A stochastic realization in a hilbert space based on "LQ decomposition" with application to subspace identification

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In this paper, we develop a new stochastic realization algorithm using canonical correlation analysis, thereby deriving the forward innovation representation along the line of (Desai et al., 1985) by means of "LQ decomposition" in a Hilbert space generated by a second-order stationary random process. As an application, we show that our abstract result is easily adapted to the case where a finite string of a time-series data is available to derive a stochastic subspace identification algorithm.