Path Planning Method for Underwater Gravity-Aided Inertial Navigation Based on PCRB

Gravity-aided inertial navigation system (GAINS) is an important development in autonomous underwater vehicle (AUV) navigation. An effective path planning algorithm plays an important role in the performance of navigation in long-term underwater missions. By combining the gravity information obtained at each position with the error information from the INS, the posterior Cram\'er-Rao bound (PCRB) of GAINS is derived in this paper. The PCRB is the estimated lower bound of position variance for navigation along the planned trajectory. And the sum of PCRB is used as the minimum cost from the initial state to the current state in the state space, and the position error prediction variance of inertial navigation system (INS) is used as the minimum estimated cost of the path from the current state to the goal state in the A* algorithm. Thus, a path planning method with optimal navigation accuracy is proposed. According to simulation results, traveling along the path planed by the proposed method can rapidly improve the positioning accuracy while consuming just slightly more distance. Even when measuring noise changes, the planned path can still maintain optimal positioning accuracy, and high positioning accuracy is possible for any trajectory located within a certain range of the planned path.