The definition of the ADMA yaw, pitch and roll angles follows the Euler angles rules. As defined in the automotive industry standards, former DIN 70000, now ISO 8855, the applied rotational sequences belong to the group of Tait-Bryan rotations around the three coordinate axes.
The standards define:
• Symbol “Ψ” (Psi) = “Yaw” = angle around Z axis
• Symbol “Θ” (Theta) = “Pitch” = angle around Y axis
• Symbol “Φ” (Phi) = “Roll” = angle around X axis
The three rotations rotate the navigation frame XYZ into the body frame XYZ using the 3x3 matrix MGNR or vice versa (using MGNRT). The axes of the frame coordinate system are defined as north, east and down axes.
Yaw-Pitch-Roll rotation sequence:
• The yaw angle Ψ measured in the frame coordinate system is rotated around the z axis. The Y axis becomes the node axis y'.
• The pitch angle Θ measured relating to the earth's surface x-y plane is rotated around the node axis y'. The result is the vehicle-fixed x’ axis.
• The roll angle Φ describes the rotation around the vehicle-fixed x axis. The vehicle-fixed axes y’’ and z’’ are created.
Transformation from navigation frame XYZ into body frame XYZ: