Simplified Design of Dual Quaternion Strapdown Inertial Navigation Integration Algorithms

Dual quaternion navigation algorithm gain higher accuracy than traditional strapdown inertial navigation algorithm at the cost of real-time performance. In order to reduce tremendous computation amount of the former, a simplified design scheme for navigation integration algorithms is presented in this paper. First, based on update principle and computation rules of dual quaternion we separate rotational and translational increment information from dual quaternion increment, and deduce exact solutions defined by the spiral vector for thrust velocity increment, gravitational velocity increment and displacement increment. Then, considering characteristics of a strapdown inertial navigation system, implementation schemes of simplified integration algorithms for dual quaternion differential equations in three frames, including thrust velocity coordinates, gravitational velocity coordinates and position coordinates, are designed separately. Under the premise of ensuring the accuracy advantage of the original dual quaternion inertial navigation algorithm, the proposed simplified algorithm significantly improve the computational efficiency. This will lay favorable foundation for engineering realization of the dual quaternion strapdown inertial navigation algorithm.