Lower and upper bounds on the optimal filtering error of certain diffusion processes
M Zakai, J Ziv - IEEE Transactions on Information Theory, 1972 - ieeexplore.ieee.org
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.
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.
Lower and Upper Bounds on the Optimal Filtering Error of Certain Diffusion Processes
HL Van Trees, KL Bell - 2007 - ieeexplore.ieee.org
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-dlstortlon function (?>-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.
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-dlstortlon function (?>-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.
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