For the navigation algorithm of the strapdown inertial navigation system, by comparing to the equations of the dual quaternion and quaternion, the superiority of the attitude algorithm based on dual quaternion over the ones based on rotation vector in accuracy is analyzed in the case of the rotation of navigation frame. By comparing the update algorithm of the gravitational velocity in dual quaternion solution with the compensation algorithm of the harmful acceleration in traditional velocity solution, the accuracy advantage of the gravitational velocity based on dual quaternion is addressed. In view of the idea of the attitude and velocity algorithm based on dual quaternion, an improved navigation algorithm is proposed, which is as much as the rotation vector algorithm in computational complexity. According to this method, the attitude quaternion does not require compensating as the navigation frame rotates. In order to verify the correctness of the theoretical analysis, simulations are carried out utilizing the software, and the simulation results show that the accuracy of the improved algorithm is approximately equal to the dual quaternion algorithm. For the navigation algorithm of the strapdown inertial navigation system, by comparing to the equations of the dual quaternion and quaternion, the superiority of the attitude algorithm based on dual quaternion over the first based on rotation vector in accuracy is analyzed in the case of the rotation of comparing the update algorithm of the gravitational velocity in dual quaternion solution with the compensation algorithm of the harmful acceleration in traditional velocity solution, the accuracy advantage of the gravitational velocity based on dual quaternion is addressed. In view of the idea of the attitude and velocity algorithm based on dual quaternion, an improved navigation algorithm is proposed, which is as as as as the rotation vector algorithm in computational complexity. According to this method, the attitude quaternion does not require compensating as the navigation frame rotates. In order to verify the correctness of the theoretical analysis, simulations a re carrying out utilizing the software, and the simulation results show that the accuracy of the improved algorithm is approximately equal to the dual quaternion algorithm.