Page - 78 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

6. Upper Level Controller Parameter Identification object picture retina h r α human eye eye lens Figure 6.7.: Projection of an object onto the human retina, adapted from [FBE01] The cost function is defined by JCF = nCF∑ i=1 (srOTF,i−s0−vvx,i τset)2 , (6.13) where the nCF is the number of available measured data sets fulfilling the required conditions for constant following. The necessary and sufficient conditions for finding the minimum read ∂JCF ∂τset = 0 and ∂2JCF ∂τ2set >0. (6.14) These conditions lead to the very compact equation τset= vv T x (srOTF−s0 InCF×1) vvTx vvx , (6.15) where the vectors vvx and srOTF contain all the measurements fulfilling the required conditions for constant following. Both vectors have a length ofnCF. The vector InCF×1 consistsofonesatnCF rows. Forthegivenmeasurements, thenumberofdatasetsequals nCF = 138878. Figure 6.8 shows the fitted straight according to eq. (2.22), with the parameters0 = 1.978m and the identified time gap τset= 1.174s. Moon et al. identified in [MY08] a time gap of 1.36s. Fancher et al. defined in [FBE01] that the selectable time gap should be in the range of 1 to 2s. In standard [Tec09], the minimum selectable time gap is set to 1s, while in standard [Tec10] it is limited by 0.8s. The identified time gap shows that the mean driver selects a time gap near the minimum regarding a safe vehicle following time of 1s. This suggests that there are many people who select time gaps below this limit. This could be proven by the fact that in the year 2007, 11.7% of the accidents documented by the police in Germany were related to too close distances to other road users, including insufficient following distances, [Sta08]. Figure 6.8 also demonstrates that there is a wide variation in human driving behaviour. 78