Efficient nonlinear data assimilation using synchronization in a particle filter

Abstract

Current data assimilation methods still face problems in strongly nonlinear cases. A promising solution is a particle filter, which provides a representation of the state probability density function (pdf) by a discrete set of particles. To allow a particle filter to work in high-dimensional systems, the proposal density freedom is explored.We used a proposal density from synchronization theory, in which one tries to synchronize the model with the true evolution of a system using one-way coupling, via the observations. This is done by adding an extra term to the model equations which will control the growth of instabilities transversal to the synchronization manifold. In this paper, an efficient ensemble-based synchronization scheme is used as a proposal density in the implicit equal-weights particle filter, a particle filter that avoids filter degeneracy by construction. Tests using the Lorenz96 model for a 1,000-dimensional system show successful results, where particles efficiently follow the truth, both for observed and unobserved variables. These first tests show that the new method is comparable to, and slightly outperforms, a well-tuned Local Ensemble Transform Kalman Filter. This methodology is a promising solution for high-dimensional nonlinear problems in the geosciences, such as numerical weather prediction. K E Y W O R D Sdata assimilation, ensemble, synchronization, nonlinear, particle filter 1 This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. APPENDIXThis appendix contains the pseudocode algorithms to run the IEWPF using the ensemble-based synchronization as a proposal, as described in Section 2.3.

A hybrid particle-ensemble Kalman filter for problems with medium nonlinearity

“…Unfortunately, however, SIR suffers a severe curse of dimensionality that has prevented its practical application to high dimensional data assimilation problems [ 6 – 8 ]. A variety of methods have been proposed to improve the performance of particle filters in high-dimensional problems, including implicit particle filters [ 9 – 11 ], the equivalent-weights particle filter [ 12 – 16 ], likelihood approximations [ 17 ], local particle filters [ 18 – 20 ] and particle filters based on kernel mappings [ 21 ] and synchronization methods [ 22 ]. Particle filters have also been hybridized with EnKFs [ 23 – 26 ] and with variational methods [ 27 ].…”

A comparison of nonlinear extensions to the ensemble Kalman filter: Gaussian Anamorphosis and Two-Step Ensemble Filters

“…The classical bootstrap or 'SIR' particle filter of [39] generates an empirical measure that provably converges weakly to the correct posterior distribution in the limit of an infinite ensemble size [27,53], but the convergence is prohibitively slow in high-dimensional systems [15,86,87]. In view of this limitation there is a large body of research aiming to design alternatives to the classical particle filter for applications with extremely high dimension, including [24,23,25,90,3,4,69,78,73,79,80,74,76,71]. Particle filters have also been hybridized with EnKFs [34,26,41] and variational methods [66].…”

A hybrid particle-ensemble Kalman filter for problems with medium nonlinearity

“…Unfortunately, however, SIR suffers a severe curse of dimensionality that has prevented its practical application to high dimensional data assimilation problems [7,47,48]. A variety of methods have been proposed to improve the performance of particle filters in high-dimensional problems, including implicit particle filters [11,12,10], the equivalent-weights particle filter [50,2,3], likelihood approximations [44], local particle filters [41,37,39] and particle filters based on kernel mappings [40] and synchronization methods [38]. Particle filters have also been hybridized with EnKFs [13,19] and with variational methods [35].…”