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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Discretization error in dynamical inverse problems: one-dimensional model case

J. M. J. Huttunen
  • Department of Physics, University of Kuopio, P.O. Box 1627, FI-70211 Kuopio, Finland. Email:
/ H. K. Pikkarainen
  • Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, A-4040 Linz, Austria. Email:
Published Online: 2007-06-27 | DOI: https://doi.org/10.1515/jiip.2007.020

We examine nonstationary inverse problems in which the time evolution of the unknown quantity is modelled by a stochastic partial differential equation. We consider the problem as a state estimation problem. The time discrete state evolution equation is exact since the solution is given by an analytic semigroup. For the practical reasons the space discretization of the time discrete state estimation system must be performed. However, space discretization causes an error and inverse problems are known to be very intolerant to both measurement errors and errors in models. In this paper we analyse the discretization error so that the statistics of the discretization error can be taken into account in the estimation. We are interested in the related filtering problem. A suitable filtering method is presented. We also verify the method using numerical simulation.

Key Words: Nonstationary inverse problems,; state-space models,; discretization error,; Kalman filtering.

Published Online: 2007-06-27

Published in Print: 2007-07-20

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 15, Issue 4, Pages 365–386, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2007.020, June 2007

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