Open access peer-reviewed Monograph

Smoothing, Filtering and Prediction

Estimating The Past, Present and Future

Authored by Garry Einicke

Commonwealth Scientific and Industrial Research Organisation, Australia

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.

Read more >Order hardcopy
Smoothing, Filtering and PredictionEstimating The Past, Present and FutureAuthored by Garry Einicke

Published: February 24th 2012

DOI: 10.5772/2706

ISBN: 978-953-307-752-9

eBook (PDF) ISBN: 978-953-51-4346-8

Copyright year: 2012

Books open for chapter submissions

41445 Total Chapter Downloads

3 Crossref Citations

61 Web of Science Citations

6 Dimensions Citations


Open access peer-reviewed

1. Continuous-Time Minimum-Mean-Square-Error Filtering

By Garry Einicke


Open access peer-reviewed

2. Discrete-Time Minimum-Mean-Square-Error Filtering

By Garry Einicke


Open access peer-reviewed

3. Continuous-Time Minimum-Variance Filtering

By Garry Einicke


Open access peer-reviewed

4. Discrete-Time Minimum-Variance Prediction and Filtering

By Garry Einicke


Open access peer-reviewed

5. Discrete-Time Steady-State Minimum-Variance Prediction and Filtering

By Garry Einicke


Open access peer-reviewed

6. Continuous-Time Smoothing

By Garry Einicke


Open access peer-reviewed

7. Discrete-Time Smoothing

By Garry Einicke


Open access peer-reviewed

8. Parameter Estimation

By Garry Einicke


Open access peer-reviewed

9. Robust Prediction, Filtering and Smoothing

By Garry Einicke


Open access peer-reviewed

10. Nonlinear Prediction, Filtering and Smoothing

By Garry Einicke


Monograph and chapters are indexed in

  • Worldcat
  • OpenAIRE
  • Google Scholar
  • AZ ebsco
  • Base
  • CNKI
  • BKCI

Order a hardcopy of the Monograph

Free shipping with DHL Express

Hardcover (ex. VAT)£119

Order now

Residents of European Union countries need to add a Book Value-Added Tax Rate based on their country of residence. Institutions and companies, registered as VAT taxable entities in their own EU member state, will not pay VAT by providing IntechOpen with their VAT registration number. This is made possible by the EU reverse charge method.

Special discount for IntechOpen contributors

All IntechOpen contributors are offered special discounts starting at 40% OFF available through your personal dashboard

Login and purchase