Brief A stochastic realization algorithm via block LQ decomposition in Hilbert space

Authors:
Hideyuki Tanaka;Tohru Katayama
Affiliations:
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Abstract

A stochastic realization problem of a stationary stochastic process is re-visited, and a new stochastically balanced realization algorithm is derived in a Hilbert space generated by second-order stationary processes. The present algorithm computes a stochastically balanced realization by means of the singular value decomposition of a weighted block Hankel matrix derived by a ''block LQ decomposition''. Extension to a stochastic subspace identification method explains how the proposed abstract algorithm is implemented in system identification.