“Estimation of Large-Scale Implicit Models Using 2-Stage Methods”

Authors: Rolf Henriksen,
Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 1985, Vol 6, No 1, pp. 3-19.

Keywords: Parameter estimation, large scale systems, two-stage methods, decentralized filtering, prediction error methods, implicit models

Abstract: The problem of estimating large scale implicit (non-recursive) models by two- stage methods is considered. The first stage of the methods is used to construct or estimate an explicit form of the total model, by constructing a minimal stochastic realization of the system. This model is then subsequently used in the second stage to generate instrumental variables for the purpose of estimating each sub-model separately. This latter stage can be carried out by utilizing a generalized least squares method, but most emphasis is put on utilizing decentralized filtering algorithms and a prediction error formulation. A note about the connection between the original TSLS-method (two-stage least squares method) and stochastic realization is also made.

PDF PDF (2282 Kb)        DOI: 10.4173/mic.1985.1.1

DOI forward links to this article:
[1] David Di Ruscio, Rolf Henriksen and Jens G. Balchen (1994), doi:10.4173/mic.1994.1.5
[2] D. Di Ruscio, R. Henriksen and J.G. Balchen (1993), doi:10.1109/CDC.1993.325869
References:
[1] ANDERSON, B.D.O., GEVERS, M.R. (1979). Identifiability of closed-loop systems using the joint input/output identification method, Proc. Vth IFAC Symposium on Identification and System Parameter Estimation, Darmstadt, F. R. Germany, p. 645, Pergamon Press.
[2] ANDERSON, B.D.O., GEVERS, M.R. (1982). Identifiability of linear stochastic systems operating under linear feedback, Automatica, 18, 195 doi:10.1016/0005-1098(82)90108-X
[3] AOKI, M. (1983). Notes in Econometric Time Series Analysis: System Theoretic Perspectives, Springer-Verlag.
[4] BASMAN, R.L (1957). A generalized classical method of linear estimation of coefficients in a structural equation, Econometrica, 25, 77 doi:10.2307/1907743
[5] CAINES, P.E., LJUNG, L. (1976). Asymptotic normality and accuracy of prediction error estimators, Research Report No. 7602, University of Toronto, Department of Electrical Engineering.
[6] CAINES, P.E., CHAN, C.W. (1976). Estimation, identification and feedback, In System Identification: Advances and Case Studies,.editors. R. K. Mehra and D. G. Lainiotis, p. 349, Academic Press.
[7] CHOW, C.G. (1964). A comparison of alternative estimators for simultaneous equations, Econometrica, 32, 532 doi:10.2307/1910177
[8] CLARKE, D.W. (1967). Generalized least-squares estimation of the parameters of a dynamic model, Proc. IFAC Symposium on Identification of Automatic Control Systems, Prague, Czechoslovakia, Paper No. 3.17.
[9] DAMEN, A.A.H., HAJDASINSKI, A.K. (1982). Practical tests with different approximate realizations based on the singular value decomposition of the Hankel matrix, Proc. VIth IFAC Symposium on Identification and System Parameter Estimation, Arlington, Virginia, USA, p. 809, Pergamon Press.
[10] DHRYMES, P.J. (1972). Simultaneous equations inference in econometrics, IEEE Trans. Automat. Control, AC-17, 427 doi:10.1109/TAC.1972.1100040
[11] FAURRE, P.L. (1976). Stochastic realization algorithms, In System Identification: Advances and Case studies,.editors R. K. Mehra and D.G. Lainiotis, p. 1, Academic Press.
[12] GEVERS, M.R. (1976). On the identification of feedback systems, Proc. IVth IFAC Symposium on Identification and System Parameter Estimation, Tbilisi, USSR, Part 3, p. 625.
[13] GOODWIN, G.C., PAYNE, R. L. (1977). Dynamic System Identification: Experiment Design and Data Analysis, Academic Press.
[14] GUSTAVSSON, I., LJUNG, L, SÖDERSTRÖM, T. (1974). Identification of linear multivariable systems operating under linear feedback control, IEEE Trans. Automat. Control, AC-19, 836 doi:10.1109/TAC.1974.1100702
[15] GUSTAVSSON, I., LJUNG, L., SÖDERSTRÖM, T. (1975). Identifiability condition for linear systems operating in closed loop, Int. J. Control, 21, 243 doi:10.1080/00207177508921984
[16] GUSTAVSSON, I., LJUNG, L., SÖDERSTRÖM, T. (1976). Identification of processes in closed loop - identifiability and accuracy aspects, Proc. IVth IFAC Symposium on Identification and System Parameter Estimation, Tbilisi, USSR, Part 1, p. 23.
[17] HAJDASINSKI, A., VAN DEN HOF, P., DAMEN, A. (1984). Naive approximate realizations of noisy data, Proc. 9th IFAC World Congress, Budapest, Hungary, Vol. X, p. 90.
[18] HENRIKSEN, R. (1979). Nonlinear filtering in econometric models, Research Memorandum No. 240, Princeton University, Econometric Research Program, Princeton, New Jersey.
[19] HO, B.L., KALMAN, R.E. (1966). Effective construction of linear state-variable models from input/output functions, Regelungstechnik, 14, p. 545.
[20] KAILATH, T. (1968). An innovations approach to least-squares estimation, Part I: Linear filtering in additive white noise. IEEE Trans. Automat, Control, AC-13, 646 doi:10.1109/TAC.1968.1099025
[21] KALMAN, R.E. (1980). Identifiability and problems of model selection in econometrics, Proc. 4th World Congress of the Econometric Society, Aix-en-Provence, France.
[22] LJUNG, L (1976). On the consistency of prediction error identification methods, In System Identification: Advances and Case Studies,.editors R. K. Mehra and D. G. Lainiotis, p. 121, Academic Press.
[23] MEHRA, R.K. (1974). Identification in control and econometrics; similarities and differences, Annals of Economic and Social Measurement, 3, p. 21.
[24] NG, T.S., GOODWIN, G.C., ANDERSON, B.D.O. (1977). Identifiability of MIMO linear systems operating in closed loop, Automatica, 13, p. 477 doi:10.1016/0005-1098(77)90068-1
[25] RISSANEN, J., KAILATH, T. (1972). Partial realization of random systems, Automatica, 8, p. 389 doi:10.1016/0005-1098(72)90098-2
[26] SANDERS, C.W., TACKER, F.C., LINTON, T.D. (1974). A new class of decentralized filters for interconnected systems, IEEE Trans. Automat. Control, AC-19, p. 259 doi:10.1109/TAC.1974.1100541
[27] SANDERS, C.W., TACKER, E.C., LINTON, T.D. (1978). Information exchange in decentralized filter via interaction estimates, Proc. 7th IFAC Triennial World Congress, Helsinki, Finland, p. 1367, Pergamon Press.
[28] SILJAK, D.D, VUKCEVIC, M.B. (1978). On decentralized estimation, Int. J. Control, 27, p. 113 doi:10.1080/00207177808922351
[29] SIN, K.S., GOODWIN, G.C. (1980). Checkable conditions for identifiability of linear systems in closed loop, IEEE Trans. Automat. Control, AC-25, p. 722 doi:10.1109/TAC.1980.1102421
[30] SINGH, M.G. (1975). Multi-level state estimation, Int. J. Syst. Sci., 6, p. 535 doi:10.1080/00207727508941836
[31] SÖDERSTRÖM, T., STOICA, P.G. (1983). Instrumental Variable Methods for System Identification, Springer-Verlag.
[32] TACKER, E.C., SANDERS, C.W. (1980). Decentralized structures for state estimation in large scale systems, Large Scale Systems, 1, p. 39.
[33] THEIL, H. (1953). Repeated least squares applied to complete equation systems, Central Planning Bureau, The Hague, The Netherlands.
[34] THEIL, H. (1971). Principles of Econometrics, John Wiley and Sons.
[35] VAN ZEE, G.A., BOSGRA, O.H. (1979). The use of realization theory in the robust identification of multivariable systems, Proc. Vth IFAC Symposium on System Identification and Parameter Estimation, Darmstadt, F.R. Germany, p. 477, Pergamon Press.
[36] WIERINGA, J. (1984). Minimal partial realization of covariance stationary sequences, Diploma thesis, The Norwegian Institute of Technology, Division of Engineering Cybernetics.
[37] WOLOVICH, W.A. (1974). Linear Multivariable Systems, Springer-Verlag.


BibTeX:
@article{MIC-1985-1-1,
  title={{Estimation of Large-Scale Implicit Models Using 2-Stage Methods}},
  author={Henriksen, Rolf},
  journal={Modeling, Identification and Control},
  volume={6},
  number={1},
  pages={3--19},
  year={1985},
  doi={10.4173/mic.1985.1.1},
  publisher={Norwegian Society of Automatic Control}
};