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2.160

Identification, Estimation, and Learning

3-0-9 units · Graduate

Provides a broad theoretical basis for estimation, identification, and learning of linear and nonlinear systems at the cross-disciplinary area of system dynamics and control, machine learning, and statistics. Recursive least squares estimate, partial least squares, Kalman filter and extended Kalman filter, Bayes filter and particle filter; parametric and non-parametric system identification, Wiener-Hopf equation, persistent excitation, unbiased estimates, asymptotic variance, experiment design; function approximation theory, neural nets, radial basis functions, Koopman operator for exact linearization of nonlinear systems, and dynamic mode decomposition. Context-oriented mini-projects: robotics, self-driving cars, biomedical engineering, wearable sensors.

Spring 2006

Topics

  • Introduction
  • Recursive Least Square (RLS) Algorithms
  • Properties of RLS
  • Random Processes, Active Noise Cancellation
  • Discrete Kalman Filter-1
  • Discrete Kalman Filter-2
  • Continuous Kalman Filter
  • Extended Kalman Filter
  • Prediction Modeling of Linear Systems
  • Model Structure of Linear Time-invariant Systems
  • Time Series Data Compression, Laguerre Series Expansion
  • Non-linear Models, Function Approximation Theory, Radial Basis Functions
  • Neural Networks
  • Error Back Propagation Algorithm
  • Perspective of System Identification, Frequency Domain Analysis
  • Informative Data Sets and Consistency
  • Informative Experiments: Persistent Excitation
  • Asymptotic Distribution of Parameter Estimates
  • Experiment Design, Pseudo Random Binary Signals (PRBS)
  • Maximum Likelihood Estimate, Cramer-Rao Lower Bound and Best Unbiased Estimate
  • Information Theory of System Identification: Kullback-Leibler Information Distance, Akaike’s Information Criterion

Readings

  • There is no primary textbook for this course. Most of the course materials have been developed based on the following references:
    Listed reading
  • Ljung, Lennart. System Identification: Theory for the User . 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1999. ISBN: 9780136566953.
    Listed reading
  • Goodwin, Graham, and Kwai Sang Sin. Adaptive Filtering, Prediction, and Control . Englewood Cliffs, NJ: Prentice-Hall, 1984. ISBN: 9780130040695.
    Listed reading
  • Burnham, Kenneth, and David Anderson. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach . 2nd ed. New York, NY: Springer, 2003. ISBN: 9780387953649.
    Listed reading
  • Brown, Robert, and Patrick Hwang. Introduction to Random Signals and Applied Kalman Filtering . 3rd ed. New York, NY: Wiley, 1996. ISBN: 9780471128397.
    Listed reading

Prerequisites & course information

Prereq: 2.151 , 6.7100[J] , 16.31 , or permission of instructor G (Fall) 3-0-9 units

Sources