Objectives  This paper proposes a multi-autonomous underwater vehicle (AUV) cooperative localization algorithm based on an adaptive fading Sage–Husa extended Kalman filter in order to increase the positioning accuracy of mult-AUVs during navigation.

  Methods  The algorithm improves the adaptive filter in the filtering algorithm, obtains the estimated value of the innovation covariance through the weighting of the fading memory index, and introduces the fading factor to adjust the prediction error covariance matrix to achieve the purpose of adjusting the filter gain. The multi-AUV cooperative navigation model is established and the basic filtering process is obtained; through the fusion of speed and position information, an accurate estimation of the position state of the follower-AUV is achieved; finally, the algorithm and the expectation maximization-EKF (EM-EKF) and EKF algorithms are used in an AUV cooperative navigation model for simulation comparison.

  Results   The results show that when the noise covariance does not match, the root mean square error (RMSE) of the proposed algorithm is reduced by 17.82% and 24.48% respectively, and the average localization error (ALE) is reduced by 17.87% and 22.54% respectively; when the noise covariance is time-varying, the RMSE of the proposed algorithm is reduced by 42.11% and 51.23% respectively, and the ALE is reduced by 34.87% and 46.90% respectively.

  Conclusions   The proposed algorithm can effectively improve the reliability, accuracy and adaptability of filtering.