|Abstract In satellite navigation system, the traditional algorithm of solving dilution of precision (DOP) and satellite positioning based on least square method is the direct matrix inverse (DMI) method. In order to overcome the disadvantages of high computational burden and poor numerical stability of traditional DMI method, an improved method of satellite positioning and DOP was presented based on the matrix U T DU decomposition, which made use of the symmetric and positive definite performance of the measurement matrix. The correctness and validity of the new method can be guaranteed by the strict mathematical theory. The numerical results show that, in comparison with the traditional DMI method, the reduction of operational volume of positioning is about 60% and that of solving DOP is about 36% by the proposed method. At the same time, the condition number of the solving matrix of the improved method has reduced considerably after decomposition and the numerical stability is significantly improved.