Errors-in-Variables Identification of Composite Noncausal-FIR/IIR Models with Application to Transmissibility Identification

Model structures used for system identification include infinite impulse response (IIR) models and finite impulse response (FIR) models. Identification using IIR models requires knowledge of the order of the system, where underestimating or overestimating the order of the system can yield poor parameter estimates. Although identification using FIR models does not require knowledge of the order of the system, FIR models cannot approximate systems with poles on or outside the unit circle. Noncausal FIR models can approximate systems with asymptotically stable and unstable poles, but not systems with poles on the unit circle. A composite noncausal-FIR/IIR (CNFI) model has an IIR part and a noncausal-FIR part, where the IIR part approximates poles on the unit circle, and the FIR part approximates the remaining part of the system. In this paper, we propose an errors-in-variables identification algorithm for CNFI models. We apply the proposed algorithm to identify transmissibilities, which are models that characterize the relationship between the outputs of an underlying system.