Page - 111 - in Maximum Tire-Road Friction Coefficient Estimation

6 Results and conclusion 5 5.5 6 6.5 0 0.5 1 1.5 Time in s 5 5.5 6 6.5 0 0.5 1 1.5 Time in s Figure 6.4.: Top: Different particles marked by gray scale converge with time to the most likely value of µmax for particle filter with resampling step (The cor- responding estimate to this particle behaviour is shown as Example 1 in Figure 6.5). Bottom: Particles are fixed and thus remain constant versus time for particle filter without resampling step (Depiction corresponding to the estimate shown in Figure 6.3). they are fed the same input. It results from the chance-based resampling algorithm that deletes unlikely states and multiplies very likely states based on the particles’ PDF. Thus, the time to convergence and the values to which the particle fitler converges vary. Once the presented particle filter converged, the estimate no longer changes, regardless ofwhether the inputsandthevalue tobeobservedhavechanged. Ithas tobementioned that changes in the estimate can no longer be identified after all particles have moved towards the current most probable value. Thus, the particles have to be reset or re- initialised after convergence in order to be able to detect changes. The following section describesandcomparestwomethodsthatenablenewspreadingofparticlesundercertain circumstances. 6.1.3. Resampling step with particle re-initialisation For initial tests, 12 fixed and 24 variable particles were used in parallel, and the most likely estimate for each of the set of particles was calculated. In a first approach, the 111