5,217 research outputs found
Data Assimilation by Conditioning on Future Observations
Conventional recursive filtering approaches, designed for quantifying the
state of an evolving uncertain dynamical system with intermittent observations,
use a sequence of (i) an uncertainty propagation step followed by (ii) a step
where the associated data is assimilated using Bayes' rule. In this paper we
switch the order of the steps to: (i) one step ahead data assimilation followed
by (ii) uncertainty propagation. This route leads to a class of filtering
algorithms named \emph{smoothing filters}. For a system driven by random noise,
our proposed methods require the probability distribution of the driving noise
after the assimilation to be biased by a nonzero mean. The system noise,
conditioned on future observations, in turn pushes forward the filtering
solution in time closer to the true state and indeed helps to find a more
accurate approximate solution for the state estimation problem
Inverse Problems and Data Assimilation
These notes are designed with the aim of providing a clear and concise
introduction to the subjects of Inverse Problems and Data Assimilation, and
their inter-relations, together with citations to some relevant literature in
this area. The first half of the notes is dedicated to studying the Bayesian
framework for inverse problems. Techniques such as importance sampling and
Markov Chain Monte Carlo (MCMC) methods are introduced; these methods have the
desirable property that in the limit of an infinite number of samples they
reproduce the full posterior distribution. Since it is often computationally
intensive to implement these methods, especially in high dimensional problems,
approximate techniques such as approximating the posterior by a Dirac or a
Gaussian distribution are discussed. The second half of the notes cover data
assimilation. This refers to a particular class of inverse problems in which
the unknown parameter is the initial condition of a dynamical system, and in
the stochastic dynamics case the subsequent states of the system, and the data
comprises partial and noisy observations of that (possibly stochastic)
dynamical system. We will also demonstrate that methods developed in data
assimilation may be employed to study generic inverse problems, by introducing
an artificial time to generate a sequence of probability measures interpolating
from the prior to the posterior
The analog data assimilation
In light of growing interest in data-driven methods for oceanic, atmospheric, and climate sciences, this work focuses on the field of data assimilation and presents the analog data assimilation (AnDA). The proposed framework produces a reconstruction of the system dynamics in a fully data-driven manner where no explicit knowledge of the dynamical model is required. Instead, a representative catalog of trajectories of the system is assumed to be available. Based on this catalog, the analog data assimilation combines the nonparametric sampling of the dynamics using analog forecasting methods with ensemble-based assimilation techniques. This study explores different analog forecasting strategies and derives both ensemble Kalman and particle filtering versions of the proposed analog data assimilation approach. Numerical experiments are examined for two chaotic dynamical systems: the Lorenz-63 and Lorenz-96 systems. The performance of the analog data assimilation is discussed with respect to classical model-driven assimilation. A Matlab toolbox and Python library of the AnDA are provided to help further research building upon the present findings.Fil: Lguensat, Redouane. Université Bretagne Loire; FranciaFil: Tandeo, Pierre. Université Bretagne Loire; FranciaFil: Ailliot, Pierre. University of Western Brittany. Laboratoire de Mathématiques de Bretagne Atlantique; FranciaFil: Pulido, Manuel Arturo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Modelado e Innovación Tecnológica. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas Naturales y Agrimensura. Instituto de Modelado e Innovación Tecnológica; ArgentinaFil: Fablet, Ronan. Université Bretagne Loire; Franci
A Bayesian Consistent Dual Ensemble Kalman Filter for State-Parameter Estimation in Subsurface Hydrology
Ensemble Kalman filtering (EnKF) is an efficient approach to addressing
uncertainties in subsurface groundwater models. The EnKF sequentially
integrates field data into simulation models to obtain a better
characterization of the model's state and parameters. These are generally
estimated following joint and dual filtering strategies, in which, at each
assimilation cycle, a forecast step by the model is followed by an update step
with incoming observations. The Joint-EnKF directly updates the augmented
state-parameter vector while the Dual-EnKF employs two separate filters, first
estimating the parameters and then estimating the state based on the updated
parameters. In this paper, we reverse the order of the forecast-update steps
following the one-step-ahead (OSA) smoothing formulation of the Bayesian
filtering problem, based on which we propose a new dual EnKF scheme, the
Dual-EnKF. Compared to the Dual-EnKF, this introduces a new update
step to the state in a fully consistent Bayesian framework, which is shown to
enhance the performance of the dual filtering approach without any significant
increase in the computational cost. Numerical experiments are conducted with a
two-dimensional synthetic groundwater aquifer model to assess the performance
and robustness of the proposed Dual-EnKF, and to evaluate its
results against those of the Joint- and Dual-EnKFs. The proposed scheme is able
to successfully recover both the hydraulic head and the aquifer conductivity,
further providing reliable estimates of their uncertainties. Compared with the
standard Joint- and Dual-EnKFs, the proposed scheme is found more robust to
different assimilation settings, such as the spatial and temporal distribution
of the observations, and the level of noise in the data. Based on our
experimental setups, it yields up to 25% more accurate state and parameters
estimates
Data Assimilation: A Mathematical Introduction
These notes provide a systematic mathematical treatment of the subject of
data assimilation
Sequential Monte Carlo Methods for System Identification
One of the key challenges in identifying nonlinear and possibly non-Gaussian
state space models (SSMs) is the intractability of estimating the system state.
Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced
more than two decades ago), provide numerical solutions to the nonlinear state
estimation problems arising in SSMs. When combined with additional
identification techniques, these algorithms provide solid solutions to the
nonlinear system identification problem. We describe two general strategies for
creating such combinations and discuss why SMC is a natural tool for
implementing these strategies.Comment: In proceedings of the 17th IFAC Symposium on System Identification
(SYSID). Added cover pag
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