A Kalman Filter Approach for Estimating Tendon Wave Speed from Skin-Mounted Accelerometers

Shear wave tensiometry is a noninvasive approach for assessing in vivo tendon forces based on the speed of a propagating shear wave. Wave speed is measured by impulsively exciting a shear wave in a tendon and then assessing the wave travel time between skin-mounted accelerometers. Signal distortion with wave travel can cause errors in the estimated wave travel time. In this study, we investigated the use of a Kalman filter to fuse spatial and temporal accelerometer measurements of wave propagation. Spatial measurements consist of estimated wave travel times between accelerometers. Temporal measurements are the change in wave arrival at a fixed accelerometer between successive impulsive taps. The Kalman filter substantially improved the accuracy of estimated wave speeds when applied to simulated tensiometer data. The variability of estimated wave speed was reduced by ~55% in the presence of random sensor noise. It was found that increasing the number of accelerometers from two to three further reduced wave speed errors by 45%. The use of redundant accelerometers (>2) also improved the robustness of wave speed measures in the presence of uncertainty in accelerometer location. We conclude that the use of a Kalman filter and redundant accelerometers can enhance the fidelity of using shear wave tensiometers to track tendon wave speed and loading during movement.