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Stochastic Estimation and Control

Graduate · Historical course

Fall 2004

Topics

  • Introduction
  • Independence
  • Expectation, Averages and Characteristic Function
  • Correlation, Covariance, and Orthogonality
  • Some Common Distributions
  • More Common Distributions
  • Linearized Error Propagation
  • More Linearized Error Propagation
  • Concept of a Random Process
  • Autocorrelation Function
  • Power Spectral Density Function
  • Gauss-Markov Process
  • Determination of Autocorrelation and Spectral Density Functions from Experimental Data
  • Introduction: The Analysis Problem
  • Pure White Noise and Bandlimited Systems
  • Nonstationary (Transient) Analysis - Initial Condition Response
  • The Wiener Filter Problem
  • The Stationary Optimization Problem - Weighting Function Approach
  • Complementary Filter
  • Estimation
  • Markov Processes
  • State Space Description
  • Monte Carlo Simulation of Discrete-Time Systems
  • Transition from the Discrete to Continuous Filter Equations
  • Divergence Problems
  • Complementary Filter Methodology

Readings

  • Brown, Robert Grover, and Patrick Y. C. Hwang. Introduction to Random Signals and Applied Kalman Filtering. New York: John Wiley & Sons, March 1992. ISBN: 0471525685.
    Listed reading
  • LEC #: 13 · TOPICS: Determination of Autocorrelation and Spectral Density Functions from Experimental Data · READINGS: Section 2.15
    Reading assignment
  • LEC #: 25 · TOPICS: Divergence Problems · READINGS: Section 6.6
    Reading assignment
Sources