Selection of System Identification Model and Identifiability Condition in the Presence of Persistent Disturbances

Abstract

In this paper, we consider an identification problem of linear systems in the presence of not only stochastic disturbances such as white noises but also persistent disturbances such as constant and sinusoidal disturbances with unknown frequencies. The object is to identify the plants in the presence of persistent disturbances and estimate the frequencies of the sinusoidal disturbances. The purpose of this paper is to select a suitable identification model and analyze its identifiability condition. First, we select the identification model whose one-step-ahead predictor corresponds to the steady-state Kalman predictor, which is the optimal one-step-ahead model. Second, we show the condition for the existence of the steady-state Kalman predictor and analyze the identifiability condition of the identification model. Finally, through a numerical example, we show the fact we can identify the system in the presence of persistent disturbances using the selected identification model if the identifiability condition is satisfied.