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Implicit particle filters for data assimilation  [PDF]
Alexandre J. Chorin,Matthias Morzfeld,Xuemin Tu
Mathematics , 2010,
Abstract: Implicit particle filters for data assimilation update the particles by first choosing probabilities and then looking for particle locations that assume them, guiding the particles one by one to the high probability domain. We provide a detailed description of these filters, with illustrative examples, together with new, more general, methods for solving the algebraic equations and with a new algorithm for parameter identification.
Implicit particle methods and their connection with variational data assimilation  [PDF]
Ethan Atkins,Matthias Morzfeld,Alexandre J. Chorin
Physics , 2012,
Abstract: The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. We present a new and more general derivation of this approach and extend the method to particle smoothing as well as to data assimilation for perfect models. We show that the minimizations required by implicit particle methods are similar to the ones one encounters in variational data assimilation and explore the connection of implicit particle methods with variational data assimilation. In particular, we argue that existing variational codes can be converted into implicit particle methods at a low cost, often yielding better estimates, that are also equipped with quantitative measures of the uncertainty. A detailed example is presented.
An Efficient Meshfreee Implicit Filter for Nonlinear Filtering Problems  [PDF]
Feng Bao,Yanzhao Cao,Clayton Webster,Guannan Zhang
Mathematics , 2015,
Abstract: In this paper, we propose a meshfree approximation method for the implicit filter developed in [2], which is a novel numerical algorithm for nonlinear filtering problems. The implicit filter approximates conditional distributions in the optimal filter over a deterministic state space grid and is developed from samples of the current state obtained by solving the state equation implicitly. The purpose of the meshfree approximation is to improve the efficiency of the implicit filter in moderately high-dimensional problems. The construction of the algorithm includes generation of random state space points and a meshfree interpolation method. Numerical experiments show the effectiveness and efficiency of our algorithm.
Small-noise analysis and symmetrization of implicit Monte Carlo samplers  [PDF]
Jonathan Goodman,Kevin K. Lin,Matthias Morzfeld
Statistics , 2014,
Abstract: Implicit samplers are algorithms for producing independent, weighted samples from multi-variate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two implicit samplers in the small noise regime. Our analysis suggests a symmetrization of the algo- rithms that leads to improved (implicit) sampling schemes at a rel- atively small additional cost. Computational experiments confirm the theory and show that symmetrization is effective for small noise sampling problems.
Data Assimilation by Conditioning on Future Observations  [PDF]
Wonjung Lee,Chris Farmer
Mathematics , 2013, DOI: 10.1109/TSP.2014.2330807
Abstract: Conventional recursive filtering approaches, designed for quantifying the state of an evolving uncertain dynamical system with intermittent observations, use a sequence of (i) an uncertainty propagation step followed by (ii) a step where the associated data is assimilated using Bayes' rule. In this paper we switch the order of the steps to: (i) one step ahead data assimilation followed by (ii) uncertainty propagation. This route leads to a class of filtering algorithms named \emph{smoothing filters}. For a system driven by random noise, our proposed methods require the probability distribution of the driving noise after the assimilation to be biased by a nonzero mean. The system noise, conditioned on future observations, in turn pushes forward the filtering solution in time closer to the true state and indeed helps to find a more accurate approximate solution for the state estimation problem.
An adaptive estimation of forecast error covariance parameters for Kalman filtering data assimilation

Xiaogu Zheng,

大气科学进展 , 2009,
Abstract: An adaptive estimation of forecast error covariance matrices is proposed for Kalman filtering data assimilation. A forecast error covariance matrix is initially estimated using an ensemble of perturbation forecasts. This initially estimated matrix is then adjusted with scale parameters that are adaptively estimated by minimizing -2log-likelihood of observed-minus-forecast residuals. The proposed approach could be applied to Kalman filtering data assimilation with imperfect models when the model error statistics are not known. A simple nonlinear model (Burgers' equation model) is used to demonstrate the efficacy of the proposed approach.
Information Filtering via Implicit Trust-based Network  [PDF]
Zhao-Guo Xuan,Zhan Li,Jian-Guo Liu
Computer Science , 2011,
Abstract: Based on the user-item bipartite network, collaborative filtering (CF) recommender systems predict users' interests according to their history collections, which is a promising way to solve the information exploration problem. However, CF algorithm encounters cold start and sparsity problems. The trust-based CF algorithm is implemented by collecting the users' trust statements, which is time-consuming and must use users' private friendship information. In this paper, we present a novel measurement to calculate users' implicit trust-based correlation by taking into account their average ratings, rating ranges, and the number of common rated items. By applying the similar idea to the items, a item-based CF algorithm is constructed. The simulation results on three benchmark data sets show that the performances of both user-based and item-based algorithms could be enhanced greatly. Finally, a hybrid algorithm is constructed by integrating the user-based and item-based algorithms, the simulation results indicate that hybrid algorithm outperforms the state-of-the-art methods. Specifically, it can not only provide more accurate recommendations, but also alleviate the cold start problem.
A case for variational geomagnetic data assimilation: insights from a one-dimensional, nonlinear, and sparsely observed MHD system
A. Fournier,C. Eymin,T. Alboussière
Nonlinear Processes in Geophysics (NPG) , 2007,
Abstract: Secular variations of the geomagnetic field have been measured with a continuously improving accuracy during the last few hundred years, culminating nowadays with satellite data. It is however well known that the dynamics of the magnetic field is linked to that of the velocity field in the core and any attempt to model secular variations will involve a coupled dynamical system for magnetic field and core velocity. Unfortunately, there is no direct observation of the velocity. Independently of the exact nature of the above-mentioned coupled system – some version being currently under construction – the question is debated in this paper whether good knowledge of the magnetic field can be translated into good knowledge of core dynamics. Furthermore, what will be the impact of the most recent and precise geomagnetic data on our knowledge of the geomagnetic field of the past and future? These questions are cast into the language of variational data assimilation, while the dynamical system considered in this paper consists in a set of two oversimplified one-dimensional equations for magnetic and velocity fields. This toy model retains important features inherited from the induction and Navier-Stokes equations: non-linear magnetic and momentum terms are present and its linear response to small disturbances contains Alfvén waves. It is concluded that variational data assimilation is indeed appropriate in principle, even though the velocity field remains hidden at all times; it allows us to recover the entire evolution of both fields from partial and irregularly distributed information on the magnetic field. This work constitutes a first step on the way toward the reassimilation of historical geomagnetic data and geomagnetic forecast.
A case for variational geomagnetic data assimilation: insights from a one-dimensional, nonlinear, and sparsely observed MHD system  [PDF]
Alexandre Fournier,Céline Eymin,Thierry Alboussière
Physics , 2007, DOI: 10.5194/npg-14-163-2007
Abstract: Secular variations of the geomagnetic field have been measured with a continuously improving accuracy during the last few hundred years, culminating nowadays with satellite data. It is however well known that the dynamics of the magnetic field is linked to that of the velocity field in the core and any attempt to model secular variations will involve a coupled dynamical system for magnetic field and core velocity. Unfortunately, there is no direct observation of the velocity. Independently of the exact nature of the above-mentioned coupled system -- some version being currently under construction -- the question is debated in this paper whether good knowledge of the magnetic field can be translated into good knowledge of core dynamics. Furthermore, what will be the impact of the most recent and precise geomagnetic data on our knowledge of the geomagnetic field of the past and future? These questions are cast into the language of variational data assimilation, while the dynamical system considered in this paper consists in a set of two oversimplified one-dimensional equations for magnetic and velocity fields. This toy model retains important features inherited from the induction and Navier-Stokes equations: non-linear magnetic and momentum terms are present and its linear response to small disturbances contains Alfv\'en waves. It is concluded that variational data assimilation is indeed appropriate in principle, even though the velocity field remains hidden at all times; it allows us to recover the entire evolution of both fields from partial and irregularly distributed information on the magnetic field. This work constitutes a first step on the way toward the reassimilation of historical geomagnetic data and geomagnetic forecast.
Cluster assimilation and collisional filtering on metal-oxide surfaces  [PDF]
Daniel A. Freedman,T. A. Arias
Physics , 2006,
Abstract: We present the first ab initio molecular dynamics study of collisions between metal-oxide clusters and surfaces. The resulting trajectories reveal that the internal degrees of freedom of the cluster play a defining role in collision outcome. The phase space of incoming internal temperature and translational energy exhibits regions where the collision process itself ensures that each cluster which does not rebound from the surface assimilates seamlessly onto it upon impact. This filtering may explain recent observations of a "fast smoothing mechanism" during pulsed laser deposition.
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