MODELING AND ANALYSIS FOR THE GPS PSEUDO-RANGE OBSERVABLE

In this paper, a digital system for the Global Positioning System (GPS ) pseudo range observable is modeled and analyzed theoretically. The o bservable is measured in a GPS receiver by accurately tracking the pse udorandom noise (PRN) code phase of the input GPS signal using a digit al energy detector and a digital delay lock loop (DDLL). The following issues are presented: 1) mathematical modeling of the digital PRN cod e acquisition and tracking system, 2) the closed-form expression deriv ation for the detection and false-alarm probabilities of the acquisiti on process and for the variance of code phase tracking error, and 3) t he linear and nonlinear performance analysis of the DDLL for optimizin g the receiver structures and parameters with tradeoff between the tra cking errors due to receiver dynamics and due to input noise.