For the underwater long baseline (LBL) positioning systems, the traditional distance intersection algorithm simplifies the sound speed to a constant, and calculates the underwater target position parameters with a nonlinear iteration. However, due to the complex underwater environment, the sound speed changes with time and space, and then the acoustic propagation path is actually a curve, which inevitably causes some errors to the traditional distance intersection positioning algorithm. To reduce the position error caused by the uncertain underwater sound speed, a new time of arrival (TOA) intersection underwater positioning algorithm of LBL system is proposed. Firstly, combined with the vertical layered model of the underwater sound speed, an implicit positioning model of TOA intersection is constructed through the constant gradient acoustic ray tracing. And then an optimization function based on the overall TOA residual square sum is advanced to solve the position parameters for the underwater target. Moreover, the parti-cle swarm optimization (PSO) algorithm is replaced with the traditional nonlinear least square method to optimize the implicit positioning model of TOA intersection. Compared with the traditional distance intersection positioning model, the TOA intersection positioning model is more suitable for the engineering practice and the optimization algorithm is more effective. Simulation results show that the proposed methods in this paper can effectively improve the positioning accuracy for the underwater target.

As a new information provider of autonomous navigation, the on-orbit landmark observation offers a new means to improve the accuracy of autonomous positioning and attitude determination. A novel autonomous navigation method based on the landmark observation and the inertial system is designed to achieve the high-accuracy estimation of the missile platform state. In the proposed method, the navigation scheme is constructed first. The implicit observation equation about the deviation of the inertial system output is derived and the Kalman filter is applied to estimate the missile platform state. Moreover, the physical observability of the landmark and the mathematical observability of the navigation system are analyzed. Finally, advantages of the proposed autonomous navigation method are demonstrated through simulations compared with the traditional celestial-inertial navigation system and the deeply integrated celestial-inertial navigation system.