1,095 research outputs found
Data assimilation in the low noise regime with application to the Kuroshio
On-line data assimilation techniques such as ensemble Kalman filters and
particle filters lose accuracy dramatically when presented with an unlikely
observation. Such an observation may be caused by an unusually large
measurement error or reflect a rare fluctuation in the dynamics of the system.
Over a long enough span of time it becomes likely that one or several of these
events will occur. Often they are signatures of the most interesting features
of the underlying system and their prediction becomes the primary focus of the
data assimilation procedure. The Kuroshio or Black Current that runs along the
eastern coast of Japan is an example of such a system. It undergoes infrequent
but dramatic changes of state between a small meander during which the current
remains close to the coast of Japan, and a large meander during which it bulges
away from the coast. Because of the important role that the Kuroshio plays in
distributing heat and salinity in the surrounding region, prediction of these
transitions is of acute interest. Here we focus on a regime in which both the
stochastic forcing on the system and the observational noise are small. In this
setting large deviation theory can be used to understand why standard filtering
methods fail and guide the design of the more effective data assimilation
techniques. Motivated by our analysis we propose several data assimilation
strategies capable of efficiently handling rare events such as the transitions
of the Kuroshio. These techniques are tested on a model of the Kuroshio and
shown to perform much better than standard filtering methods.Comment: 43 pages, 12 figure
An information field theory approach to Bayesian state and parameter estimation in dynamical systems
Dynamical system state estimation and parameter calibration problems are
ubiquitous across science and engineering. Bayesian approaches to the problem
are the gold standard as they allow for the quantification of uncertainties and
enable the seamless fusion of different experimental modalities. When the
dynamics are discrete and stochastic, one may employ powerful techniques such
as Kalman, particle, or variational filters. Practitioners commonly apply these
methods to continuous-time, deterministic dynamical systems after discretizing
the dynamics and introducing fictitious transition probabilities. However,
approaches based on time-discretization suffer from the curse of dimensionality
since the number of random variables grows linearly with the number of
time-steps. Furthermore, the introduction of fictitious transition
probabilities is an unsatisfactory solution because it increases the number of
model parameters and may lead to inference bias. To address these drawbacks,
the objective of this paper is to develop a scalable Bayesian approach to state
and parameter estimation suitable for continuous-time, deterministic dynamical
systems. Our methodology builds upon information field theory. Specifically, we
construct a physics-informed prior probability measure on the function space of
system responses so that functions that satisfy the physics are more likely.
This prior allows us to quantify model form errors. We connect the system's
response to observations through a probabilistic model of the measurement
process. The joint posterior over the system responses and all parameters is
given by Bayes' rule. To approximate the intractable posterior, we develop a
stochastic variational inference algorithm. In summary, the developed
methodology offers a powerful framework for Bayesian estimation in dynamical
systems
Enhanced particle PHD filtering for multiple human tracking
PhD ThesisVideo-based single human tracking has found wide application but multiple
human tracking is more challenging and enhanced processing techniques are
required to estimate the positions and number of targets in each frame. In
this thesis, the particle probability hypothesis density (PHD) lter is therefore
the focus due to its ability to estimate both localization and cardinality
information related to multiple human targets. To improve the tracking performance
of the particle PHD lter, a number of enhancements are proposed.
The Student's-t distribution is employed within the state and measurement
models of the PHD lter to replace the Gaussian distribution because
of its heavier tails, and thereby better predict particles with larger amplitudes.
Moreover, the variational Bayesian approach is utilized to estimate
the relationship between the measurement noise covariance matrix and the
state model, and a joint multi-dimensioned Student's-t distribution is exploited.
In order to obtain more observable measurements, a backward retrodiction
step is employed to increase the measurement set, building upon the
concept of a smoothing algorithm. To make further improvement, an adaptive
step is used to combine the forward ltering and backward retrodiction
ltering operations through the similarities of measurements achieved over
discrete time. As such, the errors in the delayed measurements generated by
false alarms and environment noise are avoided.
In the nal work, information describing human behaviour is employed
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Abstract v
to aid particle sampling in the prediction step of the particle PHD lter,
which is captured in a social force model. A novel social force model is
proposed based on the exponential function. Furthermore, a Markov Chain
Monte Carlo (MCMC) step is utilized to resample the predicted particles,
and the acceptance ratio is calculated by the results from the social force
model to achieve more robust prediction. Then, a one class support vector
machine (OCSVM) is applied in the measurement model of the PHD lter,
trained on human features, to mitigate noise from the environment and to
achieve better tracking performance.
The proposed improvements of the particle PHD lters are evaluated
with benchmark datasets such as the CAVIAR, PETS2009 and TUD datasets
and assessed with quantitative and global evaluation measures, and are compared
with state-of-the-art techniques to con rm the improvement of multiple
human tracking performance
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