Exact conversion of ECEF to geodetic coordinates

Question

I came across the paper "Exact conversion of Earth-centered Earth-fixed coordinates to geodetic coordinates", which describes a series of equations which can be used to calculate a set of geodetic coordinates from a set of ECEF coordinates. However, there seem to be a plethora of methods for doing this type of calculation, and so I'm wondering:

1. Is this method mathematically correct?
2. Does there exist a closed-form solution to the conversion problem which is widely accepted as a standard in the GIS community?

Answer 1

1. The equation continues on the following page, so it's hard to tell.
2. Yes, please see EPSG Guidance Note 7.2 in Section 2.2.1 titled "Geographic/Geocentric conversions" (EPSG code 9602) You will want the reverse conversion to get from X/Y/Z to Lat/Long/Height*.

*Note that height here is defined as height above the ellipsoid, which is often confused with elevation. Elevation is (usually) defined as height above the geoid or mean sea level.

Answer 2

1. From my research of ECEF-to-geodetic algorithms, the Zhu (1993) algorithm is accurate enough for almost all practical uses. However, there are other algorithms that have better accuracy and speed.

   The conversion from ECEF to geodetic coordinates has several solutions. In this field, when an author claims their algorithm is "exact", they might mean that it's simply closed-form (i.e. non-iterative). Or they might mean they've solved for one root of the quartic equation.

   Some other algorithms worth considering:

   • Olson (1996)
   • Bowring (1976)

2. In my opinion, GeographicLib comes close.