Page - 15 - in Integration of Advanced Driver Assistance Systems on Full-Vehicle Level - Parametrization of an Adaptive Cruise Control System Based on Test Drives

2.2. Environmental-Recognition Sensors r 1r 2r ϕ Rx11A Tx Rx22A xs ys d S Figure 2.7.: Monopulse priciple, adapted from [Win09] as described in eq. (2.3). When sending at frequency f(t), it receives the frequency f(t)−∆fr. At this measurement at time t, the frequency shift due to the Doppler Effect is omitted because it is much smaller than the change of the frequency due to the chirp. Using this frequency shift and eq. (2.4), the distance to the object can be calculated. The relative velocity is determined with the frequency shift due to the Doppler Effect, which is not determined at a single measurement point, but rather over a longer period of frequency ramps. Therefore, eq. (2.2) with f0 = f1 is used to find the relative speed r˙, [Win09]. Monopulse RADAR The Monopulse Method is used to find the azimuth angleϕ, see fig. 2.2. The method is called monopulse because only one RADAR impulse, which is emitted by antenna Tx1, is necessary to detect the angle. The two antennas Rx1 and Rx2 receive phase-shifted signals. They have a horizontal distance ofd in the sy direction of the sensor coordinate system, see fig. 2.7. Signal processing generates the sum |∑| and the difference |∆| of the two signals. Figure 2.8(a) shows the normalized signalsA1 (solid) andA2 (dashed) for the received signals of two different azimuth angles (black and grey). The error angle εdepicted in fig. 2.8(b) reads ε= |∆| |∑ |= |A1|−|A2||A1|+ |A2|. (2.8) The gradient of ε is a measure for the azimuth angleϕ, [Mah88]. Mahafza describes in [Mah88] another possibility to estimate the azimuth angle by measuring the phase shift between the two signals. Signal A2 can be described as A2 = A1 e −i∆δ, where ∆δ describes the phase shift between the two signals. The modulus of the quotient of the difference ∆ =A1−A2 and the sum ∑ =A1+A2 reads∣∣∣∣∆∑∣∣∣∣= tan(∆δ2 ) . (2.9) 15