Identification of the Deterministic Part of MIMO State Space Models Given in Innovations Form from Input-Output Data

Authors

Michel Verhaegen

Year

1994

Journal Paper

Algorithm

IV-MOESP

Source

Automatica

Identifiers

DOI 10.1016/0005-1098(94)90229-1

Abstract¶

In this paper we describe two algorithms to identify a linear, time-invariant, finite dimensional state space model from input-output data. The system to be identified is assumed to be excited by a measurable input and an unknown process noise and the measurements are disturbed by unknown measurement noise. Both noise sequences are discrete zero-mean white noise. The first algorithm gives consistent estimates only for the case where the input also is zero-mean white noise, while the same result is obtained with the second algorithm without this constraint. For the special case where the input signal is discrete zero-mean white noise, it is explicitly shown that this second algorithm is a special case of the recently developed Multivariable Output-Error State Space (moesp) class of algorithms based on instrumental variables.

Summary¶

Extends the MOESP subspace identification line from deterministic output-error realization toward stochastic MIMO systems in innovations form. The paper gives two algorithms for estimating the deterministic state-space dynamics from input-output data corrupted by process and measurement noise, and shows that one method connects directly to instrumental-variable MOESP, clarifying how MOESP-type projections can recover deterministic dynamics in mixed deterministic-stochastic settings.