Open Access
October 2005 Optimal quantization methods for nonlinear filtering with discrete-time observations
Gilles Pagès, Huyên Pham
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Bernoulli 11(5): 893-932 (October 2005). DOI: 10.3150/bj/1130077599


We develop an optimal quantization approach for numerically solving nonlinear filtering problems associated with discrete-time or continuous-time state processes and discrete-time observations. Two quantization methods are discussed: a marginal quantization and a Markovian quantization of the signal process. The approximate filters are explicitly solved by a finite-dimensional forward procedure. A posteriori error bounds are stated, and we show that the approximate error terms are minimal at some specific grids that may be computed off-line by a stochastic gradient method based on Monte Carlo simulations. Some numerical experiments are carried out: the convergence of the approximate filter as the accuracy of the quantization increases and its stability when the latent process is mixing are emphasized.


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Gilles Pagès. Huyên Pham. "Optimal quantization methods for nonlinear filtering with discrete-time observations." Bernoulli 11 (5) 893 - 932, October 2005.


Published: October 2005
First available in Project Euclid: 23 October 2005

zbMATH: 1084.62095
MathSciNet: MR2172846
Digital Object Identifier: 10.3150/bj/1130077599

Keywords: Euler scheme , Markov chain , Nonlinear filtering , numerical approximation , stationary signal , Stochastic gradient descent , Vector quantization

Rights: Copyright © 2005 Bernoulli Society for Mathematical Statistics and Probability

Vol.11 • No. 5 • October 2005
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