473 research outputs found
Scaled unscented transform Gaussian sum filter: theory and application
In this work we consider the state estimation problem in
nonlinear/non-Gaussian systems. We introduce a framework, called the scaled
unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas:
the scaled unscented Kalman filter (SUKF) based on the concept of scaled
unscented transform (SUT), and the Gaussian mixture model (GMM). The SUT is
used to approximate the mean and covariance of a Gaussian random variable which
is transformed by a nonlinear function, while the GMM is adopted to approximate
the probability density function (pdf) of a random variable through a set of
Gaussian distributions. With these two tools, a framework can be set up to
assimilate nonlinear systems in a recursive way. Within this framework, one can
treat a nonlinear stochastic system as a mixture model of a set of sub-systems,
each of which takes the form of a nonlinear system driven by a known Gaussian
random process. Then, for each sub-system, one applies the SUKF to estimate the
mean and covariance of the underlying Gaussian random variable transformed by
the nonlinear governing equations of the sub-system. Incorporating the
estimations of the sub-systems into the GMM gives an explicit (approximate)
form of the pdf, which can be regarded as a "complete" solution to the state
estimation problem, as all of the statistical information of interest can be
obtained from the explicit form of the pdf ...
This work is on the construction of the Gaussian sum filter based on the
scaled unscented transform
Truncated Moment Problem for Dirac Mixture Densities with Entropy Regularization
We assume that a finite set of moments of a random vector is given. Its
underlying density is unknown. An algorithm is proposed for efficiently
calculating Dirac mixture densities maintaining these moments while providing a
homogeneous coverage of the state space.Comment: 18 pages, 6 figure
On particle filters applied to electricity load forecasting
We are interested in the online prediction of the electricity load, within
the Bayesian framework of dynamic models. We offer a review of sequential Monte
Carlo methods, and provide the calculations needed for the derivation of
so-called particles filters. We also discuss the practical issues arising from
their use, and some of the variants proposed in the literature to deal with
them, giving detailed algorithms whenever possible for an easy implementation.
We propose an additional step to help make basic particle filters more robust
with regard to outlying observations. Finally we use such a particle filter to
estimate a state-space model that includes exogenous variables in order to
forecast the electricity load for the customers of the French electricity
company \'Electricit\'e de France and discuss the various results obtained
Nonlinear Gaussian Filtering : Theory, Algorithms, and Applications
By restricting to Gaussian distributions, the optimal Bayesian filtering problem can be transformed into an algebraically simple form, which allows for computationally efficient algorithms. Three problem settings are discussed in this thesis: (1) filtering with Gaussians only, (2) Gaussian mixture filtering for strong nonlinearities, (3) Gaussian process filtering for purely data-driven scenarios. For each setting, efficient algorithms are derived and applied to real-world problems
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