Classification, Parameter Estimation and State Estimation

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Abstract

3.1.2MAP estimation 3.1.3The Gaussian case with linear sensors 3.1.4Maximum likelihood estimation 3.1.5Unbiased linear MMSE estimation 3.2 Performance of estimators 3.2.1 Bias and covariance 3.2.2The error covariance of the unbiased linear MMSE estimator 3.3 Data fitting 3.3.1 Least squares fitting 3.3.2Fitting using a robust error norm 3.3.3Regression 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 4.1.1Models 4.1.2Optimal online estimation 4.2 Continuous state variables 4.2.1 Optimal online estimation in linear-Gaussian systems 4.2.2Suboptimal solutions for nonlinear systems 4.2.3Other filters for nonlinear systems 4.3 Discrete state variables 4.3.1 Hidden Markov models 4.3.2Online state estimation 4.3.3Offline state estimation 4.4 Mixed states and the particle filter 4.4.1 Importance sampling 4.4.2Resampling by selection 4.4.3The condensation algorithm 4.5 Selected bibliography 4.6 Exercises 5 Supervised Learning 5.1 Training sets 5.2 Parametric learning 5.2.1 Gaussian distribution, mean unknown vi CONTENTS 5.2.2 Gaussian distribution, covariance matrix unknown 5.2.3 Gaussian distribution, mean and covariance matrix both unknown 5.2.4 Estimation of the prior probabilities 5.2.5 Binary measurements 5.3 Nonparametric learning 5.3.1 Parzen estimation and histogramming 5.3.2Nearest neighbour classification 5.3.3Linear discriminant functions 5.3.4The support vector classifier 5.3.5The feed-forward neural network 5.4 Empirical evaluation 5.5 References 5.6 Exercises 6 Feature Extraction and Selection 6.1 Criteria for selection and extraction 6.1.1Inter/intra class distance 6.1.2Chernoff-Bhattacharyya distance 6.1.3Other criteria 6.2 Feature selection 6.2.1 Branch-and-bound 6.2.2 Suboptimal search 6.2.3 Implementation issues 6.3 Linear feature extraction 6.3.1 Feature extraction based on the Bhattacharyya distance with Gaussian distributions 6.3.2Feature extraction based on inter/intra class distance 6.4 References viii CONTENTS 9.1.3Feature extraction 9.1.4Feature selection 9.1.5Complex classifiers 9.1.6Conclusions 9.2 Time-of-flight estimation of an acoustic tone burst 9.2.1 Models of the observed waveform 9.2.2 Heuristic methods for determining the ToF 9.2.3 Curve fitting 9.2.4 Matched filtering 9.2.5 ML estimation using covariance models for the reflections 9.2.6 Optimization and evaluation 9.3 Online level estimation in an hydraulic system 9.3.1 Linearized Kalman filtering 9.3.2Extended Kalman filtering 9.3.3Particle filtering 9.3.4Discussion 9.4 References CONTENTS ix C.1.2Poisson distribution C.1.3Binomial distribution C.1.4Normal distribution C.1.5The Chi-square distribution C.2 Bivariate random variables C.3 Random vectors C.3.1 Linear operations on Gaussian random vectors C.3.2 Decorrelation C.4 Reference Appendix D Discrete-time Dynamic Systems D.1 Discrete-time dynamic systems D.2 Linear systems D.3 Linear time invariant systems D.3.1 Diagonalization of a system D.3.2 Stability D.4 References Appendix E Introduction to PRTools E.1 Motivation E.2 Essential concepts in PRTools E.3 Implementation E.4 Some details E.4

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