Markov chain approximations to filtering equations for reflecting diffusion processes
Herein, we consider direct Markov chain approximations to the Duncan-Mortensen-Zakai equations for nonlinear filtering problems on regular, bounded domains. For clarity of presentation, we restrict our attention to reflecting diffusion signals with symmetrizable generators. Our Markov chains are constructed by employing a wide band observation noise approximation, dividing the signal state space into cells, and utilizing an empirical measure process estimation. The upshot of our approximation is an efficient, effective algorithm for implementing such filtering problems. We prove that our approximations converge to the desired conditional distribution of the signal given the observation. Moreover, we use simulations to compare computational efficiency of this new method to the previously developed branching particle filter and interacting particle filter methods. This Markov chain method is demonstrated to outperform the two-particle filter methods on our simulated test problem, which is motivated by the fish farming industry.
Year of publication: |
2004
|
---|---|
Authors: | Kouritzin, Michael A. ; Long, Hongwei ; Sun, Wei |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 110.2004, 2, p. 275-294
|
Publisher: |
Elsevier |
Keywords: | Nonlinear filtering Reflecting diffusion Duncan-Mortensen-Zakai equation Markov chain approximation Law of large numbers Particle filters |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
CONVERGENCE OF MARKOV CHAIN APPROXIMATIONS TO STOCHASTIC REACTION DIFFUSION EQUATIONS
Kouritzin, Michael A., (2001)
-
On extending classical filtering equations
Kouritzin, Michael A., (2008)
-
Least squares estimators for discretely observed stochastic processes driven by small Lévy noises
Long, Hongwei, (2013)
- More ...