Hello,

It turns out, if we consider this local coordinate system strictly, then for any point of standing (except for P0) - there must be vertical deflections?

Yes, the vertical of P0 is orthogonal to the local plane (the vertical axis is the normal axis) and the vertical is orthogonal to the surface of the ellipsoid. Each point is transformed to local plane. The tilt of the vertical of such points must be taken into account during the adjustment.

Kind reagrds
Micha

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