## 4 Test Setup for Experimental Measurements
### Accelerometer vs. Doppler Measurements  
In addition to radar measurements, panel vibration data were also collected using piezoelectric accelerometers. These devices were positioned at specific locations around the vehicle and used during the same experiments. The purpose of this setup was to use the accelerometer data as a ground truth for validating the radar system's performance. If a strong correlation is found between the radar and accelerometer data, as will be demonstrated in the following sections, micro-Doppler radar could be considered a reliable and versatile method for vibration detection. Based on the cues provided by the cue giver as described above, we ensured that the accelerometer and radar data were synchronized. However, it is important to note the key differences between accelerometer and Doppler measurements. The radar antenna's beamwidth was large enough to cover a broad area of the vehicle, meaning it captured reflections from a wide region. In contrast, accelerometers must be mounted on a specific surface to provide accurate readings, yielding only point measurements. This meant that the accelerometers measured vibrations from the surface they were mounted on, without capturing data from the entire area illuminated by the radar. As noted in Section 3.6, micro-Doppler shifts induced by vibration are functions of angles \(\alpha\), \(\beta\), \(\alpha_{P}\), and \(\beta_{P}\), which are non-zero for surfaces away from the radar boresight. Consequently, the frequency spectrum magnitudes from vibrations captured by the radar will likely be lower than those measured by the accelerometers. Table 5 outlines the positions where the accelerometers were placed for both the Multi-Passenger Test and the PRND Test. It is important to note that the accelerometers were repositioned after completing measurements for one side or when switching vehicles. Additionally, some accelerometers were placed in different locations for different vehicles due to mounting challenges. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Experiment** & **Test info** & **Scenarios** \\ \hline \multirow{4}{*}{multi-passenger} & engine ON and in PARK & 1-Person \\  & 1 min recording & 2-Person \\  & sides: front, back, driver side, & 3-Person \\  & passenger side & 4-Person \\  & 1 min recording & OFF \\  & gear shifts at every 10 sec intervals & PERKSE \\ PRND & sides: front, back, driver side, & NEUTRAL \\  & passenger side & DRIVE \\  & & OFF \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Testing summary. During the experiments, vibration data were collected using two separate data acquisition systems (DAQs). The micro-Doppler radar data were collected as detailed in this paper while a second DAQ was used to collect vibration data from vehicle-mounted accelerometers. The secondary DAQ was a stand-alone system from a major manufacturer of data acquisition equipment. While all data were time-stamped using the local clocks of the respective DAQ, there was no absolute time synchronization between DAQs. During the data analysis, distinct vibration events, such as those caused by shifting gears, were used to correlate the micro-Doppler- and accelerometer-based vibration data. For the averaged power spectral densities and spectrograms in this work using data spanning many seconds of vehicle vibration, we believe that the cross-correlation-based synchronization provides sufficient temporal resolution. It should be noted that the micro-Doppler radar signal is an average of displacement/velocity/acceleration over the two-dimensional projected beam area based on the range to the target and the antenna beamwidths. The projected radar beam area on the vehicle chassis is almost circular and 72 cm (28 in) in diameter. The accelerometers, however, return the vibration at a fixed location on the panel. Because of this difference, the lowest order panel mode vibration should correlate well as the entire panel moves. We expect micro-Doppler and accelerometer vibration at higher order modes (higher frequency vibration) to deviate.