Premium
A dynamic likelihood approach to filtering
Author(s) -
Restrepo J. M.
Publication year - 2017
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.3143
Subject(s) - kalman filter , data assimilation , gaussian , ensemble kalman filter , computer science , mathematics , likelihood function , filter (signal processing) , filtering problem , algorithm , particle filter , bayesian probability , mathematical optimization , extended kalman filter , estimation theory , artificial intelligence , physics , quantum mechanics , meteorology , computer vision
A Bayesian data assimilation scheme is formulated for advection‐dominated or hyperbolic evolutionary problems, and observations. It uses the physics to dynamically update the likelihood in order to extend the impact of the likelihood on the posterior, a strategy that would be particularly useful when the observation network is sparse in space and time and the associated measurement uncertainties are low. The filter is applied to a problem with linear dynamics and Gaussian statistics, and compared to the exact estimate, a model outcome, and the Kalman filter estimate. By comparing to the exact estimate the dynamic likelihood filter is shown to be superior to model outcomes and to the Kalman estimate, when the observation system is sparse. The added computational expense of the method is linear in the number of observations and thus computationally efficient, suggesting that the method is practical even if the space dimensions of the physical problem are large.