## 3 Experimental Results and Analysis
### Indoor and Outdoor Loop Datasets  
Since optical reference systems are limited by space, we further evaluated the actual performance of the five frameworks on real-world indoor and outdoor loop datasets. The indoor dataset contained three sub-datasets: a small-scale multi-path and multi-motion loop dataset (termed as indoor dataset 1), a medium-scale multi-motion loop dataset (termed as indoor dataset 2), and a medium-scale walking loop dataset (termed as indoor dataset 3). All indoor datasets were collected in Building 26 on the Weijin campus of Tianjin University. Indoor datasets 1 and 2 were collected on the second floor, while indoor dataset 3 was collected on the fourth floor. Indoor dataset 1 contained 48 trajectories with four shapes (i.e., a circle (approximately 26.4 m), an eight-shaped path (approximately 27.2 m), a rectangle (approximately 34.5 m), and a straight line (up and down, approximately 34.3 m)). Indoor dataset 2 was collected along a rectangular path, and the tester moved with combined motions (i.e., walking, slow running, and crouch-walking). The motions in indoor dataset 3 included three-lap walking and free walking with normal speed. The three-lap walking experiment is performed by moving along the corridor loop three times with a normal speed. The free walking test was more challenging. The tester walked through several straight corridors, a meeting room, several staircases, an office, etc. The experimental environments were more complex, and the walking trajectory was more random. The outdoor walking experiment was performed by walking around Jingye Lake on the Weijin campus of Tianjin University. In the outdoor experiment, the test path included approximately 349 m of a straight line, and the tester walked through three  
Figure 8: Translation error (**left**) and absolute heading error (**right**) cumulative distribution function (CDF) curves of different frameworks. Figure 7: Heading error and translation error distributions of different frameworks. parking lots and over several cast-iron well lids. Further, we establish a more challenging indoor-outdoor dataset to further validate our algorithm. The dataset was collected in both indoor and outdoor environments along a path of nearly 2 km. The tester started from an indoor point on the second floor and walked towards the outdoor space through several corridors, a hall, and stairs. Then, long-term outdoor walking with short-term slow running was performed before the tester went back to the start point. Finally, the datasets were established with a total distance of 12.98 km. The information of all datasets is summarized in Table 4.  
It is difficult to use heading and translation errors to directly evaluate an algorithm's performance in an open space. Since the differences among the different frameworks are their heading drift correction methods, the SE, TTDE, and their root-mean-square errors (RMSEs) can be used to test the different heading algorithms. Figures 9 and 10 and Table 5 show that all frameworks except for ZUPT-EC achieved similar performance on indoor datasets 1 and 2. Intuitively, Figures 11 and 12 show that the ZUPT-AFM and ZUPT-MED-EC had the best heading and translation performances among the five frameworks on indoor dataset 3. Further, Figures 13-15 show that ZUPT-AFM achieved the best performance on the more challenging outdoor and indoor-outdoor datasets. Rich experiments can fully validate the performances of the five frameworks. Therefore, all of the datasets, with a total distance of 12.98 km, were leveraged to test the five algorithms. The RMSEs of the SEs and TTDEs in Table 6 show that the ZUPT-AFM and ZUPT-MED-EC performed similarly on indoor datasets 2 and 3, while ZUPT-AFM outperformed ZUPT-MED-EC on the outdoor and indoor-outdoor datasets. The long distance, long operation period, multiple motions, and experimental environment may have affected the heading and translation performance of the inertial-/magnetic-sensor-based localization system.