| P. van Overschee and B. de Moor. Subspace algorithms for the stochastic identification problem. Automatica, 29(3):649--660, March 1993. |
....will therefore be ignored in this paper. model parameters A,C,Q,R. Ideally, we would want the maximum likelihood solution from the finite sample: A(t) C(t) Q(t) R(t) arg min A,C,Q,R p(y(1) y(t) 2) The algorithm that achieves the optimum asymptotically as has been derived in [16]. Unfortunately, given the dimensionality of our problem (m , t 100) this algorithm is computationally impractical and we settle for the simplified, suboptimal algorithm proposed in [6] Once properly implemented, this algorithm runs in a few seconds on a high end PC. The order of the ....
P. Van Overschee and B. De Moor. Subspace algorithms for the stochastic identification problem. Automatica, 29:649-- 660, 1993.
.... expectation maximization (EM) approaches using particle filters [20, 3] or structured variational inference techniques [23] Our models are discrete time, continuous state dynamical systems, and the action is coded in the dynamical model (i.e. the system parameters) We use closed form algorithms [22] rather than EM as customary, to perform learning. Since the space of model is non linear, computing a distance between models is non trivial. We draw on the literature of system identification and signal processing, where the problem is an active area of research [8, 18] We propose different ....
....R; Q, a canonical realization of the process fy(t)g. Ideally, we would want the maximum likelihood solution from the finite sample, that is the argument of max A;C;Q;R p(y(1) y( jA; C; Q; R) 2) The closed form asymptotically optimal solution to this problem has been derived in [22]. From this point on, therefore, we will assume that we have available for each sample sequence a model in the form fA; C; Q; Rg. While the state transition A and the output transition C are an intrinsic characteristic of the model, the input and output noise covariances Q and R are not ....
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P. Van Overschee and B. De Moor. Subspace algorithms for the stochastic identification problem. Automatica, 29:649-- 660, 1993.
....given in closed form in equations (9) to (13) that can be implemented in a few lines of Matlab code (Figure 1) This algorithm draws on numerous results in the theory of system identification. In particular, it can be considered as an extension of the theory developed by Van Overschee and De Moor [11] to the particular case of image sequences. In traditional system identification one has few measurements and uses them to control far more states. In vision, on the other hand, one has a huge number of measurements (a 1920 dimensional vector at each time instant for video resolution) and wants to ....
.... the case of linear models driven by Gaussian noise such as (1) this problem can only be solved iteratively, and is often formulated in the framework of expectation maximization [13] Instead, we will follow the philosophy of subspace identification methods championed by Van Overschee and DeMoor [11], and compute a solution in closed form. This solution can be shown to be asymptotically efficient under suitable hypotheses. 2.2 Uniqueness and canonical model realizations The first observation concerning the model (1) is that the choice of matrices A; C; Q; R; S is not unique, in the sense ....
P. Van Overschee and B. De Moor. Subspace algorithms for the stochastic identification problem. Automatica, 29:649-- 660, 1993.
....if the dynamical model is linear, their unique representation is not. Therefore, distance must be defined in terms of the length of a geodesic path relative to a Riemannian metric in the nonlinear space of models. This paper draws on results from the theory of system identification, in particular [29], for mapping data to models. Such a map is one to one and can be computed in closed form. Each model is represented as a point on a manifold that has a Riemannian structure that has been worked out in [11] To the best of our knowledge, we are the first to pose the problem of recognizing ....
P. Van Overschee and B. De Moor. Subspace algorithms for the stochastic identification problem. Automatica, 29:649-- 660, 1993.
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Van Overschee P., De Moor B. Subspace Algorithms for the Stochastic Identification Problem. ESAT/SISTA report 1991-26, Kath. Universiteit Leuven, Dept. E.E. , Belgium. To be published in Automatica.
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Van Overschee P., De Moor B. Subspace Algorithms for the Stochastic Identification Problem. 30 th IEEE Conference On Decision and Control, Brighton, England, 11-13 December 1991, pp. 1321-1326.
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P. Van Overschee P., B. De Moor, Subspace algorithms for the stochastic identification problem, Automatica, vol. 29, no. 3, March (1993), pp. 649-660.
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P. Van Overschee, B. De Moor, "Subspace algorithms for the stochastic identification problem," Automatica, vol. 29, no. 3, Mar. 1993, pp. 649-660.
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Van Overschee P., De Moor B. (1993). Subspace Algorithms for the Stochastic Identification Problem, Automatica, Vol. 29, No. 3, pp 649660.
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Van Overschee P., De Moor B. Subspace algorithms for the stochastic identification problem. Automatica 29, 3, pp.649-660, 1993.
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Van Overschee P., De Moor B. Subspace Algorithms for the Stochastic Identification Problem. ESAT/SISTA report 1991-26, Kath. Universiteit Leuven, Dept. E.E. , Belgium. Accepted for publication in Automatica.
No context found.
Van Overschee P., De Moor B. Subspace Algorithms for the Stochastic Identification Problem. 30 th IEEE Conference On Decision and Control, Brighton, England, 11-13 December 1991, pp. 1321-1326.
No context found.
Van Overschee P., De Moor B. Subspace algorithms for the stochastic identification problem. ESAT-SISTA Report 1991-29, Department of Electrical Engineering, Katholieke Universiteit Leuven, Belgium. Accepted for publication in Automatica, 1993.
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P. Van Overschee and B. De Moor, "Subspace algorithms for the stochastic identification problem," Automatica, vol. 29, no. 3, pp. 649--660, Mar. 1993.
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Van Overschee P., De Moor B. (1993). Subspace Algorithms for the Stochastic Identification Problem, Automatica, Vol. 29, No. 3, pp 649-660.
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P. Van Overschee, B. De Moor, "Subspace algorithms for the stochastic identification problem," Automatica, vol. 29, no. 3, Mar. 1993, pp. 649-660.
....theory that is closely related to CCA and that was introduced by Shannon [18] in 1948. A slightly di#erent interpretation in terms of channel capacity and information rate is given in [17] Another area where CCA is applied, is stochastic realization and identification of dynamical models [1, 3, 5, 11, 12, 15, 16, 21, 22]. The order of the model and a state sequence can be derived from the canonical correlations and the canonical variates of the past and the future output data. Katrien De Cock is a research assistant at the K.U.Leuven. Dr. Bart De Moor is a full professor at the K.U.Leuven. Our research is ....
P. Van Overschee and B. De Moor, "Subspace algorithms for the stochastic identification problem", Automatica 29, 649--660, 1993. Available on ftp://ftp.esat.kuleuven.ac.be/ pub/SISTA/vanoverschee/reports as file stoch auto2.ps.Z.
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P. van Overschee and B. de Moor. Subspace algorithms for the stochastic identification problem. Automatica, 29(3):649--660, March 1993.
No context found.
P. Van Overschee and B. De Moor. Subspace algorithms for the stochastic identification problem. Automatica, 29:649--660, 1993.
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P. Van Overschee and B. De Moor, "Subspace algorithms for the stochastic identification problem," Automatica, vol. 29, pp. 649--660, 1993.
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P. Van Overschee and B. De Moor. Subspace algorithms for the stochastic identification problem. Automatica, 29:649-- 660, 1993.
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P. van Overschee and B. de Moor. Subspace algorithms for the stochastic identification problem. Automatica, 29(3):649--660, March 1993.
No context found.
P. Van Overschee and B. De Moor. Subspace algorithms for the stochastic identification problem. Automatica, 29:649-- 660, 1993.
No context found.
P. van Overschee and B. de Moor. Subspace algorithms for the stochastic identification problem. Automatica, 29(3):649--660, March 1993.
No context found.
P. Van Overschee and B. De Moor, "Subspace algorithms for the stochastic identification problem," Automatica, Vol. 29, No. 3, pp. 649--660, 1993.
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