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Author: Garry Einicke
Publisher: Myidentifiers - Australian ISBN Agency
ISBN: 9780648511519
Category : Education
Languages : en
Pages : 380
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Book Description
Scientists, engineers and the like are a strange lot. Unperturbed by societal norms, they direct their energies to finding better alternatives to existing theories and concocting solutions to unsolved problems. Driven by an insatiable curiosity, they record their observations and crunch the numbers. This tome is about the science of crunching. It's about digging out something of value from the detritus that others tend to leave behind. The described approaches involve constructing models to process the available data. Smoothing entails revisiting historical records in an endeavour to understand something of the past. Filtering refers to estimating what is happening currently, whereas prediction is concerned with hazarding a guess about what might happen next. 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 an eleven-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 applies 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. Chapter 11 rounds off the course by exploiting knowledge about transition probabilities. HMM and minimum-variance-HMM filters and smoothers are derived. The improved performance offered by these techniques needs to be reconciled against the significantly higher calculation overheads.
Author: Garry Einicke
Publisher: Myidentifiers - Australian ISBN Agency
ISBN: 9780648511519
Category : Education
Languages : en
Pages : 380
Get Book Here
Book Description
Scientists, engineers and the like are a strange lot. Unperturbed by societal norms, they direct their energies to finding better alternatives to existing theories and concocting solutions to unsolved problems. Driven by an insatiable curiosity, they record their observations and crunch the numbers. This tome is about the science of crunching. It's about digging out something of value from the detritus that others tend to leave behind. The described approaches involve constructing models to process the available data. Smoothing entails revisiting historical records in an endeavour to understand something of the past. Filtering refers to estimating what is happening currently, whereas prediction is concerned with hazarding a guess about what might happen next. 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 an eleven-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 applies 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. Chapter 11 rounds off the course by exploiting knowledge about transition probabilities. HMM and minimum-variance-HMM filters and smoothers are derived. The improved performance offered by these techniques needs to be reconciled against the significantly higher calculation overheads.
Author: Garry Einicke
Publisher: BoD – Books on Demand
ISBN: 9533077522
Category : Computers
Languages : en
Pages : 290
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Book Description
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.
Author: Jeremy Weissberg
Publisher:
ISBN: 9781681176062
Category :
Languages : en
Pages : 280
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Book Description
Smoothing is often used to reduce noise within an image or to produce a less pixelated image. Most smoothing methods are based on low pass filters. Smoothing is also usually based on a single value representing the image, such as the average value of the image or the middle (median) value. In image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. In smoothing, the data points of a signal are modified so individual points (presumably because of noise) are reduced, and points that are lower than the adjacent points are increased leading to a smoother signal. Smoothing may be used in two important ways that can aid in data analysis; by being able to extract more information from the data as long as the assumption of smoothing is reasonable and; by being able to provide analyses that are both flexible and robust. Filtering and prediction is about observing moving objects when the observations are corrupted by random errors. Smoothing, Filtering and Prediction - Estimating The Past, Present and Future 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.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Simo Särkkä
Publisher: Cambridge University Press
ISBN: 1108912303
Category : Mathematics
Languages : en
Pages : 438
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Book Description
Now in its second edition, this accessible text presents a unified Bayesian treatment of state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models. The book focuses on discrete-time state space models and carefully introduces fundamental aspects related to optimal filtering and smoothing. In particular, it covers a range of efficient non-linear Gaussian filtering and smoothing algorithms, as well as Monte Carlo-based algorithms. This updated edition features new chapters on constructing state space models of practical systems, the discretization of continuous-time state space models, Gaussian filtering by enabling approximations, posterior linearization filtering, and the corresponding smoothers. Coverage of key topics is expanded, including extended Kalman filtering and smoothing, and parameter estimation. The book's practical, algorithmic approach assumes only modest mathematical prerequisites, suitable for graduate and advanced undergraduate students. Many examples are included, with Matlab and Python code available online, enabling readers to implement algorithms in their own projects.
Author: Graham Eanes
Publisher:
ISBN: 9781632384508
Category :
Languages : en
Pages : 0
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Book Description
A descriptive account based on the theory as well as principles of smoothing, filtering and prediction techniques has been presented in this book. It aims to provide understanding of classical filtering, prediction techniques and smoothing techniques along with newly developed embellishments for enhancing performance in applications. It describes the domain in a vivid manner for the purpose of serving as a valuable guide for students as well as experts. It extensively discusses minimum-mean-square-error solution construction and asymptotic behavior, continuous-time and discrete-time minimum-variance filtering, minimum-variance filtering results for steady-state problems and continuous-time and discrete-time smoothing. It further elaborates on robust techniques that accommodate uncertainties within problem specifications, parameter estimation, applications of Riccati equations, etc. These afore-mentioned linear techniques have been applied to various nonlinear estimation problems towards the end of the book. Although they have a risk of assurance of optical performance, these mentioned linearizations can be employed in predictors, filters and smoothers. The book serves the objective of imparting practical knowledge amongst students interested in this field.
Author: Simo Särkkä
Publisher: Cambridge University Press
ISBN: 110703065X
Category : Computers
Languages : en
Pages : 255
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Book Description
A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
Author: Rafael A. Irizarry
Publisher: CRC Press
ISBN: 1000708039
Category : Mathematics
Languages : en
Pages : 794
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Book Description
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.
Author: Tomas Björk (matematiker.)
Publisher:
ISBN:
Category : Funktionsanalys
Languages : en
Pages : 28
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Book Description
Author: Lawrence D. Stone
Publisher: Artech House
ISBN: 1608075532
Category : Technology & Engineering
Languages : en
Pages : 315
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Book Description
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.
