## 5 Experiments
### Experimental Results  
We employed three localization algorithms to estimate pedestrian positions: the APDR algorithm, the VIO algorithm, and the autonomous localization algorithm proposed in this paper. For the VIO algorithm, we utilized the latest ORB-SLAM3. The position error at each step was calculated, providing a detailed evaluation of localization accuracy. Key evaluation metrics include average localization error, maximum error, minimum error, and standard deviation of error. These metrics allow for a comprehensive quantitative analysis of overall error levels, extreme error points, error fluctuation, and endpoint accuracy. They also facilitate a detailed comparison of the localization accuracy across different algorithms. The experiments were conducted in multiple scenarios, which present diverse and complex settings. The presence of obstacles and dynamic environmental factors adds variability, thereby increasing the demand for algorithm reliability and stability. To evaluate the algorithm's performance, three specific paths were chosen for testing: a straight-line round-trip, a curved path, and a closed-loop single circle. Each path posed unique challenges for the localization system. For instance, the straight-line round-trip path tested the consistency of straight-line motion and large-turn angle accuracy, validating the robustness of the algorithm in different typical motion states. The curved path assessed the algorithm's localization accuracy in a dynamic, directional environment. Meanwhile, the closed-loop single-circle path was used to verify both the localization and orientation accuracy of the algorithm in a typical path. During the test, subjects wore the device and traveled along the three specified paths. The total distances for each path were as follows: straight-line round-trip 137.62 m, curved path 103.05 m, and closed-loop single circle 190.06 m. The trajectory results are shown in Figure 16a-c, with corresponding local views presented in Figure 16d-f. The trajectory diagram includes the true trajectory (red curve), the trajectory of the adaptive PDR algorithm (green curve), the trajectory of visual-inertial (blue curve), and the trajectory of our algorithm (black curve). The real trajectory was obtained by reconstructing the path using a foot-point marking tool and a laser ranging tool. Points were marked each time the heel hit the ground, with distances measured using the laser ranging tool to reconstruct the actual trajectory. By comparing the trajectories of three algorithms (APDR, VIO, and our proposed autonomous localization algorithm) with the real trajectory, the results demonstrate that the proposed fusion localization algorithm can track the real trajectory both stably and accurately. This highlights the algorithm's consistency in tracking within complex environments, further validating its reliability and accuracy for real-world applications. Figure 15: Testing environment. (**a**) Indoor corridors. (**b**) Underground parking lots. (**c**) Tunnels. Figure 17a-f show the localization error over time for each trajectory, along with the corresponding error violin plots. From the error curves and distributions, it is evident that the fusion algorithm significantly reduces the error, and some of the error fluctuations exhibit more stability. Compared to the individual systems or algorithms, the fused algorithm achieves higher localization accuracy and stability, underscoring its greater potential for both practical applications and research value. Figure 16: Trajectory curves for three different paths. To quantify and compare the error levels, we performed a statistical analysis of the error data for three trajectories (APDR, VIO, and our proposed autonomous localization method) relative to the real trajectory. The analysis included maximum error, minimum error, average error, and error standard deviation.