A utilization of properties of the discrete-time Riccati equation in stochastic realization theory. (English) Zbl 0574.93015
The problem of generating families of wide-sense, stochastic realizations of a discrete-time stationary stochastic process is considered. To do this, it is known that a Riccati equation has to be solved. In this paper, the non-Riccati algorithm of A. Lindquist and T. Kailath [SIAM J. Control 12, 736-746 (1974; Zbl 0296.93037)] is used to generate families of realizations, the state covariances of which are totally ordered. Finally, the property of constant directions which the discrete-time Riccati equation enjoys is utilized to obtain families of realizations, the state covariances of which have the same value in certain directions.
MSC:
| 93B15 | Realizations from input-output data |
| 60G10 | Stationary stochastic processes |
| 93C55 | Discrete-time control/observation systems |
| 15A24 | Matrix equations and identities |
| 93E03 | Stochastic systems in control theory (general) |
Keywords:
stochastic realizations; discrete-time stationary stochastic process; non-Riccati algorithm; constant directionsCitations:
Zbl 0296.93037References:
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