Bart found out that the current definition, as used by U. Fechner and L. Fagiano is not well suited for control purposes.

You can find a different definition here: https://github.com/OpenSourceAWE/SymbolicAWEModels.jl/blob/v3-kite/examples/heading_gate.jl

• try to reproduce the results of Bart
• add a new function for calculating the heading in a better way
• update the documentation

The old definition should not be deleted so that results can be compared using both the old and the correct definitions.

The following code could be used as a starting point, but the nomenclature needs to be adapted:

"""Wind frame heading by projecting body x-axis onto wind-perpendicular plane."""
function wind_frame_heading(R_body_x, wind_vel)
    wind_norm = wind_vel / norm(wind_vel)

    minus_e_x = -R_body_x
    proj_on_wind = dot(minus_e_x, wind_norm) * wind_norm
    e_x_perp = minus_e_x - proj_on_wind

    wind_cross_z = [wind_norm[2], -wind_norm[1], 0.0]
    heading_x = dot(e_x_perp, wind_cross_zt

    heading_z = e_x_perp[3]

    heading = atan(heading_x, heading_z)
    return heading
end

R_body_x is the x vector of the rotation matrix from the world to the body reference frame.
The world reference frame is the ENU reference frame.
wind_vel is the velocity vector of the wind in ENU reference frame under the assumption that the z component is zero.