# Parameters for ED50 -> ETRS89/WGS84 seven-parameter transformation which are good for Denmark?

I am looking for parameters for a seven-parameter transformation (Rx, Ry, Rz, Tx, Ty, Tz, s) from ED50 UTM (zone 32U) to ETRS89 and/or WGS84.

The best match I could find is here: http://geodesy.spacecenter.dk/~geod/REF/3drefdk.htm

Unfortunately, it seems like these parameters produce coordinates which are off by some 50 meters or so.

Ideally, the parameters should lead to a transformation within a couple of meters of what the online calculator at http://valdemar.kms.dk/trf/ produces.

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are you comparing data to google earth ? or good gps point. If google earth , rememeber that it dosent use 4326, it uses 3587 – simplexio Feb 19 '13 at 12:21

With Arcmap, if I choose esriSRGeoTransformation_ED_1950_To_ETRS_1989_4, which they say is for Denmark, it says it is using a position vector geotransformation with:

``````dx=-81.1
dy = -89.4
dz=-115.8
rx=0.485
ry= 0.024
rz= 0.413
s=-0.54
``````
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Thanks Kirk, but that's actually the same parameters (with slightly less precision) that what geodesy.spacecenter.dk/~geod/REF/3drefdk.htm gives, and that's quite a bit off in comparison to KMS conversion. :-( – Grrrr Aug 29 '10 at 15:55
Wow, 50 meters seems a bit large. If you really trust valdemar.kms.dk/trf and like solving math equations, I guess you could plug in 7 different points and use the results to reverse engineer the parameters. With seven equations and seven unknowns it should be possible to solve for the parameters. Or ask someone how at math.stackexchange.com. – Kirk Kuykendall Aug 29 '10 at 21:15
Actually, I lied about 50 meters. For one particular point I have the difference of 121 m, and I have verified by other means that valdemar.kms.dk/trf gives the correct coordinates for that point. Your idea is pretty cool actually, I'll try that. – Grrrr Aug 29 '10 at 21:53

Ok, I did what Kirk suggested. Well, almost. Since I did not need the Z coordinate, I could get away with using a four-parameter transform. I used just two reference points for calculations, although it would be better to do a least square fit with a higher number of points. At any rate, I am getting results which are consistently within 2-3 meters or less of the values computed via http://valdemar.kms.dk/trf/ for points all over Denmark.

The parameters came out to be:

``````s = -4.509;
cx = -176.99;
cy = -89.08;
rz = 0.336"  (or 0.0000016298 rad)
``````
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In the context of the oil and gas industry, the 7-parameter Common Offshore transformation is used. Refer to this gazette notice: https://www.og.decc.gov.uk/regulation/guidance/co_systems/co_sys_03.htm for reference.

In ESRI ArcGIS, this transformation is represented by the transformation "ED_50_To_WGS_1984_18".

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