Precision of conversion from WSG84 to ECEF and ECEF to ENU?

Question

To convert from a global to a local coordinate system, I apply the following transformations.

WSG84 to ECEG:

with

and ECEF to ENU:

Let's assume that the semi-major axes a and e are known with high precision (e.g. a = 6378137.0 and e²=6.69437999014e-3), and the reference position in the second transformation is correct.

What is the precision I can expect from this transformation within a short distance from the reference position (let's say less than a mile)?

Answer 1

Both of these equations ("Geodetic/Wgs84 to ECEF" and "ECEF to ENU") are exact equations for the transformations and they do not as such introduce any error to the position.

The limiting factors for the accuracy are basically the accuracy of the ellipsoid parameters and the numerical accuracy of the actual implementation (float point numbers have limited accuracy).

What I would personally do to check out the accuracy is to try out some conversions (e.g. with Wikipedia Coordinate Conversion equations)

1. Geodetic -> ENU-> Geodetic and
2. ENU -> Geodetic -> ENU

and see how well the numbers are the same after one "full loop". My guess is that with almost any impementation the accuracy is highly limited by the actual measurement of the location (be it, in Geodetic coordinates, for example).