Dual-satellite passive positioning based on improved particle swarm optimization combined with Newton iteration

The passive positioning method utilizing the joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) from two satellites leverages the discrepancies in signal arrival time and frequency to formulate positioning equations. These equations are inherently nonlinear and possess multiple extrema, making them difficult to resolve. To overcome these computational challenges, this study introduces a novel hybrid algorithm that integrates Particle Swarm Optimization (PSO) with Levy flight and Newton iteration. The proposed optimization approach mitigates the issues related to the selection of initial values, as well as the convergence instability and suboptimal positioning accuracy commonly encountered in traditional methods. By incorporating a linearized iterative process, the method efficiently converges to the final positioning solution. The effectiveness and robustness of the proposed algorithm are corroborated by extensive simulation experiments, which confirm its capability to address the passive positioning problem based on the joint TDOA and FDOA of two satellites.