EPSG guidance note #7-2, http://www.epsg.org
Note the analogy with the Coordinate Frame rotation (code 9607) but beware of the differences! The Position Vector convention is used by IAG and recommended by ISO 19111. See methods 1033 and 1037 for similar tfms operating between other CRS types.
Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided. Transformation of coordinates from one geographic coordinate reference system into another is often carried out as a concatenation of the following operations: (geographical to geocentric) + (geocentric to geocentric) + (geocentric to geographic) The Position Vector transformation (geog2D domain) has 5 steps: (i) geographic 2D coordinates are converted to 3D using EPSG coordinate operation method code 9659; (ii) geographic 3D coordinates are converted to geocentric coordinates using EPSG coordinate operation method code 9602; (iii) the middle step of the concatenated transformation, from geocentric coordinates to geocentric coordinates, uses the Position Vector(geocentric domain) method, EPSG method code 1033; (iv) the geocentric coordinates are converted to geographic 3D using EPSG coordinate operation method code 9602; (v) finally the geographic 3D coordinates are converted to geographic 2D using EPSG coordinate operation method code 9659.
Input point: Coordinate reference system: WGS 72 (geographic 2D) Latitude = 55 deg 00 min 00 sec N Longitude = 4 deg 00 min 00 sec E This is taken to be geographic 3D with an assumed Ellipsoidal height hS = 0 m This transforms to Cartesian geocentric coords: Xs = 3 657 660.66 (m) Ys = 255 768.55 (m) Zs = 5 201 382.11 (m) Transformation parameters WGS 72 to WGS 84: tX (m) = 0.000 tY (m) = 0.000 tZ (m) = 4.5 rX (") = 0.000 = 0.0 radians rY (") = 0.000 = 0.0 radians rZ (") = 0.554 = 0.000002685868 radians dS (ppm) = 0.219 from which M = 1.000000219 Application of the 7 parameter Position Vector transformation results in WGS 84 coordinates of: Xt = 3 657 660.78 (m) Yt = 255 778.43 (m) Zt = 5 201 387.75 (m) This converts into: Latitude = 55 deg 00 min 00.090 sec N Longitude = 4 deg 00 min 00.554 sec E Ellipsoidal height = +3.22 m on the WGS 84 geographic 3D coordinate reference system. For the 2D equivalent the height is ignored.