Time domain simulation in the design of phase and frequency locked loops for GPS

When designing tracking loops for a given application we need to ensure that the resulting loops maintain lock under the worst dynamic conditions that could be expected. Analytic theory allows us to achieve this goal for continuous noiseless linear systems. Real systems are however not noiseless or linear and, as in the case of digital systems, may not be continuous. In this paper the use of time domain numerical simulation in the design of discrete-time tracking loops for GPS systems is explored. In particular aliasing effects due to the multivalued nature of discriminator functions will be computed together with the effect of nonlinear discriminator functions. It will also be shown that it is possible to include the effects of noise in the simulations