Seite - 34 - in Maximum Tire-Road Friction Coefficient Estimation

2 Estimation of the friction potential the variance between different initial slip slopes and corresponding friction potentials µmax is very high, as shown by Uchanski, [Uch01, p.122-124]. Uchanski proposedanapproachtodetect low-frictionsurfacesduringbrakingmanoeu- vres based on the wheel rotational speedsωi from the ABS sensors and a measurement of the longitudinal velocity vx, [Uch01, p.111-122]. The results also show a dependence of lower slipvalueswithµmax. Onecrucial factor is accurateandreliable slipcalculation. During braking, it is difficult to calculate a reference velocity vx using only wheel speed sensorsas thevelocity state changes tooquickly. Thusanothermethod for estimatingvx is necessary, [Uch01, p.114]. In addition, the longitudinal tire forces during braking are estimated using wheel speeds and vx in a filtering technique called optimal FIR deriva- tive, [Uch01, p.76-98]. Ray proposed a model-based approach where the most probable friction potential µmax is estimated using an adapted form of a particle filter, [Ray97], which is described in Section 5.2. The main element to estimate the friction potential is a tire model that calculates the expected longitudinal and lateral tire forces Fx and Fy for different hy- potheses of µmax. The inputs for the tire model are the tire loadFz,i, the longitudinal slip sx, the side slip angle α and the longitudinal velocity vx. These model-based hy- potheticalFx,i are then compared to longitudinal tire forces that have been estimated separately using an extended Kalman filter and a vehicle model with the vehicle’s state measurements. In a state observer model such as the particle filter, there is a measure- ment function z (cf. Equation 5.2) that contains the internal state x to be observed, which is not directly measured. In the approach mentioned, z is an estimate from an- other state observer, i.e. the extended Kalman filter. Thus, this method requires much knowledge about vehicle and tire parameters, as well as signal characteristics in order to obtain the necessary vehicle states with sufficient accuracy (e.g. the longitudinal slip sx or the slip angleα), in order to have an acceptable estimate of the horizontal tire forces. Boßdorf-Zimmer also used a Baysian filter, namely an extended Kalman filter, to estimateµmax for lateral driving states. He estimated both the slip angleα andµmax si- multaneously using a two-track vehicle and a non-linear tire model. The combined estimation is possible because the influence ofα andµmax affects the lateral tire forces in different ranges of influence, [BZ07, p.75-95], see also Figure 5.2 for the similiar rela- tion of the longitudinal tire forceFx,i and the longitudinal slip sx andµ max. 34