EKF_robot_pose: how it works?

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Hello,

I have a question for ekf_robot_pose's authors

I can't understand from the source what math model ( x(k+1) = f(x(k),u(k)) ) has been used for robot system. Maybe something like this:

Where ξ is the speed of the robot, T is the sample time, Δ is the last rotation within [t(k-1), t(k)]

My output measurement is y = [x1 x2 θ] vector. I get it from odom topic like ekf_robot_pose algorithm. My input vector is u =[ξ Δ].

What's the input vector of ekf_robot_pose algorithm? Because it seems to work only with output measurement P.S. I use only odom informations.

Thank you