Quantization Based Filtering Method using First Order Approximation and Comparison with the Particle Filtering Approach

The quantization based filtering method (see [1], [2]) is a grid based approximation method for solving 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.