Bernoulli

  • 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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 23 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.bj/1130077599

Digital Object Identifier
doi:10.3150/bj/1130077599

Mathematical Reviews number (MathSciNet)
MR2172846

Zentralblatt MATH identifier
1084.62095

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

Citation

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. https://projecteuclid.org/euclid.bj/1130077599


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