Derivation of nonlinear error equations of strapdown inertial navigation system using quaternion

Derivation method of nonlinear differential error equations of attitude and velocity of strapdown inertial navigation system (SINS) using quaternion is studied. In large numbers of references studying quaternion. researchers are often confused about the relationship among these conclusions because different kinds of expressions and denotations have been applied. Under the conventional denotation system, some new useful relations are derived. Using these new relations, the nonlinear error equations of SINS are analyzed, and the important equations and error models of SINS can be reduced. Accurate nonlinear equations of attitude and velocity error under the new denotation are given.