Page 7 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

vi CONTENTS

3.1.2 MAP estimation 55
3.1.3 The Gaussian case with linear sensors 56
3.1.4 Maximum likelihood estimation 57
3.1.5 Unbiased linear MMSE estimation 59
3.2 Performance of estimators 62
3.2.1 Bias and covariance 63
3.2.2 The error covariance of the unbiased linear
MMSE estimator 67
3.3 Data fitting 68
3.3.1 Least squares fitting 68
3.3.2 Fitting using a robust error norm 72
3.3.3 Regression 74
3.4 Overview of the family of estimators 77
3.5 Selected bibliography 79
3.6 Exercises 79

4 State Estimation 81
4.1 A general framework for online estimation 82
4.1.1 Models 83
4.1.2 Optimal online estimation 86
4.2 Continuous state variables 88
4.2.1 Optimal online estimation in linear-Gaussian
systems 89
4.2.2 Suboptimal solutions for nonlinear
systems 100
4.2.3 Other filters for nonlinear systems 112
4.3 Discrete state variables 113
4.3.1 Hidden Markov models 113
4.3.2 Online state estimation 117
4.3.3 Offline state estimation 120
4.4 Mixed states and the particle filter 128
4.4.1 Importance sampling 128
4.4.2 Resampling by selection 130
4.4.3 The condensation algorithm 131
4.5 Selected bibliography 135
4.6 Exercises 136

5 Supervised Learning 139
5.1 Training sets 140
5.2 Parametric learning 142
5.2.1 Gaussian distribution, mean unknown 143