scholarly journals Penalized ensemble Kalman filters for high dimensional non-linear systems

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248046
Author(s):  
Elizabeth Hou ◽  
Earl Lawrence ◽  
Alfred O. Hero
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Estimation Error ◽  
Covariance Structure ◽  
Full Rank ◽  
The State ◽  
High Dimensional ◽  
Ensemble Kalman Filters ◽  
Non Linear ◽  
Non Linear System

The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the well-known Kalman filter. However, its performance can suffer when the ensemble size is smaller than the state space, as is often necessary for computationally burdensome models. This scenario means that the empirical estimate of the state covariance is not full rank and possibly quite noisy. To solve this problem in this high dimensional regime, we propose a computationally fast and easy to implement algorithm called the penalized ensemble Kalman filter (PEnKF). Under certain conditions, it can be theoretically proven that the PEnKF will be accurate (the estimation error will converge to zero) despite having fewer ensemble members than state dimensions. Further, as contrasted to localization methods, the proposed approach learns the covariance structure associated with the dynamical system. These theoretical results are supported with simulations of several non-linear and high dimensional systems.

Design an Unscented Kalman Filter-Based SoC Estimator for HEV Application

2012 ◽  
Vol 588-589 ◽  
pp. 424-428 ◽  
Author(s):  
Hong Wen He ◽  
Kai Zhao ◽  
Rui Xiong
Keyword(s):  
Kalman Filter ◽  
Lithium Ion Battery ◽  
Hybrid Electric Vehicles ◽  
Unscented Kalman Filter ◽  
Estimation Error ◽  
Lithium Ion ◽  
Soc Estimation ◽  
Non Linear ◽  
Non Linear System ◽  
Method Accuracy

An unscented Kalman filter (UKF) is adopted to estimate the state of charge (SoC) of a lithium ion battery for application in hybrid electric vehicles (HEVs). Generally, the extended Kalman filter (EKF) can be selected to estimate a non-linear system state. However, it may leads to large errors since the strong non-linear and stochastic performance. In this paper, the performance of the lithium-ion battery is tested by a design of experiment, such as hysteresis, polarization, coulomb efficiency, etc. And a combined battery model is selected for SoC estimation, while the model parameter was identified by using UKF algorithm. Finally, the federal urban driving schedule (FUDS) is used to evaluate the proposed method accuracy. And the results show that the maximum SoC estimation error is less than 3%.

scholarly journals Non-linear wave data assimilation with an ANN-type wind-wave model and Ensemble Kalman Filter (EnKF)

2010 ◽  
Vol 34 (8) ◽  
pp. 1984-1999 ◽  
Author(s):  
Ahmadreza Zamani ◽  
Ahmadreza Azimian ◽  
Arnold Heemink ◽  
Dimitri Solomatine
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Wind Wave ◽  
Wave Model ◽  
Linear Wave ◽  
Wave Data ◽  
Non Linear

Machine learning based conditional mean filter: a non-linear extension of the ensemble Kalman filter 

2021 ◽  
Author(s):  
Truong-Vinh Hoang ◽  
Sebastian Krumscheid ◽  
Raul Tempone
Keyword(s):  
Machine Learning ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Machine Learning Techniques ◽  
Filter Method ◽  
Gaussian State ◽  
Correct Prediction ◽  
Conditional Mean ◽  
Non Linear ◽  
Mean Filter

<p>Filtering is an uncertainty quantification technique that refers to the inference of the states of dynamical systems from noisy observations. This work proposes a machine learning-based filtering method for tracking the high-dimensional non-Gaussian state-space models with non-linear dynamics and sparse observations. Our filter method is based on the conditional expectation mean filter and uses machine-learning techniques to approximate the conditional mean (CM). The contribution of this work is twofolds: (i) we demonstrate theoretically that the assimilated ensembles obtained using the ensemble conditional mean filter (EnCMF) provide a correct prediction of the posterior mean and have the optimal variance, and (ii) we implement the EnCMF using artificial neural networks, which has a significant advantage in representing non-linear functions that map between high-dimensionality domains, such as the CM. We implement the machine learning-based EnCMF for tracking the states of the Lorenz-63 and 96 systems under the chaotic regime. Numerical results show that the EnCMF outperforms the ensemble Kalman filter.</p>

scholarly journals Design of Adaptive Controller Exploiting Learning Concepts Applied to a BLDC-Based Drive System

Energies ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2512
Author(s):  
Pierpaolo Dini ◽  
Sergio Saponara
Keyword(s):  
Complexity Analysis ◽  
Signal Amplitude ◽  
Adaptive Controller ◽  
Power Converter ◽  
The State ◽  
Control Technique ◽  
State Representation ◽  
Servo Drive ◽  
Non Linear ◽  
Non Linear System

This work presents an innovative control architecture, which takes its ideas from the theory of adaptive control techniques and the theory of statistical learning at the same time. Taking inspiration from the architecture of a classical neural network with several hidden levels, the principle is to divide the architecture of the adaptive controller into three different levels. Each level implements an algorithm based on learning from data and therefore we can talk about learning concepts. Each level has a different task: the first to learn the required reference to the control loop; the second to learn the coefficients of the state representation of a model of the system to be controlled; and finally, the third to learn the coefficients of the state representation of the actual controller. The design of the control system is reported from both a rigorous and an operational point of view. As an application example, the proposed control technique is applied on a second-order non-linear system. We consider a servo-drive based on a brushless DC (BLDC) motor, whose dynamic model considers all the non-linear effects related to the electromechanical nature of the electric machine itself, and also an accurate model of the switching power converter. The reported example shows the capability of the control algorithm to ensure trajectory tracking while allowing for disturbance rejection with different disturbance signal amplitude. The implementation complexity analysis of the new controller is also proposed, showing its low overhead vs. basic control solutions.

scholarly journals Performance and stochastic stability of the adaptive fading extended Kalman filter with the matrix forgetting factor

2016 ◽  
Vol 14 (1) ◽  
pp. 934-945
Author(s):  
Cenker Biçer ◽  
Levent Özbek ◽  
Hasan Erbay
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Extended Kalman Filter ◽  
Stochastic Systems ◽  
Estimation Error ◽  
The State ◽  
Forgetting Factor ◽  
The Matrix ◽  
Stochastic Framework ◽  
Theoretical Results

AbstractIn this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable.The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.

scholarly journals Covariance Inflation in the Ensemble Kalman Filter: A Residual Nudging Perspective and Some Implications

2013 ◽  
Vol 141 (10) ◽  
pp. 3360-3368 ◽  
Author(s):  
Xiaodong Luo ◽  
Ibrahim Hoteit
Keyword(s):  
Kalman Filter ◽  
Numerical Experiment ◽  
Ensemble Kalman Filter ◽  
Sufficient Conditions ◽  
The State ◽  
State Estimate ◽  
Inflation Factor

Abstract This article examines the influence of covariance inflation on the distance between the measured observation and the simulated (or predicted) observation with respect to the state estimate. In order for the aforementioned distance to be bounded in a certain interval, some sufficient conditions are derived, indicating that the covariance inflation factor should be bounded in a certain interval, and that the inflation bounds are related to the maximum and minimum eigenvalues of certain matrices. Implications of these analytic results are discussed, and a numerical experiment is presented to verify the validity of the analysis conducted.

scholarly journals On Serial Observation Processing in Localized Ensemble Kalman Filters

2015 ◽  
Vol 143 (5) ◽  
pp. 1554-1567 ◽  
Author(s):  
Lars Nerger
Keyword(s):  
Ensemble Kalman Filter ◽  
Kalman Filters ◽  
Large Scale ◽  
The State ◽  
Ensemble Kalman Filters ◽  
Filter Performance ◽  
Error Covariance ◽  
Analysis Process ◽  
Scale Models ◽  
Serial Observation

Abstract Ensemble square root filters can either assimilate all observations that are available at a given time at once, or assimilate the observations in batches or one at a time. For large-scale models, the filters are typically applied with a localized analysis step. This study demonstrates that the interaction of serial observation processing and localization can destabilize the analysis process, and it examines under which conditions the instability becomes significant. The instability results from a repeated inconsistent update of the state error covariance matrix that is caused by the localization. The inconsistency is present in all ensemble Kalman filters, except for the classical ensemble Kalman filter with perturbed observations. With serial observation processing, its effect is small in cases when the assimilation changes the ensemble of model states only slightly. However, when the assimilation has a strong effect on the state estimates, the interaction of localization and serial observation processing can significantly deteriorate the filter performance. In realistic large-scale applications, when the assimilation changes the states only slightly and when the distribution of the observations is irregular and changing over time, the instability is likely not significant.

scholarly journals On the existence of equations of evolution

1984 ◽  
Vol 7 (2) ◽  
pp. 409-411
Author(s):  
J. Lubliner
Keyword(s):  
Linear System ◽  
Evolution Equation ◽  
Closed Interval ◽  
The State ◽  
Initial State ◽  
Non Linear ◽  
Non Linear System

A time-independent, non-autonomous non-linear system governed by a principle of determinism (the state at a given time is determined by the initial state and by the control history during the intervening closed interval) is shown to obey a generalized evolution equation (1.2), wherenis such that the state is continuously differentiabie with respect to time whenever the control is of classCn.

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