“Closed and Open Loop Subspace System Identification of the Kalman Filter”
Authors: David Di Ruscio,Affiliation: Telemark University College
Reference: 2009, Vol 30, No 2, pp. 71-86.
Keywords: Subspace, Identification, Closed loop, Linear Systems, Modeling
Abstract: Some methods for consistent closed loop subspace system identification presented in the literature are analyzed and compared to a recently published subspace algorithm for both open as well as for closed loop data, the DSR_e algorithm. Some new variants of this algorithm are presented and discussed. Simulation experiments are included in order to illustrate if the algorithms are variance efficient or not.
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DOI: 10.4173/mic.2009.2.3DOI forward links to this article:
| [1] David Di Ruscio (2012), doi:10.4173/mic.2012.2.1 |
| [2] David Di Ruscio (2013), doi:10.4173/mic.2013.3.2 |
| [3] David Di Ruscio (2009), doi:10.4173/mic.2009.4.2 |
| [4] Jan-Willem van Wingerden, Marco Lovera, Marco Bergamasco, Michel Verhaegen and Gijs van der Veen (2013), doi:10.1049/iet-cta.2012.0653 |
| [5] Gijs van der Veen, Jan-Willem van Wingerden and Michel Verhaegen (2013), doi:10.1109/TCST.2012.2205929 |
| [6] K. Erik J. Olofsson (2013), doi:10.1109/CDC.2013.6761026 |
| [7] Gijs van der Veen, Jan-Willem van Wingerden and Michel Verhaegen (2010), doi:10.1109/CDC.2010.5717872 |
| [8] Jinxu Cheng, Mengqi Fang and Youqing Wang (2016), doi:10.1007/s11045-016-0427-y |
| [9] Christer Dalen and David Di Ruscio (2016), doi:10.4173/mic.2016.4.2 |
| [10] Guillaume Mercere, Ivan Markovsky and Jose A. Ramos (2016), doi:10.1109/CDC.2016.7798709 |
| [11] Christer Dalen and David Di Ruscio (2017), doi:10.4173/mic.2017.4.3 |
| [12] Christer Dalen and David Di Ruscio (2018), doi:10.4173/mic.2018.1.4 |
| [13] Christer Dalen and David Di Ruscio (2018), doi:10.4173/mic.2018.4.4 |
| [14] Rajamani Doraiswami and Lahouari Cheded (2019), doi:10.5772/intechopen.81793 |
| [15] Rajamani Doraiswami and Lahouari Cheded (2018), doi:10.1049/iet-cta.2017.0829 |
| [16] Christer Dalen and David Di Ruscio (2022), doi:10.4173/mic.2022.4.1 |
[1] Chiuso, A. (2007). The role of vector autoregressive modeling in predictor-based subspace identification, Automatica, 4.6:1034-1048 doi:10.1016/j.automatica.2006.12.009
[2] Di Ruscio, D. (1994). Methods for the identification of state space models from input and output measurements, In 10th IFAC Symp. on System Identif.
[3] Di Ruscio, D. (1996). Combined Deterministic and Stochastic System Identification and Realization: DSR-a subspace approach based on observations, Modeling, Identification and Control, 1.3:193-230 doi:10.4173/mic.1996.3.3
[4] Di Ruscio, D. (1997). On subspace identification of the extended observability matrix, In 36th Conf. on Decision and Control.
[5] Di Ruscio, D. (2000). A weighted view of the partial least squares algorithm, Automatica, 36(6):831-850 doi:10.1016/S0005-1098(99)00210-1
[6] Di Ruscio, D. (2003). Subspace System Identification of the Kalman Filter, Modeling, Identification and Control, 2.3:125-157 doi:10.4173/mic.2003.3.1
[7] Di Ruscio, D. (2008). Subspace system identification of the Kalman filter: open and closed loop systems, In Proc. Intl. Multi-Conf. on Engineering and Technological Innovation.
[8] Hestenes, M. R. Stiefel, E. (1952). Methods for Conjugate gradients for Solving Linear Systems, J. Res. National Bureau of Standards, 4.6:409-436.
[9] Ho, B. L. Kalman, R. E. (1966). Effective construction of linear state-variable models from input/output functions, Regelungstechnik. 1.12:545-592.
[10] Jansson, M. (2003). Subspace identification and arx modeling, In 13th IFAC Symp. on System Identif.
[11] Jansson, M. (2005). A new subspace identification method for open and closed loop data, In IFAC World Congress.
[12] Katayama, T. (2005). Subspace Methods for System Identification, Springer.
[13] Larimore, W. E. (1983). System identification, reduced order filtering and modeling via canonical variate analysis, In Proc. Am. Control Conf. pp. 445-451.
[14] Larimore, W. E. (1990). Canonical variate analysis in identification, filtering and adaptive control, In Proc. 29th Conf. on Decision and Control. pp. 596-604.
[15] Ljung, L. McKelvey, T. (1995). Subspace identification from closed loop data, Technical Report LiTH-ISY-R-1752, Linkoping University, Sweden.
[16] Nilsen, G. W. (2005). Topics in open and closed loop subspace system identification: finite data based methods, Ph.D. thesis, NTNU-HiT, ISBN 82-471-7357-3.
[17] Overschee, P. V. de Moor, B. (1994). N4SID: Subspace Algorithms for the Identification of Combined Deterministic Stochastic Systems, Automatica, 30(1):75-93 doi:10.1016/0005-1098(94)90230-5
[18] Overschee, P. V. de Moor, B. (1996). Subspace identification for linear systems, Kluwer Acad. Publ.
[19] Qin, S. J. Ljung, L. (2003). Closed-loop subspace identification with innovation estimation, In Proc. 13th IFAC SYSID Symposium. pp. 887-892.
[20] Qin, S. J., Weilu, L., Ljung, L. (2005). A novel subspace identification approach with enforced causal models, Automatica, 4.12:2043-2053 doi:10.1016/j.automatica.2005.06.010
[21] Sotomayor, O. A. Z., Park, S. W., Garcia, C. (2003). Model reduction and identification of wastewater treatment plants - a subspace approach, Latin American Applied Research, Bahia Blanca, v.33, p. 135-140, Mais Informacoes.
[22] Sotomayor, O. A. Z., Park, S. W., Garcia, C. (2003). Multivariable identification of an activated sludge process with subspace-based algorithms, Control Engineering Practice, 11(8):961-969 doi:10.1016/S0967-0661(02)00210-1
[23] Weilu, L., Qin, J., Ljung, L. (2004). A Framework for Closed-loop Subspace Identification with Innovations Estimation, Techn. report no. 2004-07, Texas-Wisconsin Modeling and Control Consortium.
[24] Zeiger, H. McEwen, A. (1974). Approximate linear realizations of given dimensions via Ho´s algorithm, IEEE Trans. on Automatic Control, 1.2:153 doi:10.1109/TAC.1974.1100525
BibTeX:
@article{MIC-2009-2-3,
title={{Closed and Open Loop Subspace System Identification of the Kalman Filter}},
author={Di Ruscio, David},
journal={Modeling, Identification and Control},
volume={30},
number={2},
pages={71--86},
year={2009},
doi={10.4173/mic.2009.2.3},
publisher={Norwegian Society of Automatic Control}
};