Identification of Hammerstein Systems from Short Segments of Data: Application to Stretch Reflex Identification

Abstract

It is not trivial to acquire data under stationary conditions from biomedical systems since they frequently show time-varying and/or switching behaviour. It is often possible to acquire short segments of stationary data and repeat the experiment many times. However, initial conditions contribute substantially to the transient response and must therefore be accounted for explicitly. This paper presents a subspace algorithm for the identification of Hammerstein systems from short segments of data that estimates the initial condition of each segment and the parameters of the nonlinearity, as well as a state-space model for the linear part. A previously developed algorithm suffers from two issues. Firstly, all segments had to be equal lengths, and secondly the algorithm provided an over-parameterized model of the Hammerstein system rather than an individual model for each component of the cascade. We resolved the first issue by introducing a new formulation of the problem and the second one by developing an iterative method to separate the estimated parameters. Simulation results on Hammerstein model of reflex joint stiffness show the algorithm is capable of identifying accurate models even with noisy data. We also show the application of this algorithm on a set of experimental data acquired from one subject.