Data Assimilation by Conditioning of Driving Noise on Future Observations

Conventional recursive filtering approaches, designed for quantifying the state of an evolving stochastic dynamical system with intermittent observations, use a sequence of i) an uncertainty propagation step followed by ii) a step where the associated data is assimilated using Bayes' rule. Alte...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2014-08, Vol.62 (15), p.3887-3896
Main Authors: Wonjung Lee, Farmer, Chris
Format: Article
Language:English
Subjects:
Applied sciences
Bayesian statistics
Conditioning
cubature measure
Data assimilation
Detection, estimation, filtering, equalization, prediction
Driving conditions
Exact sciences and technology
Filtering
Filtration
Gaussian approximation filter
Information, signal and communications theory
Kalman filters
Linear approximation
Noise
Probability distribution
Signal and communications theory
Signal, noise
Smoothing methods
State estimation
Telecommunications and information theory
Uncertainty
Vectors
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Summary:Conventional recursive filtering approaches, designed for quantifying the state of an evolving stochastic dynamical system with intermittent observations, use a sequence of i) an uncertainty propagation step followed by ii) a step where the associated data is assimilated using Bayes' rule. Alternatively, the order of the steps can be switched to i) one step ahead data assimilation followed by ii) uncertainty propagation. In this paper, we apply this smoothing-based sequential filter to systems driven by random noise, however with the conditioning on future observation not only to the system variable but to the driving noise. Our research reveals that, for the nonlinear filtering problem, the conditioned driving noise is biased by a nonzero mean and in turn pushes forward the filtering solution in time closer to the true state when it drives the system. As a result our proposed method can yield a more accurate approximate solution for the state estimation problem.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2014.2330807