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Robust Limits of Risk Sensitive Nonlinear Filters

  • Wendell H. Fleming
  • William M. McEneaney

Abstract.

Deterministic filter models are considered, and a criterion for a deterministic filter to be robust is introduced. Among the candidates for robust deterministic filters are so-called minimax estimators. In the second part of the paper, a risk sensitive stochastic approach to nonlinear filtering is considered, in which the traditional expected mean squared error criterion is replaced by an expected exponential-of-mean squared error. Minimax filters are obtained as totally risk averse limits of risk sensitive filters.

Key words. Nonlinear filtering, Risk sensitive, Robust filtering, H∞ Filtering, Viscosity solutions, Hamilton–Jacobi–Bellman equations. 

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Copyright information

© Springer-Verlag London Limited 2001

Authors and Affiliations

  • Wendell H. Fleming
    • 1
  • William M. McEneaney
    • 2
  1. 1.Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, U.S.A. whf@cfm.brown.edu. Partially supported by NSF Grant DMS-9531276 through Brown University and by ONR Grant N0014-96-1-0267 through North Carolina State University.US
  2. 2.Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205, U.S.A. wmm@math.ncsu.edu. http://www4.ncsu.edu/~wmm/. Research partially supported by AFOSR Grant F08671-98-0-1098 and by ONR Grant N0014-96-1-0267.US

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