Methods and good practice guidelines for human joint kinematics estimation through magnetic and inertial wearable sensors

According to the World Health Organization, the ability to move is recognized as a key factor for the human well-being. From the wearable Magnetic and Inertial Measurement Units (MIMUs) signals it is possible to extract several digital mobility outcomes including the joint kinematics. To this end, it is first required to estimate the orientation of the MIMUs by means of a sensor fusion algorithm (SFA). After that, the relative orientation is computed and then decomposed to obtain the joint angles. However, the MIMUs do not provide a direct output of the physical quantity of interest which can be only determined after an ad hoc processing of their signals. It follows that the joint angle accuracy mostly depends on multiple factors. The first one is the magnitude of the MIMU measurements errors and up to date there is still a lack of methods for their characterization. A second crucial factor is the choice of the SFA to use. Despite the abundance of formulations in the literature, no-well established conclusions about their accuracy have been reached yet. The last factor is the biomechanical model used to compute the joint angles. In this context, unconstrained methods offer a simple way to decompose the relative orientation using the Euler angles but suffer from the inherent issues related to the SFA. In contrast, constrained approaches aim at increasing the robustness of the estimates by adopting models in which an objective function is minimized through the definition of physiological constraints. This thesis proposed the methods to accurately estimate the human joint kinematics starting from the MIMU signals. Three main contributions were provided. The first consisted in the design of a comprehensive battery of tests to completely characterize the sources of errors affecting the quality of the measurements. These tests rely on simple hypotheses based on the sensor working principles and do not require expensive equipment. Nine parameters were defined to quantify the signal accuracy improvements (if any) of 24 MIMUs before and after the refinement of their calibration coefficients. The second contribution was focused on the SFAs. Ten among the most popular SFAs were compared under different experimental conditions including different MIMU models and rotation rate magnitudes. To perform a “fair” comparison it was necessary to set the optimal parameter values for each SFA. The most important finding was that all the errors fall within a range from 3.8 deg to 7.1 deg thus making it impossible to draw any conclusions about the best performing SFA since no statistically significant differences were found. In addition, the orientation accuracy was heavily influenced by the experimental variables. After that, a novel method was designed to estimate the suboptimal parameter values of a given SFA without relying on any orientation reference. The maximum difference between the errors obtained using optimal and suboptimal parameter values amounted to 3.7 deg and to 0.6 deg on average. The last contribution consisted in the design of an unconstrained and a constrained methods for estimating the joint kinematics without considering the magnetometer to avoid the ferromagnetic disturbances. The unconstrained method was employed in a telerehabilitation platform in which the joint angles were estimated in real time. Errors collected during the execution of a full-body protocol were lower than 5 deg (considered the acceptability threshold). However, this method may be inaccurate after few minutes since no solutions can be taken to mitigate the drift error. To overcome this limitation a constrained method was developed based on a robotic model of the upper limb to set appropriate constraints. Errors relative to a continuous robot motion for twenty minutes were lower than 3 deg at most suggesting the feasibility of employing these solutions in the rehabilitation programs to properly plan the treatment and to accurately evaluate the outcomes.