Open access peer-reviewed Monograph

Smoothing, Filtering and Prediction

Estimating The Past, Present and Future

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.

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32790 Total Chapter Downloads

2 Crossref Citations

28 Web of Science Citations

3 Dimensions Citations

chaptersDownloads

Open access peer-reviewed

1. Continuous-Time Minimum-Mean-Square-Error Filtering
5055

Open access peer-reviewed

2. Discrete-Time Minimum-Mean-Square-Error Filtering
2695

Open access peer-reviewed

3. Continuous-Time Minimum-Variance Filtering
4352

Open access peer-reviewed

4. Discrete-Time Minimum-Variance Prediction and Filtering
2913

Open access peer-reviewed

5. Discrete-Time Steady-State Minimum-Variance Prediction and Filtering
3530

Open access peer-reviewed

6. Continuous-Time Smoothing
3045

Open access peer-reviewed

7. Discrete-Time Smoothing
2455

Open access peer-reviewed

8. Parameter Estimation
2760

Open access peer-reviewed

9. Robust Prediction, Filtering and Smoothing
2737

Open access peer-reviewed

10. Nonlinear Prediction, Filtering and Smoothing
3248

Monograph and chapters are indexed in

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