Elsevier

Automatica

Volume 30, Issue 1, January 1994, Pages 75-93
Automatica

N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems

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Abstract

Recently a great deal of attention has been given to numerical algorithms for subspace state space system identification (N4SID). In this paper, we derive two new N4SID algorithms to identify mixed deterministic-stochastic systems. Both algorithms determine state sequences through the projection of input and output data. These state sequences are shown to be outputs of non-steady state Kalman filter banks. From these it is easy to determine the state space system matrices. The N4SID algorithms are always convergent (non-iterative) and numerically stable since they only make use of QR and Singular Value Decompositions. Both N4SID algorithms are similar, but the second one trades off accuracy for simplicity. These new algorithms are compared with existing subspace algorithms in theory and in practice.

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The original version of this paper was presented at the 12th IFAC Congress which was held in Sydney, Australia, during 19–23 July 1993. The Published Proceedings of this IFAC Meeting may be ordered from: Pergamon Press Limited, Headington Hill Hall, Oxford OX3 0BW, U.K. This paper was recommended for publication in revised form by the Guest Editors.

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