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 Function
1.1.4 Common Probability Density Functions
         Uniform Density
         Gaussian Density
         Multivariable Gaussian Density
         Chi-Squared Density
1.2 Stochastic Processes
1.2.1 Stationary Processes and the (Auto) Covariance and (Auto) Correlation functions.
1.2.2 Cross-Covariance and Cross-Correlation Functions
1.2.3 Power Spectral Density
1.2.4 Linear Systems subject to stochastic input 
1.3 Quasi-stationary signals 
1.4 Stochastic Convergence 
1.4.1 Convergence in Mean
1.4.2 Convergence in Probability 
1.4.3 Convergence with Probability 1

1.4.4 Convergence in Distribution

2 Estimation Methods
2.1 Minimum Mean Square Error Estimation
2.2 Maximum A Posteriori Estimation 
2.3 Unbiased Parameter Estimation

3 Minimum Mean Square Error Parameter Estimation
3.1 The Bias-Variance Error Trade-Off
3.2 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 Models
5.1 Model Structures and Probabilistic Models
5.2 Estimation Methods
5.2.1 Maximum Likelihood Estimation
5.2.2 The Extended Invariance Principle 
5.2.3 The Prediction Error Method
5.2.4 Multi-Step Least-Squares Methods
5.2.5 Instrumental Variable Methods
5.2.6 Indirect Inference
5.3 Linear Models
5.3.1 Maximum Likelihood Estimation
5.3.2 The Prediction Error Method
5.4 Multi-Step Least-Squares Methods
5.5 Subspace Identification
5.6 Instrumental Variable Methods
5.7 Bayesian Methods
5.8 Time versus Frequency Domain Identification
5.9 Continuous Time Model Identification

6 Model Quality
6.1 Variance Quantification
6.1.1 Fundamental Geometric Principles 
6.1.2 Fundamental Structural Results 
6.1.3 Variability of Estimated Frequency Response
6.1.4 Variability of Nonlinear System Estimates
6.1.5 Bootstrap Methods

7 Experiment Design
7.1 Identifiability 
7.2 Persistence of Exciation
7.3 Input Signal Design
7.3.1 Common Input Signals 
              PRBS 
              Sums of Sine-Waves and Crest Factor Correction
7.4 Application Oriented Experiment Design
7.5 Adaptive Experiment Design 
8 Model Validation
8.1 Residual whiteness Tests 
8.2 Input to residual correlation tests
8.3 Model Error Modelling 
9 Application Examples
9.1 Closed Loop Identification
9.2 Network Models
9.3 Errors-in-Variables Models
9.4 Block-structured Nonlinear Models 

9.5 Identification for Control