# Rotation of Radar Axis in 3D plane

I'm working on a sensor fusion application. In our vehicle, 4 radars (fixed, non-rotating radars) are placed at 4 corners of the vehicles at 45 degrees with respect to x, y and z-axes of the vehicle. For proper working of the sensor-fusion algorithm we need to offset all detected objects to the center of the vehicle.

The Radar axis are oriented as below

Radars are installed on vehicle as below:

Currently I was planning to use below formula to cater 2D rotations: x ́=x cos⁡θ+y sin⁡θ y ́=y cos⁡θ-x sin⁡θ Where ((x) ́,y ́) are the new coordinates of the same point but when its Radar axis is rotated by an angle θ.

However since z-axis of the radar is not parallel to the z-axis of vehicle I'm unable to use the above formula. Kindly advice on how can I rotate the z-axis of radar to make it parallel to vehicular z-axis.

• If you are not able to rotate the radar axes to vehicle axes with a single rotation about Z axis, then you need two (or three) successive rotations. However, I am not able to visualise the axes from the diagram given in the question. Do you have a proper top view, front view and side view of the setup rather than the 3D-ish view given currently in the question ?
– AJN
Commented Feb 28, 2023 at 13:18
• Not sure what you need to obtain. However, formulation and handling will be easier when you start using vectors (for positions, orientations, speed etc.) and matrices (at least for rotations; you can determine them from misaligned radar-vectors for example). Examples. Shift: $\vec r_{new}=\vec r_{radar}+\vec r_{offset3}$; Rotation: $\vec n_{radar4} = M_4 \times \vec {Orientation}_{radar4}$, where M is a matrix. // Once you have this set of vector equations, dealing with components become "easier", i.e. less prone to errors. Commented Mar 31, 2023 at 8:18