I have ground reference point (GRP) in ECEF coordinates available to me. I wish to find a normal to the earth ellipsoid at this GRP. How do I calculate the unit normal?
Convert your EDEF coordinates into Plate-Carrée coordinates and subsequently use the WGS80 Geoïd. Determine the position of your reference point on the geoid and calculate the unit normal. As simple as that. To perform this in pratcice proceed as follows:
Perform a coordinate transformation from the local ECEF to the Plate Carrée coordinate system, for which you can find the applicable theory in any geodesy handbook and probably your highest chance on success to perform this conversion accurately will be reached when you use the geodetic handbook of your country, because you will need the coordinate system properties of the ECEF system.
The second step, e.g. the determination of the normal at an arbiitrary point on the WGS 80 geoid is a piece of cake (3D trigoniometry). Take your course in 3D trigoniometry out of you drawer again, and look up how to calculate the normal ina an oarbitrary point of a geoid. Once you have done this for an arbitrary point, take the Plate Carrée coordinates of your reference point and do exactly the same as for an arbitrary point. Simple as that. Your Scud rocket can't miss Ryad if you perform the calculation like that ;-). If you like I can give you the Plate Carrée coordinates of the Royal palace in Ryad.
Success mate, A small step for a man, a big step for humanity and womens lib.
Frank
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