Nonlinear optimization for drift removal in estimation of gait kinematics based on accelerometers

A new data processing method is described for estimation of angles of leg segments, joint angles, and trajectories in the sagittal plane from data recorded by sensors units mounted at the lateral side of leg segments. Each sensor unit comprises a pair of three-dimensional accelerometers which send data wirelessly to a PC. The accelerometer signals comprise time-varying and temperature-dependent offset, which leads to drift and diverged signals after integration. The key features of the proposed method are to model the offset by a slowly varying function of time (a cubic spline polynomial) and evaluate the polynomial coefficients by nonlinear numerical simplex optimization with the goal to reduce the drift in processed signals (angles and movement displacements). The angles and trajectories estimated by our method were compared with angles measured by an optical motion capture system. The comparison shows that the errors for angles (rms) were below 4° and the errors in stride length were below 2%. The algorithm developed is applicable for real-time and off-line analysis of gait. The method does not need any adaptation with respect to gait velocity or individuality of gait.