**5. Experiments**

In this section, we evaluate the performances of the proposed methods through experiments with the dataset we collected in a university building. We introduce the experimental scenario and data collection in Section 5.1 and the results are presented in Section 5.2; we analyzed the performances related to the landmark identification, PDR, and virus quanta concentration.

### *5.1. Experimental Scenario and Data Acquisition*

We collected our experimental data on the fourth floor of the Center-Zone-1 building of Kyushu University's Ito campus. We assume that there is no exchange of virus particles with the room space. Figure 3 shows the floor plan of the experimental area. Based on the practical scenario, the Manhattan distance is applied to measure the virus movement. Since the width (measured as 2 m) and height (assumed to be 3 m based on the practical scenario) of the hallway are generally the same, the volume of the virus coverage can be determined by the virus movement distance for the calculation of the virus quanta concentration. When the virus encounters a corner, its direction changes, leading to a shift in the virus quanta concentration to varying degrees. For a corner with two branches, the concentration is assumed to decrease by half due to the inertia effect while these viral particles continue the forward transmission. If it is a corner with three or more branches, we assume that the virus quanta would be distributed evenly in all other directions.

**Figure 3.** The floor plan of our experiment.

In data collection, five recruited participants held Pixel 4a smartphones with the required sensors integrated (e.g., accelerometer, gyroscope, and rotation sensor) and an Android application installed. The application can periodically read and store the readings of 11 channels (3 for the accelerometer, 3 for the gyroscope, and 5 for the rotation sensor) as the user walks along the prescribed routes at a normal speed in the experimental area. Moreover, participants are required to hold their smartphones at chest level, which is a reasonable position where participants can record extra information to facilitate data processing. Indeed, it is recommended that they record the timestamp and the identification of the passing landmark to construct the dataset for the landmark identification model training.

### *5.2. Analysis and Discussion*

### 5.2.1. Landmark Identification

The proposed landmark recognition model was extensively evaluated by a series of experiments and implemented using the Keras framework with the TensorFlow backend to minimize the cross-entropy loss. The model was performed using the collected data with 3863 samples. The dataset was divided into training (70%) and testing (30%) sets, randomly, without overlapping. There were a total of 11 landmarks, including 7 corners, 2 stairs, and 2 elevators.

Table 1 details the network configuration considered in our study. Since there were many combinations of parameters, to reduce the selection space, we let all of the Bi-LSTM neurons share the same value, with the 1D convolution filter and kernel sizes accessing the same setting, respectively. To achieve stable performances of different model settings, a grid search with the 10-fold cross-validation method was adopted. It worked through all of the combinations of parameters to find the best settings. It should be noted that the following study uses the bold value for each parameter when it is not otherwise specified.


**Table 1.** Landmark identification neural network configuration.

Moreover, the model configuration (the Adam optimization algorithm) was selected as the optimizer during the gradient descent. Other training hyperparameters were also evaluated and their recognition accuracies are presented in Figure 4. More specifically, the experiment was conducted with the learning rates of 0.00001, 0.00002, 0.00005, 0.0001, 0.0002, 0.0005, 0.001, 0.002, 0.005, 0.01, 0.02, and 0.05, as presented in Figure 4a. The mini-batch size was tested with 16, 20, 32, 50, 64, 100, 128, 150, 200, and 256, as shown in Figure 4b. The model configured as Table 1 achieved the highest identification accuracy of 98.4% when the learning rate was 0.0002 and the mini-batch size was 256. Additionally, early stopping criteria and a learning rate reduction strategy were applied during the

model training process in order to reduce the issue of over-fitting and to improve the model performance. The learning rate decreased with a factor of 0.5 when the accuracy was not improved for 10 epochs and the training ended if the accuracy without enhancement on the validation was set after 15 iterations. Detailed training hyperparameter settings are revealed in Table 2.

**Figure 4.** Model accuracy on various learning rates (**a**) and batch sizes (**b**), shown as the red square.



Following the considered model configuration and optimal training hyperparameters, the accuracy curve and loss curve of the training and testing processes are illustrated in Figure 5a,b. The recognition results on 11 selected landmarks of the experiment-conducted floor are presented by the confusion matrix in Figure 6.

Moreover, to evaluate the proposed network more comprehensively, further comparisons were conducted on other deep neural networks (CNN, LSTM, and LSTM-CNN without residual connections) with the same depth and training hyperparameters as shown in Table 2. Table 3 presents the obtained experimental results of accuracy, precision, recall, and F1-score using different networks. It can be seen that the proposed Bi-LSTM-CNN network achieved the highest performance in all four metrics thanks to the elaborately extracted spatial and temporal features. Therefore, the effectiveness of the proposed Bi-LSTM-CNN classification model for the landmark identification task is demonstrated with the experimental evaluation.

**Figure 5.** Accuracy (**a**) and loss (**b**) curves of the model on the selected parameters.

**Figure 6.** Confusion matrix for landmark identification.


**Table 3.** Landmark identification performances of different models in the collected dataset.

### 5.2.2. Trajectory Tracing

The path shown as the red line in Figure 3 is designed to evaluate the performance of PDR with landmark calibration and the results are presented in Figure 7a. To quantitatively evaluate the positioning accuracy, we show the accumulative error distribution in Figure 7b. It can be seen from the left figure that the original PDR has an increasing error due to the initial wrong direction, although the information of many short segments can be described relatively accurately. Due to the significant error in the heading estimation without the landmark correction, the cumulative error distribution is not displayed in the right picture. The performance of PDR with the landmark calibration is well examined, nearly 80% of the positioning errors are less than 0.4 m, and the error probability within 0.7 m is higher than 90%. From the conducted experiments, the performance of the PDR-fused landmark calibration was evaluated with a lower positioning error, as compared to the PDR without calibration.

**Figure 7.** The performance (**a**) and the accumulative error distribution (**b**) of the proposed landmarkcalibrated PDR.

### 5.2.3. Virus Quanta Concentration

As mentioned above, we regard all virus particles exhaled every 0.1 s during exhalation as virus instances. There will be many virus instances expelled during the entire movement of an infector. During the transmission of each instance, a uniform motion with a velocity of 3.9 ( m · s<sup>−</sup>1) is maintained in the first second after exhalation, and the virus quanta are evenly distributed in the space that is passed by. The initial number of quanta (*q*0 = 0), the virus quanta emission rate (*ERq*), and the removal rate of infectious viral-laden particles (*RRiv*) are 142 and 1.37, respectively, and remain the same within the experiment [29,30].

The virus-laden particles released in each interval follow the same moving pattern, leading to the same trend in the change of the quanta concentration. We chose the instantaneous concentration at the end of each shorter interval with a length of 0.1 s to represent the concentrations at all times during the entire interval, as presented in Figure 8. As can be seen in Figure 8, the overall change in concentration presents an exponentially decreasing trend, from above 88 in the first interval (0~0.1 s) to close to 0 one second later. The sharp

decrease one second later is because of an

expansioncoverage to the entire considered space.

instantaneous

 of the viral aerosol

**Figure 8.** Quanta concentration of viral particles changes over time (first 1.5 s) after being released. Red points represent the instantaneous concentration at the end of each shorter interval.

The time when people started moving can be seen at time 0 of the experiment. Figure 9 presents the virus concentration in the current environment at the time of 0 s, 0.5 s, and 5 s from left to the right (using lines to represent the considered corridor spaces). Among them, at t = 0 s, only the virus concentration near the point start can be seen to exceed 80, while most of the other parts are not covered by viral particles. At t = 0.5 s, under the combined movements of virus droplets and humans, the relatively high quanta concentrations covered more. In addition, after another 0.5 s, the particles initially expelled att=0s will spread to the overall space. At t = 5 s, the area with higher quanta concentration gradually moves forward with the movement of people. Moreover, due to the accumulated particles that diffuse into the entire environment, the quanta concentration in the overall space is increased, gradually reaching a non-negligible level compared with the concentration of the newly expelled virus instance.

**Figure 9.** Indoor virus quanta concentrations at 0 s (**a**), 0.5 s (**b**), and 5 s (**c**), respectively, from the start of the movement.
