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Calculating Vehicle Attitude with Kinematics Equations Integrator Device
March 11, 2011

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Innovators at NASA's Armstrong Flight Research Center have patented a kinematics equations integrator device and method that improve accuracy when determining the attitude of a flight vehicle. Inertial navigation systems (INS) are widely used in flight vehicle applications such as aircraft, spacecraft, missiles, and satellites. These self-contained navigation systems are used to determine flight vehicle position. However, several factors cause these systems to require correction terms and renormalization over time. This innovation uses angular velocity and initial vehicle attitude data to greatly simplify the computation required in the integration loop and transmit the result to the navigational computer for use in a flight vehicle's correcting course. The technology can be implemented in a logic circuit or as software on a microchip. The method preserves the quaternion normalization and does not require error correction terms or renormalization. As a result, this approach increases integration speed, decreases software complexity, and requires only a basic computational system for operation.


  • Accurate: Improves quality of critical attitude data
  • Faster: Increases integration speed
  • High-performance: Never requires correction or re-normalization of the quaternion
  • Efficient: Decreases the amount and complexity of required software
  • Convenient: Offers portability between various computational systems because of its non-proprietary solution


  • Military aircraft
  • General aviation aircraft
  • Helicopters
  • Satellites and other spacecraft
  • Missiles and rockets


Armstrong has one patent issued (U.S. Patent No: 6,061,611→ ) for this technology.

Commercial Opportunity

This technology is part of NASA's technology transfer program. The program seeks to stimulate development of commercial uses of NASA-developed technologies. NASA is flexible in its agreements, and opportunities exist for licensing and joint development. Armstrong is interested in a partnership to commercialize this technology.

Contact Information

If you would like more information about this technology or about NASA's technology transfer program, please contact:

Technology Transfer Office
NASA's Armstrong Flight Research Center
PO Box 273, M/S 1100
Edwards, CA 93523-0273
Phone: (661) 276-3368
E-mail: DFRC-TTO@mail.nasa.gov

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