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Attitude Determination

Attitude Determination. - Using GPS. Table of Contents. Definition of Attitude Attitude and GPS Attitude Representations Least Squares Filter Kalman Filter Other Filters The AAU Testbed Results Conclusion. What is Attitude?.

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Attitude Determination

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  1. Attitude Determination - Using GPS

  2. Table of Contents • Definition of Attitude • Attitude and GPS • Attitude Representations • Least Squares Filter • Kalman Filter • Other Filters • The AAU Testbed • Results • Conclusion Danish GPS Center

  3. What is Attitude? Orientation of a coordinate system (u,v,w) with respect to some reference system (x,y,z) Danish GPS Center

  4. When is Attitude information needed? • Controlling an Aircraft, Boat or Automobile • Onboard Satellites • Pointing of Instruments • Pointing of Weapons • Entertainment industri (VR) • Etc... Danish GPS Center

  5. Attitude sensors Currently used sensors include: • Gyroscopes • Rate gyros (+integration) • Star trackers • Sun sensors • Magnetometers • GPS Danish GPS Center

  6. Advantages of GPS • Adding new functionality to existing equipment • No cost increase • No weight increase • No moving parts (solid-state) • Measures the absolute attitude Disadvantages • Mediocre accuracy (0.1 - 1º RMS error) • Low bandwidth (5-10 Hz maximum) • Requires direct view of satellites Danish GPS Center

  7. Interferometric Principle Danish GPS Center

  8. Interferometric Principle Measurement equation: The full phase difference is the projection of the baseline vector onto the LOS vector: Danish GPS Center

  9. Attitude Matrix 9 parameters needed: When (x,y,z) is a reference system: Danish GPS Center

  10. Properties of “A” “A” rotates a vector from the reference system to the body system The transpose of “A” rotates in the opposite direction (back again) Danish GPS Center

  11. Properties of “A” Rotation does not change the size of the vectors: Every rotation has a rotation-axis (and a rotation- angle) The rotation-angle is the eigenvalue of “A” Danish GPS Center

  12. Euler sequences A sequence of rotations by the angles (,,) about the coordinate axes of the reference system Single axis: Multiple axes: Danish GPS Center

  13. Quaternions A quaternion consists of four composants Where i,j and k are hyperimaginary numbers Danish GPS Center

  14. Quaternions A quaternion can be thought of as a 4 dimensional vector with unit length: Danish GPS Center

  15. Quaternions Quaternions represent attitude as a rotation-axis and a rotation-angle Danish GPS Center

  16. Quaternions Quaternions can be multiplied using the special operator defined as: Danish GPS Center

  17. Quaternions The attitude matrix can be formed from the quaternion as: Where Danish GPS Center

  18. Least Squares Solution Including attitude information into the measurement equation Linearization of the attitude matrix Danish GPS Center

  19. Least Squares Solution Forming the phase residual Danish GPS Center

  20. Least Squares Solution Danish GPS Center

  21. Least Squares Solution Estimate update Danish GPS Center

  22. Extended Kalman Filter A Kalman filter consists of a model equation and a measurent equation Danish GPS Center

  23. Extended Kalman Filter And their linearized counterparts…. And Danish GPS Center

  24. Extended Kalman Filter Algorithm Danish GPS Center

  25. Extended Kalman Filter Tuning of the filter Noise variance determined experimentally Danish GPS Center

  26. Extended Kalman Filter Tuning of the filter Noise variance determined by ‘trial-and-error’ Danish GPS Center

  27. Extended Kalman Filter Determining the system model Danish GPS Center

  28. Other Filters Danish GPS Center

  29. Testbed Danish GPS Center

  30. Software Danish GPS Center

  31. Motor Control Danish GPS Center

  32. Motor Angles Danish GPS Center

  33. Local Horizontal System Danish GPS Center

  34. Results Based on actual and simulated data, the following performance parameters were evaluated • Accuracy • Computational efficiency • Ability to converge Danish GPS Center

  35. Accuracy Danish GPS Center

  36. Speed Danish GPS Center

  37. Convergence Danish GPS Center

  38. Convergence Danish GPS Center

  39. Conclusion • Kalman filter is by far most accurate, but also computationally very heavy • Single-point (LSQ) offers good accuracy + high speed • Vector matching algorithms has the lowest accuracy but does not suffer from convergence problems • Performance depend on satellite constellation • Results were affected by mechanical problems with levelling of the testbed Danish GPS Center

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