Identification of time-varying biological systems from ensemble data (joint dynamics application)

The theory underlying a new method for the identification of time-varying systems is described. The method uses singular value decomposition to obtain least-squares estimates of time-varying impulse response functions from an ensemble of input-output realizations. No a priori assumptions regarding the system structure or form of the time-variation are required and there are few restrictions on the input signal. Simulation studies, using a model of time-varying joint dynamics, show that the method can track rapid changes in system dynamics accurately and is robust in the presence of output noise. An application of the method is demonstrated by using it to track dynamic ankle stiffness during a rapid, voluntary, isometric contraction. During the transient phase of the contraction, low-frequency ankle stiffness gain decreased in a manner which could not be described with the second-order model of joint dynamics often used under stationary conditions.