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Attitude estimation is used to determine the spatial orientation of an object relative to a reference coordinate frame, or to provide a method for vector conversion between the reference coordinate frame and the target coordinate frame. In this paper, after the definitions of 4 kinds of attitude representations, we derive the conversion formulas between different attitude representations. Then, a complete derivation process of the attitude differential equations is provided. In the end, we describe the result of a typical experiment, which demonstrates the correctness of these conversion formulas. All these researches can help understand the meaning of the attitude accurately and master the attitude updating algorithm in different fields of applications. Keywords—attitude; conversion; quaternion; rotation

Research on Attitude Representations and Attitude Differential Equations