Optimal quantization methods for nonlinear filtering with discrete-time observations

Nonlinear Filtering with Perfect Discrete Time Observations

We consider the problem of estimating the state of a diffusion process, based on discrete time observations in singular noise. We reduce the problem to a static problem, and we show that the solution is provided by the area or co–area formula of ge~ metric measure theory, provided the observed value is a regular value of the observation function. In order to address the case of singular values,...

Sequential Monte Carlo Methods for Nonlinear Discrete-Time Filtering

Discrete-time Mixed H2/H∞ Nonlinear Filtering

In this paper, we consider the discrete-time mixed H2/H∞ filtering problem for affine nonlinear systems. Sufficient conditions for the solvability of this problem with a finite-dimensional filter are given in terms of a pair of coupled discrete-time Hamilton-Jacobi-Isaac’s equations (DHJIE) with some side conditions. Both the finite-horizon and infinitehorizon problems are discussed for the cas...

Optimal Filtering with Multirate Observations

This paper considers the problem of optimal filtering for several channels of observations occurring at different sampling rates. The problem is formulated in general terms with arbitrary sampling rates for the observations. The set of observation sequences (channels) are jointly cyclostationary and the resulting optimal filters are linear and periodically timevarying (LPTV). A formula for the ...

Online quantization in nonlinear filtering

Sequential Baysian filtering arises in many practical problems. The complexity of this problem depends very much on the underlying mathematical model. When a linear Gaussian model is assumed, the well known Kalman filter provides the desired optimal solution. However, in many situations these assumptions do not hold, even approximately. We consider here a somewhat simplified version of the gene...