A differential geometric approach to nonlinear filtering: the projection filter

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 propo...

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Bibliographic Details
Published in:IEEE transactions on automatic control 1998-02, Vol.43 (2), p.247-252
Main Authors: Brigo, D., Hanzon, B., LeGland, F.
Format: Article
Language:English
Subjects:
Applied sciences
Density measurement
Detection, estimation, filtering, equalization, prediction
Differential equations
Exact sciences and technology
Filtering
Geometry
Information, signal and communications theory
Mathematics
Nonlinear equations
Nonlinear filters
Partial differential equations
Probability
Signal and communications theory
Signal, noise
State estimation
Statistics
Stochastic processes
Telecommunications and information theory
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Summary: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 one 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.
ISSN:0018-9286
1558-2523
DOI:10.1109/9.661075