To determine the approximate position of a global positioning system receiver, the Bancroft method can provide the initial value for linearization of the observation equation, which can then be solved by the least-square (LS) method. Because the solution of LS method is not unique and the observation data have noise, the solution is ill-posed. In order to solve the problem, we introduce the regularization method combined with the optimum choice of regularization parameter. The experimental result indicates that it can enhance the resistance to bad errors, which has significance in real-time fast positioning.