[Proj] The world of ECEF aka geocentric coordinates

Duncan Agnew dagnew at ucsd.edu
Tue Feb 3 13:58:29 EST 2009

```According to

%A Tomas Soler
%A Larry D. Hothem
%T Coordinate systems used in geodesy: basic definitions and concepts
%J J. Surv. Engrg.
%V 114
%P 84-97
%D 1988

(both authors from the US National Geodetic Survey)

there are the following reference frames and coordinates:

1. The  Conventional Terrestrial Reference Coordinate Systems (CTRS)
which are geocentric, with z-axis pointing to the pole, and x through
zero longitude. They use  x,y,z for the Cartesian coordinates. There
are different realizations of this, for example the various ITRF's.
Note that with modern methods of space geodesy, the ellipsoid is
irrelevant: what is found is *only* straight-line distances between
points,
deduced from time delays. The ellipsoid chosen is just a matter of
convention and convenience.
The terminology used by the IERS is the same, with the particular
definitions adopted giving the International Terrestrial Reference
System, realized by the various International Terrestrial Reference
Frames.

2. Geodetic Coordinate Systems, Cartesian coordinates u,v,w; center
is at the center of the reference ellipsoid, w along semimajor axis,
u through the defined "zero longitude". Each datum corresponds to a
different GCS, and also includes something that gives the shape and
size of
the ellipsoid.
They use lambda, phi, and h for the ellipsoidal coordinates in such
a system, or for ellipsoidal coordinates in a CTRS with a given
ellipsoid;
they refer to these as "curvilinear geodetic coordinates".

[3. Astronomic coordinates, which depend on the local vertical. Not
used in mapping since people figured out to allow for deflections of
the vertical.]

4. Local Terrestrial Frame: origin where you like, xyz parallel to
the xyz of the CTRS. Not easy to visualize.

5. Local Geodetic Frame: origin where you like, u normal to the
ellipsoid,
e normal to u and in the geodetic meridian, n normal to both. This is
the usual enu local system, I think, and those are the letters they use.
They use alpha for geodetic azimuth, and nu for vertical angle.

[6. Local Astronomic Frame].

They do not discuss polar coordinates for the CTRS. Certainly the
standard usage is "geocentric latitude" for the polar angle. But unless
you are just approximating positions on a sphere, I'm not sure what
the point of using polar coordinates is.

I would say that the local enu should be called "Cartesian coordinates
in the local geodetic frame"--wordy, but it keeps the distinction clear
between types of coordinates and the frame they are used in.
"Rectangular"
suggests only two dimensions, and invites confusion with the Rectangular
system of land subdivision (township/range/section).

There doesn't seem to much of a consensus, does there?

Duncan Agnew

```