Identification of time-varying joint dynamics using wavelets

A wavelet-based method was investigated to identify time-varying properties of joint dynamics. Wavelet decomposition was used to expand each time-varying coefficient of an autoregressive with exogenous input (ARX) model into a finite set of basis sequences, and singular value decomposition was used to obtain more robust parameter estimates of the expansion. With a set of well-selected basis, the time-varying ARX coefficients could be well approximated by a combination of a small number of basis sequences, which simplified the identification of the time-varying parameters. The estimated time-varying ARX parameters were converted to a second-order continuous-time system characterizing joint dynamics with joint stiffness, viscosity and limb inertia. Simulation based on a time-varying joint dynamics model showed that the method tracked the time-varying system parameter closely