Output error minimizing back and forth nudging method for initial state recovery

Atte Aalto

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4 Citations (Scopus)


We show that for linear dynamical systems with skew-adjoint generators, the initial state estimate given by the back and forth nudging method with colocated feedback, converges to the minimizer of the discrepancy between the measured and simulated outputs — given that the observer gains are chosen suitably and the system is exactly observable. If the system's generator A is essentially skew-adjoint and dissipative (with not too much dissipation), the colocated feedback has to be corrected by the operator eAteAt in order to obtain such convergence. In some special cases, a feasible approximation for this operator can be found analytically. The case with wave equation with constant dissipation will be presented.

Original languageEnglish
Pages (from-to)111-117
Number of pages7
JournalSystems and Control Letters
Publication statusPublished - 1 Aug 2016
Externally publishedYes


  • Back and forth nudging
  • Observers
  • Output error minimization
  • State estimation
  • Variational data assimilation


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