# High-Fidelity Drone Simulation with Depth Camera Noise and Improved Air Drag Force Models
## 2 Depth Camera Modeling and Implementation
### Simulation Implementation and Results
The realism of our simulator can be visually verified as seen in Figures 7-9. In Figures 7 and 8, the depth data obtained from the real wall with different materials closely resemble the simulation depth data generated using the depth camera noise model. As shown in Figure 9, the depth camera noise model exhibits larger noise levels with increasing distance. To validate the proposed model, we conducted another indoor experiment using a Realsense D435 depth camera. The camera was stationary, capturing static objects from a perpendicular angle, as described in the experimental setup Section 2.2. For this experiment, we used a different cement wall than the one described in Section 2.2. The experimental setup remained consistent with the previous section. To vary the lighting conditions in real-world experiments, we utilized different LED lights (3000 Lumens, Z-9020M (Nanjing, China)). Light density was measured using a cellphone, and the recorded light density represented the average value measured in the testing area when the cellphone camera was directed from the wall towards the Realsense camera in a perpendicular direction. Three different light conditions were observed: 160 Lux, 230 Lux, and 300 Lux, all falling within the typical range of indoor lighting conditions [37]. It is worth noting that the light condition can be easily adjusted in the simulator. \begin{table}
\begin{tabular}{c c c c} \hline  & **Plastic** & **Cement** & **Formboard** \\  & **m = 0.85 (1/m)** & **m = 0.50 (1/m)** & **m = 0.55 (1/m)** \\ \hline \(R^{2}\) Value & 0.26049 & 0.7126 & 0.5438 \\ \hline \end{tabular}
\end{table} 
Table 1: Coefficient of determination (\(R^{2}\)) between standard deviations of the depth errors and simulated standard deviations of the depth using our depth noise model for different materials. Figure 6: Stereo IR depth camera error implementation in simulation. The distance between the depth camera and the wall was manually adjusted from 0.5 m to 8 m, resulting in a total of 29 camera positions, using a roller. At each distance, we captured five depth images, each with a size of 460 \(\times\) 320 pixels. The standard deviation values of the depth errors and their deviations can then be achieved. Using the depth camera model with noise for a cement wall (material value 0.5 1/m) obtained in Section 2.3, the comparison between the real standard deviations of the depth errors and the simulated standard deviations of the depth using our depth noise model for cement walls is shown in Figure 10. It is observed from Figure 10 that the average value of \(R^{2}\) is 0.74 for three light conditions, validating the accuracy of our depth noise model. Furthermore, it is also observed that the noise model is not affected by the lighting condition under 300 Lux. Similar results were also observed with the same depth camera D435 tested under different lighting conditions under 540 Lux, but at shorter distances (1 m, 1.5 m) [38]. It was shown that incorporating a noise model results in better performance in SLAM and reconstruction algorithms [38], object recognition [39], segmentation [40], 3D reconstruction [41], and camera tracking [42]. Our depth noise camera model for those applications will be validated in our future work. Figure 8: Pointcloud visualization of real world wall (**a**) with wallpaper, and (**b**) with reflective plastic. Figure 7: Pointcloud visualization of depth value with noise implemented when (**a**) m = 0.35 (1/m), (**b**) m = 0.55 (1/m). Figure 9: Simulation depth camera (**a**) without noise, and (**b**) with noise. Figure 10: Depth noise standard deviation value of cement wall in real environments and noise model using material value 0.5 m\({}^{-1}\) in **(a)** 160 Lux light density, **(b)** 230 Lux light density, and **(c)** 300 Lux light density.