Arbitrary Spatial Trajectory Reconstruction Based on a Single Inertial Sensor

Compared with visible, infrared rays, and ultrasonic positioning technologies, the signal acquisition of portable inertial sensors is not affected by the external environment, such as light and occlusion. Therefore, motion tracking based on inertial signals is a promising complement. However, accurate trajectory reconstruction based on inertial sensors is a great challenge due to intrinsic and measurement errors, especially the drift error that exacerbates the accumulative error in trajectory calculation. To address this challenge, we propose a new trajectory reconstruction method, geometric dynamic segmental reconstruction (GDSR), where we treat the movement trajectory as a combination of basic trajectories. To this end, we design a temporal and spatial interaction segmentation approach to decompose the trajectory into basic segments by combining the dynamic feature of inertial measurement unit (IMU) signals with the spatial morphological feature of motion. Accordingly, we design a geometrical model library with undetermined parameters to match these segments. For precise parameter prediction, we propose an extra-supervised learning method that integrates different prediction tasks into one framework, which can not only expand training samples, but also enable different subtasks to compete with each other, thus improving the parameter prediction accuracy of each subtask, thereby accurately approximating the trajectory segments. To quantify the trajectory reconstruction accuracy, we propose the Fréchet spline sliding error (FSSE) and length error ratio (LER) to evaluate curve similarity. The range of FSSE is [0], [2], where 0 means that the two curves have the same shape. The range of LER is [1,
$+\infty $
], where 1 means that the two curves have the same length. We test different IMUs in two experimental scenarios and one public available dataset. In all three tests, the FSSE of the GDSR method is less than 0.09, and the LER is less than 1.31, which is significantly better than all the comparison methods.