scholarly journals Adaptive Filter as Efficient Tool for Data Assimilation under Uncertainties

2020 ◽  
Author(s):  
Hong Son Hoang ◽  
Remy Baraille
Keyword(s):  
Kalman Filter ◽  
Dynamical Systems ◽  
Data Assimilation ◽  
Adaptive Filter ◽  
High Dimensional ◽  
Main Principle ◽  
Computational Power ◽  
Observational Errors ◽  
Simulation Results ◽  
Computational Resources

In this contribution, the problem of data assimilation as state estimation for dynamical systems under uncertainties is addressed. This emphasize is put on high-dimensional systems context. Major difficulties in the design of data assimilation algorithms is a concern for computational resources (computational power and memory) and uncertainties (system parameters, statistics of model, and observational errors). The idea of the adaptive filter will be given in detail to see how it is possible to overcome uncertainties as well as to explain the main principle and tools for implementation of the adaptive filter for complex dynamical systems. Simple numerical examples are given to illustrate the principal differences of the AF with the Kalman filter and other methods. The simulation results are presented to compare the performance of the adaptive filter with the Kalman filter.

scholarly journals Assessment of multilevel ensemble-based data assimilation for reservoir history matching

2019 ◽  
Vol 24 (1) ◽  
pp. 217-239
Author(s):  
Kristian Fossum ◽  
Trond Mannseth ◽  
Andreas S. Stordal
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
History Matching ◽  
Computational Cost ◽  
Ensemble Size ◽  
Matching Problems ◽  
Reservoir Models ◽  
Reservoir History Matching ◽  
Computational Resources

AbstractMultilevel ensemble-based data assimilation (DA) as an alternative to standard (single-level) ensemble-based DA for reservoir history matching problems is considered. Restricted computational resources currently limit the ensemble size to about 100 for field-scale cases, resulting in large sampling errors if no measures are taken to prevent it. With multilevel methods, the computational resources are spread over models with different accuracy and computational cost, enabling a substantially increased total ensemble size. Hence, reduced numerical accuracy is partially traded for increased statistical accuracy. A novel multilevel DA method, the multilevel hybrid ensemble Kalman filter (MLHEnKF) is proposed. Both the expected and the true efficiency of a previously published multilevel method, the multilevel ensemble Kalman filter (MLEnKF), and the MLHEnKF are assessed for a toy model and two reservoir models. A multilevel sequence of approximations is introduced for all models. This is achieved via spatial grid coarsening and simple upscaling for the reservoir models, and via a designed synthetic sequence for the toy model. For all models, the finest discretization level is assumed to correspond to the exact model. The results obtained show that, despite its good theoretical properties, MLEnKF does not perform well for the reservoir history matching problems considered. We also show that this is probably caused by the assumptions underlying its theoretical properties not being fulfilled for the multilevel reservoir models considered. The performance of MLHEnKF, which is designed to handle restricted computational resources well, is quite good. Furthermore, the toy model is utilized to set up a case where the assumptions underlying the theoretical properties of MLEnKF are fulfilled. On that case, MLEnKF performs very well and clearly better than MLHEnKF.

scholarly journals A Hybrid Particle–Ensemble Kalman Filter for Lagrangian Data Assimilation

2015 ◽  
Vol 143 (1) ◽  
pp. 195-211 ◽  
Author(s):  
Laura Slivinski ◽  
Elaine Spiller ◽  
Amit Apte ◽  
Björn Sandstede
Keyword(s):  
Kalman Filter ◽  
Velocity Field ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
High Dimensional ◽  
Salinity Field ◽  
Hybrid Particle ◽  
Highly Nonlinear ◽  
Particle Ensemble ◽  
Low Dimensional

Abstract Lagrangian measurements from passive ocean instruments provide a useful source of data for estimating and forecasting the ocean’s state (velocity field, salinity field, etc.). However, trajectories from these instruments are often highly nonlinear, leading to difficulties with widely used data assimilation algorithms such as the ensemble Kalman filter (EnKF). Additionally, the velocity field is often modeled as a high-dimensional variable, which precludes the use of more accurate methods such as the particle filter (PF). Here, a hybrid particle–ensemble Kalman filter is developed that applies the EnKF update to the potentially high-dimensional velocity variables, and the PF update to the relatively low-dimensional, highly nonlinear drifter position variable. This algorithm is tested with twin experiments on the linear shallow water equations. In experiments with infrequent observations, the hybrid filter consistently outperformed the EnKF, both by better capturing the Bayesian posterior and by better tracking the truth.

Training a convolutional neural network to conserve mass in data assimilation

2021 ◽  
Author(s):  
Yvonne Ruckstuhl ◽  
Tijana Janjic ◽  
Stephan Rasp
Keyword(s):  
Neural Network ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Quadratic Programming ◽  
Convolutional Neural Network ◽  
Ensemble Kalman Filter ◽  
High Dimensional ◽  
Forecast Errors ◽  
The Difference ◽  
Prediction Systems

<p>In previous work, it was shown that preservation of physical properties  in the data assimilation framework can significantly reduce forecast errors. Proposed data assimilation methods, such as the quadratic programming ensemble (QPEns) that can impose such constraints on the calculation of the analysis, are computationally more expensive, severely limiting their application to high dimensional prediction systems as found in earth sciences. We therefore propose to use a convolutional neural network (CNN) trained on the difference between the analysis produced by a standard ensemble Kalman Filter (EnKF) and the QPEns to correct any violations of imposed constraints. On this poster, we focus on conservation of mass and show in an idealized setup that the hybrid of a CNN and the EnKF is capable of reducing analysis and background errors to the same level as the QPEns. </p>

scholarly journals Training a convolutional neural network to conserve mass in data assimilation

2021 ◽  
Vol 28 (1) ◽  
pp. 111-119
Author(s):  
Yvonne Ruckstuhl ◽  
Tijana Janjić ◽  
Stephan Rasp
Keyword(s):  
Neural Network ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Convolutional Neural Network ◽  
Ensemble Kalman Filter ◽  
High Dimensional ◽  
Forecast Errors ◽  
The Difference ◽  
Prediction Systems ◽  
Set Up

Abstract. In previous work, it was shown that the preservation of physical properties in the data assimilation framework can significantly reduce forecast errors. Proposed data assimilation methods, such as the quadratic programming ensemble (QPEns) that can impose such constraints on the calculation of the analysis, are computationally more expensive, severely limiting their application to high-dimensional prediction systems as found in Earth sciences. We, therefore, propose using a convolutional neural network (CNN) trained on the difference between the analysis produced by a standard ensemble Kalman filter (EnKF) and the QPEns to correct any violations of imposed constraints. In this paper, we focus on the conservation of mass and show that, in an idealised set-up, the hybrid of a CNN and the EnKF is capable of reducing analysis and background errors to the same level as the QPEns.

Comparison on Three Filter Methods in Self-Alignment for SINS of the Carrier Craft

2012 ◽  
Vol 591-593 ◽  
pp. 1793-1799
Author(s):  
Yong Jun Wang ◽  
Jing Shuo Xu ◽  
Rui Hua Song ◽  
Yang Gao ◽  
Ya Zhou Di
Keyword(s):  
Kalman Filter ◽  
Adaptive Filter ◽  
State Space Model ◽  
Basic Principles ◽  
Space Model ◽  
Filter Performance ◽  
Filter Methods ◽  
Simulation Results ◽  
Better Than ◽  
Fuzzy Adaptive

Fuzzy adaptive filter and H∞ filter are introduced to solve the problem of low filter performance, which comes from uncertain noise caused by seawave and high frequence vibrancy. First, basic principles of the fuzzy adaptive filter and H∞ filter are formulated. Second, state space model of self-alignment for SINS of the carrier craft is built. Finally, according to each character, a comparison on results that Kalman filter, fuzzy adaptive filter and H∞ filter are applied to alignment for SINS of the carrier craft is made. Simulation results show that although Kalman filter has definite robustness to external uncertainty noise, weak anti-jamming ability and bad filter performance make self-alignment failed. Fuzzy adaptive filter and H∞ filter have strong ability to suppress external uncertain noise and can obtain good filtering accuracy. They both can complete self-alignment. Filtering accuracy and rapidity of fuzzy adaptive filter are better than those of H∞ filter, while robustness and curve smoothness of H∞ filter are stronger than those of other filters.

scholarly journals Ensemble Riemannian Data Assimilation: Towards High-dimensional Implementation

2021 ◽  
Author(s):  
Sagar Kumar Tamang ◽  
Ardeshir Ebtehaj ◽  
Peter Jan van Leeuwen ◽  
Gilad Lerman ◽  
Efi Foufoula-Georgiou
Keyword(s):  
Dynamical Systems ◽  
Data Assimilation ◽  
Mean Squared Error ◽  
Likelihood Function ◽  
Nonlinear Dynamical Systems ◽  
High Dimensional ◽  
Nonlinear Dynamical ◽  
Systematic Biases ◽  
Background Probability ◽  
Lorenz 96

Abstract. This paper presents the results of the Ensemble Riemannian Data Assimilation for relatively high-dimensional nonlinear dynamical systems, focusing on the chaotic Lorenz-96 model and a two-layer quasi-geostrophic (QG) model of atmospheric circulation. The analysis state in this approach is inferred from a joint distribution that optimally couples the background probability distribution and the likelihood function, enabling formal treatment of systematic biases without any Gaussian assumptions. Despite the risk of the curse of dimensionality in the computation of the coupling distribution, comparisons with the classic implementation of the particle filter and the stochastic ensemble Kalman filter demonstrate that with the same ensemble size, the presented methodology could improve the predictability of dynamical systems. In particular, under systematic errors, the root mean squared error of the analysis state can be reduced by 20 % (30 %) in Lorenz-96 (QG) model.

Data assimilation with the weighted ensemble Kalman filter

2010 ◽  
Author(s):  
Nicolas Papadakis ◽  
Etienne Mémin ◽  
Anne Cuzol ◽  
Nicolas Gengembre
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter

A Strong Tracking Cubature Kalman Filter for Nonlinear Estimation

2013 ◽  
Vol 313-314 ◽  
pp. 1115-1119
Author(s):  
Yong Qi Wang ◽  
Feng Yang ◽  
Yan Liang ◽  
Quan Pan
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Scaling Factor ◽  
Estimation Accuracy ◽  
Nonlinear State Estimation ◽  
Cubature Kalman Filter ◽  
Novel Method ◽  
Simulation Results ◽  
Tracking Filter ◽  
Nonlinear State

In this paper, a novel method based on cubature Kalman filter (CKF) and strong tracking filter (STF) has been proposed for nonlinear state estimation problem. The proposed method is named as strong tracking cubature Kalman filter (STCKF). In the STCKF, a scaling factor derived from STF is added and it can be tuned online to adjust the filtering gain accordingly. Simulation results indicate STCKF outperforms over EKF and CKF in state estimation accuracy.

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