Page - 91 - in Maximum Tire-Road Friction Coefficient Estimation

5. Tire/road friction estimator This chapteroutlines theproposedmethod for estimating the frictionpotential basedon sensor signals of avehicle equippedwithESC.Abrief introduction to recursiveBayesian state estimation (and especially the particle filter) is provided first. Both methods have proven to be suitable for state estimation problems and can deal with the presence of uncertain measurements and measurement noise. The system model to be observed, which was chosen based on the results of Section 4, is described. The advantages and disadvantages of both the observer and the model are discussed, with an emphasis on longitudinal tire force calculation, as its accuracy is crucial for the estimate’s accuracy. 5.1. Recursive Bayesian state estimation Estimating the friction potential based on measurements of the vehicle’s states can be treatedasastateestimationproblem, since the frictionpotential isa time-varyingmodel parameter that directly influences the vehicle’s state equations. In state estimation, a statex(k) that isdifficultor impossible tomeasuredirectly isobservedviameasurements of inputsandoutputs, [Bau07,p.1]. This isusuallyaccomplishedwithinanobserver that delivers an estimate xˆ(k) for the internal state based on a state model, which consists of a non-linear difference equation for x(k) and a non-linear measurement equation z(k) in the form x(k) = f(x(k−1),w(k)) (5.1) z(k) = h(x(k),v(k)), (5.2) [Wat06, p.65], with k= 1, ...,Nk being the time step. Since the state model can only represent a simplified description of the real physical process, uncertainties are unavoid- able. In addition, the necessary measurements are subject to measurement noise and model inaccuracies. These uncertainties, which are considered within Equations 5.1 and 5.2, are modelled as the process noisew(k) and the measurement noisev(k). Deviations between a real value and its measurement are subject to chance. This means that for a constant input, the outcome of the measurements will vary randomly. Rather than