128 research outputs found
An Ensemble Kalman-Particle Predictor-Corrector Filter for Non-Gaussian Data Assimilation
An Ensemble Kalman Filter (EnKF, the predictor) is used make a large change
in the state, followed by a Particle Filer (PF, the corrector) which assigns
importance weights to describe non-Gaussian distribution. The weights are
obtained by nonparametric density estimation. It is demonstrated on several
numerical examples that the new predictor-corrector filter combines the
advantages of the EnKF and the PF and that it is suitable for high dimensional
states which are discretizations of solutions of partial differential
equations.Comment: ICCS 2009, to appear; 9 pages; minor edit
Bridging the ensemble Kalman and particle filter
In many applications of Monte Carlo nonlinear filtering, the propagation step
is computationally expensive, and hence, the sample size is limited. With small
sample sizes, the update step becomes crucial. Particle filtering suffers from
the well-known problem of sample degeneracy. Ensemble Kalman filtering avoids
this, at the expense of treating non-Gaussian features of the forecast
distribution incorrectly. Here we introduce a procedure which makes a
continuous transition indexed by gamma in [0,1] between the ensemble and the
particle filter update. We propose automatic choices of the parameter gamma
such that the update stays as close as possible to the particle filter update
subject to avoiding degeneracy. In various examples, we show that this
procedure leads to updates which are able to handle non-Gaussian features of
the prediction sample even in high-dimensional situations
Deterministic Mean-field Ensemble Kalman Filtering
The proof of convergence of the standard ensemble Kalman filter (EnKF) from
Legland etal. (2011) is extended to non-Gaussian state space models. A
density-based deterministic approximation of the mean-field limit EnKF
(DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given
a certain minimal order of convergence between the two, this extends
to the deterministic filter approximation, which is therefore asymptotically
superior to standard EnKF when the dimension . The fidelity of
approximation of the true distribution is also established using an extension
of total variation metric to random measures. This is limited by a Gaussian
bias term arising from non-linearity/non-Gaussianity of the model, which exists
for both DMFEnKF and standard EnKF. Numerical results support and extend the
theory
Health monitoring for strongly non‐linear systems using the Ensemble Kalman filter
Many structural engineering problems of practical interest involve pronounced non-linear dynamics the governing laws of which are not always clearly understood. Standard identification and damage detection techniques have difficulties in these situations which feature significant modelling errors and strongly non-Gaussian signals. This paper presents a combination of the ensemble Kalman filter and non-parametric modelling techniques to tackle structural health monitoring for non-linear systems in a manner that can readily accommodate the presence of non-Gaussian noise. Both location and time of occurrence of damage are accurately detected in spite of measurement and modelling noise. A comparison between ensemble and extended Kalman filters is also presented, highlighting the benefits of the present approach. Copyright © 2005 John Wiley & Sons, Ltd
Bridging the ensemble Kalman and particle filters
In many applications of Monte Carlo nonlinear filtering, the propagation step is computationally expensive, and hence the sample size is limited. With small sample sizes, the update step becomes crucial. Particle filtering suffers from the well-known problem of sample degeneracy. Ensemble Kalman filtering avoids this, at the expense of treating non-Gaussian features of the forecast distribution incorrectly. Here we introduce a procedure that makes a continuous transition indexed by γ∈[0,1] between the ensemble and the particle filter update. We propose automatic choices of the parameter γ such that the update stays as close as possible to the particle filter update subject to avoiding degeneracy. In various examples, we show that this procedure leads to updates that are able to handle non-Gaussian features of the forecast sample even in high-dimensional situation
Score-based Data Assimilation
Data assimilation, in its most comprehensive form, addresses the Bayesian
inverse problem of identifying plausible state trajectories that explain noisy
or incomplete observations of stochastic dynamical systems. Various approaches
have been proposed to solve this problem, including particle-based and
variational methods. However, most algorithms depend on the transition dynamics
for inference, which becomes intractable for long time horizons or for
high-dimensional systems with complex dynamics, such as oceans or atmospheres.
In this work, we introduce score-based data assimilation for trajectory
inference. We learn a score-based generative model of state trajectories based
on the key insight that the score of an arbitrarily long trajectory can be
decomposed into a series of scores over short segments. After training,
inference is carried out using the score model, in a non-autoregressive manner
by generating all states simultaneously. Quite distinctively, we decouple the
observation model from the training procedure and use it only at inference to
guide the generative process, which enables a wide range of zero-shot
observation scenarios. We present theoretical and empirical evidence supporting
the effectiveness of our method
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