Smoothing, Filtering and Prediction - Estimating The Past, Present and Future

Einicke, Garry Allan

Smoothing, Filtering and Prediction - Estimating The Past, Present and Future

Edited by Garry Allan Einicke

Abstract: 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 – 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.

JEL-codes: C60 (search for similar items in EconPapers)
Date: 2012
ISBN: 978-953-307-752-9
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.intechopen.com/books/1759 (text/html)
Book downloadable chapter-by-chapter

Chapters in this book:

Continuous-Time Minimum-Mean-Square-Error Filtering: Garry Allan Einicke
Continuous-Time Minimum-Variance Filtering: Garry Allan Einicke
Continuous-Time Smoothing: Garry Allan Einicke
Discrete-Time Minimum-Mean-Square-Error Filtering: Garry Allan Einicke
Discrete-Time Minimum-Variance Prediction and Filtering: Garry Allan Einicke
Discrete-Time Smoothing: Garry Allan Einicke
Discrete-Time Steady-State Minimum-Variance Prediction and Filtering: Garry Allan Einicke
Nonlinear Prediction, Filtering and Smoothing: Garry Allan Einicke
Parameter Estimation: Garry Allan Einicke
Robust Prediction, Filtering and Smoothing: Garry Allan Einicke

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ito:pbooks:1759

DOI: 10.5772/2706

Access Statistics for this book

More books in Books from IntechOpen
Bibliographic data for series maintained by Slobodan Momcilovic ().