scholarly journals Correlation between System and Observation Errors in Data Assimilation

2018 ◽  
Vol 146 (9) ◽  
pp. 2913-2931 ◽  
Author(s):  
Tyrus Berry ◽  
Timothy Sauer
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Extreme Case ◽  
Covariance Matrices ◽  
Bayesian Filtering ◽  
Filtering Algorithm ◽  
Accurate Knowledge ◽  
Cross Correlations ◽  
Observational Errors ◽  
The Individual

Abstract Accurate knowledge of two types of noise, system and observational, is an important aspect of Bayesian filtering methodology. Traditionally, this knowledge is reflected in individual covariance matrices for the two noise contributions, while correlations between the system and observational noises are ignored. We contend that in practical problems, it is unlikely that system and observational errors are uncorrelated, in particular for geophysically motivated examples where errors are dominated by model and observation truncations. Moreover, it is shown that accounting for the cross correlations in the filtering algorithm, for example in a correlated ensemble Kalman filter, can result in significant improvements in filter accuracy for data from typical dynamical systems. In particular, we discuss the extreme case where the two types of errors are maximally correlated relative to the individual covariances.

scholarly journals Calibrating Multimodel Forecast Ensembles with Exchangeable and Missing Members Using Bayesian Model Averaging

2010 ◽  
Vol 138 (1) ◽  
pp. 190-202 ◽  
Author(s):  
Chris Fraley ◽  
Adrian E. Raftery ◽  
Tilmann Gneiting
Keyword(s):  
Kalman Filter ◽  
Pacific Northwest ◽  
Ensemble Kalman Filter ◽  
Bayesian Model ◽  
Bayesian Model Averaging ◽  
Model Averaging ◽  
Weighted Average ◽  
Multimodel Ensembles ◽  
The Individual ◽  
Ensemble Systems

Abstract Bayesian model averaging (BMA) is a statistical postprocessing technique that generates calibrated and sharp predictive probability density functions (PDFs) from forecast ensembles. It represents the predictive PDF as a weighted average of PDFs centered on the bias-corrected ensemble members, where the weights reflect the relative skill of the individual members over a training period. This work adapts the BMA approach to situations that arise frequently in practice; namely, when one or more of the member forecasts are exchangeable, and when there are missing ensemble members. Exchangeable members differ in random perturbations only, such as the members of bred ensembles, singular vector ensembles, or ensemble Kalman filter systems. Accounting for exchangeability simplifies the BMA approach, in that the BMA weights and the parameters of the component PDFs can be assumed to be equal within each exchangeable group. With these adaptations, BMA can be applied to postprocess multimodel ensembles of any composition. In experiments with surface temperature and quantitative precipitation forecasts from the University of Washington mesoscale ensemble and ensemble Kalman filter systems over the Pacific Northwest, the proposed extensions yield good results. The BMA method is robust to exchangeability assumptions, and the BMA postprocessed combined ensemble shows better verification results than any of the individual, raw, or BMA postprocessed ensemble systems. These results suggest that statistically postprocessed multimodel ensembles can outperform individual ensemble systems, even in cases in which one of the constituent systems is superior to the others.

scholarly journals Combining Hybrid and One-Step-Ahead Smoothing for Efficient Short-Range Storm Surge Forecasting with an Ensemble Kalman Filter

2019 ◽  
Vol 147 (9) ◽  
pp. 3283-3300
Author(s):  
Naila F. Raboudi ◽  
Boujemaa Ait-El-Fquih ◽  
Clint Dawson ◽  
Ibrahim Hoteit
Keyword(s):  
Kalman Filter ◽  
Storm Surge ◽  
Ensemble Kalman Filter ◽  
Computational Cost ◽  
Forecast Model ◽  
Bayesian Filtering ◽  
Background Error ◽  
One Step ◽  
Ensemble Transform Kalman Filter ◽  
Storm Surge Forecasting

Abstract This work combines two auxiliary techniques, namely the one-step-ahead (OSA) smoothing and the hybrid formulation, to boost the forecasting skills of a storm surge ensemble Kalman filter (EnKF) forecasting system. Bayesian filtering with OSA-smoothing enhances the robustness of the ensemble background statistics by exploiting the data twice: first to constrain the sampling of the forecast ensemble with the future observation, and then to update the resulting ensemble. This is expected to improve the behavior of EnKF-like schemes during the strongly nonlinear surges periods, but requires integrating the ensemble with the forecast model twice, which could be computationally demanding. The hybrid flow-dependent/static formulation of the EnKF background error covariance is then considered to enable the implementation of the filter with a small flow-dependent ensemble size, and thus less model runs. These two methods are combined within an ensemble transform Kalman filter (ETKF). The resulting hybrid ETKF with OSA smoothing is tested, based on twin experiments, using a realistic setting of the Advanced Circulation (ADCIRC) model configured for storm surge forecasting in the Gulf of Mexico and assimilating pseudo-observations of sea surface levels from a network of buoys. The results of our numerical experiments suggest that the proposed filtering system significantly enhances ADCIRC forecasting skills compared to the standard ETKF without increasing the computational cost.

scholarly journals Groundwater flow inverse modeling in non-MultiGaussian media: performance assessment of the normal-score Ensemble Kalman Filter

2011 ◽  
Vol 8 (4) ◽  
pp. 6749-6788 ◽  
Author(s):  
L. Li ◽  
H. Zhou ◽  
H. J. Hendricks Franssen ◽  
J. J. Gómez-Hernández
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Random Function ◽  
Bimodal Distribution ◽  
Function Model ◽  
Normal Score ◽  
Mean And Variance ◽  
Assimilation Process ◽  
Flow Configurations ◽  
The Individual

Abstract. The normal-score ensemble Kalman filter (NS-EnKF) is tested on a synthetic aquifer characterized by the presence of channels with a bimodal distribution of its hydraulic conductivities. Fourteen scenarios are analyzed which differ among them in one or various of the following aspects: the prior random function model, the boundary conditions of the flow problem, the number of piezometers used in the assimilation process, or the use of covariance localization in the implementation of the Kalman filter. The performance of the NS-EnKF is evaluated through the ensemble mean and variance maps, the connectivity patterns of the individual conductivity realizations and the degree of reproduction of the piezometric heads. The results show that (i) the localized NS-EnKF can identify correctly the channels when a large number of conditioning piezometers are used even when an erroneous prior random function model is used, (ii) localization plays an important role to prevent filter inbreeding and results in a better logconductivity characterization, and (iii) the NS-EnKF works equally well under very different flow configurations.

scholarly journals Applying an ensemble Kalman filter to the assimilation of AERONET observations in a global aerosol transport model

2009 ◽  
Vol 9 (6) ◽  
pp. 23835-23873 ◽  
Author(s):  
N. A. J. Schutgens ◽  
T. Miyoshi ◽  
T. Takemura ◽  
T. Nakajima
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Transport Model ◽  
Current Model ◽  
Aerosol Transport ◽  
Model Uncertainties ◽  
Variable Model ◽  
Mixing Ratios ◽  
Observational Errors ◽  
Assimilation System

Abstract. We present a global aerosol assimilation system based on an ensemble Kalman filter, which we believe leads to a significant improvement in aerosol fields. The ensemble allows realistic, spatially and temporally variable model covariances (unlike other assimilation schemes). As the analyzed variables are mixing ratios (prognostic variables of the aerosol transport model), there is no need for the extra assumptions required by previous assimilation schemes analyzing aerosol optical thickness (AOT). We describe the implementation of this assimilation system and in particular the construction of the ensemble. This ensemble should represent our estimate of current model uncertainties. Consequently, we construct the ensemble around randomly modified emission scenarios. The system is tested with AERONET observations of AOT and Angström exponent (AE). Particular care is taken in the prescribing the observational errors. The assimilated fields (AOT and AE) are validated through independent AERONET, SKYNET and MODIS Aqua observations. We show that, in general, assimilation of AOT observations leads to improved modelling of global AOT, while assimilation of AE only improves modelling when the AOT is high.

scholarly journals An Efficient Particle Filtering Algorithm based on Ensemble Kalman Filter Proposal Density

2021 ◽  
Author(s):  
Prakash Tamboli
Keyword(s):  
Kalman Filter ◽  
Computational Efficiency ◽  
Ensemble Kalman Filter ◽  
Particle Filtering ◽  
Filtering Algorithm ◽  
Effective Particle

The paper presents an effective particle filtering using the Ensemble Kalman Filter based proposal density to improve the computational efficiency

scholarly journals An Efficient Particle Filtering Algorithm based on Ensemble Kalman Filter Proposal Density

2021 ◽  
Author(s):  
Prakash Tamboli
Keyword(s):  
Kalman Filter ◽  
Computational Efficiency ◽  
Ensemble Kalman Filter ◽  
Particle Filtering ◽  
Filtering Algorithm ◽  
Effective Particle

The paper presents an effective particle filtering using the Ensemble Kalman Filter based proposal density to improve the computational efficiency

scholarly journals Groundwater flow inverse modeling in non-MultiGaussian media: performance assessment of the normal-score Ensemble Kalman Filter

2012 ◽  
Vol 16 (2) ◽  
pp. 573-590 ◽  
Author(s):  
L. Li ◽  
H. Zhou ◽  
H. J. Hendricks Franssen ◽  
J. J. Gómez-Hernández
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Random Function ◽  
Bimodal Distribution ◽  
Function Model ◽  
Normal Score ◽  
Mean And Variance ◽  
Flow Configurations ◽  
Multigaussian Distribution ◽  
The Individual

Abstract. The normal-score ensemble Kalman filter (NS-EnKF) is tested on a synthetic aquifer characterized by the presence of channels with a bimodal distribution of its hydraulic conductivities. This is a clear example of an aquifer that cannot be characterized by a multiGaussian distribution. Fourteen scenarios are analyzed which differ among them in one or various of the following aspects: the prior random function model, the boundary conditions of the flow problem, the number of piezometers used in the assimilation process, or the use of covariance localization in the implementation of the Kalman filter. The performance of the NS-EnKF is evaluated through the ensemble mean and variance maps, the connectivity patterns of the individual conductivity realizations and the degree of reproduction of the piezometric heads. The results show that (i) the localized NS-EnKF can characterize the non-multiGaussian underlying hydraulic distribution even when an erroneous prior random function model is used, (ii) localization plays an important role to prevent filter inbreeding and results in a better logconductivity characterization, and (iii) the NS-EnKF works equally well under very different flow configurations.

scholarly journals Sensorless-BLDC motor speed control with ensemble Kalman filter and neural network

2019 ◽  
Vol 10 (1) ◽  
pp. 1 ◽  
Author(s):  
Muhammad Rif'an ◽  
Feri Yusivar ◽  
Benyamin Kusumoputro
Keyword(s):  
Neural Network ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Operational Reliability ◽  
Brushless Dc Motor ◽  
Motor Speed ◽  
Filtering Algorithm ◽  
Brushless Dc ◽  
Terminal Voltage ◽  
Non Linear Systems

The use of sensorless technology at BLDC is mainly to improve operational reliability and play a role for wider use of BLDC motors in the future. This research aims to predict load changes and to improve the accuracy of estimation results of sensorless-BLDC. In this paper, a new filtering algorithm is proposed for sensorless brushless DC motor based on Ensemble Kalman filter (EnKF) and neural network. The proposed EnKF algorithm is used to estimate speed and rotor position, while neural network is used to estimate the disturbance by simulation. The proposed algorithm requires only the terminal voltage and the current of three phases for estimated speed and disturbance. A model of non-linear systems is carried out for simulation. Variations in disturbances such as external mechanical loads are given for testing the performance of the proposed algorithm. The experimental results show that the proposed algorithm has sufficient control with error speed of 3 % in a disturbance of 50 % of the rated-torque. Simulation results show that the speed can be tracked and adjusted accordingly either by disturbances or the presence of disturbances.

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