# Estimating yaw angle and yaw rate for a frontal vehicle

I would like to know if it is possible (and if it is possible how can it be done) to estimate the yaw angle and yaw rate of a vehicle in front of me knowing the following information:

-my speed (x,y,z),my position(x,y,z),my yaw angle and my yaw rate

-the relative speed to me(on x and y) of the vehicle/robot to which I want to find the yaw and yaw rate

-the position(x,y,z) of a point on the vehicle( corner of a vehicle) the length, width and height of the vehicle

You need to state some other piece of information, which might be obvious in your mind:

• Are the two vehicles exactly the same?
• Do you know the motion equations of them?

Any angular acceleration is a torque divided by the inertia moment, and by numeric integration or any other method, you usually can calculate the angular rate and instantaneous value. This is the correct method as far as I know.

I only can guess of sort of rather not series methods to try to guess the yaw of that vehicle, which would imply the usage of rule of three. But I insist on that, more data is needed, and that calculus is no reliable at all.

• To answer you questions: The vehicles are not the same, I do not know the motion equation between them. I have all the motion(velocity , acceleration, pitch, yaw, roll,pitch-rate, roll-rate, yaw-rate, position etc) information regarding my robot, and also relative speed, position, length, width, height of the robot in front of me. What I can say is that the two objects can move in a straight line or in a curve. – Mircea Paul Muresan May 29 '17 at 13:41
• Then, you cannot estimate the yaw angle or rate of the first robot. – galtor May 29 '17 at 14:53

If you had such information for at least two different times, that could be combined to determine the yaw and yaw rate. The "point on the other vehicle" information would need to be the same point on the vehicle for both times. (With such information about only one time, the best you could do is make a "guess" such as "not moving" or "same yaw and yaw rate as me".)

You would need to use the information about your own vehicle to convert the information about the other vehicle from relative to absolute coordinates. The change in the other vehicle's position would give you the yaw. The change in the point on the other vehicle, relative to the center of the other vehicle, would represent motion in a circle around that center: the yaw rate.

BTW, since you are interested in determining yaw and yaw rate based on measurements of position, you may find this project useful as an example. I used radar and lidar measurements to estimate the position, yaw, and yaw rate of a vehicle. By combining multiple measurements, it was possible to estimate position more precisely than any of the individual measurements and to estimate yaw and yaw rate which were never directly measured.

https://github.com/ericlavigne/CarND-Unscented-Kalman-Filter