Extended Theory of Early-Late Code Tracking for a Bandlimited GPS Receiver

Abstract

Code-tracking accuracy, an important attribute of GPS receivers, depends both on characteristics of the signal being tracked and on the design of the receiver. A simple expression has been available to predict code-tracking accuracy for early-late processing of signals with sinc-squared spectra in white noise for an infinite front-end bandwidth receiver. However, the literature has not indicated when this approximation holds. This paper provides a more exact analysis of code-tracking accuracy for early-late discriminators processing conven-tional binary phase shift keyed signals in white noise. New analytical expressions apply for various front-end bandwidths, discriminator spacings, and code-tracking loop bandwidths, while using linear models based on a small-error assumption. A theoretical lower bound is also supplied, indicating inherent limits on accuracy for given conditions. While evaluation of the exact expressions requires numerical integrations, new algebraic approximations are also provided. Numerical results compare the various expressions and approximations.