Iterative observer-based state and parameter estimation for linear systems

Atte Aalto*

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review


We propose an iterative method for joint state and parameter estimation using measurements on a time interval [0, T] for systems that are backward output stabilizable. Since this time interval is fixed, errors in initial state may have a big impact on the parameter estimate. We propose to use the back and forth nudging (BFN) method for estimating the system's initial state and a Gauss-Newton step between BFN iterations for estimating the system parameters. Taking advantage of results on the optimality of the BFN method, we show that for systems with skew-Adjoint generators, the initial state and parameter estimate minimizing an output error cost functional is an attractive fixed point for the proposed method. We treat both linear source estimation and bilinear parameter estimation problems.

Original languageEnglish
Pages (from-to)265-288
Number of pages24
JournalESAIM - Control, Optimisation and Calculus of Variations
Issue number1
Publication statusPublished - 1 Jan 2018
Externally publishedYes


  • Back and forth nudging
  • Output error minimization
  • Parameter estimation
  • System identification


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