Numerical simulation of GNSS code tracking loops using Euler-Maruyama method

Abstract

The Euler-Maruyama (EM) method for the numerical integration of stochastic differential equations is applied to simulate tracking loops for Global Navigation Satellite System (GNSS) signals. Use of a large step size and two-point pseudorandom numbers allow for computationally efficient simulation of statistics such as the mean time to lose lock (MTLL). To demonstrate this method, non-coherent delay-lock loops are simulated using the EM method. The MTLL computed from an ensemble of 50 sample paths is compared to a numerical integration of the Fokker-Plank equation. The dependence of computational time and error on step size is evaluated.