In uncertain marine environment, auxiliary sensors of the unmanned marine vehicle (UMV) integrated navigation system may be abnormal at any time, reducing the navigation accuracy. To address this problem, this article presents a novel data-based anomaly location and recovery (ALR) algorithm for the strapdown inertial navigation system (SINS)/Doppler velocity log (DVL)/pressure sensor (PS) integrated navigation system. The ALR algorithm uses long short-term memory (LSTM) networks to establish the relationship between filter parameters and the location of anomalies. Considering the dependence of data-driven algorithms on extensive datasets and the challenges in obtaining a substantial amount of navigation experimental data, the LSTM networks incorporate a transfer learning approach to transfer anomaly-related features exacted from sufficient virtual data to real tasks. In addition, variations in the distribution of the same class navigation data at different stages contribute to the intraclass diversity of samples. To avoid the diagnosis delay of gradual anomalies caused by intraclass diversity, we designed a dual LSTM network module with a self-staging strategy. Subsequently, an anomaly recovery module is implemented based on the Janus structure of DVL beams. Simulations and lake-trial experiments indicate the effectiveness of the proposed ALR method, particularly under a limited dataset, thereby enhancing accuracy and reliability in fault-tolerant navigation.