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In order to improve the precision of navigation positioning, a more accurate solution of GPS positioning equations is required. A new algorithm is developed and improvement of existing algorithms has been made in this paper to improve the precision. For each algorithm, simulation is made respectively. Simulation results show that compared to old ones, the new algorithm can improve the solution precision by 29.41%. The improvement of existing algorithms can increase the solution precision by 34.55% and 6.72%. As a result, the precision of navigation positioning can be improved correspondingly. In the end, the direction of future research is discussed.