Abstract: The original dual-quaternion navigation algorithm involves many complex operations and requires a large amount of computation. A  implified algorithm is proposed for dual-quaternion navigation to make extraction of gravitational velocity and position vectors easier. The notation of the simplified algorithm is unambiguous. After that, the formula for extracting non-gravitational velocity is further simplified. Simulation shows that the simplified method provides the same precision as the original dual-quaternion algorithm, both being better than the traditional strap-down navigation algorithm. The computation complexity of the proposed method is the least among the three, while position error of the approximate algorithm is close to that of the original dual-quaternion algorithm.