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How do I find a projection to a target CRS (Coordinate Reference System) based on a number of reference points?

Reference Points

Lat Lng                                -> Unknown CRS (X, Y)

29.999999999999456, 10.0               -> 0, 0
29.999942188937776, 10.099416075499747 -> 10000, 0
52.51051013417886, 13.430682115106462  -> 229459, 2511140
52.420591784398034, 12.98406698769891  -> 200000, 2500000
52.44802435357121, 11.492633733515229  -> 100000, 2500000

From the data above it seems, the unknown CRS has its origin at 30.0, 10.0 and the unit is in meters. My closest guess based on the tools recommended in related questions are:

Esri:102014 - Europe_Lambert_Conformal_Conic

Esri:102031 - Europe_Equidistant_Conic

However, trying to transform the coordinates using the CRS above does not yield the correct target reference points.

Disclaimer: I have read the related questions (Determining unknown Coordinate System using QGIS? and Find CRS (coordinate reference system) based on known location and coordinates?)

The EPSG-Registry and Projfinder tools recommended in those questions did not yield a result.

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Chris2M
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    If you have access to ArcGIS Desktop, create xy data layers for both sets of coordinates (include an ID field and give the corresponding points the same ID. Identify the lat/lon values as ETRS89 or WGS84. Leave the other values as "unknown coordinate system". Start with 102013 and start adjusting the false easting/northing values of the data frame's coordinate system to see if you can get a match. – mkennedy Jan 30 '17 at 18:45
  • I do not have access to ArcGIS. However, you gave me the idea to "bruteforce" the various parameters of the projections that gave the "closest" results. Using the org.geotools java api and some parameter fuzzing techniques I found the projection is accurately described by Lambert_Conformal_Conic_2SP with central_meridian=10,latitude_of_origin=30,standard_parallel_1=40,standard_parallel_2=60 :) – Chris2M Jan 30 '17 at 21:22

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