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Guidance, Navigation and Control Short Course

Understand the principles of navigation by inertial, celestial, and radio (including GPS) methods, the principles of guidance and control of 6-DOF motion, the characteristics and noise models of sensors, and the dynamic behavior of controlled and guided systems.

Dr. Brian Stevens (Director) and Dr. J. Clayton Kerce

Engineers and scientists involved in the design or evaluation of guidance, navigation, and control systems for land, sea, and air vehicles, and projectiles.

  • Discover how sensor errors arise, propagate, and are modeled & simulated
  • Understand the Kalman Filter and concepts of Estimation Theory
  • Master the kinematics and dynamics of 6-DOF motion
  • Explore principles of Geodesy and the WGS-84 datum
  • Examine systems for navigation on the Earth
  • Understand gyro and accelerometer principles and error sources
  • Learn the techniques of missile guidance


  1. Review material for GNC relevant mathematics (available in advance)
    • Navigation
      • Models of Earth’s shape; WGS-84; Coordinate Systems; Gravity & Gravitation
      • Map Projections; Plane & Spherical distance calculations; Astro-Navigation
      • Radio Navigation; Hyperbolic Systems; VOR; DME; TACAN
      • GPS; Principles; Sources of Error; Differential GPS systems
    • Systems Theory
      • Mathematical Models; State Equations; Numerical Simulation
      • Equilibrium and Linearization; Numerical solution; Aircraft Example
      • Analytical Solutions of Linear State Equations; Modal Analysis
      • Low energy trajectory planning for satellite control & navigation
    • Kinematics & Dynamics of Rigid-Body 6-DOF Motion
      • Vector Analysis; Relative Motion; Attitude Representations; Quaternions
      • Translational and Rotational Dynamics; Stability of Spinning Bodies
      • Aerodynamic Effects; Spinning Artillery Round example.
    • Control Problems in GNC
      • Review of relevant control theory
      • Inertial Stabilization; Mechanization; Disturbance Inputs
      • Pointing Control; Control of multi-axis gimbals
      • Tracking Control; Tracking dynamics; Target tracking example with Kalman track-filter
      • Multivariable Design Example: Aircraft automatic landing; Steady State conditions, linearization, transfer functions,compensation, initialization, simulation.
    • Probability & Random Processes in GNC
      • Review of Probability and Random Process Theory, leading to:
      • Descriptions of Errors; Noise Analysis; Monte-Carlo Simulation
      • Shaping Filters; Complementary Filtering; Covariance Analysis
      • Least Squares; the Kalman Filter; Nonlinear Dynamics; Divergence & Bias
      • Factorization; Choice of Variables; Tracking example; Estimation Theory
    • Inertial Navigation
      • Accelerometers and Gyroscopes: Types & Principles, Error Sources
      • Stabilized Platform & Strapdown Nav. Systems; Alignment; Errors
    • Guidance
      • Command Guidance v. Homing Guidance
      • Proportional Navigation, Augmented P.N, Modern Guidance Laws
      • Missile Autopilots; Missile Homing loop Analysis
      • Guidance Filters; Kalman Filter example and simulation
      • Monte Carlo Simulation; Adjoint Analysis

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