A New Optimization-Based Attitude Estimator with a Closed form Solution Using Magnetometer and Gyro Data

Attitude determination in space missions is of a great importance. Especially, small satellite attitude determination faces two main challenges: a limited number of attitude sensors and weak computational resources. The two aforementioned issues represent the main motivation of this work, where a magnetometer and a rate gyro are employed in a simple and fast algorithm to determine satellite attitude. A part of the attitude is measured with the magnetometer and the other is estimated using the satellite kinematics with optimization. The proposed method solves the optimization problem with an analytical approach based on a closed form relation. Consequently, it does not need an initial time to converge. The new method has two adjustable parameters to compromise between estimation accuracy and computation time. The conventional Extended Kalman Filter, as a method with relatively low computational effort, is compared with the proposed method. The simulation results show that the algorithm not only has a better accuracy than EKF but also it requires impressively less computation time.