Approximate nonlinear filtering by projection on exponential manifolds of densities
type: Item
instance of: scholarly article
title: Approximate nonlinear filtering by projection on exponential manifolds of densities
zbMATH Open document ID: 0930.93074
DOI: 10.2307/3318714
author: Damiano Brigo
author: B. Hanzon
author: François Le Gland
published in: Bernoulli
publication date: 2000-01-31T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bj/1172617201
review text: The nonlinear Kushner-Stratonovich filtering equation for the state and observation equations \[ dX_{t}=f_{t}(X_{t}) dt+\sigma _{t}(X_{t}) dW_{t}, X_{0}, \] \[ dY_{t}=h_{t}(X_{t}) dt+dV_{t}, Y_{0}=0, \] is projected on the finite-dimensional manifold of the family of probability densities \(p(\cdot ,\theta), \theta \in \Theta \subseteq \mathbb{R}^{m}.\) It is shown that the parameters \(\theta _{t}\) of the projection filter density \(p(\cdot ,\theta _{t})\) satisfy a finite-dimensional SDE the explicit form of which is given in the paper. The most constructive results are obtained for exponential densities. The known concept of assumed density filter (ADF) is compared with the projection filter. Simulation results comparing the projection filter and the optimal filter for the cubic sensor problem are presented.
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 1334560
zbMATH Keywords: differential geometry and statistics
zbMATH Keywords: approximation of Kushner-Stratonovich filtering equation
zbMATH Keywords: projection filter
zbMATH Keywords: assumed density filter
reviewed by: Grigori N. Milstein
MaRDI profile type: Publication
OpenAlex ID: W2077991515
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description: scientific article; zbMATH DE number 1334560