Identification of a Hammerstein model of the stretch reflex EMG using separable least squares

The Hammerstein cascade, a zero-memory nonlinearity followed by a linear filter, is often used to model nonlinear biological systems. Using this structure, some high-order nonlinear systems can be represented accurately using relatively few parameters. However, because the model output is not a linear function of its parameters, in general they cannot be estimated in closed form. Currently, an iterative technique, which alternates between estimating the linear element from a cross-correlation, and then fitting a polynomial to the nonlinearity via linear regression, is used to identify these cascades. In this paper, separable least squares (SLS) optimization methods are proposed as a means of simultaneously estimating both the linear and nonlinear elements, in an exact least squares framework. A SLS algorithm for the identification of Hammerstein cascades is developed and used to analyze stretch reflex EMG data from a spinal cord injured patient. Results are compared to those obtained using the traditional, iterative, algorithm