Score Evaluation Within the Extended Square-Root Information Filter

  • Maria V. Kulikova
  • Innokenti V. Semoushin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3991)


A newly developed algorithm for evaluating the Log Likelihood Gradient (score) of linear discrete-time dynamic systems is presented, based on the extended Square-Root Information Filter (eSRIF). The new result can be used for efficient calculations in gradient-search algorithms for maximum likelihood estimation of the unknown system parameters. The theoretical results are given with the examples showing the superior perfomance of this computational approach over the conventional one.


Very Large Scale Integration Linear Dynamic System Linear State Space Model Unknown System Parameter Numerical Score Evaluation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Goodwin, G.C., Payne, R.L.: Dynamic System Identification: Experiment Design and Data Analysis. Academic, New York (1977)MATHGoogle Scholar
  2. 2.
    Goodrich, R.L., Caines, P.E.: Linear System Identification from Non-stationary Cross-sectional Data. IEEE Trans. Automat. Contr. AC-24, 403–411 (1979)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Yared, K.I.: On Maximum Likelihood Identification of Linear State Space models, Mass. Inst. Technol., Cambridge, MA, Rep. LIDS-TH-920 (1979)Google Scholar
  4. 4.
    Wilson, D.A., Kumar, A.: Derivative Computations for the Log Likelihood Function. IEEE Trans. Automat. Contr. AC-27, 230–232 (1982)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Segal, M., Weinstein, E.: A New Method for Evaluating the Log-Likelihood Gradient (Score) of Linear Dynamic Systems. IEEE Trans. Automat. Contr. AC-33, 763–766 (1988)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Segal, M., Weinstein, E.: A New Method for Evaluating the Log-Likelihood Gradient, the Hessian, and the Fischer Information Matrix for Linear Dynamic Systems. IEEE Trans. Automat. Contr. AC-35, 682–687 (1989)MATHMathSciNetGoogle Scholar
  7. 7.
    Leland, R.P.: A New Formula for the Log-Likelihood Gradient for Continuous-Time Stochastic Systems. IEEE Trans. Automat. Contr. AC-40, 1295–1300 (1995)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Leland, R.P.: An Improved Log-Likelihood Gradient for Continuous-Time Stochastic Systems with Deterministic Input. IEEE Trans. Automat. Contr. AC-41, 1207–1210 (1996)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Kaminski, P.G., Bryson, A.E., Schmidt, S.F.: Discrete Square Root Filtering: A survey of Current Techniques. IEEE Trans. on Aut. Cont. AC-16(6), 727–735 (1971)CrossRefGoogle Scholar
  10. 10.
    Bierman, G.J., Belzer, M.R., Vandergraft, J.S., Porter, D.W.: Maximum likelihood estimation using square root information filters. IEEE Trans. on Autom. Contr. 35(12), 1293–1298 (1990)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Park, P., Kailath, T.: New square-root algorithms for Kalman filtering. IEEE Trans. on Autom. Contr. 40(5), 895–899 (1995)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Grewal, M.S., Andrews, A.P.: Kalman Filtering: Theory and Practice. Prentice-Hall, Englewood Cliffs (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Maria V. Kulikova
    • 1
  • Innokenti V. Semoushin
    • 2
  1. 1.School of Computational and Applied MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa
  2. 2.Ulyanovsk State UniversityUlyanovskRussia

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