Quantization based filtering method using first order approximation

The quantization based filtering method 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 comparison with sequential Monte Carlo methods is made. Numerical results are presented for both particular cases of linear Gaussian models and stochastic volatility models