Folding Techniques for Low Complexity Acquisition of Modern GNSS Signals
In global navigation satellite system (GNSS) because of the long pseudo-random-noise (PRN) code period and high chip rate of the code rapid code acquisition is challenging. The difficulty is how to rapidly detect the correct cell from numerous code frequency cells. To speed up the search process several folding techniques have been proposed in the literature which directly reduces the code phases to be searched by folding either the local signal or the incoming signal. Unfortunately all the folding techniques work on the basis of a non-realistic assumption that there is no sign transition in the data set due to the navigation message bits. In this study we consider different variants of the already available folding methods such as extended replica folding acquisition search technique (XFAST) and discuss their performance in the presence of data sign transition
Given ?>0 andp?(0,1), we consider the following problem: findu such that $$\begin{gathered} - \Delta u + \lambda [u]_ + ^p = 0in\Omega , \hfill \\ u = 1on\partial \Omega , \hfill \\ \end{gathered} $$ whereΩ??2 is a smooth convex domain. We prove optimalH 1 andL ? error bounds for the standard continuous piecewise linear Galerkin finite element approximation. In addition we analyse a more practical approximation using numerical integration on the nonlinear term. Finally we consider a modified nonlinear SOR algorithm, which is shown to be globally convergent, for solving the algebraic system derived from the more practical approximation.