An Initial Attitude Determination Method for Geomagnetic Field and Gyro Data Fusion with Kalman Filter

This paper presents an initial attitude determination algorithm using a magnetometer and gyroscopes. Firstly, it measures the geomagnetic field vectors in spacecraft's body-fixed frame (BFF) at two different points (point a and b with the corresponding BBF described as BFFA and BFFB) on orbit track and calculates their theoretical projections in reference frame (RF) with the international geomagnetic field model (IGRF). Secondly, the algorithm utilizes gyro rate integration to calculate the relative quaternion that rotates the spacecraft's BBF from BFFA to BFFB. Thirdly, it converts the coordinate of the first measured vector from BBFA to BBFB with the relative quaternion. Finally, utilizing two unparalleled vectors with their projections in RF and BFFB, the spacecraft's attitude at point b is estimated. The estimation results are directly influenced by measurement noise and by gyro drift but is still accurate enough as initial input for Kalman Filter (KF), which is sensitive to initial estimation errors. Simulations are carried out that demonstrate the efficiency of the algorithm in the particular case of high initial estimation errors.