Nonlinear filtering : Interacting particle resolution

@article{Moral1997NonlinearF,
  title={Nonlinear filtering : Interacting particle resolution},
  author={Pierre Del Moral},
  journal={Comptes Rendus De L Academie Des Sciences Serie I-mathematique},
  year={1997},
  volume={325},
  pages={653-658}
}
  • P. Moral
  • Published 1 September 1997
  • Mathematics
  • Comptes Rendus De L Academie Des Sciences Serie I-mathematique

Measure-valued processes and interacting particle systems. Application to nonlinear filtering problems

In the paper we study interacting particle approximations of discrete time and measure-valued dynamical systems. These systems have arisen in such diverse scientic disciplines as physics and signal

Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering

This paper focuses on interacting particle systems methods for solving numerically a class of Feynman-Kac formulae arising in the study of certain parabolic differential equations, physics, biology,

Convergence of Empirical Processes for Interacting Particle Systems with Applications to Nonlinear Filtering

In this paper, we investigate the convergence of empirical processes for a class of interacting particle numerical schemes arising in biology, genetic algorithms and advanced signal processing. The

Wiener Chaos and Nonlinear Filtering

The paper discusses two algorithms for solving the Zakai equation in the time-homogeneous diffusion filtering model with possible correlation between the state process and the observation noise with main existing results about these Wiener chaos algorithms summarized.

Generalised particle filters

This thesis contains a rigorous analysis of the approximation of the solution of the filtering problem using Gaussian mixtures, deduce the L-convergence rate and obtain the central limit theorem for the approximating system.

PARTICLE APPROXIMATIONS TO THE FILTERING PROBLEM IN CONTINUOUS TIME

In this chapter, we survey some recent results on the particle system approximations to stochastic filtering problems in continuous time. First, a weighted particle system representation of the

Stability of Nonlinear Filters and Branching Particle Approximations to The F iltering Problems

Various particle filters have been proposed and their convergence to the optimal filter are obtained for finite time intervals. However, uniform convergence results have been established only for

A PARTICLE FILTER FOR NONLINEAR FILTERING WITH L\'EVY JUMPS

Nonlinear filtering where the signal and observation processes are corrupted by a Gaussian and a compound Poisson process is interested, and a so-called Luenberger observer is constructed to construct an estimator of the state process and an estimators of the density process.

A branching particle system approximation for nonlinear stochastic filtering

The optimal filter π = {πt, t ∈ [0, T]} of a stochastic signal is approximated by a sequence {πtn} of measure-valued processes defined by branching particle systems in a random environment (given by
...

References

SHOWING 1-10 OF 18 REFERENCES

Nonlinear Filtering Using Random Particles

This paper is concerned with extending the particle solution of nonlinear discrete-time filtering problems developed in [Ph.D. thesis, Universite Paul Sabatier, Tolouse, France, 1994], [Contrat

The Nonlinear Filtering Problem

In Chapter 4, we were concerned with the problem of approximations for the singularly perturbed system (4.1.1), (4.1.2), and with the associated problem of control approximations. In this chapter, we

Convergence of a Branching Particle Method to the Solution of the Zakai Equation

A sequence of branching particle systems Un convergent in distribution to the solution of the Zakai equation is constructed, which can be used to solve numerically the filtering problem.

Asymptotic behavior of the nonlinear filtering errors of Markov processes

Novel approach to nonlinear/non-Gaussian Bayesian state estimation

An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters, represented as a set of random samples, which are updated and propagated by the algorithm.

Nonlinear filtering and measure-valued processes

Summary. We construct a sequence of branching particle systems with time and space dependent branching mechanisms whose expectation converges to the solution of the Zakai equation. This gives an

Optimal nonlinear filtering in GPS/INS integration

The application of optimal nonlinear/non-Gaussian filtering to the problem of INS/GPS integration in critical situations is described, and particle filtering theory is introduced and GPS/INS integration simulation results are discussed.

On invariant measures of filtering processes

In the paper invariant measures of both discrete and continuous time filtering processes are studied. A generalization of the famous Kunita's result [6] to the case of locally compact signal state

Des resultats de non existence de filtre de dimension finie

We show that a necessary condition for the existence of a universal finite dimensionally computable filter is that the Lie algebra $ naturally associated with the Zakai' equation, be finite

Filtrage non-linéaire: résolution particulaire à la Monte Carlo

Les problemes de filtrage optimal consistent a estimer un processus a partir de son observation partielle bruitee. A l'exception notable de la situation lineaire-gaussienne, les filtres optimaux ne