scholarly journals Ensemble Variational Assimilation as a Probabilistic Estimator. Part II: The fully non-linear case

2018 ◽  
Author(s):  
Mohamed Jardak ◽  
Olivier Talagrand
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
Objective Function ◽  
Ensemble Kalman Filter ◽  
The Other ◽  
Linear Case ◽  
Absolute Minimum ◽  
Strong Constraint ◽  
Variational Assimilation ◽  
Lorenz 96

Abstract. In Part II, the method of Ensemble Variational Assimilation (EnsVAR) is implemented in fully nonlinear conditions on the Lorenz-96 chaotic 40-parameter model. In the case of strong-constraint assimilation, it requires to be used in association with the method of Quasi-Static Variational Assimilation (QSVA). It then produces ensembles which possess as much reliability and resolution as in the linear case, and its performance is at least as good as that of Ensemble Kalman Filter and Particle Filter. On the other hand, ensembles consisting of solutions that correspond to the absolute minimum of the objective function (as identified from the minimizations without QSVA) are signif- icantly biased. In the case of weak-constraint assimilation, EnsVAR is fully successful without need to resort to QSVA.

scholarly journals Ensemble variational assimilation as a probabilistic estimator – Part 2: The fully non-linear case

2018 ◽  
Vol 25 (3) ◽  
pp. 589-604 ◽  
Author(s):  
Mohamed Jardak ◽  
Olivier Talagrand
Keyword(s):  
Kalman Filter ◽  
Objective Function ◽  
Ensemble Kalman Filter ◽  
The Other ◽  
Linear Case ◽  
Absolute Minimum ◽  
Strong Constraint ◽  
Variational Assimilation ◽  
Non Linear ◽  
Lorenz 96

Abstract. The method of ensemble variational assimilation (EnsVAR), also known as ensemble of data assimilations (EDA), is implemented in fully non-linear conditions on the Lorenz-96 chaotic 40-parameter model. In the case of strong-constraint assimilation, it requires association with the method of quasi-static variational assimilation (QSVA). It then produces ensembles which possess as much reliability and resolution as in the linear case, and its performance is at least as good as that of ensemble Kalman filter (EnKF) and particle filter (PF). On the other hand, ensembles consisting of solutions that correspond to the absolute minimum of the objective function (as identified from the minimizations without QSVA) are significantly biased. In the case of weak-constraint assimilation, EnsVAR is fully successful without need for QSVA.

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

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248266
Author(s):  
Ian Grooms ◽  
Gregor Robinson
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
Ensemble Kalman Filter ◽  
Orthogonal Transformation ◽  
Hybrid Filter ◽  
Hybrid Particle ◽  
Particle Ensemble ◽  
Non Gaussian ◽  
Two Stages ◽  
Lorenz 96

A hybrid particle ensemble Kalman filter is developed for problems with medium non-Gaussianity, i.e. problems where the prior is very non-Gaussian but the posterior is approximately Gaussian. Such situations arise, e.g., when nonlinear dynamics produce a non-Gaussian forecast but a tight Gaussian likelihood leads to a nearly-Gaussian posterior. The hybrid filter starts by factoring the likelihood. First the particle filter assimilates the observations with one factor of the likelihood to produce an intermediate prior that is close to Gaussian, and then the ensemble Kalman filter completes the assimilation with the remaining factor. How the likelihood gets split between the two stages is determined in such a way to ensure that the particle filter avoids collapse, and particle degeneracy is broken by a mean-preserving random orthogonal transformation. The hybrid is tested in a simple two-dimensional (2D) problem and a multiscale system of ODEs motivated by the Lorenz-‘96 model. In the 2D problem it outperforms both a pure particle filter and a pure ensemble Kalman filter, and in the multiscale Lorenz-‘96 model it is shown to outperform a pure ensemble Kalman filter, provided that the ensemble size is large enough.

scholarly journals Ensemble variational assimilation as a probabilistic estimator – Part 1: The linear and weak non-linear case

2018 ◽  
Vol 25 (3) ◽  
pp. 565-587 ◽  
Author(s):  
Mohamed Jardak ◽  
Olivier Talagrand
Keyword(s):  
Probability Distribution ◽  
Simple Procedure ◽  
Linear Case ◽  
Bayesian Probability ◽  
Variational Assimilation ◽  
Non Linear ◽  
Abstract Data ◽  
Gaussian Case ◽  
Low Dimensional ◽  
Lorenz 96

Abstract. Data assimilation is considered as a problem in Bayesian estimation, viz. determine the probability distribution for the state of the observed system, conditioned by the available data. In the linear and additive Gaussian case, a Monte Carlo sample of the Bayesian probability distribution (which is Gaussian and known explicitly) can be obtained by a simple procedure: perturb the data according to the probability distribution of their own errors, and perform an assimilation on the perturbed data. The performance of that approach, called here ensemble variational assimilation (EnsVAR), also known as ensemble of data assimilations (EDA), is studied in this two-part paper on the non-linear low-dimensional Lorenz-96 chaotic system, with the assimilation being performed by the standard variational procedure. In this first part, EnsVAR is implemented first, for reference, in a linear and Gaussian case, and then in a weakly non-linear case (assimilation over 5 days of the system). The performances of the algorithm, considered either as a probabilistic or a deterministic estimator, are very similar in the two cases. Additional comparison shows that the performance of EnsVAR is better, both in the assimilation and forecast phases, than that of standard algorithms for the ensemble Kalman filter (EnKF) and particle filter (PF), although at a higher cost. Globally similar results are obtained with the Kuramoto–Sivashinsky (K–S) equation.

Kalman/Particle Filter for Integrated Navigation System

2013 ◽  
Vol 756-759 ◽  
pp. 2142-2146 ◽  
Author(s):  
Zhun Jiao ◽  
Rong Zhang
Keyword(s):  
Kalman Filter ◽  
Particle Filter ◽  
Navigation System ◽  
The Other ◽  
New Method ◽  
Integrated Navigation ◽  
Computation Complexity ◽  
Integrated Navigation System ◽  
Simulation Results

Particle filter is introduced. Since the particle filter would bring hard computation, a new Kalman/Particle mixed filter used on SINS/GPS integrated navigation system was proposed. The new method divides the system into two sub-models, one is linear, the other one is nonlinear, and then implement Kalman filter and particle filter separately. The simulation results show that their performance is almost equal, but the computation complexity of the Kalman/particle filter is much lower than traditional particle filter.

scholarly journals A Bayesian approach to multivariate adaptive localization in ensemble-based data assimilation with time-dependent extensions

2019 ◽  
Vol 26 (2) ◽  
pp. 109-122 ◽  
Author(s):  
Andrey A. Popov ◽  
Adrian Sandu
Keyword(s):  
Kalman Filter ◽  
Bayesian Approach ◽  
Ensemble Kalman Filter ◽  
Time Dependent ◽  
Multivariate Approach ◽  
Filter Performance ◽  
Geophysical Model ◽  
Correlation Information ◽  
Lorenz 96 ◽  
Univariate Approach

Abstract. Ever since its inception, the ensemble Kalman filter (EnKF) has elicited many heuristic approaches that sought to improve it. One such method is covariance localization, which alleviates spurious correlations due to finite ensemble sizes by using relevant spatial correlation information. Adaptive localization techniques account for how correlations change in time and space, in order to obtain improved covariance estimates. This work develops a Bayesian approach to adaptive Schur-product localization for the deterministic ensemble Kalman filter (DEnKF) and extends it to support multiple radii of influence. We test the proposed adaptive localization using the toy Lorenz'96 problem and a more realistic 1.5-layer quasi-geostrophic model. Results with the toy problem show that the multivariate approach informs us that strongly observed variables can tolerate larger localization radii. The univariate approach leads to markedly improved filter performance for the realistic geophysical model, with a reduction in error by as much as 33 %.

scholarly journals An Estimate of Inflation Factor and Analysis Sensitivity in Ensemble Kalman Filter

2016 ◽  
Author(s):  
Guocan Wu
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
Estimation Accuracy ◽  
Error Matrix ◽  
Spatially Correlated ◽  
Inflation Factor ◽  
Analysis Error ◽  
Lorenz 96 ◽  
Assimilation Scheme

Abstract. The estimation accuracy of forecast error matrix is crucial to the assimilation result. Ensemble Kalman filter (EnKF) is a widely used ensemble based assimilation method, which initially estimate the forecast error matrix using a Monte Carlo method with the short-term ensemble forecast states. However, this estimate needs to be further improved using inflation technique. In this study, the forecast error inflation factor is estimated based on cross validation and the analysis sensitivity is also investigated. The improved EnKF assimilation scheme is validated by assimilating spatially correlated observations to the atmosphere-like Lorenz-96 model. The experiment results show that, the analysis error is reduced and the analysis sensitivity to observations is improved.

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