Sensory Fusion of Magnetoinertial Data Based on Kinematic Model With Jacobian Weighted-Left-Pseudoinverse and Kalman-Adaptive Gains

Abstract

This paper presents a sensory fusion method for estimation of joint angles of serial kinematic chains with rotational degrees of freedom based on magnetoinertial measurements—Magnetoinertial tracking based on JAcobian PseudoInverse (MIJAPI). The concept takes into account the mechanism kinematic model, and the computation relies on the differential kinematics inversion (inverse kinematics solution based on the Jacobian inverse). A Moore–Penrose weighted left pseudoinverse of the mechanism Jacobian matrix is applied to solve a (typically) overdetermined system (redundant measurements resulting from constraints related to attachments of magnetoinertial sensors) in a least-squares approach. Calculation of a gain matrix for correcting the estimated angles is based on Kalman-adaptive algorithm. The quality of the proposed approach was compared to different solutions based on the Unscented Kalman filter. In terms of computational complexity, the MIJAPI concept outperforms the Kalman-based approaches. Better results were also noticed in conditions with significant measurement disturbances and sensor misalignments. The method is applicable in the fields of human motion tracking/analysis as well as robotics.