This paper examines projective and differential geometry of attitude errors in various parameterizations. It begins with a review of algebra and kinematics of attitude parameterizations, which leads to a discussion of similarities between projective mappings characteristic of attitude rates and those characteristic of additive and multiplicative errors. The paper then demonstrates how differential equations governing propagation of these errors in various parameterizations follow naturally from the underlying algebraic structure of the rotation tensor. Next, it is shown how the fundamental algebraic and geometric properties of attitude parameterizations yield elegant general closed-form expressions for the attitude error transition matrices and how these matrices can be modified when switching from the original parameterizations to their shadow counterparts. The closed-form expressions of the error transition matrices are also leveraged in the development of the error expansion and nonlinearity metrics. Finally, various results presented in the paper are assembled together to derive general expressions for sequential attitude estimation based on extended Kalman filtering. These include a novel closed-form discrete-time covariance update, which is more accurate and faster to compute than numerical approximations using matrix exponential. The paper illustrates many of its general derivations with examples that include the classical, modified, and generalized Rodrigues parameters, the rotation vector, and the quaternion vector part.
Projective and Differential Geometry of Attitude Errors with Applications to Estimation
Journal of Guidance, Control, and Dynamics ; 36 , 5 ; 1254-1266
2013-09-01
Article (Journal)
Electronic Resource
English
Projective Geometry of Attitude Parameterizations with Applications to Estimation (AAS 12-241)
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