scholarly journals EEG-fMRI Fusion: Adaptations of the Kalman Filter for Solving a High-Dimensional Spatio-Temporal Inverse Problem

10.5772/16490 ◽  
2011 ◽  
Author(s):  
Thomas Deneux
Keyword(s):  
Inverse Problem ◽  
Kalman Filter ◽  
High Dimensional ◽  
Spatio Temporal

scholarly journals Spatio-Temporal Context, Correlation Filter and Measurement Estimation Collaboration Based Visual Object Tracking

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2841
Author(s):  
Khizer Mehmood ◽  
Abdul Jalil ◽  
Ahmad Ali ◽  
Baber Khan ◽  
Maria Murad ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Object Tracking ◽  
Environmental Changes ◽  
Correlation Filter ◽  
Temporal Context ◽  
Visual Object ◽  
Target Model ◽  
Change Of Scale ◽  
Tracking Model ◽  
Spatio Temporal

Despite eminent progress in recent years, various challenges associated with object tracking algorithms such as scale variations, partial or full occlusions, background clutters, illumination variations are still required to be resolved with improved estimation for real-time applications. This paper proposes a robust and fast algorithm for object tracking based on spatio-temporal context (STC). A pyramid representation-based scale correlation filter is incorporated to overcome the STC’s inability on the rapid change of scale of target. It learns appearance induced by variations in the target scale sampled at a different set of scales. During occlusion, most correlation filter trackers start drifting due to the wrong update of samples. To prevent the target model from drift, an occlusion detection and handling mechanism are incorporated. Occlusion is detected from the peak correlation score of the response map. It continuously predicts target location during occlusion and passes it to the STC tracking model. After the successful detection of occlusion, an extended Kalman filter is used for occlusion handling. This decreases the chance of tracking failure as the Kalman filter continuously updates itself and the tracking model. Further improvement to the model is provided by fusion with average peak to correlation energy (APCE) criteria, which automatically update the target model to deal with environmental changes. Extensive calculations on the benchmark datasets indicate the efficacy of the proposed tracking method with state of the art in terms of performance analysis.

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.

scholarly journals The Kalmag Model as a Candidate for IGRF-13

2020 ◽  
Author(s):  
Julien Baerenzung ◽  
Matthias Holschneider ◽  
Johannes Wicht ◽  
Vincent Lesur ◽  
Sabrina Sanchez
Keyword(s):  
Inverse Problem ◽  
Kalman Filter ◽  
Vector Field ◽  
Geomagnetic Field ◽  
Time Window ◽  
Field Measurements ◽  
Covariance Matrices ◽  
Smoothing Algorithm ◽  
Mean Fields ◽  
Observable Field

Abstract We present a new model of the Geomagnetic field spanning the last 20 years and called Kalmag. Deriving from the assimilation of CHAMP and SWARM vector field measurements, it separates the different contributions to the observable field through parameterized prior covariance matrices. To make the inverse problem numerically feasible it has been sequentialized in time though the combination of a Kalman filter and a smoothing algorithm. The model provides reliable estimates of past, present and future mean fields and associated uncertainties. The version presented here is an update of our IGRF candidates, the amount of assimilated data has been doubled and the considered time window has been extended from [2000.5,2019.74] to [2000.5,2020.33].

Optical reservoir computing for high-dimensional spatio-temporal chaotic systems prediction (Conference Presentation)

2020 ◽  
Author(s):  
Mushegh Rafayelyan ◽  
Jonathan Dong ◽  
Yongqi Tan ◽  
Florent Krzakala ◽  
Sylvain Gigan
Keyword(s):  
Chaotic Systems ◽  
High Dimensional ◽  
Reservoir Computing ◽  
Spatio Temporal
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