Aiming at the ill-posed problems of observation equation in satellite navigation rapid positioning, a method that unites the adaptive weighted differential evolution (DE) algorithm and Tikhonov regularization is proposed. Based on a thorough analysis of the optimization process of the DE algorithm, an adaptively changed weighting factor is applied in the mutation process. Also, the regularization term is introduced to the objective function of DE to solve the equation steadily. Simulation results show that, when the condition number is about 10⁵, the new method has the least number of iterations compared with other intelligent optimization algorithms such as the genetic algorithm (GA) and the basic DE algorithm. The accuracy of the new method is about 5 times, 2 times, 1.5 times and 1 times higher than the traditional truncated singular value decomposition (TSVD) method, the Tikhonov regularization method, the GA and the basic DE algorithm respectively. When gross errors exist in observation vectors, the accuracy of the new method is basically the same. Therefore, the proposed method has good soundness.