Subspace identification algorithm for stochastic systems equipped with zeros close to unit circle

Abstract

In identifying a stochastic system possessing zeros close to the unit circle, the effect of the initial state appears in the estimates. This paper derives a stochastic subspace identification algorithm for such a system. A new stochastic realization algorithm is developed based on the covariance matrices of the state and the white-noise input, by taking the initial state and positive realness into account. A subspace identification algorithm is obtained by applying the realization algorithm to a finite string of data. Numerical simulation results show that the proposed algorithm provides favorable results compared with the conventional ones.