Page - 114 - in Maximum Tire-Road Friction Coefficient Estimation

6 Results and conclusion 2.5 3 3.5 4 4.5 5 0 0.05 0.1 0.15 0.2 0.25 Time in s b) Difference between µmax(sampled particles) and µmax(fixed particles) Limit Time in s a) Standard deviation of sampled particles 2.5 3 3.5 4 4.5 5 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Limit ˆ ˆ Figure 6.6.: Top: Standard deviation (SD) of variable particles (black) and SD limit of 0.1 (gray) versus time during a braking manoeuvre with deceleration of ≈−4.5 m/s2 for aµ step manoeuvre. Bottom: Difference ∆µˆmax between µˆmax(fixed particles) and µˆmax(variable particles) and the limit of 0.2 versus time for the same manoeuvre. tialisation methods. Whereas in the case of SD, the number of re-initialisations is high, see Figure 6.9 (top), the infrequent re-initialisation using ∆µˆmax as shown in Figure 6.9 (bottom) favors higher deviations between the reference value and the estimate which is not corrected versus time. Table 6.2 shows the MAE and maximum absolute errors for the estimates shown in Figure 6.8. For the short periods of time where a change in µmax is not yet detected, the maximum absolute error of about 0.75 is quite high for all three cases. For this manoeuvre in general, the estimate µˆmax(fixed particles) shows the best accuracy with 114