Modified Kalman Filter for Generation of Attitude Error Corrections

A system for utilizing a modified Kalman filter for generating attitude error correction values for a spacecraft, the system comprising:

• primary attitude inertial sensors on board the spacecraft providing attitude measurements at frequent and regular intervals;
• secondary attitude positional sensors providing attitude measurements at irregular or infrequent intervals;
• and
• an attitude error correction filter module of a flight computer configured to
• receive the attitude measurements from the primary attitude inertial sensors and the secondary attitude positional sensors, and
• compute attitude error correction values for the attitude measurements from the primary attitude inertial sensors based on the attitude measurements from the secondary attitude sensors using expanded equations derived for a subset of a plurality of block sub-matrices partitioned from the matrices of the Kalman filter, a remainder of the plurality of block sub-matrices are pre-calculated, wherein
• a covariance propagation and update of the Kalman filter is calculated and updated in a single step,
• the expanded equations derived for the subset of the plurality of block sub-matrices utilize body-reference frame Kalman filter equations, and
• the attitude error correction values are converted back to earth-centered inertial frame reference value before being provided to an attitude control module of the flight computer.