Analytic accelerometer–magnetometer attitude determination without reference information

Attitude determination using the accelerometer–magnetometer combination is basically an applied mathematical problem. Commonly, such attitude determination tasks should be accomplished with reference information of sensors, e.g. the magnetometer’s reference vector, from calibration processes. However, this piece of important information cannot be accurately acquired or would differ with the change of body’s position. In this paper, to solve such problem, the conventional accelerometer–magnetometer combination fusion equations are transformed into a brand new set of equations, which are free of reference information. Quaternion solutions to the novel equations are obtained via analytic computation techniques. According to the unique design, the proposed attitude estimator owns very fast computation speed compared with representative methods including iterative ones and algebraic ones. Experiments and simulations are carried out to give demonstrations and comparisons, which verify the correctness and effectiveness of the proposed method. The results also show that using the proposed quaternion solution, fusion with gyroscope can be more efficiently obtained.