MultiSensor Extended Kalman Filter for Spacecraft Attitude Determination

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Multi-Sensor Extended Kalman Filter for
Spacecraft Attitude Determination

• Tena Wang
• ASE/EM Dept
• UT-Austin

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Background/Motivation

• Sensor suites are useful for maximizing the
  advantages of each sensor while minimizing the
  disadvantages.
• As missions become more ambitious, spacecraft
  navigation will require more versatility, which
  may not be realizable with just one or two
  sensors.
• In the past, not many missions had the option of
  using sensor suites because of each sensors
  cost, form factor, and weight.
• However, now, smaller, cheaper sensors are being
  offered from such manufacturers as Ball
  Aerospace, AeroAstro, and Boeing.
• This research investigated how several different
  sensor measurements would be combined together,
  and what the results of such combinations would
  be.

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List of Filters Discussed

• Previous Work GPS and Magnetometer (GM) EKF for
  FASTRAC satellites
• Thesis Work
• GPS, Magnetometer, Star Tracker (GMST) EKF
• Cascade Filter GPS, Magnetometer, Star Tracker,
  Gyro (GMST-Gyro) EKF

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Multi-Sensor Extended Kalman Filter

• To add multiple sensor measurements to EKF
• Sensor measurement models, Gsensor.
• The following were augmented
• The observation vector, y
• The sensitivity matrix, H
• The measurement covariance matrix, R
• A dynamic model was not included
• Adding a gyro was different from adding the star
  tracker.

Tapley, B., Schutz, R., Born, G. Statistical
Orbit Determination, Elsevier Academic Press,
Amsterdam, 2004.
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GMST EKF

• State vector
• The star tracker measurements were modeled as a
  quaternion
• Star tracker measurements were generated with the
  following equation
• 12 different cases were tested in which the
  random error and the weighting of the data were
  varied.
• For reference, the following were the weights
  given to the GPS and magnetometer data
• GPS SNR data R1.0 if numsatslt5 and R3.0
  otherwise
• Magnetometer data R1.0
• Standard deviations were calculated
• Attitude solutions were plotted

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GMST EKF Results

• As error increases, the standard deviation
  increases.
• Generally, as the data is weighted less, the
  standard deviations increases because the GPS and
  magnetometer data are driving the solution.
• For reference, the standard deviations for the GM
  attitude solution were the following
• Roll 0.66971 deg
• Pitch 0.75682 deg
• Yaw 2.23854 deg
• 3 Axis 2.45608 deg
• In the cases outlined in red, there was not a
  clear trend as the weight was decreased.

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GMST EKF Results (continued)
Test Case 4 Random Error5400 arcseconds ,
R0.001
Test Case 1 Zero Random Error, R0.001
Test Case 9 Zero Random Error , R10.0
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Cascade Filter (GMST-Gyro)

• State vector
• The gyro measurement model was the following
• where g is the gyro-measured spacecraft
  angular velocity
• ?true is the true spacecraft velocity
• ß is the gyro bias or gyro drift
• ?1 is the random error vector modeled as a
  zero-mean Gaussian white noise in each of the
  spacecraft axes
• Two cases tested
• Without bias
• With bias (10-5 rad/s)

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GMST-Gyro (without bias) Results
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GMST-Gyro (with bias) Results
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Conclusions/Recommendations

• Star tracker and gyro measurements were combined
  with GPS and magnetometer measurements, and the
  results indicate that filters are working as
  expected.
• Assuming typical star tracker measurement
  accuracies, combining the star tracker
  measurements to the GPS and magnetometer
  measurements increased the accuracy of the
  attitude estimate.
• The gyro would be useful for cases in which high
  frequency measurements were needed such as when
  the spacecraft is tumbling at a high rate.
• This filter was only tested with one orbit
  scenario and should be tested with others.
• Other sensors models and measurements should be
  added to test other combinations.

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• Questions?