Non-Gaussian Filters for Nonlinear Continuous-Discrete Models

Development of Nonlinear Lattice-Hammerstein Filters for Gaussian Signals

In this paper, the nonlinear lattice-Hammerstein filter and its properties are derived. It is shown that the error signals are orthogonal to the input signal and also backward errors of different stages are orthogonal to each other. Numerical results confirm all the theoretical properties of the lattice-Hammerstein structure.

Gaussian filters for nonlinear filtering problems

In this paper we develop and analyze real-time and accurate filters for nonlinear filtering problems based on the Gaussian distributions. We present the systematic formulation of Gaussian filters and develop efficient and accurate numerical integration of the optimal filter. We also discuss the mixed Gaussian filters in which the conditional probability density is approximated by the sum of Gau...

Fast Nonlinear Filter for Continuous-Discrete Time Multiple Models∗

A fast algorithm is proposed for computing on line the optimal nonlinear filter in the continuous-discrete time, multiple model setting. Using the finite element approximation on a spatial grid with N points and performing part of the computations off line, the on-line complexity of the algorithm is shown to be O(N) for all dimensions of the state process. The error of the approximation is also...

Fast Continuous-Discrete DAF-Filters

This paper introduces a new method for nonlinear continuous-discrete filtering. It is shown that the Fokker-Planck -Equation can be solved numerically by using distributed approximating functionals (DAFs). The approximation is very accurate and resolves the time interval between observations in one calculation step. Additionally, the operator matrix has to be evaluated only once and not necessa...

Non-Gaussian and Nonparametric Models for Continuous Spatial Data