Seite - 145 - in Maximum Tire-Road Friction Coefficient Estimation

E. Longitudinal velocity estimation An accurate monitoring of the vehicle’s longitudinal velocity vx is necessary for the calculation of the longitudinal slips sx,i as described in Section 5.5.1. The following sections present different approaches to estimate vx with the required accuracy. These approaches are divided into methods that only use the ESC sensors, in observer-based methods, in radar-based methods and in methods based on global navigation satellite system (GNSS). This classification is based on Uchanski, who mentions measuring or estimating vx either by a vehicle speed observer, by using radar sensors or by using data from a , [Uch01, p.114]. The following sections also discuss promising solutions for automotive series-application regarding costs. E.1. Estimation of the longitudinal velocity using only ESC sensors The reference velocity vx can be calculated using only the wheel speeds ωi for certain driving states. With a free rolling wheel (e.g. when accelerating on a non-driven axle), a referencevelocityvx canbecalculated foraknowneffective tire radiusre,i. Nevertheless, at least one wheel has to be slip-free. This generally excludes all four-wheel driven vehicles and all vehicles during braking. An additional problem is the accuracy that can be reached. As mentioned by Dieckmann, [Die92, p.19-22, 110], it is possible to estimate sx with a high resolution when the wheel rotational speeds are observed for several revolutions. Due to this principle, this only works when ωi does not change quickly. In addition, the observed wheel needs to be slip-free, as mentioned above. Again, free rolling conditions have to be used for calibration to compensate for differences in the effective tire radius re,i between front and rear axle, [Die92, p.110-111]. One promising idea is to estimate sx simultaneously to µ max, as mentioned in Section 5.3. This is possible because the influences ofµmax and sx,i are in different ranges ofFx,i, cf. [BZ07, p.84-86]. Nevertheless, this was not investigated, as this special focus was beyound the scope of this thesis.