Moving horizon estimation for tire-road friction during braking

Estimation of tire-road friction forces has an important role in anti-lock brake systems (ABS), as well as for vehicle stability control systems, and road condition monitoring systems. We investigate the use of a moving horizon observer for estimation of multiple friction model parameters as well as the longitudinal wheel slip state under typical ABS braking scenarios, using wheel speed measurement and information on the brake torque. It is well known that data may not be persistently exicting for every period of time in such scenarios, expecially when estimating several friction model parameters simultaneously. The algorithm therefore has regularization mechanisms to ensure graceful degradation of the state and parameter estimation performance in cases when data are not persistently exciting. Simulations with a quarter car dynamic model and the four-parameter longitudinal Magic-formula friction model illustrates the performance of the algorithm.