**Page description appears here**

“Combined Deterministic and Stochastic System Identification and Realization: DSR - A Subspace Approach Based on Observations”

Authors: David Di Ruscio,
Affiliation: Telemark University College
Reference: 1996, Vol 17, No 3, pp. 193-230.

     Valid XHTML 1.0 Strict

Keywords: System identification, subspace methods, stochastic and deterministic systems, state-space methods, time series analysis

Abstract: A numerically stable and general algorithm for identification and realization of a complete dynamic linear state space model, including the system order, for combined deterministic and stochastic systems from time series is presented. A special property of this algorithm is that the innovations covariance matrix and the Markov parameters for the stochastic sub-system are determined directly from a projection of known data matrices, without e.g. recursions of non-linear matrix Riccatti equations. A realization of the Kalman filter gain matrix is determined from the estimated extended observability matrix and the Markov parameters. Monte Carlo simulations are used to analyze the statistical properties of the algorithm as well as comparing with existing algorithms.

PDF PDF (4546 Kb)        DOI: 10.4173/mic.1996.3.3

DOI forward links to this article:
  [1] A. Sæther, C. Arakaki, C. Ratnayake and D. Di Ruscio (2009), doi:10.1080/02726350902991007
  [2] S. Joe Qin, Weilu Lin and Lennart Ljung (2005), doi:10.1016/j.automatica.2005.06.010
  [3] Dionisio Bernal (2013), doi:10.1016/j.ymssp.2013.02.012
  [4] David Di Ruscio (2003), doi:10.4173/mic.2003.3.1
  [5] Dionisio Bernal (2011), doi:10.1002/stc.383
  [6] Bernt Lie, David Di Ruscio, Rolf Ergon, Bjørn Glemmestad, Maths Halstensen, Finn Haugen, Saba Mylvaganam, Nils-Olav Skeie and Dietmar Winkler (2009), doi:10.4173/mic.2009.3.4
  [7] Rolf Ergon (1998), doi:10.4173/mic.1998.2.2
  [8] Dionisio Bernal (2013), doi:10.1016/j.ymssp.2013.10.020
  [9] Rolf Ergon (1998), doi:10.1016/S0169-7439(98)00168-3
  [10] Jin Wang and S.Joe Qin (2002), doi:10.1016/S0959-1524(02)00016-1
  [11] Dionisio Bernal (2006), doi:10.1061/(ASCE)0733-9399(2006)132:6(651)
  [12] David Di Ruscio (2009), doi:10.4173/mic.2009.4.2
  [13] David Di Ruscio (2009), doi:10.4173/mic.2009.2.3
  [14] David Di Ruscio (2013), doi:10.4173/mic.2013.3.2
  [15] Dionisio Bernal (2004), doi:10.1061/(ASCE)0733-9399(2004)130:9(1083)
  [16] D. Bernal (2014), doi:10.1533/9781782422433.1.67
  [17] Håkon Viumdal, Saba Mylvaganam and David Di Ruscio (2014), doi:10.4173/mic.2014.3.1
  [18] Dionisio Bernal, Michael Döhler, Salma Mozaffari Kojidi, Kenny Kwan and Yang Liu (2015), doi:10.1193/101812EQS311M
  [19] Jan-Willem van Wingerden, Marco Lovera, Marco Bergamasco, Michel Verhaegen and Gijs van der Veen (2013), doi:10.1049/iet-cta.2012.0653
  [20] Weilu Lin, S.J. Qin and L. Ljung (2004), doi:10.1109/CDC.2004.1430374
  [21] Aleksandra Marjanovic, Goran Kvascev and Zeljko Durovic (2012), doi:10.1109/CCA.2012.6402447
  [22] Martin Grossl (2013), doi:10.1109/SysTol.2013.6693941
  [23] Omar Mohamed, Dalal Younis, Hawa Abdelwahab, Amer Anizei and Belgasem T. Elobidy (2014), doi:10.1109/ICUMT.2014.7002138
  [24] Christer Dalen, David Di Ruscio and Roar Nilsen (2015), doi:10.4173/mic.2015.3.5
  [25] Omar Mohamed, Ashraf Khalil, Marwan Limhabrash and Jihong Wang (2015), doi:10.1109/AEECT.2015.7360556
  [26] Christer Dalen and David Di Ruscio (2016), doi:10.4173/mic.2016.1.4
  [27] Carlos F. Alcala, Ricardo Dunia and S. Joe Qin (2012), doi:10.3182/20120829-3-MX-2028.00238
  [28] Morten Bakke, Tor A. Johansen and Sigurd Skogestad (2010), doi:10.3182/20100705-3-BE-2011.00099
  [29] Cristian Cruz and Eduardo Miranda (2016), doi:10.1061/(ASCE)ST.1943-541X.0001628
  [30] Christer Dalen and David Di Ruscio (2016), doi:10.4173/mic.2016.4.2
  [31] D. Bernal (2018), doi:10.1016/j.ymssp.2017.04.043
  [32] Christer Dalen and David Di Ruscio (2017), doi:10.4173/mic.2017.4.3
  [33] Christer Dalen and David Di Ruscio (2018), doi:10.4173/mic.2018.1.4
  [34] Kalil Erazo, Debarshi Sen, Satish Nagarajaiah and Limin Sun (2019), doi:10.1016/j.ymssp.2018.07.041
  [35] Abhinav Narasingam and Joseph Sang-Il Kwon (2018), doi:10.1016/j.compchemeng.2018.08.010
  [36] Christer Dalen and David Di Ruscio (2018), doi:10.4173/mic.2018.4.4
  [37] Cristian Cruz and Eduardo Miranda (2019), doi:10.1016/j.engstruct.2019.01.056
  [38] O.M. Brastein, B. Lie, R. Sharma and N.-O. Skeie (2019), doi:10.1016/j.enbuild.2019.03.018

[1] DI RUSCIO, D. (1994). Methods for the identification of state space models from input and output measurements, SYSID 94, The 10th IFAC Symposium on System Identification, Copenhagen, July 4-6.
[2] DI RUSCIO, D. (1995). A method for the identification of state space models from input and output measurements, Modeling, Identification and Control, vol. 16, no. 3. Program commercial available by Fantoft Process AS, Box 306, N-1301 Sandvika.
[3] DI RUSCIO. D. (1995). A method for identification of combined deterministic and stochastic systems, Proceedings of the third European Control Conference, ECC95, Roma, September 5-8, pp. 429-434.
[4] DI RUSCIO, D., HOLMBERG, A. (1996). Subspace identification for dynamic process analysis and modeling, Control Systems 96, Halifax, Nova Scotia, May 1996.
[5] GOLUB, G.H., VAN LOAN, C.F. (1983). Matrix Computations, North Oxford Academic Publishers Ltd.
[6] LARIMORE, W.E. (1983). System identification, reduced order filtering and modeling via canonical variate analysis, Proc. of the American Control Conference, San Francisco, USA, pp. 445-451.
[7] LARIM0RE, W.E. (1990). Canonical Variate Analysis in Identification, Filtering and Adaptive Control, Proc. of the 29th Conference on Decision and Control, Honolulu, Hawaii, December 1990, pp. 596-604.
[8] LJUNG, L. (1991). System Identification Toolbox, The Mathworks, Inc.
[9] FAURRE, P.L. (1976). Stochastic realization algorithms, In R.K. Mehra and D.G. Lainiotis (eds), System Identification: Advances and Case Studies, Academic Press doi:10.1016/S0076-5392(08)60868-1
[10] KALMAN, R.E., FALB, P.L., ARBIB, M.A. (1969). Topics in mathematical system theory, McGraw-Hill Book Company.
[11] KUNG, S.Y. (1978). A new identification and Model Reduction Algorithm via Singular Value Decomposition, Conf on Circuits, Systems and Computers, Pacific Grove, CA, November 1978, pp. 705-714.
[12] MOORE., B.C. (1981). Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction, IEEE Trans. on Automatic Control, Vol. AC-26, pp. 17-31.
[13] VAN OVERSCHEE, P., DE MOOR, B. (1994). N4SID: Subspace Algorithms for the Identification of Combined Deterministic Stochastic Systems, Automatica, vol. 30, no. 1, pp. 75-94 doi:10.1016/0005-1098(94)90230-5
[14] VAN OVERSCHEE, P. (1995). Subspace Identification: theory-implementation-application, PhD thesis, Katholieke Universiteit Leuven, Belgium.
[15] VAN OVERSCHEE, P., DE MOOR, B. (1996). A Unifying Theorem for Three Subspace System Identification Algorithms, Automatica, vol. 31, no. 12, pp. 1853-1864 doi:10.1016/0005-1098(95)00072-0
[16] VERHAGEN, M. (1994). Identification of the deterministic part of MIMO state space models given on innovations form from input output data, Automatica, vol. 30, no. 1, pp. 61-74 doi:10.1016/0005-1098(94)90229-1
[17] VIBERG, M. (1995). Subspace-Based Methods for the Identification of Linear Time-invariant Systems, Automatica, vol. 31, no. 12, pp. 1835-1851 doi:10.1016/0005-1098(95)00107-5

  title={{Combined Deterministic and Stochastic System Identification and Realization: DSR - A Subspace Approach Based on Observations}},
  author={Di Ruscio, David},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}


Oct 2018: MIC reaches 3000 DOI Forward Links. The last 1000 took 2 years and 5 months.

May 2016: MIC reaches 2000 DOI Forward Links. The first 1000 took 34 years, the next 1000 took 2.5 years.

July 2015: MIC's new impact factor is now 0.778. The number of papers published in 2014 was 21 compared to 15 in 2013, which partially explains the small decrease in impact factor.

Aug 2014: For the 3rd year in a row MIC's impact factor increases. It is now 0.826.

Dec 2013: New database-driven web-design enabling extended statistics. Article number 500 is published and MIC reaches 1000 DOI Forward Links.

Jan 2012: Follow MIC on your smartphone by using the RSS feed.


July 2011: MIC passes 1000 ISI Web of Science citations.

Mar 2010: MIC is now indexed by DOAJ and has received the Sparc Seal seal for open access journals.

Dec 2009: A MIC group is created at LinkedIn and Twitter.

Oct 2009: MIC is now fully updated in ISI Web of Knowledge.