Observations Preprocessing and Quantization for Nonlinear Filters
SIAM Journal on Control and Optimization
Foundations of Quantization for Probability Distributions
Foundations of Quantization for Probability Distributions
A tutorial on particle filters for online nonlinear/non-GaussianBayesian tracking
IEEE Transactions on Signal Processing
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The quantization based filtering method (see [G. Pagès and H. Pham, Bernoulli, 11 (2005), pp. 893-932; G. Pagès, H. Pham, and J. Printems, Optimal quantization methods and applications to numerical problems in finance, in Handbook of Computational and Numerical Methods in Finance, S. T. Rachev, ed., Birkhäuser, Boston, 2004, pp. 253-297]) is a grid based approximation method to solve nonlinear filtering problems with discrete time observations. It relies on off-line preprocessing of some signal grids in order to construct fast recursive schemes for filter approximation. We give here an improvement of this method by taking advantage of the stationary quantizer property. The key ingredient is the use of vanishing correction terms to describe schemes based on piecewise linear approximations. Convergence results are given and numerical results are presented for the particular cases of linear Gaussian model and stochastic volatility models.