## 5 Simulation and Experiments
### Dataset Experiment  
To inspect the effectiveness of the algorithm in real-world scenarios, this paper employs the EuRoC ROOM01 and MainHall02 datasets [28] for validation. Since this study investigates the performance of the loosely coupled visual-inertial algorithm itself instead of visual odometry, one of the state-of-the-art visual SLAM algorithms, monocular ORB-SLAM V3 [29], serves as the visual black-box approach. Given that this algorithm has been confirmed to exhibit exceptional ATE performance, this paper focuses on RPE comparisons of different algorithms by employing EVO tools [30] to analyze trajectories. The ICEKF operates with the IMU data at 200 Hz, and meanwhile the visual measurement runs at 20 Hz. To facilitate the comparison, each frame from the visual measurement with ORB-SLAM is considered a keyframe. The coefficients are \(\mu_{v}=0.9\) and \(\mu_{\omega}=0.5\), and the initial scale factor is determined based on the prior results of the visual algorithm as \(\lambda=2.04\). Given that the hardware setup and scenario are fixed in the dataset, the initial covariance matrix \(\mathbf{P}_{k|k}\) of the ICEKF can be easily adjusted via multiple runs. In the first run, the initial \(\mathbf{P}_{k|k}\) is selected randomly, and eventually stabilizes as the algorithm progresses. The final updated \(\mathbf{P}_{k|k}\) is utilized to run the scenario test again, which greatly increases the convergence speed and provides high resilience against noise. For applications in unknown environments, initial covariance estimation can be conducted in a similar scenario to further improve convergence efficiency. Dataset experiments with monocular ORB-SLAM, its IMU variant, and the monocular MSCKF with an IMU were performed. The entire experiment processes are shown in Figures 9 and 10. The contrast between the three-dimensional position output of the ICEKF and the ground truth is shown in Figures 11 and 12. The three-dimensional position errors and the orientation errors between the output of the ICEKF and the ground truth after applying alignment using [PERSON]'s method [30] from the two dataset tests are shown in Figures 13-16. Figure 8: The initial estimate set and the converging process. Trajectory analysis using EVO is conducted, in which the ICEKF with the results from ORB-SLAM and its IMU variant, as well as the data obtained from the monocular MSCKF [31], are compared against the ground truth, with the statistical RPE results presented in Tables 3 and 4. The comparative results indicate that the ICEKF ensures real-time measurement through high-frequency IMU updates and achieves an accuracy comparable to that of the monocular ORB-SLAM and its IMU variant while outperforming the monocular MSCKF. Although the trajectory does not reach the high accuracy of ORB-SLAM-based methods owing to the lack of posterior batch optimization processing, the computational complexity of the coupled part of the algorithm is only \(\mathbf{O}(n)\), which benefits localization applications. Moreover, the algorithm framework can be directly utilized with other localization algorithms to improve their measurement stability in complex environments. Figure 10: Dataset experiments (MainHall02): (a) monocular ORB-SLAM, (b) monocular ORB-SLAM with IMU, and (c) monocular MSCKF. Figure 9: Dataset experiments (ROOM01): (a) monocular ORB-SLAM, (b) monocular ORB-SLAM with IMU, and (c) monocular MSCKF. Figure 11: Position output of the ICEKF and the ground truth (ROOM01). Figure 12: Position output of the ICEKF and the ground truth (MainHall02). Figure 13: Position error between the ICEKF and the ground truth (ROOM01). Figure 16: Orientation error between the ICEKF and the ground truth (MainHall02). Figure 14: Orientation error between the ICEKF and the ground truth (ROOM01). Figure 15: Position error between the ICEKF and the ground truth (MainHall02).