Application of Neural Networks to External Parameter Estimation for Nonlinear Vehicle Models

In this article, we propose a method of combining neural networks (NN) with nonlinear state-space models (SSM). Such model parts that are well understood can be integrated into the state space, while the NN can estimate such parts that are uncertain or hard to model. We apply the method to vehicle state estimation on a race track. Therefore, we derive a nonlinear two-track model with a scaled magic formula and adaptively estimate the tire parameters—stiffnesses and maximum friction potential—with the NN. The results show that the NN is able to reach an excellent estimation performance and generalizes over different model parameters, such as tire type, tread depth, surfaces conditions, and maneuvers. The trained model is furthermore integrated into an Extended Kalman Filter (EKF) to estimate the longitudinal speed, lateral speed, and yaw rate of the vehicle.