Page - 147 - in Maximum Tire-Road Friction Coefficient Estimation

E Longitudinal velocity estimation Villagra et al. propose estimating vx and vy using bax, bay,ωz andωi based on alge- braic estimation approaches, [VdFM08]. To estimate only vx, an estimate of vy is also necessary. The sensitivity of the results toµmax seems to be low. It has to be mentioned that no vehicle parameters are necessary. Nevertheless, no experimental results were shown, but just experiments with simulated data. Rajamani et al. discussed the estimation of vx based on two different sensor com- binations, [RPPL12]. For the first approach, the wheel speeds and an accelerometer are used to estimate vx within an observer. Although this approach takes into account aerodynamic drag and estimating the climbing resistance, it showed some shortcomings in the form of under-damped estimation dynamics and was not suitable, according to the authors. The second approach is described within the GNSS-based approaches. E.3. Radar-based estimation of the longitudinal velocity Radar sensors are already available in vehicles equipped with adaptive cruise control (ACC). The necessary accuracy with which the relative velocity ∆vx to other objects (including stationary objects) has to be detected for ACC are≤2 m/s or≤3 % of ∆vx. This high accuracy of the relative velocity makes it possible to improve the on-board calculation of the vehicle’s own velocity vx, [WDS09, p.492]. The resolution with which the relative velocity ∆vx between the vehicle and another object can theoretically be measureddependsonthemeasurementtimeT andthefrequencyrangef0, [Win09b]. For automotiveapplicationsworld-widethetransmitted frequencyf0 ismostoften76.5GHz. Given the light speed cL= 299792458 m/s 2 and a typical measurement timeT= 0.04 s, the theoretical resolution ∆v¯x of the relative velocity is ∆v¯x= cL 2 ·f0 ·T = 299792458 2 ·76.5 ·109 ·0.04≈ 0.05 m/s, (E.1) [Win09b]. As an example for the real achieved accuracy, the Bosch LRR3 radar sensor currentlyused inseriesapplication forACChasanaccuracyof∆vxof0.1m/s, [Win09b]. Nevertheless, this is the accuracy of the relative speed to other objects. It cannot be assumedthatthishighaccuracycanalsobeachievedfortherelativevelocitybetweenthe vehicle and the road. This accuracy also depends on the mounting height of the sensor, the direction of the centre of the transmitted signal and especially on the reflection capability of the road. The reflection capability depends in general on the type of object, its geometry and its orientation. Metal objects (e.g. stationary objects such 147