Transcript Attitude Determination

Attitude Estimation
Thomas Bak
Institute of Electronic Systems
Aalborg University
[email protected]
Outline
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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?
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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)
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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’ Model 13-515
Barnes,
2.5x2.5 cm sun sensor
Double-Triangle Sun
Sensor Module
Figure 1
Honeywell magnetometer
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Problem Formulation – Wahba’s problem
r1
b1
r3
b2
r2
Reference
b3
Spacecraft body
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Attitude Determination Methods
In general the solutions fall into two groups:
1. Deterministic (point-by-point) solutions, where the attitude is
found based on two or more vector observations from a single point
in time,
2. 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 (cont’d)
1. 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
2. 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 (cont’d)
3. Find the sun position in an inertial frame at the same time and position
points using SunV1.m . Generate 100 sun position reference vectors.
4. Generate 100 random spacecraft attitudes in terms of quaternions by rotation
about the z-axis. The quaternions describe rotation from inertial to spacecraft
frame.
5. 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.
6. 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.
7. 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
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