When do nonlinear filters achieve maximal accuracy?

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Abstract

The nonlinear filter for an ergodic signal observed in white noise is said to achieve maximal accuracy if the stationary filtering error vanishes as the signal to noise ratio diverges. We give a general characterization of the maximal accuracy property in terms of various systems theoretic notions. When the signal state space is a finite set explicit necessary and sufficient conditions are obtained, while the linear Gaussian case reduces to a classic result of Kwakernaak and Sivan [IEEE Trans. Automatic Control, AC-17 (1972), pp. 79-86].

Original languageEnglish (US)
Pages (from-to)3151-3168
Number of pages18
JournalSIAM Journal on Control and Optimization
Volume48
Issue number5
DOIs
StatePublished - Jan 1 2009

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

Keywords

  • Maximal accuracy
  • Nonlinear filtering
  • Small noise limit
  • Systems theory

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