vi PROBABILISTIC ROBOTICS
3.2.1 Linear Gaussian Systems 34
3.2.2 The Kalman Filter Algorithm 36
3.2.3 Illustration 37
3.2.4 Mathematical Derivation of the KF 39
3.3 The Extended Kalman Filter 48
3.3.1 Linearization Via Taylor Expansion 49
3.3.2 The EKF Algorithm 50
3.3.3 Mathematical Derivation of the EKF 51
3.3.4 Practical Considerations 53
3.4 The Information Filter 55
3.4.1 Canonical Representation 55
3.4.2 The Information Filter Algorithm 57
3.4.3 Mathematical Derivation of the Information Filter 58
3.4.4 The Extended Information Filter Algorithm 60
3.4.5 Mathematical Derivation of the Extended Information
Filter 61
3.4.6 Practical Considerations 62
3.5 Summary 64
3.6 Bibliographical Remarks 65
4 NONPARAMETRIC FILTERS 67
4.1 The Histogram Filter 68
4.1.1 The Discrete Bayes Filter Algorithm 69
4.1.2 Continuous State 69
4.1.3 Decomposition Techniques 73
4.1.4 Binary Bayes Filters With Static State 74
4.2 The Particle Filter 77
4.2.1 Basic Algorithm 77
4.2.2 Importance Sampling 80
4.2.3 Mathematical Derivation of the PF 82
4.2.4 Properties of the Particle Filter 84
4.3 Summary 89
4.4 Bibliographical Remarks 90
5 ROBOT MOTION 91
5.1 Introduction 91
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