Page - 113 - in Maximum Tire-Road Friction Coefficient Estimation

6 Results and conclusion particles was always used. A particle distribution that is different than the initial one (e.g. based on the particles’ PDF) might improve an estimate, but this was not inves- tigated. In addition, the SD limit can be optimized. This re-initialisation method has the advantage that no fixed particles need to be calculated in parallel. In a third step, an alternative initialisation strategy for the variable particles was implemented using the difference between the estimates of the variable and the fixed particles. If the difference between µˆmax(fixed particles) and µˆmax(variable particles) was higher than a set limit of 0.2, it was assumed that there had been a change of µmax, and the current variable particles were replaced with particles with the initial distribution. This criterion was exceeded less frequently during the manoeuvre shown in Figure 6.6 than when using the SD limit discussed above, which led to a smoother estimate. Again, it may be possible to improve the estimate by adjusting the set limit (e.g. independenceonthecovariance)andbyanalternative selectionof thedistribution of the new particles. Table 6.2 shows the impact of the choice of re-initialisation on the estimate’s accuracy, which is discussed further below. 6.2. Strong braking manoeuvre with varyingµmax To evaluate the performance of the two proposed particle re-initialisation methods, a so-called µ step manoeuvre, in which the road surface changes during the manoeuvre, was selected. Thus, during a braking manoeuvre with a deceleration of≈−4.5 m/s2 as shown in Figure 6.7, the test vehicle drove from dry road (µmax≈ 1) to icy road (µmax≈ 0.3). The resulting estimates using both fixed particles and variables particles re-initialised by SD or ∆µˆmax, as shown in Figure 6.8. It can also be seen in Figure 6.8 that the estimate using variable particles re-initialised by SD (light gray) is very noisy, due to the high number of re-initialisations. It is interesting that it is even noisier than the method using no resampling step (black dotted). Nevertheless, the changes in µmax aredetectedquicklywithbothmethodsmentioned. In contrast, the estimateusing variable particles that are re-initialised based on ∆µˆmax (dark gray) is very smooth, but needs more time to detect the decrease in µmax. Furthermore, for this case, the real value is not as well met as with fixed particles or re-initialisation using SD limits. This occurs because the particles are not newly distributed, which suggests that the limit of 0.2 may be too high. Figure 6.9 shows the behaviour of the particles versus time for the two different ini- 113