988 research outputs found
Surrogate Test to Distinguish between Chaotic and Pseudoperiodic Time Series
In this communication a new algorithm is proposed to produce surrogates for
pseudoperiodic time series. By imposing a few constraints on the noise
components of pseudoperiodic data sets, we devise an effective method to
generate surrogates. Unlike other algorithms, this method properly copes with
pseudoperiodic orbits contaminated with linear colored observational noise. We
will demonstrate the ability of this algorithm to distinguish chaotic orbits
from pseudoperiodic orbits through simulation data sets from theR\"{o}ssler
system. As an example of application of this algorithm, we will also employ it
to investigate a human electrocardiogram (ECG) record.Comment: Accepted version, to appear in Phys. Rev.
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
Recursive Bayesian Filters for Data Assimilation
A thesis on some recursive Bayesian filters for data assimilatio
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