22,217 research outputs found
Path sampling for particle filters with application to multi-target tracking
In recent work (arXiv:1006.3100v1), we have presented a novel approach for
improving particle filters for multi-target tracking. The suggested approach
was based on drift homotopy for stochastic differential equations. Drift
homotopy was used to design a Markov Chain Monte Carlo step which is appended
to the particle filter and aims to bring the particle filter samples closer to
the observations. In the current work, we present an alternative way to append
a Markov Chain Monte Carlo step to a particle filter to bring the particle
filter samples closer to the observations. Both current and previous approaches
stem from the general formulation of the filtering problem. We have used the
currently proposed approach on the problem of multi-target tracking for both
linear and nonlinear observation models. The numerical results show that the
suggested approach can improve significantly the performance of a particle
filter.Comment: Minor corrections, 23 pages, 8 figures. This is a companion paper to
arXiv:1006.3100v
Bayesian quantification for coherent anti-Stokes Raman scattering spectroscopy
We propose a Bayesian statistical model for analyzing coherent anti-Stokes
Raman scattering (CARS) spectra. Our quantitative analysis includes statistical
estimation of constituent line-shape parameters, underlying Raman signal,
error-corrected CARS spectrum, and the measured CARS spectrum. As such, this
work enables extensive uncertainty quantification in the context of CARS
spectroscopy. Furthermore, we present an unsupervised method for improving
spectral resolution of Raman-like spectra requiring little to no \textit{a
priori} information. Finally, the recently-proposed wavelet prism method for
correcting the experimental artefacts in CARS is enhanced by using
interpolation techniques for wavelets. The method is validated using CARS
spectra of adenosine mono-, di-, and triphosphate in water, as well as,
equimolar aqueous solutions of D-fructose, D-glucose, and their disaccharide
combination sucrose
Multiple object tracking using an automatic veriable-dimension particle filter
Object tracking through particle filtering has been widely addressed in recent years. However, most works assume a constant number of objects or utilize an external detector that monitors the entry or exit of objects in the scene. In this work, a novel tracking method based on particle filtering that is able to automatically track a variable number of objects is presented. As opposed to classical prior data assignment approaches, adaptation of tracks to the measurements is managed globally. Additionally, the designed particle filter is able to generate hypotheses on the presence of new objects in the scene, and to confirm or dismiss them by gradually adapting to the global observation. The method is especially suited for environments where traditional object detectors render noisy measurements and frequent artifacts, such as that given by a camera mounted on a vehicle, where it is proven to yield excellent results
A population Monte Carlo scheme with transformed weights and its application to stochastic kinetic models
This paper addresses the problem of Monte Carlo approximation of posterior
probability distributions. In particular, we have considered a recently
proposed technique known as population Monte Carlo (PMC), which is based on an
iterative importance sampling approach. An important drawback of this
methodology is the degeneracy of the importance weights when the dimension of
either the observations or the variables of interest is high. To alleviate this
difficulty, we propose a novel method that performs a nonlinear transformation
on the importance weights. This operation reduces the weight variation, hence
it avoids their degeneracy and increases the efficiency of the importance
sampling scheme, specially when drawing from a proposal functions which are
poorly adapted to the true posterior.
For the sake of illustration, we have applied the proposed algorithm to the
estimation of the parameters of a Gaussian mixture model. This is a very simple
problem that enables us to clearly show and discuss the main features of the
proposed technique. As a practical application, we have also considered the
popular (and challenging) problem of estimating the rate parameters of
stochastic kinetic models (SKM). SKMs are highly multivariate systems that
model molecular interactions in biological and chemical problems. We introduce
a particularization of the proposed algorithm to SKMs and present numerical
results.Comment: 35 pages, 8 figure
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
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