🛰️Spacecraft Attitude Control Unit 8 – Spacecraft Attitude Determination Methods

Fundamentals of Spacecraft Attitude

• Spacecraft attitude refers to the orientation of the spacecraft with respect to a reference frame
• Attitude control is crucial for maintaining the desired orientation and pointing direction of the spacecraft
• Attitude determination involves estimating the current attitude using various sensors and algorithms
• Spacecraft attitude is typically described using three angles: roll, pitch, and yaw
• Attitude control systems employ actuators such as reaction wheels, thrusters, or magnetic torquers to adjust the spacecraft's orientation
• Disturbance torques, such as gravitational, aerodynamic, and solar radiation pressure, can perturb the spacecraft's attitude
• Attitude stability is essential for ensuring the proper functioning of onboard instruments and communication systems

Coordinate Systems and Reference Frames

• Coordinate systems provide a framework for describing the position and orientation of the spacecraft
• The body-fixed frame is attached to the spacecraft and rotates with it, with axes typically aligned with the spacecraft's principal axes of inertia
• The inertial reference frame is a non-rotating frame, often centered at the Earth's center (Earth-Centered Inertial frame) or the Sun (Sun-Centered Inertial frame)
• The orbital reference frame is defined by the spacecraft's orbit, with the z-axis pointing towards the Earth's center, the y-axis normal to the orbital plane, and the x-axis completing the right-handed triad
• Coordinate transformations, such as rotation matrices or quaternions, are used to convert between different reference frames
• Local vertical, local horizontal (LVLH) frame is commonly used for Earth-orbiting spacecraft, with the x-axis pointing along the velocity vector, the z-axis towards the Earth's center, and the y-axis completing the triad
• Celestial reference frames, such as the International Celestial Reference Frame (ICRF), are based on the positions of distant celestial objects and used for high-precision attitude determination

Attitude Representation Methods

• Attitude representation methods describe the orientation of the spacecraft relative to a reference frame
• Euler angles (roll, pitch, yaw) provide an intuitive representation of attitude but suffer from singularities and gimbal lock
• Direction cosine matrix (DCM) is a 3x3 orthogonal matrix that represents the rotation between two coordinate frames
  • DCM is composed of nine elements that satisfy orthogonality and unity constraints
  • DCM is commonly used for attitude transformations and computations
• Quaternions are four-dimensional vectors that provide a singularity-free and computationally efficient attitude representation
  • Quaternions consist of a scalar part and a vector part, with the vector part representing the rotation axis and the scalar part related to the rotation angle
  • Quaternions are used extensively in attitude estimation and control algorithms
• Rodrigues parameters, also known as Gibbs vector, represent attitude using a three-dimensional vector
• Modified Rodrigues parameters (MRP) provide a minimal attitude representation with improved numerical stability compared to Rodrigues parameters

Sensors for Attitude Determination

• Sun sensors measure the direction of the Sun relative to the spacecraft and provide two-axis attitude information
  • Coarse sun sensors have a wide field of view and are used for initial attitude acquisition
  • Fine sun sensors have a narrow field of view and higher accuracy for precise attitude determination
• Star trackers capture images of the star field and compare them with a star catalog to determine the spacecraft's attitude
  • Star trackers provide high-accuracy three-axis attitude information and are widely used in modern spacecraft
  • Star identification algorithms, such as the pyramid algorithm or the grid algorithm, are used to match the observed stars with the catalog
• Magnetometers measure the Earth's magnetic field vector in the spacecraft's body frame, providing two-axis attitude information
• Gyroscopes measure the angular velocity of the spacecraft and are used for short-term attitude propagation
  • Rate gyros measure the angular velocity directly
  • Fiber-optic gyros (FOGs) and ring laser gyros (RLGs) are commonly used due to their high accuracy and reliability
• Horizon sensors detect the Earth's horizon and provide pitch and roll information relative to the local vertical
• Global Positioning System (GPS) receivers can be used for attitude determination by measuring the carrier phase differences between multiple antennas

Attitude Determination Algorithms

• Attitude determination algorithms estimate the spacecraft's attitude using sensor measurements and mathematical models
• Deterministic methods, such as TRIAD or QUEST, use a minimum set of vector measurements to compute the attitude
  • TRIAD algorithm requires two non-parallel vector measurements and provides a closed-form solution
  • QUEST (Quaternion Estimator) algorithm is an optimization-based method that minimizes the attitude error using multiple vector measurements
• Recursive estimation techniques, such as the Kalman filter, use a dynamic model of the spacecraft and sensor measurements to estimate the attitude and its uncertainty
  • Extended Kalman Filter (EKF) linearizes the nonlinear attitude dynamics and measurement models for state estimation
  • Unscented Kalman Filter (UKF) uses a deterministic sampling approach to capture the nonlinearities without explicit linearization
• Batch estimation methods, such as the Batch Least Squares (BLS) algorithm, process a batch of sensor measurements to estimate the attitude over a specific time interval
• Particle filters, also known as Sequential Monte Carlo methods, represent the attitude probability distribution using a set of weighted particles
• Attitude determination algorithms often incorporate sensor fusion techniques to combine measurements from multiple sensors and improve estimation accuracy

Error Sources and Calibration

• Sensor errors, such as bias, scale factor, and misalignment, can introduce inaccuracies in attitude determination
  • Bias refers to a constant offset in the sensor measurements
  • Scale factor represents the ratio between the true and measured values
  • Misalignment errors occur when the sensor axes are not perfectly aligned with the spacecraft's body axes
• Spacecraft flexibility and thermal distortions can cause discrepancies between the assumed and actual sensor orientations
• Calibration techniques are used to estimate and compensate for sensor errors and improve attitude determination accuracy
  • On-orbit calibration methods, such as the batch least-squares approach or the Kalman filter-based approach, estimate the calibration parameters using in-flight data
  • Ground-based calibration is performed before launch to characterize sensor performance and determine calibration coefficients
• Star catalog errors, such as incorrect star positions or magnitudes, can affect the accuracy of star tracker-based attitude determination
• Atmospheric effects, such as refraction and scintillation, can introduce errors in horizon sensor measurements
• Magnetic field modeling errors, due to the complex and time-varying nature of the Earth's magnetic field, can impact magnetometer-based attitude determination

Advanced Techniques and Future Trends

• Attitude determination using multiple spacecraft formations, such as formation flying or satellite swarms, enables collaborative and distributed sensing
• Deep learning and machine learning techniques are being explored for attitude determination, particularly for star pattern recognition and sensor fusion
  • Convolutional Neural Networks (CNNs) have shown promise in star identification tasks, reducing computational complexity and improving robustness
  • Recurrent Neural Networks (RNNs) can capture temporal dependencies in attitude estimation problems
• Autonomous attitude determination systems aim to reduce the reliance on ground-based processing and enable real-time onboard attitude estimation
• Sensor advancements, such as miniaturized star trackers, MEMS gyroscopes, and quantum sensors, offer improved accuracy, reliability, and power efficiency
• Integration of attitude determination with other spacecraft subsystems, such as guidance, navigation, and control, enables more efficient and coordinated operations
• Fault-tolerant attitude determination algorithms, such as the Interacting Multiple Model (IMM) approach, can handle sensor failures and maintain attitude estimation performance
• Adaptive attitude determination techniques can adjust the estimation algorithms based on the operating conditions and sensor availability

Practical Applications and Case Studies

• Earth observation satellites require precise attitude determination for accurate pointing and image geo-referencing
  • Landsat series satellites use star trackers and gyroscopes for high-accuracy attitude determination
  • Sentinel-2 satellites employ multiple star trackers and a GPS receiver for attitude estimation
• Communication satellites rely on accurate attitude determination for antenna pointing and beam steering
  • Intelsat satellites use a combination of star trackers, sun sensors, and gyroscopes for attitude determination
  • Iridium NEXT constellation satellites determine attitude using star trackers and Earth horizon sensors
• Interplanetary missions have stringent attitude determination requirements for navigation, scientific observations, and data transmission
  • Cassini mission to Saturn used star trackers, sun sensors, and gyroscopes for attitude determination during its orbital operations
  • New Horizons mission to Pluto and the Kuiper Belt relies on a star tracker, an inertial measurement unit (IMU), and a sun sensor for attitude estimation
• Small satellite missions, such as CubeSats, face unique challenges in attitude determination due to limited power, space, and computational resources
  • AAUSAT3 CubeSat mission used a combination of magnetometers, sun sensors, and a MEMS gyroscope for attitude determination
  • BRITE constellation of nanosatellites employs a miniaturized star tracker and a set of coarse sun sensors for attitude estimation
• Formation flying missions require relative attitude determination between multiple spacecraft
  • PRISMA mission demonstrated autonomous formation flying and relative attitude determination using GPS receivers and an vision-based sensor system
  • Proba-3 mission plans to use a laser-based metrology system for high-precision relative attitude determination between two spacecraft