When do nonlinear filters achieve maximal accuracy?

Details When do nonlinear filters achieve maximal accuracy? When do nonlinear filters achieve maximal accuracy?

2009-01-08

arxiv.org/abs/0901.1084v2

SIAM J. Control Optim. 48, 3151-3168 (2009)

Mathematics

Probability

18 pages

Scientific paper

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 (1972).

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