Identification of nonlinear continuous-time Hammerstein model via HMF-method

A frequency weighted least squares (FWLS) formulation is given for identifying the parameters of Hammerstein-type nonlinear continuous-time systems (1930) based on input and noise contaminated output data observed over a finite time interval. The Hartley modulating functions (HMF) method (1942) starts from a priori knowledge of the Hammerstein system structure with unknown parameters. The approach converts the nonlinear differential equation describing the nonlinear system into a Hartley spectrum equation and circumvents the need to estimate unknown initial conditions through the use of certain modulation properties. The unknown system parameters can then be estimated in the frequency domain by a FWLS-algorithm. A root mean square normalized error criterion is applied to measure the bias of the estimate for different values of the mode number and order of the Hartley transformation as well as for different levels of the noise-to-signal ratio in order to investigate some computational considerations associated with the methodology. The illustrative Monte Carlo simulation studies suggest that this method lies in the potential of being able to accurately estimate the parameters of a nonlinear continuous-time Hammerstein system in the presence of significant output measurement disturbances