[a1k0n]

I'm aware of one paper which tries to fit a local polynomial model to the lateral dynamics, and they have a different model for different positions on the track (it requires really good localization to work): https://arxiv.org/abs/1610.06534

I had some of the vehicle parameters as part of my EKF for a while, but it led to some instabilities in the control.

The main problem is that it's really hard to know what the car's instantaneous lateral velocity is. I think the best you can do is check the difference of velocity*gyro yaw rate and lateral accelerometer measurement to get a noisy lateral acceleration measurement, and that can tell you how well your tires are hooking up. I might try fitting a least-squares model on the fly with something like that.