A Differential Geometric Approach to Nonlinear Filtering: The Projection Filter

D. Brigo; B. Hanzon; F. LeGland

doi:10.1109/9.661075

A Differential Geometric Approach to Nonlinear Filtering: The Projection Filter

D. Brigo, B. Hanzon, F. LeGland

Research output: Contribution to Journal › Article › Academic

Abstract

This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is proposed which allows us to simplify the projection filter equation and to define an a posteriori measure of the local error of the projection filter approximation. Finally, simulation results are discussed for the cubic sensor problem.

Original language	English
Pages (from-to)	247-252
Number of pages	5
Journal	IEEE Transactions on Automatic Control
Volume	43
Issue number	2
DOIs	https://doi.org/10.1109/9.661075
Publication status	Published - 1998

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@article{e4ea901ee2424068ae8812eb8861f5dc,

title = "A Differential Geometric Approach to Nonlinear Filtering: The Projection Filter",

abstract = "This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is proposed which allows us to simplify the projection filter equation and to define an a posteriori measure of the local error of the projection filter approximation. Finally, simulation results are discussed for the cubic sensor problem.",

author = "D. Brigo and B. Hanzon and F. LeGland",

year = "1998",

doi = "10.1109/9.661075",

language = "English",

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pages = "247--252",

journal = "IEEE Transactions on Automatic Control",

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publisher = "Institute of Electrical and Electronics Engineers Inc.",

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T1 - A Differential Geometric Approach to Nonlinear Filtering: The Projection Filter

AU - Brigo, D.

AU - Hanzon, B.

AU - LeGland, F.

PY - 1998

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N2 - This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is proposed which allows us to simplify the projection filter equation and to define an a posteriori measure of the local error of the projection filter approximation. Finally, simulation results are discussed for the cubic sensor problem.

AB - This paper presents a new and systematic method of approximating exact nonlinear filters with finite dimensional filters, using the differential geometric approach to statistics. The projection filter is defined rigorously in the case of exponential families. A convenient exponential family is proposed which allows us to simplify the projection filter equation and to define an a posteriori measure of the local error of the projection filter approximation. Finally, simulation results are discussed for the cubic sensor problem.

U2 - 10.1109/9.661075

DO - 10.1109/9.661075

M3 - Article

SN - 0018-9286

VL - 43

SP - 247

EP - 252

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 2

ER -

A Differential Geometric Approach to Nonlinear Filtering: The Projection Filter

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