# Pedestrian Counting Based on Piezoelectric Vibration Sensor
## 3 Problem Formulation
### Problem Analysis  
Figure 2 visualizes the original signals before denoising for the cases from 0 to 4 persons. These figures show the characteristics of time-specific signals captured by sensors. Intuitively, when the number of pedestrians is increased from 0 to 2, or from 3 to 4, the waveforms look different. However, it is not easy to differentiate whether the vibration signals are generated by 2 or 3 persons with only time domain information.  
As discussed in Section 2.2, previous work [15] investigated the validation of the vibration features in Table 1 for counting the number of walking people. Figure 3 presents the results of the impulse load test experiment conducted in [15], where Figure 3a-d show the predictive capability of the vibration features in Table 1, respectively. Figure 3a shows the cross-correlation of the same SE from different sensors, representing the predictive capability of space-differential features. Figure 3b shows the cross-correlation of the same trace from the same sensor, representing the predictive capability of time-differential features. Figure 3c shows the step event duration. Figure 3d shows the step event signal entropy, representing the predictive capability of energy-specific features. [PERSON] et al. [15] showed in Figure 3b,c that features (2) and (3) are only appropriate if the detection task is to distinguish whether the number of the pedestrians is 1 or more than 1, but they are uninformative to determine the exact number of pedestrians if there are 2 or more than 2 people. Similarly, feature (4) is only useful in the cases where there is more than one individual, making it difficult to distinguish the number of people when there are less than 2. Furthermore, the generation of features (2) and (3) required that there should be a maximum of one group of pedestrians in the detected area. Intuitively, when there are two groups of people, the signal from the first group of people may be mixed with the signal from the second group. The detected signal from the sensor is a mixture of both groups of people. As a result, it is challenging to differentiate whether the \"SoI\" is from the footsteps of the first or the second group of pedestrians. Similarly, the \"SoI duration\" is meaningless when the signals from two groups of pedestrians are mixed. Meanwhile, different groups of people may move at different speeds, where some groups may run while others walk at an average speed. These different moving events may occur simultaneously and the corresponding signals may be mixed up. On the other hand, when pedestrians  
Figure 1: Data acquisition devices and experiment setup.  
walk in the monitored area, the spatial difference of the floor vibration signal source from each individual is clear, which can be captured and detected with multiple sensors. This information is encoded in the space-differential feature (1) in Table 1. To summarize, only feature (1) can be effectively used to predict the number of walking people in a more practical scenario.  
Figure 2: (**a**–**e**) present the vibration signal in the time domain. The figures show samples of time-specific signal fragments from one of the sensors.  
Similar to cross correlation computing in [15], convolutional computation shares a similar symbolic calculation form. We assume that the convolutional computation of the same walking step event signal among different sensors will extract useful spatial features for pedestrian counting tasks. Our approach uses a deep neural network with convolutional layers to extract features from step event data and detect the number of pedestrians. The experimental results are presented in Section 5.