9,936 research outputs found
Kalman-Takens filtering in the presence of dynamical noise
The use of data assimilation for the merging of observed data with dynamical
models is becoming standard in modern physics. If a parametric model is known,
methods such as Kalman filtering have been developed for this purpose. If no
model is known, a hybrid Kalman-Takens method has been recently introduced, in
order to exploit the advantages of optimal filtering in a nonparametric
setting. This procedure replaces the parametric model with dynamics
reconstructed from delay coordinates, while using the Kalman update formulation
to assimilate new observations. We find that this hybrid approach results in
comparable efficiency to parametric methods in identifying underlying dynamics,
even in the presence of dynamical noise. By combining the Kalman-Takens method
with an adaptive filtering procedure we are able to estimate the statistics of
the observational and dynamical noise. This solves a long standing problem of
separating dynamical and observational noise in time series data, which is
especially challenging when no dynamical model is specified
Mathematical control of complex systems
Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
Particle filtering in high-dimensional chaotic systems
We present an efficient particle filtering algorithm for multiscale systems,
that is adapted for simple atmospheric dynamics models which are inherently
chaotic. Particle filters represent the posterior conditional distribution of
the state variables by a collection of particles, which evolves and adapts
recursively as new information becomes available. The difference between the
estimated state and the true state of the system constitutes the error in
specifying or forecasting the state, which is amplified in chaotic systems that
have a number of positive Lyapunov exponents. The purpose of the present paper
is to show that the homogenization method developed in Imkeller et al. (2011),
which is applicable to high dimensional multi-scale filtering problems, along
with important sampling and control methods can be used as a basic and flexible
tool for the construction of the proposal density inherent in particle
filtering. Finally, we apply the general homogenized particle filtering
algorithm developed here to the Lorenz'96 atmospheric model that mimics
mid-latitude atmospheric dynamics with microscopic convective processes.Comment: 28 pages, 12 figure
Stochastic reaction networks with input processes: Analysis and applications to reporter gene systems
Stochastic reaction network models are widely utilized in biology and
chemistry to describe the probabilistic dynamics of biochemical systems in
general, and gene interaction networks in particular. Most often, statistical
analysis and inference of these systems is addressed by parametric approaches,
where the laws governing exogenous input processes, if present, are themselves
fixed in advance. Motivated by reporter gene systems, widely utilized in
biology to monitor gene activation at the individual cell level, we address the
analysis of reaction networks with state-affine reaction rates and arbitrary
input processes. We derive a generalization of the so-called moment equations
where the dynamics of the network statistics are expressed as a function of the
input process statistics. In stationary conditions, we provide a spectral
analysis of the system and elaborate on connections with linear filtering. We
then apply the theoretical results to develop a method for the reconstruction
of input process statistics, namely the gene activation autocovariance
function, from reporter gene population snapshot data, and demonstrate its
performance on a simulated case study
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