Optimal Estimation Methods

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This course serves to teach traditional concepts and recent advances in estimation, and to relate these concepts to modern dynamic systems found in aerospace disciplines. This course stresses modeling of physical problems into mathematical terms. Examples will be given from both spacecraft and aircraft systems.

TEXT: “Optimal Estimation of Dynamic Systems,” by J.L. Crassidis and J.L. Junkins, Chapman & Hall/CRC, Boca Raton, FL, 2011.

  • Review of Statistics
    • Random Variables
    • Gaussian Processes
    • Covariance and Correlation Function
    • Maximum Likelihood
  • Least Squares Estimation
    • Linear Batch Estimation
    • Linear Sequential Estimation
    • Nonlinear Estimation
  • Examples
    • Vehicle Attitude Determination
    • GPS Navigation
  • State Estimation
    • Review of State-Space Systems
    • Response to Gaussian Inputs
    • Linear Kalman Filter
    • Neighboring-Optimal Linear Estimator
    • Extended Kalman Filter for Nonlinear Systems
  • Examples
    • Position and Velocity Tracking
    • Review of Attitude Dynamics
    • Attitude Estimation Using Dynamics
    • Bias Estimation and Calibration of Gyros
  • Advanced Topics
    • Covariance Decompositions
    • Smoothing Algorithms

Years Taught: Fall '15, Fall '14, Fall '13, Spring '01