Lower and upper bounds on the optimal filtering error of certain diffusion processes

  • Authors:

  • M. Zakai;J. Ziv

  • Affiliations:

  • -;-

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

The optimal nonlinear filtering of certain vector-valued diffusion processes embedded in white noise is considered. We derive upper and lower bounds on the minimal causal mean-square error. The derivation of the lower bound is based on information-theoretic considerations, namely the rate-distortion function (varepsilon-entropy). The upper bounds are based on linear-filtering arguments. It is demonstrated that for a wide class of high-precision systems, the upper and lower bounds are tight within a factor of 2 or better.