Laws & Regulations

PRS92 Transformation Parameters

For GPS users, the following transformation parameters will be necessary when undertaking local surveys. They relate the WGS84 Datum, to which all GPS data is referenced to PRS92 on the Luzon Datum. These parameters are applied to WGS84 geocentric Cartesian coordinates to give Cartesian coordinates of the PRS92 datum which will then be transformed to geographical PRS92 coordinates.

PARAMETER WGS84 → PRS92 PRS92 → WGS84
$\Delta X$ 127.62153 -127.622
$\Delta Y$ 67.24339 -67.245
$\Delta Z$ 47.04738 -47.0433
ROT X -3.06803 3.068
ROT Y 4.90297 -4.903
ROT Z 1.57807 -1.578
SCALE 1.06002 -1.06002

The general similarity transformation formula that relates two sets of coordinates is shown below.
\[ \begin{pmatrix} X_2 \\\ Y_2 \\\ Z_2 \end{pmatrix} = \begin{pmatrix} \Delta X \\\ \Delta Y \\\ \Delta Z \end{pmatrix} + (1 + S_c \times 10^{-6}) \begin{pmatrix} 1 & R_Z & -R_Y \\\ -R_Z & 1 & R_X \\\ R_Y & -R_X & 1 \end{pmatrix} \begin{pmatrix} X_1 \\\ Y_1 \\\ Z_1 \end{pmatrix} \]
Where:
$X_2$, $Y_2$, $Z_2$ are the transformed cartesian coordinates
$\Delta X$, $\Delta Y$, $\Delta Z$ are the shifts for the change in origin
$R_X$, $R_Y$, $R_Z$ are the rotations of each axis
$S_c$ is the scale change in parts per million
$X_1$, $Y_1$, $Z_1$ are the coordinates to be transformed

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