7,776 research outputs found
Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography
This work addresses the inverse problem of electrocardiography from a new
perspective, by combining electrical and mechanical measurements. Our strategy
relies on the defini-tion of a model of the electromechanical contraction which
is registered on ECG data but also on measured mechanical displacements of the
heart tissue typically extracted from medical images. In this respect, we
establish in this work the convergence of a sequential estimator which combines
for such coupled problems various state of the art sequential data assimilation
methods in a unified consistent and efficient framework. Indeed we ag-gregate a
Luenberger observer for the mechanical state and a Reduced Order Unscented
Kalman Filter applied on the parameters to be identified and a POD projection
of the electrical state. Then using synthetic data we show the benefits of our
approach for the estimation of the electrical state of the ventricles along the
heart beat compared with more classical strategies which only consider an
electrophysiological model with ECG measurements. Our numerical results
actually show that the mechanical measurements improve the identifiability of
the electrical problem allowing to reconstruct the electrical state of the
coupled system more precisely. Therefore, this work is intended to be a first
proof of concept, with theoretical justifications and numerical investigations,
of the ad-vantage of using available multi-modal observations for the
estimation and identification of an electromechanical model of the heart
Chaotic dynamics and the role of covariance inflation for reduced rank Kalman filters with model error
The ensemble Kalman filter and its variants have shown to be robust for data assimilation in high dimensional geophysical models, with localization, using ensembles of extremely small size relative to the model dimension. However, a reduced rank representation of the estimated covariance leaves a large dimensional complementary subspace unfiltered. Utilizing the dynamical properties of the filtration for the backward Lyapunov vectors, this paper explores a previously unexplained mechanism, providing a novel theoretical interpretation for the role of covariance inflation in ensemble-based Kalman filters. Our derivation of the forecast error evolution describes the dynamic upwelling of the unfiltered error from outside of the span of the anomalies into the filtered subspace. Analytical results for linear systems explicitly describe the mechanism for the upwelling, and the associated recursive Riccati equation for the forecast error, while nonlinear approximations are explored numerically
Spatio-angular Minimum-variance Tomographic Controller for Multi-Object Adaptive Optics systems
Multi-object astronomical adaptive-optics (MOAO) is now a mature wide-field
observation mode to enlarge the adaptive-optics-corrected field in a few
specific locations over tens of arc-minutes.
The work-scope provided by open-loop tomography and pupil conjugation is
amenable to a spatio-angular Linear-Quadratic Gaussian (SA-LQG) formulation
aiming to provide enhanced correction across the field with improved
performance over static reconstruction methods and less stringent computational
complexity scaling laws.
Starting from our previous work [1], we use stochastic time-progression
models coupled to approximate sparse measurement operators to outline a
suitable SA-LQG formulation capable of delivering near optimal correction.
Under the spatio-angular framework the wave-fronts are never explicitly
estimated in the volume,providing considerable computational savings on
10m-class telescopes and beyond.
We find that for Raven, a 10m-class MOAO system with two science channels,
the SA-LQG improves the limiting magnitude by two stellar magnitudes when both
Strehl-ratio and Ensquared-energy are used as figures of merit. The
sky-coverage is therefore improved by a factor of 5.Comment: 30 pages, 7 figures, submitted to Applied Optic
- …