Smoothing, Filtering and Prediction
Smoothing, Filtering and Prediction

Author: Garry Einicke

Publisher: BoD – Books on Demand

Published: 2012-02-24

Total Pages: 290

ISBN-13: 9533077522

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This book describes the classical smoothing, filtering and prediction techniques together with some more recently developed embellishments for improving performance within applications. It aims to present the subject in an accessible way, so that it can serve as a practical guide for undergraduates and newcomers to the field. The material is organised as a ten-lecture course. The foundations are laid in Chapters 1 and 2, which explain minimum-mean-square-error solution construction and asymptotic behaviour. Chapters 3 and 4 introduce continuous-time and discrete-time minimum-variance filtering. Generalisations for missing data, deterministic inputs, correlated noises, direct feedthrough terms, output estimation and equalisation are described. Chapter 5 simplifies the minimum-variance filtering results for steady-state problems. Observability, Riccati equation solution convergence, asymptotic stability and Wiener filter equivalence are discussed. Chapters 6 and 7 cover the subject of continuous-time and discrete-time smoothing. The main fixed-lag, fixed-point and fixed-interval smoother results are derived. It is shown that the minimum-variance fixed-interval smoother attains the best performance. Chapter 8 attends to parameter estimation. As the above-mentioned approaches all rely on knowledge of the underlying model parameters, maximum-likelihood techniques within expectation-maximisation algorithms for joint state and parameter estimation are described. Chapter 9 is concerned with robust techniques that accommodate uncertainties within problem specifications. An extra term within Riccati equations enables designers to trade-off average error and peak error performance. Chapter 10 rounds off the course by applying the afore-mentioned linear techniques to nonlinear estimation problems. It is demonstrated that step-wise linearisations can be used within predictors, filters and smoothers, albeit by forsaking optimal performance guarantees.

Bayesian Filtering and Smoothing
Bayesian Filtering and Smoothing

Author: Simo Särkkä

Publisher: Cambridge University Press

Published: 2013-09-05

Total Pages: 255

ISBN-13: 110703065X

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A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.

Introduction to Data Science
Introduction to Data Science

Author: Rafael A. Irizarry

Publisher: CRC Press

Published: 2019-11-20

Total Pages: 836

ISBN-13: 1000708039

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Introduction to Data Science: Data Analysis and Prediction Algorithms with R introduces concepts and skills that can help you tackle real-world data analysis challenges. It covers concepts from probability, statistical inference, linear regression, and machine learning. It also helps you develop skills such as R programming, data wrangling, data visualization, predictive algorithm building, file organization with UNIX/Linux shell, version control with Git and GitHub, and reproducible document preparation. This book is a textbook for a first course in data science. No previous knowledge of R is necessary, although some experience with programming may be helpful. The book is divided into six parts: R, data visualization, statistics with R, data wrangling, machine learning, and productivity tools. Each part has several chapters meant to be presented as one lecture. The author uses motivating case studies that realistically mimic a data scientist’s experience. He starts by asking specific questions and answers these through data analysis so concepts are learned as a means to answering the questions. Examples of the case studies included are: US murder rates by state, self-reported student heights, trends in world health and economics, the impact of vaccines on infectious disease rates, the financial crisis of 2007-2008, election forecasting, building a baseball team, image processing of hand-written digits, and movie recommendation systems. The statistical concepts used to answer the case study questions are only briefly introduced, so complementing with a probability and statistics textbook is highly recommended for in-depth understanding of these concepts. If you read and understand the chapters and complete the exercises, you will be prepared to learn the more advanced concepts and skills needed to become an expert.

Forecasting: principles and practice
Forecasting: principles and practice

Author: Rob J Hyndman

Publisher: OTexts

Published: 2018-05-08

Total Pages: 380

ISBN-13: 0987507117

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Forecasting is required in many situations. Stocking an inventory may require forecasts of demand months in advance. Telecommunication routing requires traffic forecasts a few minutes ahead. Whatever the circumstances or time horizons involved, forecasting is an important aid in effective and efficient planning. This textbook provides a comprehensive introduction to forecasting methods and presents enough information about each method for readers to use them sensibly.

Optimal Filtering
Optimal Filtering

Author: Brian D. O. Anderson

Publisher: Courier Corporation

Published: 2012-05-23

Total Pages: 370

ISBN-13: 0486136892

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Graduate-level text extends studies of signal processing, particularly regarding communication systems and digital filtering theory. Topics include filtering, linear systems, and estimation; discrete-time Kalman filter; time-invariant filters; more. 1979 edition.

Bayesian Multiple Target Tracking, Second Edition
Bayesian Multiple Target Tracking, Second Edition

Author: Lawrence D. Stone

Publisher: Artech House

Published: 2013-12-01

Total Pages: 315

ISBN-13: 1608075532

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This second edition has undergone substantial revision from the 1999 first edition, recognizing that a lot has changed in the multiple target tracking field. One of the most dramatic changes is in the widespread use of particle filters to implement nonlinear, non-Gaussian Bayesian trackers. This book views multiple target tracking as a Bayesian inference problem. Within this framework it develops the theory of single target tracking, multiple target tracking, and likelihood ratio detection and tracking. In addition to providing a detailed description of a basic particle filter that implements the Bayesian single target recursion, this resource provides numerous examples that involve the use of particle filters. With these examples illustrating the developed concepts, algorithms, and approaches -- the book helps radar engineers develop tracking solutions when observations are non-linear functions of target state, when the target state distributions or measurement error distributions are not Gaussian, in low data rate and low signal to noise ratio situations, and when notions of contact and association are merged or unresolved among more than one target.

The Electrical Engineering Handbook,Second Edition
The Electrical Engineering Handbook,Second Edition

Author: Richard C. Dorf

Publisher: CRC Press

Published: 1997-09-26

Total Pages: 2758

ISBN-13: 9781420049763

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In 1993, the first edition of The Electrical Engineering Handbook set a new standard for breadth and depth of coverage in an engineering reference work. Now, this classic has been substantially revised and updated to include the latest information on all the important topics in electrical engineering today. Every electrical engineer should have an opportunity to expand his expertise with this definitive guide. In a single volume, this handbook provides a complete reference to answer the questions encountered by practicing engineers in industry, government, or academia. This well-organized book is divided into 12 major sections that encompass the entire field of electrical engineering, including circuits, signal processing, electronics, electromagnetics, electrical effects and devices, and energy, and the emerging trends in the fields of communications, digital devices, computer engineering, systems, and biomedical engineering. A compendium of physical, chemical, material, and mathematical data completes this comprehensive resource. Every major topic is thoroughly covered and every important concept is defined, described, and illustrated. Conceptually challenging but carefully explained articles are equally valuable to the practicing engineer, researchers, and students. A distinguished advisory board and contributors including many of the leading authors, professors, and researchers in the field today assist noted author and professor Richard Dorf in offering complete coverage of this rapidly expanding field. No other single volume available today offers this combination of broad coverage and depth of exploration of the topics. The Electrical Engineering Handbook will be an invaluable resource for electrical engineers for years to come.

Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with Engineering Applications
Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with Engineering Applications

Author: Norbert Wiener

Publisher: Martino Fine Books

Published: 2013-11

Total Pages: 174

ISBN-13: 9781614275176

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2013 Reprint of 1949 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. This is the second book by Norbert Wiener on time series and communication engineering. While the first one, "Cybernetics," treated the subject from a general standpoint and was more philosophical than mathematical, the present volume is more technical than theoretical, and forms a kind of companion piece to the first. It is intended as a tool for engineers working in the field of electrical communication and related subjects. The book consists of an introduction, five chapters, and three appendices. After explaining the general outline of the problem in the introduction, the author gives in Chapter I a review of generalized harmonic analysis which is necessary for the understanding of the following chapters. Chapters II and III are devoted to the problems of prediction and filtering respectively. In Chapter IV there is given a brief account of the theory of multiple prediction, that is, the theory of prediction when we deal with more than one time series at the same time. Finally, in Chapter V there is given a short discussion on the application of similar methods to a problem of approximate differentiation.

Stochastic Processes and Filtering Theory
Stochastic Processes and Filtering Theory

Author: Andrew H. Jazwinski

Publisher: Courier Corporation

Published: 2013-04-15

Total Pages: 404

ISBN-13: 0486318192

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This unified treatment of linear and nonlinear filtering theory presents material previously available only in journals, and in terms accessible to engineering students. Its sole prerequisites are advanced calculus, the theory of ordinary differential equations, and matrix analysis. Although theory is emphasized, the text discusses numerous practical applications as well. Taking the state-space approach to filtering, this text models dynamical systems by finite-dimensional Markov processes, outputs of stochastic difference, and differential equations. Starting with background material on probability theory and stochastic processes, the author introduces and defines the problems of filtering, prediction, and smoothing. He presents the mathematical solutions to nonlinear filtering problems, and he specializes the nonlinear theory to linear problems. The final chapters deal with applications, addressing the development of approximate nonlinear filters, and presenting a critical analysis of their performance.