Calculating Speed Between Two Cars

[kacem]

Hi,
I found a programming problem that calculated the speed between two cars as below and I would like to know how the calculation is done.
it is about determining the speed of two cars. The coordinate reference system (y,x) is attached to the ego vehicle (as shown in the attached figure).
The speed of the lead car is estimated with the radar of the ego vehicle.
As mentioned in the program reference: The true ground speed of a radar-reported object from the relative speed and the ego vehicle speed is calculated as follows:

(Vxi,Vyi) : relative object speed
egoSpeed : ego vehicle speed
[Vx,Vy] : ground object speed

Vx = Vxi + egoSpeed :Calculate longitudinal ground speed
theta = atan2(Vyi,Vxi) :Calculate heading angle
Vy = Vx * tan(theta) :Calculate lateral ground speed

Is there anyone who can explain how Vx and Vy are calculated? and why he uses the term "ground"?
Thank you.

 

[berkeman]

Welcome to the PF.

Is there anyone who can explain how Vx and Vy are calculated? and why he uses the term "ground"?

Those equations are just showing the vector addition of the two vehicle speeds to get the speed of the front vehicle with respect to the ground.

Have you learned any vector math in your schoolwork so far? If not, we can probably suggest some learning resources to help you get up to speed on these kinds of questions.

 

[A.T.]

I found a programming problem ...

Where is the code from? It seems wrong:
Theta is the movement direction relative to the chase car based on : theta = atan2(Vyi,Vxi)
But it is used to relate the velocity components relative to ground : Vy = Vx * tan(theta)

 

[kacem]

Where is the code from? It seems wrong:
Theta is the movement direction relative to the chase car based on : theta = atan2(Vyi,Vxi)
But it is used to relate the velocity components relative to ground : Vy = Vx * tan(theta)

Hi,
That's why I asked this question. It is about Matlab code from Matlab Mathworks Website, you can find it in calculateGroundSpeed section:
https://fr.mathworks.com/help/driving/examples/forward-collision-warning-using-sensor-fusion.html

 

[A.T.]

Hi,
That's why I asked this question. It is about Matlab code from Matlab Mathworks Website, you can find it in calculateGroundSpeed section:
https://fr.mathworks.com/help/driving/examples/forward-collision-warning-using-sensor-fusion.html

Well, I don't get it either. Why even calculate that angle, if you can do simple vector addition:

[Vx,Vy] = [egoSpeed + Vxi, Vyi]

But maybe I'm misunderstanding what the inputs and outputs are supposed to represent.