Attitude Estimation

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Attitude Estimation

• Thomas Bak
• Institute of Electronic Systems
• Aalborg University
• tb_at_control.auc.dk

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Outline

• Motivation
• Sensors
• Problem formulation Wahba
• Single point methods
• Filtering

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What is Attitude Determination?

• How do we estimating the orientation of a
  spacecraft by making remote observations of
  celestial bodies or reference points?

4
Motivation

• Satellites generally carry instruments to
• Do scientific work
• Do reconnaissance
• Provide communication links
• Perform weather observation
• Results in mission requirements
• The attitude of the satellite be controlled to
  point antennas, sensors, solar panels etc.
• On board control requires the attitude to be
  determined
• Alternatively the attitude is required in science
  data processing (on the ground)

5
Attitude Sensors 1

• Rate sensors
• For initial acquisition modes, where the spin
  rate of the spacecraft must be controlled to
  attain a first inertial lock
• Coarse Pointing Sensors
• Coarse control is carried out using sun sensors,
  magnetometer Earth sensors, GPS etc.
• Fine Pointing Sensors
• Fine pointing control is almost invariably by
  star camera. Recently, designs have converged
  towards simple camera systems recording 2D images
  using a Charged Coupled Device (CCD)

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Attitude Sensors 2
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Attitude Sensors - Examples
DTU Advanced Stellar Compass camera head unit
TANS Vector GPS
Barnes, 2.5x2.5 cm sun sensor
Honeywell magnetometer
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Problem Formulation Wahbas problem
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Attitude Determination Methods

• In general the solutions fall into two groups
• Deterministic (point-by-point) solutions, where
  the attitude is found based on two or more vector
  observations from a single point in time,
• Filters, recursive stochastic estimators that
  statistically combine measurements from several
  sensors and often dynamic and/or kinematic models
  in order to achieve an estimate of the attitude.

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Deterministic (point-by-point)

• Requires 2 or more measurements
• Numerous solutions are available

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Assignment

• Note Examples of Matlab code is found at the
  address www.control.auc.dk/tb/best/
• The directory www.control.auc.dk/tb/best/matlab/
  holds a number of files used in the exercise. The
  main references are given in the text below.
• The purpose of this exercise is to demonstrate a
  simple three-axis attitude determination using
  sun and magnetic field data. Data is generated
  for a satellite in a 800 km orbit with a slow
  rotation about the z-axis. Reference data as well
  as simulated measurements are generated, the SVD
  algorithm applied and finally the results are
  compared.

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Assignment (contd)

• In Matlab generate 100 points simulating the
  inertial position and Julian date (time) of a
  satellite in Earth orbit. Hint, use provided
  program, svddemo.m
• Using the provided function, BDipole.m calculate
  the Earth magnetic field vector in the position
  points and time found in 1). The result is 100
  magnetic reference vectors in an inertial frame.

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Assignment (contd)

• Find the sun position in an inertial frame at the
  same time and position points using SunV1.m .
  Generate 100 sun position reference vectors.
• Generate 100 random spacecraft attitudes in terms
  of quaternions by rotation about the z-axis. The
  quaternions describe rotation from inertial to
  spacecraft frame.
• Rotate the sun and magnetic reference vectors
  into the spacecraft frame using the Q2Mat.m,
  which generates rotation matrices that may be
  multiplied with vectors to generate body frame
  sun and magnetic vectors.
• Use the two sets of vectors (magnetic field
  reference and spacecraft frame sun reference
  and spacecraft frame) in the SVD single point
  attitude determination algorithm.
• Compare results from the SVD attitude
  determination algorithm with the direction
  cosines generated in 5) or convert the SVD
  direction cosine solution to quaternions using
  Mat2Q.m and compare the quaternions from 4)

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References