Identification of a Hammerstein Model of the Stretch Reflex EMG using Cubic Splines

The use of cubic splines, instead of polynomials, in representing static nonlinearities in block structured models is considered. A system identification algorithm for the Hammerstein structure, a static nonlinearity followed by a linear filter, is developed in which the static nonlinearity is represented by a cubic spline. The identification algorithm, based on a separable least squares Levenberg-Marquardt optimization, is used to identify a Hammerstein model of the stretch reflex EMG recorded from a spinal cord injured patient. The resulting model provides more accurate predictions of the reflex EMG, even in novel data, than more conventional models which use polynomial representations of the nonlinearity. Furthermore, the spline based optimization appears to be less sensitive to its initialization than a similar polynomial-based approach. Keywords— nonlinear system identification, physiological modeling, separable least squares, mean squared optimization, LevenbergMarquardt iteration