• Bernoulli
  • Volume 11, Number 5 (2005), 893-932.

Optimal quantization methods for nonlinear filtering with discrete-time observations

Gilles Pagès and Huyên Pham

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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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Bernoulli, Volume 11, Number 5 (2005), 893-932.

First available in Project Euclid: 23 October 2005

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Euler scheme Markov chain nonlinear filtering numerical approximation stationary signal stochastic gradient descent vector quantization


Pagès, Gilles; Pham, Huyên. Optimal quantization methods for nonlinear filtering with discrete-time observations. Bernoulli 11 (2005), no. 5, 893--932. doi:10.3150/bj/1130077599.

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