Contents
Preface for the First Edition xiii
Preface for the Second Edition xv
Acronyms and Abbreviations xvii
Notation xix
1 Introduction 1
1.1 (2ed update) A Little History 1
1.2 Sensors, Measurements, and Problem Definition 3
1.3 How This Book Is Organized 4
1.4 Relationship to Other Books 5
Part I Estimation Machinery 7
2 Primer on Probability Theory 9
2.1 Probability Density Functions 9
2.1.1 (2ed update) Definitions 9
2.1.2 (2ed update) Marginalization, Bayes’ Rule, Inference 11
2.1.3 (2ed update) Expectations and Moments 11
2.1.4 Statistically Independent, Uncorrelated 13
2.1.5 Shannon and Mutual Information 13
2.1.6 (2ed new) Quantifying the Difference Between PDFs 14
2.1.7 (2ed new) Random Sampling 14
2.1.8 Sample Mean and Covariance 15
2.1.9 Normalized Product 15
2.1.10 (2ed update) Cram´er-Rao Lower Bound and Fisher Information 16
2.2 Gaussian Probability Density Functions 17
2.2.1 (2ed update) Definitions 17
2.2.2 Joint Gaussian PDFs, Their Factors, and Inference 18
2.2.3 Statistically Independent, Uncorrelated 19
2.2.4 (2ed new) Information Form of a Gaussian 20
2.2.5 (2ed new) Marginals of a Joint Gaussian 20
2.2.6 Linear Change of Variables 21
2.2.7 Passing a Gaussian through a Nonlinearity 23
2.2.8 Normalized Product of Gaussians 27
2.2.9 (2ed new) Chi-Squared Distribution and Mahalanobis Distance 28
2.2.10 (2ed update) Shannon Information of a Gaussian 29
2.2.11 Mutual Information of a Joint Gaussian PDF 30
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