A convex optimization approach to GPS receiver tracking loop design

In this paper, the application of convex optimization theory to GPS (Global Positioning System) receiver tracking loops is investigated. We design an H_∞ controller for the receiver tracking loop based on an LMI (Linear Matrix Inequality) approach. The H_∞ controller is particularly attractive because it is a robust design in the sense that small disturbances lead to small tracking errors. Furthermore, it easily accommodates the inclusion of plant uncertainties as part of the plant model. By adding unstructured or structured perturbations to the plant model, it is possible to design controller that ensure stability robustness and performance robustness of the closed-loop system. In order to apply the H_∞ optimal design, we first rewrite the GPS receiver tracking loop into a two-input two-output generalized plant model, and then the H_∞ controller is design by using an LMI approach. The LMI is a convex optimization problem in which a local solution is guaranteed to be a global minimizer. By using a software-based GPS L5 signal generator, various levels of disturbances are derived as test inputs to evaluate the performance of the resulting tracking loop.