An efficient approximation of the Kalman filter for multiple systems coupled via low-dimensional stochastic input

Pogorelyuk, Leonid; Rowley, Clarence W.; Kasdin, N. Jeremy

doi:10.1016/j.automatica.2020.108972

Cited by 6 publications

(2 citation statements)

References 18 publications

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“…Regarding the performance differences between MP and DMD, under specific conditions the MP and DMD methods are expected to produce the same results 14 . An example of this can be seen in the noise‐free phantom with constant frequencies in Figure 2.…”

Section: Discussionmentioning

confidence: 90%

“…Yet, the truncation method decreases the scan efficiency by excluding collected measurements during post‐processing; whereas the MP implementation described previously 13 requires a multi‐step approach with low‐pass and high‐pass filtering operations before the spectral analysis. Moreover, the MP technique is not capable of estimating frequencies and amplitudes simultaneously, 14 and is not capable of obtaining the dynamic system matrix 15 …”

Section: Introductionmentioning

confidence: 99%

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Dynamic mode decomposition of dynamic MRI for assessment of pulmonary ventilation and perfusion

Ilicak

Ozdemir

Zapp

et al. 2023

Magnetic Resonance in Med

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To introduce dynamic mode decomposition (DMD) as a robust alternative for the assessment of pulmonary functional information from dynamic non-contrast-enhanced acquisitions.Methods: Pulmonary fractional ventilation and normalized perfusion maps were obtained using DMD from simulated phantoms as well as in vivo dynamic acquisitions of healthy volunteers at 1.5T. The performance of DMD was compared with conventional Fourier decomposition (FD) and matrix pencil (MP) methods in estimating functional map values. The proposed method was evaluated based on estimated signal amplitude in functional maps across varying number of measurements. Results: Quantitative assessments performed on phantoms and in vivo measurements indicate that DMD is capable of successfully obtaining pulmonary functional maps. Specifically, compared to FD and MP methods, DMD is able to reduce variations in estimated amplitudes across different number of measurements. This improvement is evident in the fractional ventilation and normalized perfusion maps obtain from phantom simulations with frequency variations and noise, as well as in the maps obtained from in vivo measurements. Conclusions:A robust method for accurately estimating pulmonary ventilation and perfusion related signal changes in dynamic acquisitions is presented. The proposed method uses DMD to obtain functional maps reliably, while reducing amplitude variations caused by differences in number of measurements.

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Section: Discussionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Dynamic mode decomposition of dynamic MRI for assessment of pulmonary ventilation and perfusion

Ilicak

Ozdemir

Zapp

et al. 2023

Magnetic Resonance in Med

View full text Add to dashboard Cite

show abstract

A moment-based Kalman filtering approach for estimation in ensemble systems

de Lima,

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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A persistent challenge in tasks involving large-scale dynamical systems, such as state estimation and error reduction, revolves around processing the collected measurements. Frequently, these data suffer from the curse of dimensionality, leading to increased computational demands in data processing methodologies. Recent scholarly investigations have underscored the utility of delineating collective states and dynamics via moment-based representations. These representations serve as a form of sufficient statistics for encapsulating collective characteristics, while simultaneously permitting the retrieval of individual data points. In this paper, we reshape the Kalman filter methodology, aiming its application in the moment domain of an ensemble system and developing the basis for moment ensemble noise filtering. The moment system is defined with respect to the normalized Legendre polynomials, and it is shown that its orthogonal basis structure introduces unique benefits for the application of Kalman filter for both i.i.d. and universal Gaussian disturbances. The proposed method thrives from the reduction in problem dimension, which is unbounded within the state-space representation, and can achieve significantly smaller values when converted to the truncated moment-space. Furthermore, the robustness of moment data toward outliers and localized inaccuracies is an additional positive aspect of this approach. The methodology is applied for an ensemble of harmonic oscillators and units following aircraft dynamics, with results showcasing a reduction in both cumulative absolute error and covariance with reduced calculation cost due to the realization of operations within the moment framework conceived.

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Multi-Sensor Fusion Boolean Bayesian Filtering for Stochastic Boolean Networks

Li¹,

Yang²

2023

IEEE Trans. Neural Netw. Learning Syst.

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An efficient approximation of the Kalman filter for multiple systems coupled via low-dimensional stochastic input

Cited by 6 publications

References 18 publications

Dynamic mode decomposition of dynamic MRI for assessment of pulmonary ventilation and perfusion

Dynamic mode decomposition of dynamic MRI for assessment of pulmonary ventilation and perfusion

A moment-based Kalman filtering approach for estimation in ensemble systems

Multi-Sensor Fusion Boolean Bayesian Filtering for Stochastic Boolean Networks

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