6,604 research outputs found
Tracking interacting dust: comparison of tracking and state estimation techniques for dusty plasmas
When tracking a target particle that is interacting with nearest neighbors in
a known way, positional data of the neighbors can be used to improve the state
estimate. Effects of the accuracy of such positional data on the target track
accuracy are investigated in this paper, in the context of dusty plasmas. In
kinematic simulations, notable improvement in the target track accuracy was
found when including all nearest neighbors in the state estimation filter and
tracking algorithm, whereas the track accuracy was not significantly improved
by higher-accuracy measurement techniques. The state estimation algorithm,
involving an extended Kalman filter, was shown to either remove or
significantly reduce errors due to "pixel locking". It is concluded that the
significant extra complexity and computational expense to achieve these
relatively small improvements are likely to be unwarranted for many situations.
For the purposes of determining the precise particle locations, it is concluded
that the simplified state estimation algorithm can be a viable alternative to
using more computationally-intensive measurement techniques.Comment: 11 pages, 6 figures, Conference paper: Signal and Data Processing of
Small Targets 2010 (SPIE
Inverse Problems and Data Assimilation
These notes are designed with the aim of providing a clear and concise
introduction to the subjects of Inverse Problems and Data Assimilation, and
their inter-relations, together with citations to some relevant literature in
this area. The first half of the notes is dedicated to studying the Bayesian
framework for inverse problems. Techniques such as importance sampling and
Markov Chain Monte Carlo (MCMC) methods are introduced; these methods have the
desirable property that in the limit of an infinite number of samples they
reproduce the full posterior distribution. Since it is often computationally
intensive to implement these methods, especially in high dimensional problems,
approximate techniques such as approximating the posterior by a Dirac or a
Gaussian distribution are discussed. The second half of the notes cover data
assimilation. This refers to a particular class of inverse problems in which
the unknown parameter is the initial condition of a dynamical system, and in
the stochastic dynamics case the subsequent states of the system, and the data
comprises partial and noisy observations of that (possibly stochastic)
dynamical system. We will also demonstrate that methods developed in data
assimilation may be employed to study generic inverse problems, by introducing
an artificial time to generate a sequence of probability measures interpolating
from the prior to the posterior
Gamma-Rays from Intergalactic Shocks
Structure formation in the intergalactic medium (IGM) produces large-scale,
collisionless shock waves, where electrons can accelerate to highly
relativistic energies. Such electrons can Compton scatter cosmic microwave
background photons up to gamma-ray energies. We study the radiation emitted in
this process using a hydrodynamic cosmological simulation of a LCDM universe.
This radiation, extending beyond TeV energies, has roughly constant energy flux
per decade in photon energy, in agreement with the predictions of Loeb & Waxman
(2000). Assuming that a fraction xi_e=0.05 of the shock thermal energy is
transferred to relativistic electrons, as inferred from collisionless
non-relativistic shocks in the interstellar medium, we find that the radiation
energy flux, e^2(dJ/de)~ 50-160 eV cm^-2 s^-1 sr^-1, constitutes ~10% of the
extragalactic gamma-ray background. The associated point-sources are too faint
to account for the ~60 unidentified EGRET gamma-ray sources, but GLAST should
resolve several sources associated with large-scale IGM structures for
xi_e~0.03, and many more sources for larger xi_e. The intergalactic origin of
the radiation can be verified through a cross-correlation with, e.g., the
galaxy distribution that traces the same structure. Its shock-origin may be
tested by a cross-correlation with radio synchrotron radiation, emitted as the
same electrons gyrate in post-shock magnetic fields. We predict that GLAST and
Cherenkov telescopes such as MAGIC, VERITAS and HESS should resolve gamma-rays
from nearby (redshifts z < 0.01) rich galaxy clusters, perhaps in the form of a
\~5-10 Mpc diameter ring-like emission tracing the cluster accretion shock,
with luminous peaks at its intersections with galaxy filaments detectable even
at z~0.025.Comment: 55 pages, 13 figures, accepted ApJ, added discussion to clarify some
points, for high resolution:
http://www.weizmann.ac.il/~keshet/IGM_Shocks.htm
Deterministic Mean-field Ensemble Kalman Filtering
The proof of convergence of the standard ensemble Kalman filter (EnKF) from
Legland etal. (2011) is extended to non-Gaussian state space models. A
density-based deterministic approximation of the mean-field limit EnKF
(DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given
a certain minimal order of convergence between the two, this extends
to the deterministic filter approximation, which is therefore asymptotically
superior to standard EnKF when the dimension . The fidelity of
approximation of the true distribution is also established using an extension
of total variation metric to random measures. This is limited by a Gaussian
bias term arising from non-linearity/non-Gaussianity of the model, which exists
for both DMFEnKF and standard EnKF. Numerical results support and extend the
theory
- …