Page - 112 - in Maximum Tire-Road Friction Coefficient Estimation

6 Results and conclusion 0.6 0.7 0.8 0.9 1 1.1 1.2 4.8 5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 Time in s Reference Resampling, Ex. 1 Resampling, Ex. 2 Resampling, Ex. 3 Figure 6.5.: Threeestimationexamplesofµmax foradrivingmanoeuverwitha longitudi- nal acceleration of bax≈4.5 m/s2 with variable particles ofµmax converging due to resampling. Mean absolute errors (MAE) and maximum absolute error of the three estimates are shown in Table 6.1. Table 6.1.: Mean absolute error (MAE) and maximum absolute error for driving ma- noeuver with bax≈ 4.5 m/s2 Example Mean absolute error (MAE) Maximum absolute error Fixed Particles 0.1725 0.7860 Variable Particles, Ex. 1 0.0798 0.1445 Variable Particles, Ex. 2 0.0299 0.1486 Variable Particles, Ex. 3 0.0494 0.1209 weighted sum of both estimates was used, which unfortunately combined the disadvan- tages of both estimators. Once the estimate of the variable particles converged, it did not change anymore with time, whereas the estimate of the fixed particles contributed noise to the final estimate. In a second step, it was considered that the state of convergence of the estimate is known because of the current distribution of the variable particles. Thus, by observ- ing the standard deviation (SD) of the particles at each time step, it is evident when particles are no longer changing over time and thus should be re-initialised. A limit of the standard deviation of 0.1 was attempted, see Figure 6.6. It can be seen that for the investigatedmanouevre shown inFigure6.2, theSDwasoftenbelowthis limit, resulting in many re-initialisations of the particles. This makes the estimate noisy, but enables fast detection of changes in µmax. During re-initialisation, the initial distribution of 112