Estimating inertial measurement unit error without any external reference information has always been a difficult problem. The method based on the reconstruction of the gravitational apparent motion in the inertial frame can estimate the accelerometer bias, but a long identification time is needed to get high alignment accuracy. In order to reduce the convergence time and improve the accuracy of estimation, a fast estimation method based on repetitive navigation under the excitation of swing motion is proposed. Two data processing methods, the forward-forward loop and the backward-forward loop, are studied and compared in this paper. In addition, the influence of data length on the experiment result was analyzed. The simulation and experimental results show that the forward-forward loop calculation cannot solve the contradiction between speed and accuracy, while the backward-forward loop calculation can effectively estimate the accelerometer bias and realize self-alignment, with a short alignment time and high alignment accuracy.