An Improved LEO Positioning Solution Algorithm Based on the LM Algorithm

This study derived a solution method for Doppler shift positioning of low Earth orbit (LEO) satellites and built a simulation environment for satellite constellation. Addressing the numerical instability and convergence issues of the Gauss-Newton (G-N) iterative algorithm in the solution process, an improved solution method based on the Levenberg-Marquardt (LM) algorithm was proposed. By conducting experiments with different error terms introduced and comparing the experimental results of various methods, it was found that the LM algorithm exhibited superior positioning accuracy in both single-error and mixed-error scenarios. Furthermore, to tackle the sensitivity of the Doppler shift positioning algorithm for low Earth orbit satellites to initial values, a grid search-based method for determining initial values was proposed, thereby reducing the impact of initial values on the positioning results.