28±0.03

+0.05±0.02

+0.52±0.01

-0.80±0.03

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31 stations used

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ETRFyyITRFyy 70 + 41 / 152

2005 ETRF2005ITRF2005 (00.0)

ETRFyyITRFyy Memo Vers. 6 / 770 + 41 / 152 stations

70 stationsworldwide 31 stations

TTTSRRRPxxxx000

Gurtner / Ihde

Jumps31 stations stable part of Europe

Rxxxx000

TTTSRRRPxxxxxxx

2000 ETRF2000

R---xxxx

ITRF2000 (97 0)

ITRF2000 (00.0)

1997 ITRF1997 (97.0)TTTSRRR

Memo Vers. 5ITRF2000 (97.0)

Altamimi

?? stations

1996TTTSRRRPxxxxxxxRxxxxxxxITRF1996 (97.0)

M B h / Alt i i S ifi ti f f f fi i i th l i f EUREF GPS iMemo: Boucher / Altamimi, Specification for reference frame fixing in the analysis of EUREF GPS campaign

Residuals ???2005-ETRF2000

mm

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Least squares transformation

Proposal by Altamimi

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Remarks to Rigorous Solution

Rotation angles divided by (reference epoch – 1989.0) approximate rotation rate of Euroasian plateapproximate rotation rate of Euroasian plateThey also contain contributions of systematic errorsAll the parameters soak up systematic errors of datum realizations and errors of regional nature

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realizations and errors of regional nature

Parameters are mathematical transformation parameters and

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8-2 don't have to be physically interpreted Formal errors are

unimportant.

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el Maintains full internal accuracy of the original ITRFyy solutionYields the smallest possible residuals/jumps w/r to the reference solution (vtPv = min) closest to the users' needs

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posi reference solution (v Pv min) closest to the users needs

Could be further improved by using densified reference network

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Current situation

S f ETRS89 li ti f ll b d ITRFSo far ETRS89 realizations are fully based on ITRFyy solutions

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European IGS stations and SLR/VLBI being part of ITRFyy

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8-2 European IGS stations and SLR/VLBI being part of ITRFyy

2000: Inclusion of EPN into ITRF2000 solution

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So far, ETRS89 realizations have not been optimized for maximum consistency between subsequent

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Further improvements, future concepts

European Permanent Network:200 permanent stations availableTime series of weekly solutionsAccumulated solutions

Use EPN for the maintenance of the ETRS89

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008 Excellent internal accuracy

Time resolution, spatial densityVelocity field

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8-2 Velocity field

EPN processing based on ITRF/IGSyy ( orbits, ERPs,..., SLR,...)ETRS89 realizations „independent“ from ITRFyy:

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el DensityFrequency...

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posi Optimized for long-term consistency between subsequent

realizationsITRFyy ETRFyy: Availability of positions/velocities of

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reference stations and of transformation parameters

Open questions (1)

How to make use of EPN? In detail?How often will there be updates to the parameters and reference coordinates?Based on which solutions? Based on which reference?

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Based on which solutions? Based on which reference?How do the mathematical models of the optimization function and the transformations look like? What to do with “scale” diff ?

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What to do with annual (or other) variations of ITRFyy/IGSyy-based positions?

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pEPN positionsCampaign-based positions

How to refer user results to the respective realization (naming

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posi How to refer user results to the respective realization (naming,

traceability, citation, uniqueness)?

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Open questions (2)

Do we need to modify the definition of ETRS89?

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008 I don't think so!

Definition is simpleS ff l

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8-2 Sufficiently vague

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Need to modify/extend specifications for the realization/maintenance of ETRS89

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posi realization/maintenance of ETRS89

e.g., quantification of the “stable part”

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Documents

Realization of ETRS89: Alternatives, future concepts/mkuhar/Zalozba/WG_Brussels_ETRS89-Gu… · Least-squares estimation of transformation parametes 31 defining points used fortheestimationof