Outline

0 Introduction

1 Essentials of Signals, Systems and Stochastic Processes 1.1 Probability Theory .1.1.1 Random Variables 1.1.2 Probability Distribution, Density and Events Bayesian Perspective Joint and Marginal Probability Conditional Probability and Bayes’ rule Operations on Random Variables 1.1.3 Expectation Variance, Covariance and Correlation Moments and the Moment Generating Function1.1.4 Common Probability Density Functions Uniform Density Gaussian Density Multivariable Gaussian Density Chi-Squared Density1.2 Stochastic Processes1.2.1 Stationary Processes and the (Auto) Covariance and (Auto) Correlation functions.1.2.2 Cross-Covariance and Cross-Correlation Functions1.2.3 Power Spectral Density1.2.4 Linear Systems subject to stochastic input 1.3 Quasi-stationary signals 1.4 Stochastic Convergence 1.4.1 Convergence in Mean1.4.2 Convergence in Probability 1.4.3 Convergence with Probability 1

1.4.4 Convergence in Distribution

2 Estimation Methods2.1 Minimum Mean Square Error Estimation2.2 Maximum A Posteriori Estimation 2.3 Unbiased Parameter Estimation3 Minimum Mean Square Error Parameter Estimation3.1 The Bias-Variance Error Trade-Off3.2 Risk and Average Risk. The Bayes Estimator Risk estimation methods

SURE, Empirical Bayes, Variational Bayes

3.3 Linear in the Parameters Models

4 Linear in the Parameters Models ¶

5 Dynamical Models5.1 Model Structures and Probabilistic Models5.2 Estimation Methods5.2.1 Maximum Likelihood Estimation5.2.2 The Extended Invariance Principle 5.2.3 The Prediction Error Method5.2.4 Multi-Step Least-Squares Methods5.2.5 Instrumental Variable Methods5.2.6 Indirect Inference5.3 Linear Models5.3.1 Maximum Likelihood Estimation5.3.2 The Prediction Error Method5.4 Multi-Step Least-Squares Methods5.5 Subspace Identification5.6 Instrumental Variable Methods5.7 Bayesian Methods5.8 Time versus Frequency Domain Identification5.9 Continuous Time Model Identification¶

5.10 Grey-Box Identification¶

6 Model Quality6.1 Variance Quantification6.1.1 Fundamental Geometric Principles 6.1.2 Fundamental Structural Results 6.1.3 Variability of Estimated Frequency Response6.1.4 Variability of Nonlinear System Estimates6.1.5 Bootstrap Methods7 Experiment Design7.1 Identifiability 7.2 Persistence of Exciation7.3 Input Signal Design7.3.1 Common Input Signals PRBS Sums of Sine-Waves and Crest Factor Correction7.4 Application Oriented Experiment Design7.5 Adaptive Experiment Design 8 Model Validation8.1 Residual whiteness Tests 8.2 Input to residual correlation tests8.3 Model Error Modelling 9 Application Examples9.1 Closed Loop Identification9.2 Network Models9.3 Errors-in-Variables Models9.4 Block-structured Nonlinear Models

9.5 Identification for Control