“Recursive prediction error methods for online estimation in nonlinear state-space models”

Authors: Dag Ljungquist and Jens G. Balchen,
Affiliation: Norsk Hydro and NTNU, Department of Engineering Cybernetics
Reference: 1994, Vol 15, No 2, pp. 109-121.

Keywords: Recursive estimation, line-search methods, recursive prediction error methods, system identification

Abstract: Several recursive algorithms for online, combined state and parameter estimation in nonlinear state-space models are discussed in this paper. Well-known algorithms such as the extended Kalman filter and alternative formulations of the recursive prediction error method are included, as well as a new method based on a line-search strategy. A comparison of the algorithms illustrates that they are very similar although the differences can be important for the online tracking capabilities and robustness. Simulation experiments on a simple nonlinear process show that the performance under certain conditions can be improved by including a line-search strategy.

PDF PDF (1541 Kb)        DOI: 10.4173/mic.1994.2.4

DOI forward links to this article:
[1] Jens G. Balchen (2000), doi:10.4173/mic.2000.1.1
[2] C. Bohn and H. Unbehauen (2001), doi:10.1049/ip-cta:20010235
[3] Remko Baur, Qi Zhao, Jan Peter Blath, Franz Kallage, Matthias Schultalbers and Christian Bohn (2014), doi:10.1109/CCA.2014.6981603
[4] A. Tarasow, C. Bohn, M. Vinaske, G. Wachsmuth and R. Serway (2010), doi:10.3182/20100712-3-DE-2013.00169
[5] Tomá Polóni, Arnfinn Aas Eielsen, Boris Rohal -Ilkiv and Tor Arne Johansen (2013), doi:10.1115/1.4024008
[6] M R Ananthasayanam, M Shyam Mohan, Naren Naik and R M O Gemson (2016), doi:10.1007/s12046-016-0562-z
[1] ANDERSON, B.D.O. MOORE, J.B., (1979). Optimal Filtering, Prentice Hall, Englewood Cliffs, NJ.
[2] DE WOLF, D.G., WIBERG, D.M. (1993). An ordinary differential equation technique for continuous-time parameter estimation, IEEE Trans. Automat. Contr., 34, 514-528 doi:10.1109/9.250521
[3] LJUNG, L. (1979). Asymptotic behavior of the extended Kalman filter as a parameter estimator for linear systems, IEEE Trans. Aut. Control, 24, 36-50 doi:10.1109/TAC.1979.1101943
[4] LJUNG, L. (1987). System Identification, Theory for the User, Prentice-Hall, Englewood Cliffs, New Jersey.
[5] LJUNG, L. SÖDERSTRÖM, T. (1983). Theory and Practice of Recursive Identification, MIT Press, Cambridge, Massachusetts.
[6] LJUNGQUIST, D. (1990). Online Estimation in Nonlinear State-Space Models with Application to Catalytic Cracking, Dr. ing. thesis, Report no. 90-89-W, Department of Engineering Cybernetics, NTH, Trondheim, Norway.
[7] LJUNGQUIST, D. (1992). Recursive Estimation Algorithms for Nonlinear State-Space Models, Statoil report no. 761.01-01, Trondheim, Norway.
[8] SCHLEE, F.H., STANDISH, C.J. TODA, N.F. (1967). Divergence in the Kalman filter, AIAA Journal, 5, 1141-1120 doi:10.2514/3.4146
[9] SORENSEN, H.W. (1985). Kalman Filtering: Theory and Application, IEEE Press, The Institute of Electrical and Electronics Engineers, Inc., New York.
[10] SOONG, T.T. (1965). On a priori statistics in minimum-variance estimation problems, Trans. of the ASME. Journal of Basic Engineering.
[11] WOLFE, M.A. (1978). Numerical Methods for Unconstrained Optimization, Van Nostrand Reinhold, Berkshire, England.

  title={{Recursive prediction error methods for online estimation in nonlinear state-space models}},
  author={Ljungquist, Dag and Balchen, Jens G.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}