question about formula(1) in the paper

[Amazingmum]

Hi author，
In formula (1), alpha is the heading Angle. Could you please tell me how this Angle is defined and which coordinate system is used as the reference? The sensor coordinate system, or the coordinate system at the rear of the vehicle.
Tks for your attention~

[ramdrop]

Hi, sorry for the late reply. All variables in Eq.(1) are defined in the radar frame, i.e., the sensor coordinate system. Please refer to the figure in [27] for further guidance.

[27] D. Kellner, M. Barjenbruch, J. Klappstein, J. Dickmann, and K. Dietmayer, “Instantaneous ego-motion estimation using Doppler radar,” in 16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013), Oct. 2013, pp. 869–874.

[Amazingmum]

thanks.
One more thing:
the v in the ransac_range_v.py ：
v = (pcl[:, 6]**2 + pcl[:, 7]**2)**0.5 # target's absolute velocity in radar frame

v_comp = (pcl[:, 8]**2 + pcl[:, 9]**2)**0.5 # target's absolute velocity in global frampcli

i know the pcl is radar data read from pcd file，but not clear about the v and v_comp.

target's absolute velocity in radar frame：it means that the v is relative to ground and expressed in radar frame.
(actually,radar can measure the target's speed relative to the radar.
if the target is not moving，it is right to say absolute velocity.
if the target is moving ，it is not absolute velocity.
So，the v is not very clear)