Name
Abstract | ||
|---|---|---|
We review the manifold projection method for stochastic nonlinear filtering in a more general setting than in our previous paper in Geometric Science of Information 2013. We still use a Hilbert space structure on a space of probability densities to project the infinite dimensional stochastic partial differential equation for the optimal filter onto a finite dimensional exponential or mixture family, respectively, with two different metrics, the Hellinger distance and the L-2 direct metric. This reduces the problem to finite dimensional stochastic differential equations. In this paper we summarize a previous equivalence result between Assumed Density Filters (ADF) and Hellinger/Exponential projection filters, and introduce a new equivalence between Galerkin method based filters and Direct metric/Mixture projection filters. This result allows us to give a rigorous geometric interpretation to ADF and Galerkin filters. We also discuss the different finite-dimensional filters obtained when projecting the stochastic partial differential equation for either the normalized (Kushner-Stratonovich) or a specific unnormalized (Zakai) density of the optimal filter. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/978-3-319-25040-3_76 | GEOMETRIC SCIENCE OF INFORMATION, GSI 2015 |
DocType | Volume | ISSN |
Conference | 9389 | 0302-9743 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| John Armstrong | 1 | 1 | 1.30 |
| Damiano Brigo | 2 | 17 | 8.42 |