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A Uniform Convergence Theorem for the Numerical Solving of the Nonlinear Filtering Problem (1998)
| Content Provider | CiteSeerX |
|---|---|
| Author | Moral, P. Del |
| 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 non linear 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 non linear filtering equation. 1 Introduction The basic model for the general Non Linear Filtering problem consists of a time inhomogeneous Markov process X and a non linear observation Y with observation noise V . Namely, let (X; Y ) be the Markov process taking value... |
| File Format | |
| Volume Number | 35 |
| Journal | Journal of Applied Probability |
| Language | English |
| Publisher Date | 1998-01-01 |
| Access Restriction | Open |
| Subject Keyword | Uniform Convergence Theorem Numerical Solving Nonlinear Filtering Problem Filtering Problem Time Inhomogeneous Markov Process Recursive Solution Main Result Non Linear Observation Non Linear Filtering Problem Markov Process Noisy Partial Information Simple Ergodic Condition Discrete Time Optimal Filter Signal Semigroup Basic Model Observation Noise Monte Carlo Particle System Approach Notable Exception Linear-gaussian Situation General Optimal Filter First Uniform Convergence Result General Non Linear Filtering Problem Stochastic Process Monte Carlo Particle Filter Particle Approximation |
| Content Type | Text |
| Resource Type | Article |
