INVESTIGADORES
LUCINI Maria magdalena
congresos y reuniones científicas
Título:
Estimation of Model Error Covariances for nonlinear dynamical systems using Particle Filters and the Expectation-Maximization algorithm'
Autor/es:
LUCINI MARIA MAGDALENA; VAN LEEWUEN, PETER JAN; PULIDO, MANUEL ARTURO
Reunión:
Conferencia; National Earth Observation Conference, NCEP,; 2018
Resumen:
Model error covariances play a central role in the perfomance of particle filters applied to nonlinearstate-space models.However, these covariances are largely unknown in most of the applications,including models used in geophysics and engineering.In this work, we propose the combination of the Expectation-Maximization algorithm (EM) with anefficient particle filter to estimate the model error covariance. A batch of observations is used to findthe elements of this model error covariance.Since the relation between the observations and the model error covariance is via the evolving stateof the system under this covariance matrix, this is a complicated problem. Based on the EM algorithmprinciples, the proposed solution method encompasses two stages: the expectation stage, in which aparticle filter is used with the present estimate of the model error covariance as given to find theprobability density function that maximizes the likelihood of the observations, followed by amaximization stage in which this expectation is maximized as function of the elements of the modelerror covariance. Since the problem is highly nonlinear an analytical solution for this maximum cannotbe found.This methodology shows to be converging towards true model error covariances in twin experimentsusing the Lorenz-96 system, but at different rates and with different accuracies depending on systemparameters. We explore the causes for these differences and discuss application to high-dimensionalsystems.