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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

enter image description here

Radars are installed on vehicle as below:

enter image description here

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.

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    $\begingroup$ 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 ? $\endgroup$
    – AJN
    Commented Feb 28, 2023 at 13:18
  • $\begingroup$ 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. $\endgroup$
    – MS-SPO
    Commented Mar 31, 2023 at 8:18

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In the Cartesian system were each vector is an compound number, should be able to do a dot product with the vehicles Z axis to get the required projection or any axis for that matter.

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