Local Cartesian System and Earth`s curvature

by Micha ⌂, Bad Vilbel, Wednesday, July 14, 2021, 08:43 (18 days ago) @ lyoyha

Hello lyoyha,

Is there a mistake in the formula?

Thank you for critical read the equation. This equation seems to be valid and can be found at Wikipedia, cf. From ECEF to ENU. The order is, however, east, north, up (which should be y, x, z instead of x, y, z). I changed the order to:

$\begin{pmatrix}y_i \\ x_i \\ z_i\end{pmatrix} = \begin{pmatrix} -\sin\lambda_0 & \cos\lambda_0 & 0 \\ -\sin\phi_0\cos\lambda_0 & -\sin\phi_0\sin\lambda_0 & \cos\phi_0 \\ \cos\phi_0\cos\lambda_0 & \cos\phi_0\sin\lambda_0 & \sin\phi_0 \end{pmatrix} \begin{pmatrix} X_i - X_0 \\ Y_i - Y_0 \\ Z_i - Z_0 \end{pmatrix}$

(EDIT: You are referred to the subindex, right? I corrected the equation and replaced the r by 0. Thanks!)

Can you confirm this equation?

Kind regards
Micha

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