## 1 Introduction  
The autonomous underwater vehicle (AUV) has a wide application prospect in civil and military fields due to its independent and autonomous operation ability. For AUVs that undertake ultra-long distance, large depth, and all-weather submersible missions, they need to autonomously and accurately navigate in the submersible state until the task is completed. The current main underwater positioning and navigation technology of AUVs is the inertial navigation system (INS). Due to the inherent defects of accelerometer zero bias and gyro drift, position errors of the INS will accumulate with time and fail to meet the requirements of AUVs [1]. Terrain-aided navigation (TAN) helps the INS correct the position and has the advantages of autonomy, concealment, and no accumulation of error over time. First, the position sequence graph is determined using INS positions. Then, the sequence that best matches the INS position sequence graph is found on the map, and the INS is corrected to the optimal matching sequence. This is the principle in which TAN corrects the cumulative errors of the INS. The key technology of TAN is the matching algorithm [2, 3]. The common matching algorithms are as follows: terrain contour matching (TERCOM), Sandia inertial TAN (SITAN), and iterative closest contour point (ICCP) [4]. SITAN uses the extended Kalman filter (KF) on the inertial terrain reference. It has good real-time performance and maneuverability but requires relatively accurate initial position error. Moreover, the algorithm is sensitive to the linearization of nonlinear observation models, and low linearization accuracy leads to filter divergence [5]. ICCP realizes position matching through repeated rigid transformation, and the matching effect is good when the initial error is small. However, when the initial error is large, mismatching will occur, and the real-time performance of ICCP is poor [6,7]. TERCOM involves correlation analysis, easily operated in practice. However, it has high computational complexity, a long output cycle, and is sensitive to course angle error [8,9]. The traditional terrain matching algorithm cannot meet the requirements for real-time navigation updates, and phenomena such as reduced positioning accuracy, algorithm instability, and long matching time are likely to occur. Terrain matching is a problem of optimization. With the development of intelligent computing, swarm intelligence optimization algorithms can be applied to INS terrain matching. [PERSON] et al. [10] used a chaotic search-based hybrid particle swarm optimization (PSO) to enhance the local development ability of PSO. Through the experiment, it is found that the newly proposed algorithm could effectively reduce the positioning error. [PERSON] et al. [11] proposed introducing PSO with convergence factors to the terrain matching of strapdown inertial navigation system (SINS) for uniform speed direct navigation experiments. The results showed that compared with TERCOM, PSO with convergence factors had higher matching accuracy and shorter matching time. However, when the initial error was large, the matching error was relatively high, which necessitated further improvement. [PERSON] et al. [12] enhanced the performance of PSO by modifying the inertia weight and acceleration factor. The improved PSO was applied to the autonomous navigation of the unmanned surface vehicle, thus improving the stability of autonomy. PSO can be combined with other algorithms to improve its performance. [PERSON] et al. [13] combined PSO with the sine and cosine algorithm (SCA) and levy flight (LF), and found that the new algorithm could find global optimal solutions of different reference functions faster and improve the robustness of the system. [PERSON] et al. [14] found a novel algorithm named SAPSO by combining PSO with simulated annealing. Although using this algorithm could improve the matching accuracy of navigation, it was time-consuming.