Multi-Beacon Long Baseline Positioning Method Based on Fixed-Point Homotopy

The target is considered as a particle in the traditional long baseline (LBL) underwater positioning model. When multiple acoustic signal senders are installed on the target and the shape of the target cannot be ignored, the positioning error of the traditional model is large. Therefore, the multi-beacon LBL positioning model is constructed based on the position inconsistency correction. Due to the multi-beacon LBL positioning model is a nonlinear equations system, the analytical solution of the target position parameters cannot be obtained. Therefore, the iterative method is needed to obtain numerical solution of the position parameters. Traditional iterative methods are sensitive to the selection of initial value, and improper initial value can easily lead to local minimum in the iteration. The fixed-point homotopy method with large-range convergence is proposed in this paper to reduce the influence of the initial value on the iteration process. The numerical continuation method is used to solve the fixed-point homotopy equation, and the underwater target position parameters can be effective estimated. The simulation results show that compared with Levenberg-Marquardt (L-M) iteration, Gauss-Newton (G-M) iteration and Netwon homotopy, the position parameters of the multi-beacon LBL positioning model can be effectively estimated by the fixed-point homotopy under the same initial value, and the positioning accuracy of the multi-beacon system can be improved.