Filtrage non lineaire avec observation sur une variete

Poniter, Monique; Szpirglas, J.

doi:10.1080/17442508508833352

Cited by 14 publications

(14 citation statements)

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“…Stochastic filtering problems where the observation has its values in a differentiable manifold constitute an important extension of the classical additive white noise setting. They were studied in the pioneering work of Duncan [1], which was expanded by Caines [2], and also by Pontier and Szpirglas [3,4]. While these two contributions consider different observation models, their overall methodologies are comparable.…”

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confidence: 99%

“…Precisely, they combine the machinery of stochastic differential geometry with standard theoretical tools, based on innovation or on change of probability. The current paper studies the same model as in [3,4]. It proceeds along similar lines, but builds on more recent development in the geometry of diffusions.…”

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confidence: 99%

“…In general, this requires a choice of affine connection. This has been taken to be a Levi-Civita connection in [1] and [3,4]. In [2], it was an unspecified metric connection.…”

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confidence: 99%

“…In [2], it was an unspecified metric connection. The idea here is that a significant improvement can be made, in studying the filtering problem of [3,4], when a Le Jan-Watanabe connection is used which is constructed in a specific way from the observation model. This is obtained by adapting a result in [5].…”

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confidence: 99%

“…The main difference among [1,2] and [3,4] is the following. In the former, the observation model is given by a horizontal stochastic differential equation in the frame bundle of the underlying manifold.…”

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On Filtering with Observation in a Manifold: Reduction to a Classical Filtering Problem

Said¹,

Manton²

2013

SIAM J. Control Optim.

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The current paper deals with filtering problems where the observation process, conditioned on the unknown signal, is an elliptic diffusion in a differentiable manifold. Precisely, the observation model is given by a stochastic differential equation in the underlying manifold. The main new idea is to use a Le Jan-Watanabe connection, instead of a usual Levi-Civita connection, in performing the operation of antidevelopment (both connections can be constructed from a stochastic differential equation as in the observation model). The following results are obtained. First, it is shown that antidevelopment reduces the original filtering problem to a classical one, i.e. an additive white noise model. Second, a new form of the Zakai and filtering equations is derived which has a structure very similar to that of classical equations. Currently, there are few well understood general numerical solution methods for filtering problems with observation in a manifold. Reduction to classical filtering problems seems desirable as it allows proven existing numerical methods for classical problems to be applied immediately. In view of practical implementation of this approach, the paper also gives an explicit pathwise construction of the antidevelopment.

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confidence: 99%

“…In general, this requires a choice of affine connection. This has been taken to be a Levi-Civita connection in [1] and [3,4]. In [2], it was an unspecified metric connection.…”

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confidence: 99%

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confidence: 99%

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confidence: 99%

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