6,604 research outputs found

    Tracking interacting dust: comparison of tracking and state estimation techniques for dusty plasmas

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    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

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    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

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    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

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    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 κ\kappa between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF when the dimension d<2κd<2\kappa. 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
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