Non-coherent, differentially coherent and quasi-coherent integration on GNSS pilot signal acquisition or assisted acquisition

Abstract

Fused with mobile communication, Global Navigation Satellite System (GNSS) has entered the era of indoor applications, though it was initially constructed to address the issue of outdoor or open sky navigation. A pilot channel is added to modern signals to enhance tracking sensitivity and stability. In pursuit of higher acquisition sensitivity, two algorithms - differentially coherent and quasi-coherent integration - are proposed and analyzed respectively to achieve pilot channel acquisition in terms of its periodicity in nature. Each detection statistics corresponding is dealt with through the study of probability density function (PDF) theoretically in the presence of expected signal (hypothesis H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ) as well as in the absence (hypothesis H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ), which are verified individually by numerical evaluation or simulation. The eventual assessment is accomplished by presenting the probability of correct detection (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> ) with respect to various carrier to noise density ratios (C/N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> ) and a fixed probability of false alarm (P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FA</sub> ). To this end, the cross-correlation function of incoming signal and local replica is derived mathematically, and proved to be self-consistent over different accumulation time interval.