Attitude Estimation Thomas Bak Institute of Electronic Systems Aalborg University tb@control.auc.dk

Outline Motivation Sensors Problem formulation – Wahba Single point methods Filtering

What is Attitude Determination? How do we estimating the orientation of a spacecraft by making remote observations of celestial bodies or reference points?

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)

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)

Attitude Sensors 2

Attitude Sensors - Examples DTU Advanced Stellar Compass – camera head unit TANS Vector GPS Barnes’ Model 13-515 Double-Triangle Sun Sensor Module Figure 1 Barnes, 2.5x2.5 cm sun sensor Honeywell magnetometer

Problem Formulation – Wahba’s problem

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.

Deterministic (point-by-point) Requires 2 or more measurements Numerous solutions are available:

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.

Assignment (cont’d) 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.

Assignment (cont’d) 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)

References