A driver assistance system (10) assists the driver in controlling the direction of a moving vehicle along a contrived centerline between lane markings by regulating a steering bias applied to a steering system of the vehicle. An electric motor (22) coupled to the steering mechanism provides a torque input to the steering in response to an estimate of electric current provided by an observer. The observer has a friction term matrix element (a.sub.55), which is correlated with friction in the steering mechanism. A controller (24) is provided, which establishes a desired or ideal frequency function of lateral displacement data (102), samples lateral displacement to provide a real frequency function of lateral displacement data (104), compares the real frequency function with the ideal frequency function (106), and updates or leaves unaltered the friction term (a.sub.55) based on the result of comparison.