A least-squares identification algorithm for estimating squat exercise mechanics using a single inertial measurement unit

This study investigated the possibility of estimating lower-limb joint kinematics during a squat exercise performed in the sagittal plane based on data collected from a single inertial measurement unit located on the lower trunk. The human body was modeled as a three-degrees-of-freedom planar chain and the relevant joint angles (ankle, knee, and hip) are represented by Fourier series. A least-squares approach based on the minimization of the difference between the measured and estimated linear accelerations and the angular velocity of the lower trunk was used to solve the related analytical problem. The approach was validated on ten healthy young volunteers (ten trials each) using a force plate and a stereophotogrammetric system to collect reference data. The root mean square differences between the estimated joint angles and those reconstructed with the stereophotogrammetric system were lower than 4° with correlation coefficients higher than 0.99. The ankle joint resultant vertical force component was estimated with an accuracy of about 3% and a high correlation coefficient of r=0.95, whereas much lower percentage accuracies were found for the horizontal force and couple components. The latter accuracies were similar to those affecting these force and couple components as estimated through inverse dynamics and the stereophotogrammetric data in conjunction with the same mechanical model, which suggests that only minor errors were introduced by the proposed algorithm and measurement tools.