Contents

Preface

Foreword

1 Introduction

1.1 The scope of the book

1.1.1 Classification

1.1.2 Parameter estimation

1.1.3 State estimation

1.1.4 Relations between the subjects

1.2 Engineering

1.3 The organization of the book

1.4 References

2 Detection and Classification

2.1 Bayesian classification

2.1.1 Uniform cost function and minimum error rate

2.1.2 Normal distributed measurements; linear and quadratic classifiers

2.2 Rejection

2.2.1 Minimum error rate classification with reject option

2.3 Detection: the two-class case

2.4 Selected bibliography

2.5 Exercises

3 Parameter Estimation

3.1 Bayesian estimation

3.1.1 MMSE estimation

3.1.2 MAP estimation

3.1.3 The Gaussian case with linear sensors

3.1.4 Maximum likelihood estimation

3.1.5 Unbiased linear MMSE estimation

3.2 Performance of estimators

3.2.1 Bias and covariance

3.2.2 The error covariance of the unbiased linear MMSE estimator

3.3 Data fitting

3.3.1 Least squares fitting

3.3.2 Fitting using a robust error norm

3.3.3 Regression

3.4 Overview of the family of estimators

3.5 Selected bibliography

3.6 Exercises

4 State Estimation

4.1 A general framework for online estimation

4.1.1 Models

4.1.2 Optimal online estimation

4.2 Continuous state variables

4.2.1 Optimal online estimation in linear-Gaussian systems

4.2.2 Suboptimal solutions for nonlinear systems

4.2.3 Other filters for nonlinear systems

4.3 Discrete state variables

4.3.1 Hidden Markov models

4.3.2 Online state estimation

4.3.3 Offline state estimation

4.4 Mixed states ...

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