Kalman Filter for Satellite Attitude Determination

Satellite attitude determination is one of the core technologies in spacecraft control, aiming to estimate a satellite's orientation state (such as pitch, roll, and yaw angles) in three-dimensional space in real-time using sensor measurement data. The Kalman filter has become a classic algorithm in this field due to its excellent noise suppression and dynamic tracking capabilities.

Core Principles The Kalman filter achieves optimal estimation through a two-stage recursive process of "prediction-update": Prediction Phase: Based on the satellite dynamics model (such as rigid body motion equations), predict the attitude angles and angular velocities at the next time step, while updating the state covariance to reflect model uncertainty. Update Phase: When sensor data (e.g., from star trackers and gyroscopes) arrives, the predicted values are weighted and fused with the measurements. The weights are determined by both the sensor noise covariance and prediction errors, ultimately outputting the optimal estimate.

MATLAB Implementation Essentials Dynamics Modeling: Establish satellite attitude quaternion or Euler angle differential equations, discretize them, and use them as the state transition matrix. Sensor Fusion: Gyroscopes provide high-frequency angular velocity data but suffer from drift, while star trackers offer low-frequency but absolute attitude references. The filter must balance these characteristics. Key Tuning Parameters: The covariance matrices of process noise (model confidence) and observation noise (sensor accuracy) directly affect the filter's stability.

Extended Applications For complex scenarios (such as model mismatch during maneuvers), adaptive Kalman filters or UKF (Unscented Kalman Filter) can be combined to enhance robustness. During simulation, it is recommended to inject Gaussian white noise to simulate real sensor data and verify the algorithm's anti-interference capability.

(Note: In actual development, issues such as quaternion normalization and Euler angle singularities must be addressed.)