A stochastic subspace system identification algorithm for state-space systems in the general 2-D Roesser model form

References

• Alenany, A. , Mercère, G. , & Ramos, J. A. (2017). Subspace identification of 2-D CRSD Roesser models with deterministic-stochastic inputs: A state computation approach. IEEE Transactions on Control Systems Technology, 25 (3), 1108–1115.
   Web of Science ®Google Scholar
• Attasi, S. (1976). Modelling and recursive estimation for double indexed sequences. In R. Mehra & D. Lainiotis (Eds.), System identification: Advances and case studies (pp. 289–348). New York, NY: Academic Press.
   Google Scholar
• Barry, P. , Gran, R. , & Waters, C. (1976). Two-dimensional filtering: A state space approach. In Proceedings of the IEEE conference on decision and control (pp. 613–618). Clearwater, FL: IEEE.
   Google Scholar
• Dillabough, M. (2007). Discrete state-space models for distributed parameter systems ( Unpublished master's thesis). Subdury: School of Graduate Studies, Laurentian University.
   Google Scholar
• Ding, T. (2007). Systems theoretic approach to textured image and video processing ( Unpublished doctoral dissertation). Pennsylvania, PA: The Pennsylvania State University.
   Google Scholar
• Ding, T. , Sznaier, M. , & Camps, O. (2006). Robust identification of 2-D periodic systems with applications to texture synthesis and classification. In Proceedings of the IEEE conference on decision and control (pp. 3678–3683). San Diego, CA: IEEE.
   Google Scholar
• Farah, M. , Mercère, G. , Ouvrard, R. , & Poinot, T. (2016). Combining least-squares and gradient-based algorithms for the identification of a co-current flow heat exchanger. International Journal of Control, 1–13. doi: 10.1080/00207179..2016.1234717.
   Google Scholar
• Farah, M. , Mercère, G. , Ouvrard, R. , Poinot, T. , & Ramos, J. (2014). Identification of 2-D Roesser models by using linear fractional representations. In Proceedings of the European control conference (pp. 382–387). Strasbourg, France: IEEE.
   Google Scholar
• Fornasini, E. , & Marchesini, G. (1978). Doubly-indexed dynamical systems: State-space models and structural properties. Mathematical Systems Theory, 12 , 59–72.
   Google Scholar
• Fraanje, R. , & Verhaegen, M. (2005). A spatial canonical approach to multidimensional state-space identification for distributed parameter systems. In Proceedings of the international workshop on multidimensional systems (pp. 217–222), Wuppertal, Germany. IEEE.
   Google Scholar
• Galkowski, K. (2000). Higher order discretization of 2-D systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47 (5), 713–722.
   Google Scholar
• Givone, D. , & Roesser, R. (1972). Multidimensional linear iterative circuits – General properties. IEEE Transactions on Computers, 21 , 1067–1073.
   Web of Science ®Google Scholar
• Habibi, A. (1972). Two-dimensional Bayesian estimate of images. Proceedings of the IEEE, 60 , 878–883.
   Web of Science ®Google Scholar
• Kaczorek, T. (1985). Two dimensional linear systems , Berlin Heidelberg, Germany: Springer Verlag.
   Google Scholar
• Kailath, T. (1980). Linear systems , Englewood Cliffs, NJ: Prentice-Hall.
   Google Scholar
• Katayama, T. (2005). Subspace methods for system identification , London, UK: Springer Verlag.
   Google Scholar
• Katayama, T. , & Kosaka, M. (1979). Recursive filtering algorithm for a two-dimensional system. IEEE Transactions of Automatic Control, 24 , 130–132.
   Web of Science ®Google Scholar
• Kung, S. , Levy, B. , Morf, M. , & Kailath, T. (1977). New results in 2-D system theory, Part II: 2-D state-space models-realization and the notions of controllability, observability, and minimality. Proceedings of the IEEE, 65 , 945–961.
   Web of Science ®Google Scholar
• Kurek, J. (1985). The general state-space model for a two-dimensional linear digital system. IEEE Transactions on Automatic Control, 30 (6), 600–602.
   Web of Science ®Google Scholar
• Lashgari, B. (1981). Two-dimensional approximation, model reduction and minimum variance error estimation ( Unpublished doctoral dissertation). Los Angeles, CA: University of Southern California.
   Google Scholar
• Lashgari, B. , & Silverman, L. (1986). Recursive estimation of two-dimensional processes with application to image processing. Circuits Systems and Signal Processing, 5 , 212–226.
   Web of Science ®Google Scholar
• Lashgari, B. , Silverman, L. , & Abramatic, J. (1983). Approximation of 2-D separable in denominator filters. IEEE Transactions on Circuits and Systems, 30 , 107–121.
   Google Scholar
• Lele, S. , & Mendel, J. (1987). Modeling and recursive state estimation for two-dimensional noncausal filters with applications in image restoration. IEEE Transactions on Circuits and Systems, 34 , 1507–1517.
   Google Scholar
• Mardia, K. , Kent, J. , & Bibby, J. (1979). Multivariate analysis , San Diego, California: Academic Press.
   Google Scholar
• Owens, D. , Amann, N. , Rogers, E. , & French, M. (2000). Analysis of linear iterative learning control schemes – A 2-D systems/repetitive processes approach. Multidimensional Systems and Signal Processing, 11 , 125–177.
   Web of Science ®Google Scholar
• Ramos, J. A. , & Mercère, G. (2016a). Image modeling based on a 2-D stochastic subspace system identification algorithm. Multidimensional Systems and Signal Processing, 28 , 1133–1165.
   Web of Science ®Google Scholar
• Ramos, J. A. , & Mercère, G. (2016b). Subspace algorithms for identifying separable-in-denominator 2D systems with deterministic-stochastic inputs. International Journal of Control, 89 (12), 2584–2610. Retrieved from http://dx.doi.org/10.1080/00207179.2016.1172258
   Web of Science ®Google Scholar
• Ramos, J. A. , & Mercère, G. (2017). Computation of the state bias and initial states for stochastic state space systems in the general 2-D roesser model form. ( ArXiv: submit/2131248 [cs.SY] 14 Jan 2018).
   Google Scholar
• Rao, C. (1964). The use and interpretation of principal component analysis in applied research. Sankhya, A, 26 , 329–359.
   Google Scholar
• Roesser, R. (1975). A discrete-state-space model for linear image processing. IEEE Transactions on Automatic Control, 20 , 1–10.
   Web of Science ®Google Scholar
• Strintzis, M. (1976). Comments on “Two-dimensional Bayesian estimate of images”. Proceedings of the IEEE, 64 , 1255–1257.
   Web of Science ®Google Scholar
• Van Overschee, P. , & De Moor, B. (1996). Subspace identification for linear systems. Theory, implementation, and applications , Dordrecht, The Netherlands: Kluwer Academic Publishers.
   Google Scholar
• Verhaegen, M. (1994). Identification of the deterministic part of MIMO state space model given in innovations form from input-output data. Automatica, 30 (1), 61–74.
   Web of Science ®Google Scholar
• Verhaegen, M. , & Verdult, V. (2007). Filtering and system identification: A least squares approach , New York, NY: Cambridge University Press.
   Google Scholar
• Voorsluys, M. , (2015). Subspace identification of Roesser models for large-scale adaptive optics ( Unpublished master's thesis). Delft, The Netherlands: Delft University of Technology.
   Google Scholar
• Wang, Z. (2014). Model based fault detection for two dimensional systems ( Unpublished doctoral dissertation). Ontario, Canada: School of Graduate Studies, Laurentian University.
   Google Scholar
• Wang, Z. , Bovik, A. , Sheikh, H. , & Simoncelli, E. (2004). Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing, 13 , 600–612.
   PubMed Web of Science ®Google Scholar
• Williams, D. (1991). Probability with martingales , Cambridge, United Kingdom: Cambridge University Press.
   Google Scholar
• Wirski, R. T . (2010). Synthesis of 2-D state-space equations for orthogonal separable denominator systems. In Proceedings of the ICSES international conference on signals and electronic circuits (pp. 285–288). Gliwice, Poland: IEEE.
   Google Scholar
• Yang, R. , Xie, L. , & Zhang, C. (2006). H 2 and mixed H 2/H ∞ control of two-dimensional systems in Roesser model. Automatica, 42 , 1507–1514.
   Web of Science ®Google Scholar