The Ensemble Kalman filter: a signal processing perspective

Roth, Michael; Hendeby, Gustaf; Fritsche, Carsten; Gustafsson, Fredrik

doi:10.1186/s13634-017-0492-x

Cited by 59 publications

(32 citation statements)

References 77 publications

(260 reference statements)

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“…, M-see SI Section B for details. Adding an artificial noise to our predictions prevents ensemble values from getting too close to each other after repeated correction steps 33 .…”

Section: Sequential Forecasting With Ensemble-based Kalman Filtermentioning

confidence: 99%

Systematic biases in disease forecasting - the role of behavior change

Eksin

Paarporn

Weitz³

2018

Preprint

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In a simple susceptible-infected-recovered (SIR) model, the initial speed at which infected cases increase is indicative of the long-term trajectory of the outbreak. Yet during real-world outbreaks, individuals may modify their behavior and take preventative steps to reduce infection risk. As a consequence, the relationship between the initial rate of spread and the final case count may become tenuous. Here, we evaluate this hypothesis by comparing the dynamics arising from a simple SIR epidemic model with those from a modified SIR model in which individuals reduce contacts as a function of the current or cumulative number of cases. Dynamics with behavior change exhibit significantly reduced final case counts even though the initial speed of disease spread is nearly identical for both of the models. We show that this difference in final size projections depends critically in the behavior change of individuals. These results also provide a rationale for integrating behavior change into iterative forecast models. Hence, we propose to use a Kalman filter to update models with and without behavior change as part of iterative forecasts. When the ground truth outbreak includes behavior change, sequential predictions using a simple SIR model perform poorly despite repeated observations while predictions using the modified SIR model are able to correct for initial forecast errors. These findings highlight the value of incorporating behavior change into baseline epidemic and dynamic forecast models.

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“…, M-see SI Section B for details. Adding an artificial noise to our predictions prevents ensemble values from getting too close to each other after repeated correction steps 33 .…”

Section: Sequential Forecasting With Ensemble-based Kalman Filtermentioning

confidence: 99%

Systematic biases in disease forecasting - the role of behavior change

Eksin

Paarporn

Weitz³

2018

Preprint

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“…They calculated the posterior PDF in a local sense; therefore, the methods are also referred to as the local numerical approximation approach. An alternative to deterministic sampling for approximating an arbitrary PDF is random sampling (e.g., the popular mixture KF (Chen and Liu, 2000), ensemble KF (Evensen, 2003;Roth et al, 2017b), Monte Carlo KF (Song, 2000), and Gaussian/GM PF (Kotecha and Djurić, 2003a;2003b)), which still strives to maintain AGC. This allows asymptotically exact integral evaluation, albeit with much higher computational complexity.…”

Section: Nonlinearitymentioning

confidence: 99%

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Liu

et al. 2017

Frontiers Inf Technol Electronic Eng

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Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov-Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed 'Gaussian conjugacy' in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity.

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“…The Lorenz-96 chaotic model consisting of a state vector of dimension 40 has been used as a common test bed for the EnKF [7]. Recently, the EnKF has been proposed for general highly dimensional problems [32]. Similar to the This work is licensed under a Creative Commons Attribution 4.0 License.…”

Section: Ensemble Kalman Filtermentioning

confidence: 99%

Cubature Ensemble Kalman Filter for Highly Dimensional Strongly Nonlinear Systems

Meng

Leib

2020

IEEE Access

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The Ensemble Kalman filter (EnKF) was introduced for highly dimensional systems, but it has poor performance in the presence of strong nonlinearities. The Cubature Kalman filter (CKF) has outstanding performance in strongly nonlinear systems, however, it is limited by high dimensionality. In this work, we provide a comparison between the EnKF and the CKF to elaborate the problems of each scheme in highly dimensional strongly nonlinear systems. To address these problems, we introduce a Cubature Ensemble Kalman filter (CEnKF) that is a combination between both types of filters making it more suitable for highly dimensional strongly nonlinear systems. These algorithms are tested by extensive computer simulations on several models for chaotic dynamical systems. In addition, the computational complexity of the CKF/EnKF/CEnKF is analyzed. Simulation results show that the CEnKF, given a large enough ensemble size, can perform better than the EnKF and CKF for highly dimensional strongly nonlinear systems with high measurement noise intensity. The CEnKF also has better stability than the EnKF, and it performs as good as the CKF with a large enough ensemble size. INDEX TERMS Cubature Kalman filter, Ensemble Kalman filter, highly dimensional systems, strongly nonlinear estimation.

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The Ensemble Kalman filter: a signal processing perspective

Cited by 59 publications

References 77 publications

Systematic biases in disease forecasting - the role of behavior change

Systematic biases in disease forecasting - the role of behavior change

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Cubature Ensemble Kalman Filter for Highly Dimensional Strongly Nonlinear Systems

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