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Modern Geomatics Technologies and Applications

Mathematics in Geomatics Engineering: Application to Code Generation of GNNS Satellites

1*
Hassan Emami , Amir Bagheri 2

1 Department of Geomatics, Marand Faculty of Engineering, University of Tabriz, Tabriz-Iran, h_emami@tabrizu.ac.ir,
h_emami@ut.ac.ir, ORCID: 0000-0002-0171-6487.

2 Department of Basic Sciences, Marand Faculty of Engineering, University of Tabriz, Tabriz-Iran, a_bageri@tabrizu.ac.ir
Abstract

This work demonstrates a realistic application of mathematics in the Geomatics and engineering. Mathematics
and engineering work together as they are right hand to each other because mathematics is the bone structure and
engineering is the physical body. The Global Navigation Satellite System (GNSS) uses of satellites to provide autonomous
Geo-spatial positioning. GNSS satellites continuously transmit signals at two or more frequencies. These signals contain
Pseudorandom noise (PRN) codes and navigation data to allow users to compute both the travel time from the satellite to
the receiver and the satellite coordinates at any time. The PRN codes are an important element of code division multiple
access (CDMA) based satellite navigation systems. Each satellite within a GNSS constellation has a unique PRN code that
it transmits as part of the C/A navigation message. This code allows any receiver to identify exactly which satellite(s) it is
receiving. The PRN codes have special mathematical properties which allow all satellites to transmit at the same frequency
without interfering with each other. These code also allow precise range measurements between satellite and user receivers.
PRN codes generator contains two shift registers known as gold polynomials. In this research, PRN codes generation of
GNNS Satellites using different polynomials is presented and discussed.

Keywords: Global Navigation Satellite System, Applied mathematics, Geomatics, PRN codes.

1. Introduction
Mathematics is defined as the study of quantities and relations with the help of numbers and symbols. So, mathematics
and engineering work together as they are right hand to each other because engineering uses mathematical operations in the
calculation of their projects. Mathematics is the mother of all sciences and engineering. Also, we can strongly say that
mathematics is the bone structure and engineering is the physical body [1]. It is a powerful language, which we use to describe
models in engineering, and also in other sciences. Furthermore, mathematics in engineering is focuses on applications of
mathematics to science and engineering. In contrast, Geomatics engineering is a specialized segment of engineering, focuses on
the monitoring, implementation, and maintenance of global geospatial information. Geospatial information is any information
that has positioned attributes associated with it. Geomatics engineering focuses on spatial information (i.e. information that has
a location). The location is the primary factor used to integrate a very wide range of data for spatial analysis and visualization.
The satellite navigation (SATNAV) systems are a branch of Geomatics engineering. These systems, uses of satellites to provide
autonomous Geo-spatial positioning. Today, there are numerous SATNAV systems operating around the world. Some are global
and others only provide service within a certain region. The term Global Navigation Satellite System (GNSS) is defined as the
collection of all SATNAV systems and their augmentations [2]. The GNSS systems are the U.S. Global Positioning System
(GPS), the Chinese BeiDou Navigation Satellite System (BDS), the European Galileo system, the Russian Federation GLObal
Navigation Satellite System (GLONASS), India’s Navigation with Indian Constellation (NavIC), and Japan’s Quasi-Zenith
Satellite System (QZSS) [3, 4]. The GNSS includes constellations of Earth orbiting satellites that broadcast their locations in
space and time, networks of ground control stations, and the receivers that calculate ground positions by trilateration. Figure 1
shows four popular GNSS systems.

Positioning by GNSS systems is based on a very simple principle. However, a very high level of technological skill is
required to make it work. The satellites send an electromagnetic signal and the user has a receiver equipped with a clock. The
position of the satellites known at each instant of time. The position of the receiver is unknown. We begin by considering

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