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CH5115: Parameter and State Estimation

This course is aimed at introducing foundational concepts related to estimation theory and methods for parameter and state estimation, with applications to distributional fitting, regression and state estimation in dynamical systems. The contents of the course include introduction to estimation, information metrics, goodness of estimators (bias, variance, consistency), methods of estimation (LS, MLE, Bayesian), recursive estimators, Kalman filters and their variants (EKF, UKF).

Objectives: 

 

The objectives of this course are three-fold: (i) to provide foundational concepts on parameter and state estimation for dynamical systems including theory and methods (ii) equip the students with the concepts of information metrics in estimation and (iii) train the students in applying these concepts to estimation problems in engineering, biological and other systems of interest using modern tools of data analysis (e.g., MATLAB).

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Pre-requisites and FAQ

 

Course Contents:

 

  1. Introduction: Overview of estimation; Importance and value of estimation in inferencing, modelling, prediction, control, monitoring and all other fields of data-driven process analysis; Course overview. 

  2. Review of mathematical and statistical essentials: Optimization and linear algebra basics; Random variables and probability distributions; Random signals, correlation functions and spectral density; White- and coloured noise

  3. Foundational concepts: Formal introduction to estimation; Types of estimation problems; Classification of estimators; Soft introduction to goodness of estimators, concepts of significance testing and confidence regions

  4. Information metrics for estimation: Notion of information in estimation; Fisher’s information, Bayesian information measures.

  5. Goodness of estimators: Ensemble properties - bias, variance, mean square error, efficiency, Cramer-Rao inequality; Asymptotic (large sample) properties - asymptotic bias and consistency; 

  6. Distribution of parameter estimates and confidence regions: Sampling distributions of estimators; Central limit theorem; Confidence regions; Significance testing

  7. Parameter estimation methods in distribution fitting and regression: Method of moments; Least squares estimators and their variants; Maximum likelihood estimators; Bayesian estimators; Conjugate and informative priors; Regularised (penalised) methods; Applications to distribution fitting and data-driven modelling.

  8. Recursive / sequential parameter estimation methods: Recursive LS and weighted LS; Sequential Bayesian estimation; Applications to online estimation in engineering and biological systems.

  9. Optimal state estimation in dynamical systems: Review of state-space models; Introduction to state estimation problem; Notions of observability (linear systems), controllability and minimal realization; Kalman filter; Extended and unscented Kalman filters for state estimation in non-linear systems; Applications to state estimation in engineering, biological and energy systems. 

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Note: All examples in soft learning, computations and exercises will be carried out in MATLAB.

 

Text Books:

 

  1. Arun K. Tangirala (2015). Principles of System Identification: Theory and Practice, CRC Press.

  2. John L. Crassidis and John L. Junkins (2012). Optimal Estimation of Dynamic Systems, CRC Press, 2nd Ed.. 

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Reference Books:

  1. Adriaan van den Bos (2007). Parameter Estimation for Scientists and Engineers, John Wiley & Sons.

  2. Chaw-Bing Chang and Keh-Ping Dunn (2007). Applied State Estimation and Association, MIT Press.

  3. F. van der Heijden, R.P.W. Duin, D. de Ridder and D.M.J. Tax (2004). Classification, Parameter Estimation and State Estimation: An Engineering Approach using MATLAB, John Wiley & Sons.

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