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Jul 31, 20246 min read

System Identification & Data Analysis

Cheat Sheet

Mind Maps:

Perquisites:

Contents and Program:

Estimation Theory
  • Course Introduction
  • Random variables. Probability distributions. Mean and covariance. Conditional probability. Gaussian variables.
  • Estimation theory. Parametric estimation. Properties of estimators. Maximum likelihood estimators. Least squares and Gauss-Markov estimators. Bayesian estimation. Minimum mean square error estimators.
  • Stochastic processes and time-series prediction. Distributions, mean and covariance function. Stationary processes. Frequency domain representation. Stochastic dynamic systems. Time-series models: AR, MA, ARMA. Time-series prediction.
System Identification
  • System identification theory. Identification of linear systems: prediction error methods. Input-output models: ARX, ARMAX, OE, BJ. Least squares estimator for linear regression models. Model validation.
  • Practical system identification. Use of software tools for system identification.
State Estimation
  • State estimation for linear systems. Non stationary stochastic systems. The state estimation problem and the Kalman filter. Asymptotic properties of the Kalman filter. Recursive system identification.
  • State estimation for nonlinear systems. State estimation in nonlinear stochastic systems. The Extended Kalman Filter. Advanced nonlinear filtering techniques: unscented filter; sequential Monte Carlo methods.

Lectures

Probability & Statistics

SI&DA - Lecture 1 ‘Recap of Random Variables (RVs) - Part I’ ✓ SI&DA - Lecture 2 ‘Recap of Random Variables (RVs) - Part II’ ✓ SI&DA - Lecture 3 ‘Recap of Conditional Distributions’ ✓ SI&DA - Lecture 4 ‘Estimation Theory - Part I’ ✓ SI&DA - Lecture 5 ‘Estimation Theory - Part II’ SI&DA - Lecture 6 ‘Maximum Likelihood Method’ SI&DA - Lecture 7 ‘Linear Estimation Problems’ SI&DA - Lecture 8 ‘Bayesian Estimation’ SI&DA - Lecture 9 ‘Stochastic Processes’ SI&DA - Lecture 10 ‘Example of Stochastic Processes’ SI&DA - Lecture 11 ‘Linear Stochastic System’ SI&DA - Lecture 12 ‘Frequency Domain Analysis of Stochastic Systems’ SI&DA - Lecture 13 ‘MA AR and ARMA Processes’ SI&DA - Lecture 14 ‘Time Series Prediction’

System Identification

SI&DA - Lecture 15 ‘System Identification’ SI&DA - Lecture 16 ‘LTI Models’ SI&DA - Lecture 17 ‘Model Selection Criteria’ SI&DA - Lecture 18 ‘Optimal Model Choice’ SI&DA - Lecture 19 ‘Model Validation - Part I’ SI&DA - Lecture 20 ‘Model Validation - Part II’

State Evaluation

SI&DA - Lecture 21 ‘State Estimation Problem’ SI&DA - Lecture 22 ‘Derivation of the Kalman Filter - Part I’ SI&DA - Lecture 23 ‘Derivation of the Kalman Filter - Part II’ SI&DA - Lecture 24 ‘Properties of the Kalman Filter’ SI&DA - Lecture 25 ‘Asymptotic Behaviour of the Kalman Filter’ SI&DA - Lecture 26 ‘Applications for the Kalman Filter’ SI&DA - Lecture 27 ‘Recursive Parameter Estimation’ SI&DA - Lecture 28 ‘The Extended Kalman Filter’ SI&DA - Lecture 29 ‘The Continuous-Discrete Kalman Filter’ SI&DA - Lecture 30 ‘The Unscented Kalman Filter - from Online Resources’ SI&DA - Lecture 30 ‘The Unscented Kalman Filter’ SI&DA - Lecture 31 ‘The Particle Filter’

Index

Course Introduction

Random variables

Estimation Theory

Exercises and Examples:

CollectionOfSIandDAExample Random variables ~ Ex.: “Uniform PDF” Random variables ~ Ex.: “Gaussian PDF or Normal” Random variables ~ Ex.: “CDF and PDF of a Coin Toss” Random variables ~ Homework 1 Random variables ~ Homework 2

Estimation Theory ~ Ex.: “Estimation Problem with Noise” Estimation Theory ~ Ex.: “Sample Mean” Estimation Theory ~ Ex.: “Another Unbiased Estimator” Estimation Theory ~ Ex.: “Sample Variance” Estimation Theory ~ Homework 3 Estimation Theory ~ Ex.: “Consistency of the Sample Mean”

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