The complex underwater environment often causes signal propagation delay or measurement outliers, resulting in the issues of measurement loss and non-Gaussian noise, leading to a decrease in the accuracy of underwater autonomous positioning. To address these issues, this paper proposes an underwater autonomous positioning method based on Bayesian inference and statistical similarity measurement. Firstly, this positioning method utilizes a maximum posterior estimation method to determine whether there is measurement loss. Secondly, if the measurement information at this moment is received, this method will utilize the fixed-point iteration approach to maximize the lower bound of statistical similarity measurement, approximating the real noise covariance matrices, thus obtaining more accurate state estimation and error covariance matrices. On the contrary, if no measurement information is received, only one-step predicted state estimation and error covariance matrices are output to improve this method's robustness. The simulation and marine experiment show that the proposed underwater autonomous positioning method has higher positioning accuracy and better robustness compared to other positioning methods.