A uniform convergence theorem for the numerical solving of the nonlinear filtering problem
- 1 December 1998
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 35 (4), 873-884
- https://doi.org/10.1239/jap/1032438382
Abstract
The filtering problem concerns the estimation of a stochastic process X from its noisy partial information Y. With the notable exception of the linear-Gaussian situation, general optimal filters have no finitely recursive solution. The aim of this work is the design of a Monte Carlo particle system approach to solve discrete time and nonlinear filtering problems. The main result is a uniform convergence theorem. We introduce a concept of regularity and we give a simple ergodic condition on the signal semigroup for the Monte Carlo particle filter to converge in law and uniformly with respect to time to the optimal filter, yielding what seems to be the first uniform convergence result for a particle approximation of the nonlinear filtering equation.Keywords
This publication has 8 references indexed in Scilit:
- Nonlinear Filtering Using Random ParticlesTheory of Probability and Its Applications, 1996
- Asymptotic Stability of the Optimal Filter with Respect to Its Initial ConditionSIAM Journal on Control and Optimization, 1996
- Novel approach to nonlinear/non-Gaussian Bayesian state estimationIEE Proceedings F Radar and Signal Processing, 1993
- Exact finite-dimensional filters for certain diffusions with nonlinear driftStochastics, 1981
- Asymptotic behavior of the nonlinear filtering errors of Markov processesJournal of Multivariate Analysis, 1971
- Prescribing a System of Random Variables by Conditional DistributionsTheory of Probability and Its Applications, 1970
- Addendum: On Stochastic Equations in the Theory of Conditional Markov ProcessesTheory of Probability and Its Applications, 1967
- Conditional Markov ProcessesTheory of Probability and Its Applications, 1960