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This paper derives an algorithm for identifying linear stochastic systems, by taking the effect of the initial state into account. The proposed algorithm computes coefficients by using the extended observability matrix for deleting the effect. Numerical simulation shows that the proposed method outperforms existence methods.
In this paper, we consider a stochastic realization problem with finite covariance data based on “LQ decomposition” in a Hilbert space, and re-derive a non-stationary finite-interval realization ([4, 5]). We develop a new algorithm of computing system matrices of the finite-interval realization by LQ decomposition, followed by the SVD of a certain block matrix. Also, a stochastic subspace identification...
A finite-interval stochastically balanced realization is analyzed based on the idealized assumption that an exact finite covariance sequence is available. It is proved that a finite-interval balanced realization algorithm [Maciejowski, J. M. (1996). Parameter estimation of multivariable systems using balanced realizations. In S. Bittanti, & G. Picci (Eds.), Identification, adaptation, learning...
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”...
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