Looking at this:


[lat,lon,h] = ned2geodetic(xNorth,yEast,zDown,lat0,lon0,h0,spheroid))

The obvious question is by how much the current location on local Cartesian NED (xNorth,yEast,zDown) can be far away from the reference point (lat0,lon0,h0)?

For example if the reference point is in Australia and the current location is in the US, does those "mathematical tricks" still will be valid?

I assume that there is an intermediate step of-

Local Cartesian NED to geocentric ECEF: https://www.mathworks.com/help/map/ref/ned2ecef.html

Since they also using Geodetic reference point - probably first converting the Geodetic reference point to ECEF, and then there is the questioned "mathematical tricks" to "add" current local Cartesian NED to that reference point (already represented in ECEF) so the current local Cartesian NED will be in ECEF - Thus the "mathematical tricks" are some sort of Cartesian/Vectorial manipulations, I suspect how long they holding in the context of maps, geodesy etc?

Regarding converting Geodetic reference point into ECEF in the intermediate step mentioned above, and in the final step converting back current Cartesian point (already in ECEF) to Geodetic, they use:

Transform geocentric (ECEF) to geodetic coordinates: https://www.mathworks.com/help/map/ref/ecef2geodetic.html

Assuming this is pretty much straight forward formulas with known limitations (Characteristics of different methods to convert ECEF to LLA) So I don't see how they interfere here...

  • 1
    I was working with both formulas (ecef2geodetic) then (ecef2enu) for different coordinates around the world. They did the job. But I still cannot get your question!
    – Moh
    Commented Jun 16, 2019 at 13:35

1 Answer 1


I don't think there are practical limitations to ned2geodetic.

  • The conversion from LLA to ECEF coordinates has closed form solution.

  • The rotation of NED vector to ECEF has closed form solution.

  • Vector addition in ECEF is trivial.

  • Conversion of ECEF coordinates to LLA as implemented in Matlab is not closed form solution. However, the algorithm employed is documented to have good accuracy and well behaved, unless the point lies close to the center of the earth (~50km).

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