In this paper, two data assimilation methods based on sequential Monte Carlo sampling are studied and compared: the ensemble Kalman filter and the particle filter. Each of these techniques has its own advantages and drawbacks. In this work, we try to get the best of each method by combining them. The proposed algorithm, called the weighted ensemble Kalman filter, consists to rely on the Ensemble Kalman Filter updates of samples in order to define a proposal distribution for the particle filter that depends on the history of measurement. The corresponding particle filter reveals to be efficient with a small number of samples and does not rely anymore on the Gaussian approximations of the ensemble Kalman filter. The efficiency of the new algorithm is demonstrated both in terms of accuracy and computational load. This latter aspect is of the utmost importance in meteorology or in oceanography since in these domains, data assimilation processes involve a huge number of state variables driven by highly non‐linear dynamical models. Numerical experiments have been performed on different dynamical scenarios. The performances of the proposed technique have been compared to the ensemble Kalman filter procedure, which has demonstrated to provide meaningful results in geophysical sciences.
We present a hierarchical Bayesian modelling (HBM) framework for estimating riverine fish population size from successive removal data via electrofishing. It is applied to the estimation of the population of Atlantic salmon (Salmo salar) juveniles in the Oir River (France). The data set consists of 10 sampling sites sampled by one or two removals over a period of 20 years (1986–2005). We develop and contrast four models to assess the effect of temporal variations and habitat type on the density of fish and the probability of capture. The Bayes factor and the deviance information criterion are used to compare these models. The most credible and parsimonious model is the one that accounts for the effects of the years and the habitat type on the density of fish. It is used to extrapolate the population size in the entire river reach. This paper illustrates that HBM successfully accommodates large but sparse data sets containing poorly informative data for some units. Its conditional structure enables it to borrow strength from data-rich to data-poor units, thus improving the estimations. Predictions of the population size of the entire river reach can be derived, while accounting for all sources of uncertainty.Nous proposons un cadre de modélisation bayésien hiérarchique (HBM) pour estimer l’abondance d’une population de juvéniles de saumon atlantique (Salmo salar) dans la rivière Oir (France) par la méthode des retraits successifs par pêche électrique. Le jeu de données est composé de 10 sites d’échantillonnage, chacun ayant été échantillonné par un ou deux passages sur une période de 20 ans (1986–2005). Quatre modèles sont développés pour introduire les variations inter-annuelles et les effets du type d’habitat sur la densité et sur la probabilité de capture. Ces modèles sont comparés à l’aide du facteur de Bayes et d’un critère d’information basé sur la déviance. Le modèle retenu est celui qui prend en compte l’effet de l’année et du type d’habitat sur la densité de juvéniles de saumons. Il est utilisé pour extrapoler la population de saumon à l’ensemble du cours d’eau. Cet article illustre que les HBM permettent de traiter des jeux de données de grande taille dont l’information portée par chaque unité échantillonnée est hétérogène. La structure conditionnelle permet d’améliorer les estimations car elle organise un transfert d’information entre les unités. Le modèle permet d’obtenir des prédictions de l’abondance sur l’ensemble du cours d’eau, tout en prenant en compte les différentes sources d’incertitude
In this paper we propose a new motion estimator for image sequences depicting fluid flows. The proposed estimator is based on the Helmholtz decomposition of vector fields.
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