Autonomous underwater vehicles (AUVs) are susceptible to non-line-of-sight (NLOS) errors and noise bias at receiving stations during the application of hydroacoustic localization systems, leading to a degradation in positioning accuracy. To address this problem, this paper optimizes the Chan-Taylor algorithm. Initially, we propose the Weighted Modified Chan-Taylor (WMChan-Talor) algorithm, which introduces dynamic weights into the Chan algorithm to correct noise variance at measurement stations, thereby improving the accuracy of AUV positioning. Computer simulations validate the effectiveness of the WMChan-Taylor algorithm in enhancing positioning accuracy. To further address the accuracy degradation caused by noise deviations across different receiving stations, we introduce an error-corrected WMChan-Taylor algorithm. This algorithm utilizes a standard residual function to eliminate significant delays caused by large errors at receiving stations and applies standard residual weighting to improve the combined positioning solution. The performance of the error-corrected WMChan-Taylor algorithm is demonstrated through both computer and semi-physical simulation experiments, confirming its capability to isolate noisier stations and thus enhance overall positioning accuracy.