The primary problem faced by the integrated navigation system based on the inertial navigation system (INS) and global positioning system (GPS) is providing reliable navigation and positioning solutions during GPS failure. Thus, this study proposes an innovative integrated navigation algorithm to address the limitation of precise positioning when GPS fails. First, for the limitation of noise interference in INS, noise reduction technology based on ensemble empirical mode decomposition (EEMD) is proposed to improve the quality of the INS signal and enhance the noise reduction effect. Second, an INS/GPS integrated framework based on the sparrow search algorithm (SSA) and extreme learning machine (ELM) is proposed. During normal GPS conditions, SSA-ELM is used to develop a high-precision prediction model to estimate differences between INS and GPS. When the GPS signal is interrupted, the difference predicted by SSA-ELM is used as the measurement input and the INS is corrected. To confirm the effectiveness of this method, a real ship experiment is conducted with other commonly used methods. The experimental results demonstrate that the proposed method can improve positioning accuracy and reliability when GPS is interrupted.