NAVSTAR/GPS Global positioning system may be applied in ballistic missiles (BM) for determination of its position on the ballistic phase of its trajectory. The methods for solution of GPS system of equations are the iterative, algebraic, and direct methods. We have applied these methods for simulated ballistic trajectories. The results presented in this paper showed that the iterative one is slower but its final error is smaller. Therefore, a new modified method which is faster and less erroneous; is proposed.. The navigation algorithms are elaborated, using the modified method, and are executed by different types of microprocessors and the results are presented. The optimum processor which provides the minimum execution time is specified. Impact of the navigation processor speed on the ballistic missile-guidance process resides in the fact that a reduced execution time of the navigation algorithm provides better possibility for delivery of higher number and almost continuous generation of guidance commands to the ballistic missile along the majority of its flight trajectory within certain time interval, which will result in an improvement of its performance. The guidance process may be improved through the application of high-speed processors. A performance improvement criterion is defined and a performance improvement (PI) factor is evaluated. The results show that an improvement of about 66.7% may be attained.