Page - 12 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

2. Adaptive Cruise Control t 0 1 1− τ received signal emitted signal 0T DRT Figure 2.3.: Emitted and received pulses of a Pulsed Doppler RADAR, adapted from [Men99] where f0 = 1 T0 is the emitted carrier frequency of the RADAR sensor, [Men99]. The received signal has a frequency of fDR=f0 +∆fr˙, where fDR= 1 TDR , see fig. 2.3. FMCW RADAR In contrast to the Pulsed Doppler RADAR, the Frequency-Modulated Continuous Wave (FMCW) RADAR sends and receives continuous electromagnetic waves. Using the rule f(t) =f1 + f2−f1 T t, (2.3) the sending frequency f(t) is modulated with linear ramps of the length T between f1 and f2. Figure 2.4 shows an example for three frequency ramps emitted by an FMCW RADARsensor. Thefinite speedofpropagationofRADARwaves,described ineq. (2.1), causes a frequency shift between the emitted and received signals of ∆fr=f1−f(t) =−f2−f1 T 2r c . (2.4) This effect is superimposed by the Doppler Effect of eq. (2.2). Therefore, the equation of the measured frequency difference between emitting and receiving signals of an object at distance rwith the relative velocity r˙ reads ∆f=−f2−f1 T 2r c −f02r˙ c . (2.5) The detection of a single object requires two different ramps, while a third ramp must be added in order to detect more than one object. The graphical representation of the problem can be performed in the r-r˙ plane, [Men99]. The solution for the distance and the relative velocity is at the point of the intersection of the different ramps. Figure 2.5 shows an example of a situation with three different ramps and four objects. 12