System identification with piecewise-constant finite impulse response model and its statistical property

Finite impulse response (FIR) models have attracted much attention in system identification in recent years. However, finite impulse response models have many parameters, and it is sometimes difficult to identify them under conditions with limited computational resources. This paper considers a finite impulse response model with a reduced number of parameters. In particular, supposing the purpose of the model is to estimate the unit step response at a given time, it is shown that one of the desirable models for this purpose is a model in which the impulse response values are piecewise constants. The statistical properties of such a piecewise-constant FIR model obtained by system identification are clarified. The usefulness of the proposed method is confirmed through numerical examples.