Quaternions and Attitude Representation

The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as well as mathematical complications involved in using them. This technical note gives a brief overview and discusses the quaternions, which are fourth dimensional extended complex numbers and used to represent orientation. Their relationship to other modes of attitude representation such as Euler angles and Axis-Angle representation is also explored and conversion from one representation to another is explained. The conventions, intuitive understanding and formulas most frequently used and indispensable to any quaternion application are stated and wherever possible, derived.