Satellite Attitude Determination AERO4701 Space Engineering 3 Week 5
Last Week Looked at GPS signals and pseudorange error terms Looked at GPS positioning from pseudorange data Looked at GPS error sources, looked at DOP measures, satellite geometry
Overview First Hour Satellite Attitude Determination Overview of common sensors used
Attitude Determination Used mainly for feedback for attitude control, also used for imaging and geo-location of observations made by onboard instruments, mapping etc. We can represent the orientation or attitude of our satellite body fixed frame w.r.t some navigation frame of reference using Direction Cosine Matrix (DCM), Euler angles or Quaternions Commonly represent w.r.t a LGV or LGDV frame
Direction Cosine Matrix (DCM)
Euler Angles
Quaternions Describe rotation between frames by a single rotation of magnitude d about a vector described by the angles [a,b,c] Quaternions use redundant parameter to avoid singularity present in Euler angles at pitch = 90 o
Inertial Navigation Euler Angles Quaternions
Inertial Sensors Ring laser gyros: laser light travels in two paths around the unit, rotation causes a difference in the path length which can be measured by the interference patterns of the two light beams Accuracies as high as 10-3, 10-4 deg/hour drift rates Commercial Ring-Laser Gyros
Inertial Sensors Inertial navigation common for ballistic missiles, no need for external reference data Old ICBM gimballed unit uses mechanical gyros for accelerometer platform levelling Most accurate gyro: experiment on Gravity Probe B, used to test tiny angular variations due to space time curvature of the Earth Gravity Probe B ICBM gimbaled IMU
Magnetometers Measures the Earth s magnetic field direction and strength in sensor fixed coordinates Uses internal model of Earth s magnetic field to calculate two attitude angles Accuracies ~0.5-1 deg
Magnetometers Earth s magnetic field is approximated using the International Geomagnetic Reference Field (IGRF) model Local magnetic field vector can then be calculated using onboard computer model and knowledge of orbital position Only two angles can be measured at any one time (orientation angle around magnetic field cannot be measured) Orientation of the local magnetic field w.r.t LGV frame changes as a function of latitude, make three angle attitude estimation possible over the time span of a full orbit
Sun Sensors Measure the angular position of the sun Based on orbital position and time of day, satellite can use measurement to help estimate orientation Can only provide two angles of orientation similarly to magnetometers
Star Sensors/Trackers Consists of a high accuracy camera with image processing to measure vectors to known celestial objects (mostly stars) High accuracy attitude estimation but potentially at the cost of more expensive equipment (cameras) and much more computer processing
Star Sensors/Trackers From image, stars are extracted from background noise, correlation of shapes found based on a star catalog Sometime colour and brightness are also used in correlation process At least two known stars needed to estimate 3-angle attitude Original Image Star Extraction Pattern Matching C A γ B Base star At least two vectors for attitude determination
Star Sensors/Trackers Older systems would have an astronaut manually align the spacecraft with a known star Computer would record attitude and use this to reset an on board inertial navigation system
Earth/Horizon Scanners Earth/Horizon scanners use the Earth s horizon to estimate the roll and pitch angles of the vehicle Mostly detected in IR; accuracy depends on blurring from atmosphere on horizon
Earth/Horizon Scanners Conical horizon scanner works on same principle but has a moving scanner Tilt angles can be measured by time ratio that scanner scans the Earth vs. space
Tilt Angles vs. Roll and Pitch
Attitude GPS GPS can be used to compute attitude by measuring the relative position of multiple antennas mounted to a structure Requires a reasonably large baseline with at least 3 antennas for 3-angle attitude determination
Summary