Instrument variable method based on nonlinear transformed instruments for Hammerstein system identification

Abstract

An extended instrumental variable (EIV) method is considered for the stochastic Hammerstein system (ARMAX and general model structure). The EIV method provides consistent parameter estimates by eliminating noise-induced bias in the least square (LS) method. To estimate the parameters, the Hammerstein model is formulated using the bilinear parameterization. The bilinear model is identified by introducing the nonlinear instrumental variables obtained from transformed delayed outputs using nonlinear mapping and polynomial basis of delayed inputs. These instruments are analyzed in full generality by computing the bounds on expected relationship between instruments and noise for the general noise disturbance structure. Then, a specific case with hyperbolic tangent (tanh) transformation is considered. Comparative performance analysis of the proposed IV method with the existing IV method, the data filtering-based LS methods, and the extended LS method shows improvement in the statistical properties of parameters estimates.