paparazzi/doc/pprz_geodetic/ned_enu.tex

\section{NED / ENU}
North-East-Down or East-North-Up coordinates are fixed in the local tangent plane. 

NED and ENU coordinates are defined using
\begin{equation}
p_{NED} = \begin{pmatrix} x \\ y \\ z \end{pmatrix} \qquad
p_{ENU} = \begin{pmatrix} x \\ y \\ z \end{pmatrix}
\end{equation}
available for the following simple types
\begin{itemize}
\item int32\_t - \texttt{NedCoor\_i} and \texttt{EnuCoor\_i}
\item float - \texttt{NedCoor\_f} and \texttt{EnuCoor\_f}
\item double - \texttt{NedCoor\_d} and \texttt{EnuCoor\_d}
\end{itemize}

\subsection{Transformation between NED and ENU}
The transformation between NED and ENU is rather simple. It can be expressed using a rotational matrix:
\begin{equation}
p_{NED} = \begin{pmatrix}
0 & 1 &  0 \\
1 & 0 &  0 \\
0 & 0 & -1
\end{pmatrix}
p_{ENU} \qquad p_{ENU} = \begin{pmatrix}
0 & 1 &  0 \\
1 & 0 &  0 \\
0 & 0 & -1
\end{pmatrix} p_{NED}
\end{equation}
or directly switching the values
\begin{equation}
\begin{pmatrix}x \\ y \\  z \end{pmatrix}_{NED} = 
\begin{pmatrix}y \\ x \\ -z \end{pmatrix}_{NED}
\end{equation}
\inHfile{ENU\_OF\_TO\_NED(po, pi)}{pprz\_geodetic}
\inHfile{INT32\_VECT2\_ENU\_OF\_NED(o, i)}{pprz\_geodetic\_int}
\inHfile{INT32\_VECT2\_NED\_OF\_ENU(o, i)}{pprz\_geodetic\_int}
\inHfile{INT32\_VECT3\_ENU\_OF\_NED(o, i)}{pprz\_geodetic\_int}
\inHfile{INT32\_VECT3\_NED\_OF\_ENU(o, i)}{pprz\_geodetic\_int}



\subsection{Transformation from NED/ENU}
\subsubsection*{to ECEF}
\input{transformations/ned_enu2ecef}


\subsection{Transformation to NED/ENU}
\subsubsection*{from ECEF}
\input{transformations/ecef2ned_enu}

\subsubsection*{from LLA}
\input{transformations/lla2ned_enu}