Data assimilation with the weighted ensemble Kalman filter

Abstract

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.

Bayesian parameter estimation and model selection for strongly nonlinear dynamical systems

“…The parameter estimation of each proposed model is handled by an efficient M-H MCMC method (i.e., [23][24][25]) that involves the computation of likelihood function using EnKF and PF-EnKF. For the likelihood computation, the state estimation is performed using the ensemble Kalman filter (EnKF) and a particle filter [26,27] with the EnKF estimates providing proposal distributions [17][18][19][20]. For model selection, the marginal likelihood (evidence) [3,13,28] is estimated Fig.…”

“…In PF, the probability density function is approximated by a set of weighted Monte Carlo samples named particles as (e.g., [10,[17][18][19][20]26,27])…”

“…In particular, we extend the Bayesian framework [9,10,12,13,15] to compute the likelihood function using an efficient particle filter (PF-EnKF) that exploits the estimates of the ensemble Kalman filter (EnKF) [16] to construct the proposal distribution [17][18][19][20]. The effectiveness of the proposed Bayesian algorithm is demonstrated for the model selection problem of a strongly nonlinear dynamical system having multiple fixed points.…”

Comparison and combination of EAKF and SIR-PF in the Bayesian filter framework

“…Recent advances in geophysical data assimilation with the particle filter framework can also be found in (van Leeuwen, 2009;Bocquet et al, 2010). Many recent studies involve the development of an observation-related proposal density for the assimilation of nonGaussian systems (Chorin et al, 2010;Papadakis et al, 2010;van Leeuwen, 2010van Leeuwen, , 2011Ambadan and Tang, 2011;Morzfeld and Chorin, 2012), some of which are very efficient in the observation system simulating experiments. However, the computational cost of these methods seems still very expensive, and the PDF of predictive errors should be approximated to update the weights, which is difficult in practical applications.…”

A method for tracking time-evolving sound speed profiles using Kalman filters

“…6 Briefly, the particles are first moved via two successive steps (the predictive and the corrective steps) following the procedure of the ensemble Kalman filter. Then a weight for each corrected particle is computed, and the state estimation is obtained by a summation of the weighted particles.…”