ECEF and LTP coordinates

[Seth Teller <seth@graphics.lcs.mit.edu>]

guys,

here is a latex excerpt that describes absolute (Earth)
coordinates, and local (campus, LTP) coordinates.  i'm
cc'ing mike bosse and zach bodnar, who may be able to
tell you how to convert LTP coordinates to MIT campus
coordinates.

prof. t.


\subsection{Coordinate Information}

The coordinate information file {\tt coord.ltp} resides at the top of
the data hierarchy.  It specifies an external coordinate system for
reference, and the dataset's origin and coordinate axes expressed in
this coordinate system.  Here is a coordinate information file for the
dataset:
\begin{verbatim}
CITY_LOCAL_TANGENT_PLANE
DATUM WGS84
LTP_LATITUDE_DEG 42.363371136 
LTP_LONGITUDE_DEG -71.090968114
LTP_ALTITUDE_M 46.41
LTP_TO_ECEF_XFORM_ROW1 -0.67383016 -0.535169569 0.509457014 3255071.19
LTP_TO_ECEF_XFORM_ROW2 0.738886267 -0.488049937 0.464601273 2968474.63
LTP_TO_ECEF_XFORM_ROW3           0  0.689493141 0.724292212 4596736.62
LTP_TO_ECEF_XFORM_ROW4 0 0 0 1
\end{verbatim}

The {\tt DATUM} element specifies the WGS84 ECEF datum
\cite{Hofmann:GPS:1997} as an external reference.  The first three
{\tt LTP} fields specify the latitude, longitude, and altitude of our
coordinate system origin (in this case, a GPS base station on the roof
of our building) with respect to the base datum.  Finally, the four
{\tt LTP\_TO\_ECEF} fields supply the rows of a $4 \times 4$ matrix
which converts a column vector $(x,y,z,1)^T$, expressed in LTP
coordinates, to ECEF coordinates.

\wfig{3.0in}{coordinates.eps}{ECEF and LTP coordinates.}{coordinates}

In ECEF coordinates (which are right-handed), the origin is at the
center of the reference ellipsoid, the positive $x$ axis goes through
the equator and the prime meridian, the positive $z$ axis goes through
the North pole, and the positive $y$ axis is orthogonal to the $x$ and
$z$ axes.  In LTP coordinates (also right-handed), $\hat{x}$ points
due East (in the local level plane), $\hat{y}$ points due North (in
the local level plane), and $\hat{z}$ points up (i.e., aligned with
the gravity vector).  Note that $\hat{z}$ does not necessarily align
with the direction to the ECEF origin, since ECEF coordinates model
the Earth as an ellipse \cite{Hofmann:GPS:1997}.