Usually, when doing millimeter-wave radar tracking, the issue of the coordinate system is not particularly considered. In fact, the motion model and algorithm assume that the coordinate system is stationary, but in fact the millimeter-wave is installed on the vehicle and moves with the vehicle. There are both translational and There is also rotation. If the assumption of a stationary coordinate system is still used, it will bring obvious errors.
The following attempts to illustrate this problem.
Assuming that the target is fixed, the millimeter-wave radar is installed on the vehicle and moves with the vehicle, as shown in the figure below. The target coordinates are always (10, 10), the self-vehicle is at (0, 0) at time t0, and the angle of the coordinate system is 0°; at time t1, it is at (1, 1), the angle of the coordinate system is 10°, and at time t2 is at (2, 2) , the angle of the coordinate system is 20°, and there is a certain rotation.
The target coordinates at time t0 are (10, 10),
The target coordinates in the coordinate system at time t1 are (cx1, cy1)=(9,9) and then rotate θ1=10°, then there is
x1 = cx1*cosθ1 + cy1*sinθ1
y1 = -cx1*sinθ1 + cy1*cosθ1Bring cx1, cy1 and cosθ1, sinθ1 into x1=10.4256, y1=7.3008
The target coordinates of the coordinate system at time t2 are (cx2, cy2) = (8, 8) and then rotate θ2 = 20°, then
x2 = cx2*cosθ2 + cy2*sinθ2
y2 = -cx2*sinθ2 + cy2*cosθ2Bring cx2, cy2 and cosθ2, sinθ2 into x2=10.2536, y2=4.7816
Therefore, from time t0 to time t1, in the vehicle coordinate system
Rvx1 = (x1 - x0)/Δt = 0.4256m/s
Rvy1 = (y1 - y0)/Δt = -2.6992m/sAnd in the world coordinate system
vx1 = -1m/s
vy1 = -1m/sFrom time t1 to time t2, in the vehicle coordinate system
Rvx2 = (x2 - x1)/Δt = -0.272m/s
Rvy2 = (y2 - y2)/Δt = -2.5192m/sAnd in the world coordinate system
vx2 = -1m/s
vy2 = -1m/sThe speed of the target seen in the self-vehicle coordinate system is different from that in the world coordinate system, mainly because the self-vehicle has rotational motion, not just translational motion. If the ego vehicle is only translational, the calculated velocity is consistent with the world coordinate system.
In the case of ego car rotation, the relative speed can be calculated by unifying the front and rear coordinates.
In the ego vehicle coordinate system at time t1
x0 = 11.584, y0 = 8.112, then we have
Mvx1 = - 1.1584m/s
Mvy1 = -0.8112m/sIn the ego vehicle coordinate system at time t2
x1 = 11.5353, y1 = 5.3793, then we have
Mvx2 = -1.2817m/s
Mvy2 = -0.5977m/sIt can be seen that the speed error after compensation is smaller, and the estimation is more accurate during extrapolation.
To give another more intuitive example, the self-vehicle moves in a circle around the origin of the coordinates, with a radius of 10, each cycle is 50ms, and the rotation between cycles is 1° (0.349rad).
If the difference between the two frames is simply made, the relative horizontal and vertical speed of the target is always changing, and should be a constant value in fact.
If the coordinate conversion compensation is done between the coordinates, the accurate relative speed can be obtained, which can also be derived through the formula.
vx = -r*(yawrate*Δt)/Δt = -r*yawrate = -3.49m/s
vy = 0m/s