Increase of accuracy of the small satellite attitude determination using redundancy techniques

Abstract

The paper deals with an algebraic method of attitude determination accuracy and the ways of increasing it. This method was examined with three different vector pairs: (1) Earth's magnetic field and Sun vector, (2) Earth's magnetic field and Nadir vector, (3) Sun vector and Nadir vector. In order to determine the accuracy of the attitude, analytical relations were found for the attitude angles (pitch, roll and yaw). These relations include terms of the measured and theoretical vectors, used in the attitude determination. As a scalar criterion for the determination of the spacecraft attitude accuracy the variance of angle determination was used. According to the results obtained, the accuracy of the algorithms was compared and the intervals where the algorithms give the most accurate results were determined. Thus, the intervals where the applied algorithms do not provide the required accuracy were determined and the reasons for worsening of the accuracy were examined (where the reference vectors are close to parallel or/and the value of pitch angle approaches ( π 2 +nπ) , this two-vector algorithm gives “bad” results). The effect of various factors on the attitude determination were examined and those which most affect the accuracy were determined. In order to increase the attitude determination accuracy, the redundant data processing algorithm, based on the Maximum Likelihood method, was used to carry out the statistical operation on the measurements of the three algorithms mentioned above and appropriate formulas were derived. As a result, the attitude was determined with high accuracy in the wide range (even when the reference vectors were almost parallel).