Page - 108 - in Maximum Tire-Road Friction Coefficient Estimation

6 Results and conclusion It can also be seen around second 5 that the hypotheses ofFx(particles), which depend on sx, show a steeper slope for the simulated manoeuvre thanFx(MD,i). 4.5 5 5.5 6 6.5 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Time in s µmax F x (particles) F x (M D,i ) µmax=0.1 µmax=0.5 µmax=1.2 Figure 6.1.: Hypotheses for longitudinal tire forcesFx,i (gray) for different particles (e.g. values) ofµmax, but with the same inputs for longitudinal slip sx, side slip angleα and tire loadFz,i. The thick black line denotes the expected longi- tudinal tire force based on the vehicle’s acceleration bax. 6.1.1. Results without resampling step Section5.2describedtheparticular stepswithin theparticlefilterandalsomentionedan implementationwithout the resampling step. Without this step, theparticles ofµmax do not change with time. Thus, the hypotheses of the longitudinal tire forces are always calculated for the same particles. At every time step, the particles ofµmax are assigned probabilities, which then makes it possible to calculate an estimate using the probability of each particle as its weight for each time step. Since the probabilities of the particles are calculated based on the difference between the hypothesized values ofFx,i andFx,i(MD,i) for every time step, every small deviation between the expected and the current inputs results in an inaccurate estimate. In the best case, the estimate just appears noisy. These deviations occur due to measurement uncertainties, especially in the determination of sx andMD,i. Deviations also arise due 108