For the multiple autonomous underwater vehicles (AUV) cooperative localization system based on two alternate leaders, by the two-stage cascade filtering method, an adaptive filtering algorithm for multiple AUV cooperative localization is proposed. The state estimation of follower AUV is decomposed into two parts: heading estimation and position estimation, which is able to reduce the influence on the poor observability of heading angle estimation as a result of using the range-only measurements and improve the position estimation performance under range measurement error model uncertainty. In addition, the algorithm complexity criterion is introduced to analyze the proposed cooperative localization algorithm. The simulation experimental results indicate that the performance of proposed algorithm is superior to the traditional approach, in terms of both localization accuracy and complexity.