Tracking with Particle Filter for High-dimensional Observation and State Spaces


Book Description

This title concerns the use of a particle filter framework to track objects defined in high-dimensional state-spaces using high-dimensional observation spaces. Current tracking applications require us to consider complex models for objects (articulated objects, multiple objects, multiple fragments, etc.) as well as multiple kinds of information (multiple cameras, multiple modalities, etc.). This book presents some recent research that considers the main bottleneck of particle filtering frameworks (high dimensional state spaces) for tracking in such difficult conditions.




Nonlinear Data Assimilation


Book Description

This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.




Theoretical Aspects of Spatial-Temporal Modeling


Book Description

This book provides a modern introductory tutorial on specialized theoretical aspects of spatial and temporal modeling. The areas covered involve a range of topics which reflect the diversity of this domain of research across a number of quantitative disciplines. For instance, the first chapter provides up-to-date coverage of particle association measures that underpin the theoretical properties of recently developed random set methods in space and time otherwise known as the class of probability hypothesis density framework (PHD filters). The second chapter gives an overview of recent advances in Monte Carlo methods for Bayesian filtering in high-dimensional spaces. In particular, the chapter explains how one may extend classical sequential Monte Carlo methods for filtering and static inference problems to high dimensions and big-data applications. The third chapter presents an overview of generalized families of processes that extend the class of Gaussian process models to heavy-tailed families known as alpha-stable processes. In particular, it covers aspects of characterization via the spectral measure of heavy-tailed distributions and then provides an overview of their applications in wireless communications channel modeling. The final chapter concludes with an overview of analysis for probabilistic spatial percolation methods that are relevant in the modeling of graphical networks and connectivity applications in sensor networks, which also incorporate stochastic geometry features.




Handbook of HydroInformatics


Book Description

Advanced Machine Learning Techniques includes the theoretical foundations of modern machine learning, as well as advanced methods and frameworks used in modern machine learning. Handbook of HydroInformatics, Volume II: Advanced Machine Learning Techniques presents both the art of designing good learning algorithms, as well as the science of analyzing an algorithm's computational and statistical properties and performance guarantees. The global contributors cover theoretical foundational topics such as computational and statistical convergence rates, minimax estimation, and concentration of measure as well as advanced machine learning methods, such as nonparametric density estimation, nonparametric regression, and Bayesian estimation; additionally, advanced frameworks such as privacy, causality, and stochastic learning algorithms are also included. Lastly, the volume presents Cloud and Cluster Computing, Data Fusion Techniques, Empirical Orthogonal Functions and Teleconnection, Internet of Things, Kernel-Based Modeling, Large Eddy Simulation, Patter Recognition, Uncertainty-Based Resiliency Evaluation, and Volume-Based Inverse Mode. This is an interdisciplinary book, and the audience includes postgraduates and early-career researchers interested in: Computer Science, Mathematical Science, Applied Science, Earth and Geoscience, Geography, Civil Engineering, Engineering, Water Science, Atmospheric Science, Social Science, Environment Science, Natural Resources, Chemical Engineering. - Key insights from 24 contributors in the fields of data management research, climate change and resilience, insufficient data problem, etc. - Offers applied examples and case studies in each chapter, providing the reader with real world scenarios for comparison. - Defines both the designing of good learning algorithms, as well as the science of analyzing an algorithm's computational and statistical properties and performance guarantees.




Data Assimilation for the Geosciences


Book Description

Data Assimilation for the Geosciences: From Theory to Application brings together all of the mathematical,statistical, and probability background knowledge needed to formulate data assimilation systems in one place. It includes practical exercises for understanding theoretical formulation and presents some aspects of coding the theory with a toy problem. The book also demonstrates how data assimilation systems are implemented in larger scale fluid dynamical problems related to the atmosphere, oceans, as well as the land surface and other geophysical situations. It offers a comprehensive presentation of the subject, from basic principles to advanced methods, such as Particle Filters and Markov-Chain Monte-Carlo methods. Additionally, Data Assimilation for the Geosciences: From Theory to Application covers the applications of data assimilation techniques in various disciplines of the geosciences, making the book useful to students, teachers, and research scientists. Includes practical exercises, enabling readers to apply concepts in a theoretical formulation Offers explanations for how to code certain parts of the theory Presents a step-by-step guide on how, and why, data assimilation works and can be used




Data Assimilation


Book Description

This book reviews popular data-assimilation methods, such as weak and strong constraint variational methods, ensemble filters and smoothers. The author shows how different methods can be derived from a common theoretical basis, as well as how they differ or are related to each other, and which properties characterize them, using several examples. Readers will appreciate the included introductory material and detailed derivations in the text, and a supplemental web site.




Filtering Complex Turbulent Systems


Book Description

The authors develop a systematic applied mathematics perspective on the problems associated with filtering complex turbulent systems. The book contains background material from filtering, turbulence theory and numerical analysis, making it suitable for graduate courses as well as for researchers in a range of disciplines where applied mathematics is required.




Modeling, Stochastic Control, Optimization, and Applications


Book Description

This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.




Advanced Concepts for Intelligent Vision Systems


Book Description

This book constitutes the refereed proceedings of the 13th International Conference on Advanced Concepts for Intelligent Vision Systems, ACIVS 2011, held in Ghent, Belgium, in August 2011. The 66 revised full papers presented were carefully reviewed and selected from 124 submissions. The papers are organized in topical sections on classification recognition, and tracking, segmentation, images analysis, image processing, video surveillance and biometrics, algorithms and optimization; and 3D, depth and scene understanding.




Sequential Monte Carlo Methods in Practice


Book Description

Monte Carlo methods are revolutionizing the on-line analysis of data in many fileds. They have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques.