gnssreﬂectometry aboardtheinternationalspacestation geros ... · navigation satellite systems...

Satellite GeodesyInstitute of Geodesy and Geoinformation ScienceTechnische Universität Berlin

GNSS Reflectometryaboard the International Space StationGEROS-ISS: Numerical Simulation of

Expected Observation Coverage

A Thesis presented forthe Degree of Master of Science

Author: Vera LeisterDate: 01.10.2015

First Assessor: Prof. Dr. Harald SchuhSecond Assessor: Dr. Jens Wickert

Hiermit erkläre ich, dass ich die vorliegende Arbeit selbstständig und eigenhändig sowieohne unerlaubte fremde Hilfe und ausschließlich unter Verwendung der aufgeführtenQuellen und Hilfsmittel angefertigt habe.

Zusammenfassung

GEROS-ISS steht für GNSS REflectometry, Radio Occultation und Scatterometry anBord der Internationalen Raumstation (ISS) und ist ein wissenschaftliches Experiment,welches 2011 der Europäischen Raumfahrtsgesellschaft (ESA) vorgeschlagen wurde. DasExperiment durläuft momentan Phase A und die Installation an der ISS ist für 2019vorgesehen.Der Hauptfokus von GEROS liegt auf Erdbeobachtung durch von Wasser, Eis undLand reflektierten Global Navigation Satellite System (GNSS) Signalen. Die mesosk-alige Bestimmung des Meeresspiegels und die Berechnung von Windgeschwindigkeitenüber der Meeresoberfläche stehen bei dieser Mission im Vordergrund. Sekundäre Mis-sions Ziele sind die Charakterisierung von Geländeoberflächen und Radio-Okkultationfür globale Atmosphärensondierung.Diese Master Arbeit ist Bestandteil der GEROS-ISS Vorbereitung und fokussiert diegeometrische Simulation und Visualisierung der Lage der Reflektionsmessungen. Dieglobale Beobachtungsabdeckung in Bezug auf verschiedene GNSS Konstellationen (GPS,GLONASS, Galileo und BeiDou) werden verglichen und für verschiedene Zeitintervalleanalysiert. Als Simulationszeiträume wurden ein Tag und eine Woche gewählt. Für dasGPS-System wurde ebenfalls eine Simulation über einen Zeitraum von einem Monatdurchgeführt. Eine Sichtbarkeitsmaske, welche die Sichtfeldeinschränkungen der GE-ROS Antenne durch die Konstruktion der ISS beschreibt, wurde implementiert undAuswirkungen auf die potentielle Abdeckung ausgewertet.

Abstract

GEROS-ISS stands for GNSS REflectometry, Radio Occultation and Scatterometry on-board the International Space Station. It is a scientific experiment, proposed to theEuropean Space Agency (ESA) in 2011 to be installed aboard the International SpaceStation ISS. GEROS-ISS is currently in phase A of realisation, the launch is foreseenfor 2019.The main focus of GEROS is the dedicated use of signals from Global Navigation Satel-lite Systems (GNSS), reflected from water, ice and land surfaces, and also refracted bythe atmosphere for Earth system observation. The main mission goals are the determ-ination of the mesoscale sea surface height and the derivation of wind velocities overocean surfaces. Secondary mission goals are land surface characterisation and radiooccultation for global atmosphere sounding.

This study is part of the GEROS-ISS mission preparation and focuses on the geomet-rical simulation and visualisation of the locations of the expected GNSS reflectometrymeasurements. The global observation coverage with respect to the different GNSS con-stellations (GPS, GLONASS, Galileo and BeiDou) are compared and analysed for vari-ous time intervals. In this study, 32 GPS satellites, 27 Galileo satellites, 24 GLONASSsatellites and 24 BeiDou satellites are considered. For orbit propagation within theMATLAB simulation Broadcast Ephemeris (BRC) data for the GPS orbits and TwoLine Element (TLE) data for the GLONASS, Galileo and BeiDou orbits as well as forthe ISS orbit was used. The reflection points were computed, applying the sphericalmirror equation [Martin-Neira 1993], for a time period of one day and one week re-spectively. For the coverage, a bin size of 1◦x1◦ and a sampling rate of 12 secondsis defined. The various Global Navigation Satellite Systems provide a similar reflec-tion coverage structure with some variation in latitude distribution due to the diversesatellite constellations. The number of satellites has an obvious impact on the reflec-tion density. For the simulation period of one day for GPS (125,755 specular points),GLONASS (95,784), Galileo (107,216) and BeiDou (98,207), a fragmentary reflectioncoverage occurs. The coverage structure is aligned to the ground track structure ofthe ISS and bound to tropical and mid-latitudes through the ISS orbital inclination at51.6◦. An equator-symmetric coverage with an accumulation of specular points alongthe minimum and maximum latitude of the ISS occurs. The coverage is fairly consistentin dependency on longitude. The combination of all 107 GNSS (426,962) satellites leadsto a realtively dense coverage between 50◦N and 50◦S with a number of 114 blank binsafter one day.After a simulation period of one week the individual systems provide a dense coveragebetween 50◦N-50◦S with less than three blank bins. The combination of all 107 GNSSsatellites leads to 2,998,141 specular points with a gapless coverage between 60◦N-60◦S.The observation density is approximatly 60 observations per sampling. The mean re-visit time depends on the latitude and ranges between one and 10 hours.

For the GPS system, reflection events for a month-long period were computed and thecoverage structure shows consistency with an increase in the overall number of reflectionpoints, 3,886,564.A specific visibility mask for the GNSS reflectometry antenna aboard the ISS, takinginto account the realistic ISS geometry, has been implemented and the impact on the po-tential reflection coverage is evaluated in detail. The resulting field of views, near-nadirand grazing, and the influence of the limitation in the port-side field of view throughthe ASIM payload are studied separately. Furthermore all limitations are combined andthe coverage loss assessed. The overall number decreases by about 70%. A coveragestructure, with a non-symmetric latitude distribution and a higher density at the min-imum latitude of the ISS, 51.6◦S, and a cutoff at 52◦N, evolves. The observation densityresults in approximatly 10 observations per sampling and mean revisit time varies fromone to 30 hours.

Declaration of Authorship

The work in this thesis is based on research carried out at the Technical University ofBerlin, the Department of Geodesy and Geoinformation technology in cooperation withthe Department of Geodesy and Remote Sensing of the German Research Centre forGeosciences (GFZ) in Potsdam, Germany. No part of this thesis has been submittedelsewhere for any other degree or qualification and it is all my own work unless referencedto the contrary in the text.

Acknowledgements

I would like to express my gratitude to my supervisor Dr. Maximilian Semmling for theuseful comments, remarks and engagement through the learning process of this masterthesis. Furthermore I would like to thank my assesor Dr. Jens Wickert for his valuableadvice and consistent guidance. I would also like to thank my frist assessor Prof. Dr.Harald Schuh for the chance to write this thesis in the inspiring environment of theGerman Research Centre for Geosciences (GFZ). Thanks to the expertise support andhelpfulness by Dr. Georg Beyerle.

Thanks to my family and friends for their unconditional support and special thanksto Cameron, who has supported me throughout the entire process, both by keeping meharmonious and helping me put pieces together.

Contents

1 Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Global Navigation Satellite Systems: GNSS 32.1 GNSS Segments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Space Segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.2 Control Segment . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1.3 User Segment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Global Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.1 GPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 GLONASS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.3 Galileo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.4 BeiDou . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3 GNSS Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.1 Carrier Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.2 Ranging Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.3 Navigation Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.4 GNSS Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4.1 Code Pseudorange . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4.2 Phase Pseudorange . . . . . . . . . . . . . . . . . . . . . . . . . 12

3 GNSS Reflectometry 133.1 Method and Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.2 Specular and Diffuse Scattering . . . . . . . . . . . . . . . . . . . . . . . 153.3 The Concept of GNSS-R Altimetry . . . . . . . . . . . . . . . . . . . . . 163.4 GNSS Reflectometry Missions . . . . . . . . . . . . . . . . . . . . . . . . 17

3.4.1 TechDemoSat-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.4.2 CYGNSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4.3 GEROS-ISS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4.3.1 Mission Idea . . . . . . . . . . . . . . . . . . . . . . . . 183.4.3.2 Mission Goals . . . . . . . . . . . . . . . . . . . . . . . 203.4.3.3 Status . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4.3.4 Scientific Studies . . . . . . . . . . . . . . . . . . . . . . 21

4 Numerical Simulation of Observation Coverage of GEROS-ISS 234.1 Description of the Simulation Software . . . . . . . . . . . . . . . . . . . 23

4.1.1 Satellite Orbit Simulation . . . . . . . . . . . . . . . . . . . . . . 234.1.2 Specular Point Computation . . . . . . . . . . . . . . . . . . . . 25

4.1.2.1 Trigonometric approach . . . . . . . . . . . . . . . . . . 25

4.1.2.2 Spherical Mirror Equation . . . . . . . . . . . . . . . . . 274.1.2.3 Specular Point Simulation . . . . . . . . . . . . . . . . . 29

4.2 Reflection Coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.2.1 Simulation Period - One Day . . . . . . . . . . . . . . . . . . . . 304.2.2 Simulation Period - One Week . . . . . . . . . . . . . . . . . . . 364.2.3 Simulation Period - One Month . . . . . . . . . . . . . . . . . . . 404.2.4 Analysis of Observation Coverage . . . . . . . . . . . . . . . . . 41

4.2.4.1 Comparison of Simulation Periods . . . . . . . . . . . . 414.2.4.2 Latitude and Longitude Distribution . . . . . . . . . . . 424.2.4.3 Temporal Distribution . . . . . . . . . . . . . . . . . . . 45

4.3 Visibility Mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.3.1 Nadir Angle Constraints . . . . . . . . . . . . . . . . . . . . . . . 49

4.3.1.1 Near-Nadir Field of View . . . . . . . . . . . . . . . . . 504.3.1.2 Grazing Field of View . . . . . . . . . . . . . . . . . . . 524.3.1.3 Near-Nadir and Grazing Field of View . . . . . . . . . 54

4.3.2 Azimuth Constraint . . . . . . . . . . . . . . . . . . . . . . . . . 564.3.3 Azimuth and Nadir Angle Constraint . . . . . . . . . . . . . . . . 58

4.4 Case Study Southern Africa . . . . . . . . . . . . . . . . . . . . . . . . . 63

5 Conclusions and Outlook 65

A GNSS Ground Track Plots 67

List of Figures

2.1 Global Navigation Satellite Systems . . . . . . . . . . . . . . . . . . . . 32.2 Galileo Ground Segment . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Composition of GNSS Signal . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1 Multistatic GNSS Reflectometry System . . . . . . . . . . . . . . . . . . 143.2 Specular and Diffuse Reflection . . . . . . . . . . . . . . . . . . . . . . . 163.3 Schematic Overview of the GEROS Experiment . . . . . . . . . . . . . 193.4 Oceanic Observations Carry Signals with a Wide Range of Related Pro-

cesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.1 MATLAB Simulation Software Overview . . . . . . . . . . . . . . . . . 244.2 Reflection Geometry Trigonometric Approach . . . . . . . . . . . . . . . 264.3 Reflection Geometry Spherical Mirror Equation . . . . . . . . . . . . . . 284.4 GPS Coverage - Simulation Period one Day . . . . . . . . . . . . . . . . 314.5 GPS, ISS and Specular Point Ground Track . . . . . . . . . . . . . . . . 324.6 GPS Coverage and Ground Track of the ISS - Simulation Period one Day 324.7 GLONASS Coverage - Simulation Period one Day . . . . . . . . . . . . . 334.8 Galileo Coverage - Simulation Period one Day . . . . . . . . . . . . . . . 334.9 Beiodu Coverage - Simulation Period one Day . . . . . . . . . . . . . . . 344.10 GNSS Coverage - Simulation Period one Day . . . . . . . . . . . . . . . 354.11 GPS Coverage - Simulation Period one Week . . . . . . . . . . . . . . . 374.12 GLONASS Coverage - Simulation Period one Week . . . . . . . . . . . . 384.13 Galileo Coverage - Simulation Period one Week . . . . . . . . . . . . . . 384.14 BeiDou Coverage - Simulation Period one Week . . . . . . . . . . . . . . 394.15 GNSS Coverage - Simulation Period one Week . . . . . . . . . . . . . . . 394.16 GPS Coverage - Simulation Period one Month . . . . . . . . . . . . . . . 414.17 Latitude Distribution of GPS, GLONASS, Galileo and BeiDou . . . . . 434.18 Latitude Distribution of GNSS Reflection Coverage . . . . . . . . . . . 434.19 Longitude Distribution of GPS, GLONASS, Galileo and BeiDou . . . . . 444.20 Longitude Distribution of GNSS Coverage . . . . . . . . . . . . . . . . . 444.21 Temporal Observation Density of GNSS Reflection Coverage . . . . . . . 454.22 Mean Revisit Time of GNSS Reflection Coverage . . . . . . . . . . . . . 464.23 GEROS-ISS Field of View . . . . . . . . . . . . . . . . . . . . . . . . . 474.24 Reflection Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.25 Visibility Mask GEROS-ISS . . . . . . . . . . . . . . . . . . . . . . . . . 484.26 Nadir Angle Distribution - Simulation Period one Day . . . . . . . . . . 494.27 Nadir Angle Distribution - Simulation Period one Week . . . . . . . . . 494.28 GPS, ISS and Specular Point Ground Track in Nadir FoV . . . . . . . . 504.29 GNSS Reflection Coverage with Near-Nadir FoV - Simulation Period one

Day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

LIST OF FIGURES

4.30 GNSS Reflection Coverage with Near-Nadir FoV - Simulation Period oneWeek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.31 GPS, ISS and Specular Point Ground Track in Grazing FoV . . . . . . . 524.32 GNSS Reflection Coverage with Grazing FoV - Simulation Period one Day 534.33 GNSS Reflection Coverage with Grazing FoV - Simulation Period one Week 534.34 GNSS Reflection Coverage with Near-Nadir and Grazing FoV - Simula-

tion Period one Day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.35 GNSS Reflection Coverage with Near-Nadir and Grazing FoV - Simula-

tion Period one Week . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.36 GNSS Reflection Coverage with Azimuth Constraint - Simulation Period

one Day . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.37 GNSS Reflection Coverage with Azimuth Constraint - Simulation Period

one Week . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.38 GNSS Reflection Coverage Applying Visibility Mask- Simulation Period

one Week . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.39 GNSS Reflection Coverage Applying Visibility Mask - Simulation Period

one Week . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.40 GNSS Latitude Distribution Applying Visibility Mask - Simulation Period

one Week . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.41 GNSS Longitude Distribution Applying Visibility Mask - Simulation Period

one Week . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.42 Temporal Observation Density of GNSS Reflection Coverage Applying

Visibility Mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.43 Mean Revisit Time of GNSS Reflection Coverage Applying Visibility Mask 624.44 Reflection Coverage South Africa - Simulation Period one Week . . . . . 644.45 Reflection Coverage South Africa Applying Visibility Mask - Simulation

Period one Week . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

A.1 GPS Ground Track Coverage - Simulation Period one Week . . . . . . . 67A.2 GLONASS Ground Track Coverage - Simulation Period one Week . . . . 68A.3 Galileo Ground Track Coverage - Simulation Period one Week . . . . . . 68A.4 BeiDou Ground Track Coverage - Simulation Period one Week . . . . . 69

List of Tables

2.1 Comparison of GPS, GLONASS, Galileo and BeiDou . . . . . . . . . . 42.2 Current and Future GPS Satellite Constellations . . . . . . . . . . . . . 72.3 Carrier Frequencies of Global Navigation Satellite Systems . . . . . . . 10

4.1 Comparison of Reflection Coverage of GPS, GLONASS, Galileo, BeiDouand GNSS after one Day . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2 Comparison of Reflection Coverage of GPS, GLONASS, Galileo, BeiDouand GNSS after one week . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.3 Reflection Coverage of GPS after Simulation Period of one Month . . . . 404.4 GNSS Reflection Coverage in the Near-Nadir FoV . . . . . . . . . . . . . 524.5 GNSS Reflection Coverage for the Grazing FoV . . . . . . . . . . . . . . 544.6 GNSS Reflection Coverage combining the near-nadir and grazing FoV . 564.7 GNSS Reflection Coverage applying the azimuth angle constraint . . . . 584.8 GNSS Reflection Coverage Applying Visibility Mask . . . . . . . . . . . 604.9 GNSS Reflection Coverage of Southern Africa Region . . . . . . . . . . . 63

Chapter 1

Introduction

1.1 Motivation

Satellite remote sensing has provided major advances in understanding the climate sys-tem and its changes, through quantifying processes and spatial-temporal states of theatmosphere, land and oceans [Yang et al. 2013].Sea level is driven by climate conditions, which are influenced by climate change andvariability. Satellite altimetry observations using the TOPEX/Poseidon satellite,launched by NASA and Centre National d’Etudes Spatiales (CNES), mapped oceansurface topography from 1992 to 2006. This mission as well as its follow-on and othermissions, observed a global mean sea level rise.Since altimetry missions place both transmitter and receiver on the same spacecraft,the distribution pattern of the resulting sea heights are bound to the particular groundtrack of the altimeter satellite [Wagner et al. 2003].Therefore other techniques such as GNSS Reflectometry (GNSS-R) provide potentialin improving and enhancing ocean observation coverage. GNSS-R, the use of GlobalNavigation Satellite Systems (GNSS) reflected signals is a powerful and potentiallydisruptive technology for remote sensing: wide coverage, passive, precise, long-term,all-weather and multi-purpose [Ruffini 2006].Wagner et al. 2003 analysed the value of ocean reflections of GPS signals to enhancesatellite altimetry in terms of data distribution for TOPEX/Poseidon and CHAMP.Previous air-borne GNSS-R measurements such as GEOHALO and the Zeppelin exper-iment, estimating surface heights and resolving anomalies of the sea surface topography,acknowledge the potential of using reflectometry to improve the detection of mesoscaleocean eddies [Semmling et al. 2014, Semmling et al. 2013].To obtain GNSS-R based sea surface observations on a global scale, satellites as receiverplatforms are required. The recent scientific experiment GEROS-ISS stands for GNSSREflectometry, Radio Occultation and Scatterometry onboard the International SpaceStation [Wickert et al. 2014b,Wickert et al. 2014a]. It primarily focuses on exploitingreflected signals of opportunity from the GNSS satellites to measure key parameters ofocean surfaces such as sea surface height (SSH) and mean square slopes (MSS), relevantto characterise climate change. Addressing the distribution limitations of conventionalaltimetry measurements, GEROS-ISS promises wide spatial coverage for SSH and MSSmeasurements. Therefore this thesis studies the numerical simulation of expected ob-servation coverage of GEROS-ISS and is part of the mission preparation.

1

2 CHAPTER 1. INTRODUCTION

1.2 Objectives

The main objective of this thesis will be the geometrical simulation and visualisation ofthe expected locations of the GNSS reflectometry measurements from the GEROS-ISSmission.Goals for this study are calculations for various GNSS constellations of GPS, GLONASS,Galileo and BeiDou, whereby global reflection coverage of the various GNSS constel-lations is compared. In addition, the combined reflection coverage of all four GlobalNavigation Satellite Systems is studied.Different simulation periods are chosen and the temporal distribution of the reflectioncoverage is analysed. A simulation period of one day and one week is chosen. In addi-tion, a month-long simualtion is carried out for the GPS system.The coverage structures and densities of the various Global Navigation Satellite Systemsare compared and analysed in detail. The temporal observation density as well as themean revisit time of observed areas is examined. Furthermore, a specific visibility maskof the GNSS antenna aboard the ISS is applied. The resulting field of views, such asnear-nadir and grazing field of view, as well as the influence of limitations in the fieldof view through the construction of the ISS are studied separately and later combined.The impact on coverage loss, due to the application of a visibility mask, is evaluated.The impact on the global reflection coverage as well as the temporal distribution isanalysed and evaluated.

Chapter 2

Global Navigation SatelliteSystems: GNSS

Global Navigation Satellite Systems (GNSS) are designed to provide users on the groundand to some extent in space with precise position and navigation information, see Za-vorotny et al. 2014, Ruffini 2006. Four global systems currently exist: The US’s GlobalPositioning System (GPS), Russia’s GLONASS, the European Galileo and China’sBeiDou, also called COMPASS. Besides the Global Navigation Satellite Systems, re-gional systems such as the Japanese Quasi-Zenith Satellite System (QZSS) also exist,but are not considered in this study. The systems are characterised as highly precise,continuous, all-weather and real-time through the use of microwave (L-band) signalstravelling through the Earth’s Atmosphere, see Jin et al. 2014, Hofmann-Wellenhofet al. 2008, Misra et al. 2001. Direct signals are used for navigation, positioning andtiming purposes. Each GNSS satellite broadcasts radio signals in two or more L-bandfrequencies (1-2 GHz) with a wavelength of approximately 20 cm.Several existing and numerous potential applications are implied through these charac-teristics. One example is the use of GNSS signals for Remote Sensing of geophysicalparameters.Refracted GNSS signals received aboard Earth orbiting satellites (GNSS Radio Oc-cultation) together with ground based GNSS observations can provide high-resolutiontropospheric water vapour, temperature, pressure and tropopause parameters as well asionospheric electron content (TEC) and vertical electron density profiles [Wickert et al.2007].Reflected signals from ocean and land surfaces can be used to determine ocean height,wind speed, wind direction at ocean surface, soil moisture, ice and snow thickness, e.g.Alonso-Arroyo et al. 2015, Rivas et al. 2010, Zavorotny et al. 2000.

Figure 2.1 Global Navigation Satellite Systems: The figure shows illustrations of theconstellations of the GNSS systems GPS, GLONASS, Galileo and Beidou. [DefenseIndustry Daily 2015, Spaceflight Now 2015, ESA 2015c, Encyclopedia Astronautica2015]

3

4 CHAPTER 2. GLOBAL NAVIGATION SATELLITE SYSTEMS: GNSS

Fullyoperational

by

Inclinationof OrbitalPlanes[degrees]

Number ofPlanes

Altitude[km]

Number ofSatellites in

WalkerConstella-

tionGPS 1995 55 6 20,180 24GLONASS 1995 64.8 3 19,140 24

Galileo expected2020 56 3 23,222 27

BeiDou expected2020 55 3 21,528 24

Table 2.1: A comparison of GPS, GLONASS, Galileo and BeiDou [NOAA 2015, ESA2015c]. The global BeiDou system consists of 24 Medium Earth Orbit satellites (MEO)at an altitude of 21,528 km in Walker constellation, five Inclined GeoSynchronous Orbitsatellites (IGSO) at an altitude of 35,786 km, and five geostationary satellites (GEO),positioned at 58.75◦E, 80◦E, 110.5◦E, 140◦E and 160◦E [China Satellite NavigationOffice 2013]

2.1 GNSS Segments

GNSS consist of a space segment containing a satellite constellation, a control segmentwith control stations for monitoring, controlling and updating on the satellite constel-lation and the user segment comprising of receivers to obtain position, velocity andtime (PVT) of static and mobile users all over the globe at all times using at least foursatellites of the constellation in view, see Hofmann-Wellenhof et al. 2008, Misra et al.2001, Seeber 1989. The structure of a Global Navigation Satellite System is well definedby the initial designs of the U.S. and USSR. The Galileo and BeiDou systems followedthis structure.

2.1.1 Space Segment

To ensure a continuous global positioning capability, the constellation is designed con-sidering the availability of at least four satellites, since four unknowns at any epochneed to be solved: Three components of position plus the clock bias. This means thesatellites need to be simultaneously visible at every site, see Hofmann-Wellenhof et al.2008. There are certain criteria for the design of a constellation: User position accuracy,satellite availability, service coverage and the satellite’s geometry. Furthermore criterialike the size and weight of the satellites need to be considered as well, since they cor-relate with launch vehicle constraints such as costs of deployment, maintenance andfuel replenishment. The degree of perturbing effects, which influence the maintenancemanoeuvres, are defined by the satellite orbit. A distinction is made between Low EarthOrbits (LEO), Medium Earth Orbits (MEO) and Geostationary Orbits (GEO) in termsof altitude.The GNSS satellites are equipped with precise atomic clocks, navigational payload andantennas and various auxiliary equipment to operate the system such as a power supplyand a propulsion system for orbit adjustments and stability control.The pseudo-range from the user to the satellite can be measured with the signal of thesatellite. The spatial position of the satellite can be determined by the user with amessage, broadcast by each satellite. If the pseudo-range and spatial position are given,

2.1. GNSS SEGMENTS 5

the users position on earth can be determined by resection.The satellites can be identified by various identification numbers e.g. launch sequencenumber or orbital position number.

2.1.2 Control Segment

The control segment consists of a master control station, monitoring stations and tele-metry telecommand antennas located all over the world [Hofmann-Wellenhof et al.2008]. The master control station coordinates all activities whilst the monitor stationsform the tracking network. The communication link to the satellites is provided throughthe ground antennas. The segment, responsible for steering the whole system, has thefollowing tasks: Tracking of the satellites for the determination and prediction of or-bital and clock parameters, monitoring of the signals broadcast by satellites and sendinginformation to satellites for the navigation message. It is also responsible for possibleencryption of data and the protection of services against unauthorised users.

Figure 2.2 Galileo’s ground segment encompasses twin European Galileo ControlCentres and uplink stations on remote sites across the world. They are all inter-connected via a robust satcom network. It includes Galileo Sensor Stations (GSSs)to provide coverage for clock synchronization and orbit measurements; UpLinkStations (ULSs) to uplink navigation and integrity data to the Galileo satellitenavigation payloads for rebroadcast to users; Telemetry, Tracking and CommandStations (TT&Cs) to manage the satellite platforms; an In-Orbit Test (IOT) siteat Redu for satellite payload testing and a trio of Medium-Earth Orbit Local UserTerminals (MEOLUTs) for search and rescue activities [GPS World 2015]

2.1.3 User Segment

The user segment can be grouped as user categorised, GNSS receivers and various in-formation services, see Misra et al. 2001.The user categories are classified into military and civilian users as well as authorisedand unauthorised users. Not all signals and services of the GNSS are accessible forcivilian and unauthorised users.GNSS receivers process the signals received from the satellites and estimate the user’sposition. The receiver’s functionalities are the identification of the satellites in view,estimation of the distance of satellite to user and Triangulation.


GNSS status information and data for users is provided by several governmental andprivate information services. In general, the information contains constellation statusreports, scheduled outages and orbital data. The orbital data is provided as an al-manac, eligible for satellite visibility predictions, and precise ephemeris data for precisepositioning.

2.2 Global Systems

2.2.1 GPS

In the beginning of 1960s several U.S. governmental organisations such as the Depart-ment of Defence (DOD), the National Aeronautics and Space Administration (NASA)and the Department of Transportation (DOT) were interested in developing satellitesystems for positioning, see NOAA 2015.From 1964 till 1966 the first satellite navigation system, Transit, with a constellationof five satellites, was operated by the United States Navy [Rothacher 2005]. Due tolimitations of this system, a more universal navigation solution with greater accuracywas required. The U.S. Navy developed the Timation satellite that proved the abilityof placing accurate clocks in space in 1967. In the 1970s the first worldwide radio navig-ation system was established: The ground-based Omega Navigation System with phasecomparison and signal transmission from pairs of stations. The Defence Navigation Sys-tem (DNSS), later named as Navstar, was created in 1973. To identify the constellationof Navstar satellites the name Navstar-GPS, abbreviated as GPS, was used. Until July1993 24 satellite were launched and the GPS system was declared as fully operationalon 17th July 1995 [Hofmann-Wellenhof et al. 2008].The system was broadcasting two signals: C/A code available for civilian use and themore precise encrypted code reserved for military use. The selective availability, whichis the feature where the signal available for civilian use could be intentionally degraded,was discontinued in 2000 and every user on the globe was allowed to receive a nondegraded signal. Between 1997 and 2009, 20 satellites of block IIR and IIR-M werelaunched and constitute a large quantity of the current GPS constellation. The civilencoded signal in the L2 band was made available for civilian users by the block IIR-Msatellites. The block IIF generation of GPS satellites provide an additional safety-of-lifesignal on the L5 frequency. In May 2010 the first IIF satellite was launched and hasoperated since August 2010. The future generation of GPS satellites, GPSIII, holds thefourth civilian GPS signal L1C, designed to enable interoperability between GPS andinternational satellite navigation systems. In January 2015, the GPS constellation of 30satellites consists of three Block IIA, twelve Block IIR, seven Block IIR(M) and eightBlock IIF satellites, see table 2. The current status of the GPS constellation can befound under: http://tycho.usno.navy.mil/gpscurr.html. All GPS satellites broadcast byemploying the Code Division Multiple Access (CDMA) technique as a channel accessmode.The official GPS space segment is composed of 24 satellites plus operational sparesdistributed over six orbital planes, separated by 60 degrees right ascension, 55 degreesinclined and with an orbital radius of about 26,600 km. Each satellite orbits the Earthexactly twice each sidereal day, repeating the same ground track once per day. Hence thesame constellation geometry can be observed every SI (International System of Units)day with approximately four minutes displacement. A primary Master Control Stationat Schriever Air Force Base (Colorado, U.S.) and ten dedicated ground antennas andmonitor stations around the globe compose the GPS ground-segment.

2.2. GLOBAL SYSTEMS 7

Legacy Satellites Modernised Satellites

Block IIA Block IIR BlockIIR(M) Block IIF GPS III

Opera-tional 3 12 7 8 in production

- CoarseAcquisition

(C/A) code onL1 frequencyfor civil users

- C/A code onL1

- All legacysignals

- All blockIIR(M) signals

- All Block IIFsignals

- P(Y) code onL1, L2

-2nd civilsignal on L2

(L2C)

- 3rd civilsignal on L5

frequency (L5)

- 4th civilsignal on L1

(L1C)

Fea-tures

- Precise P(Y)code on L1, L2frequencies formilitary users

- On-boardclock

monitoring

- New militaryM code signalsfor enhancedjam resistance

- Advancedatomic clock

- Enhancedsignal

reliability,accuracy and

integrity

- Flexiblepower levels formilitary signals

- Improvedaccuracy,

signal strengthand quality

No SelectiveAvailability

Satellites 9+:laser reflectors;search and

rescue payloadDesignLifespan[years]

7.5 7.5 7.5 12 15

Launch 1990-1997 1997-2004 2005-2009 since 2010 planned 2016

Table 2.2: Current and future GPS satellite constellations: The different GPS satellitetypes Block IIA, IIR, IIR(M), IIF and GPS III are listed with their features in thistable. Status: 13.01.2015 [NOAA 2015]

2.2.2 GLONASS

In 1972 the former Union of Soviet Socialist Republics (USSR) started the developmentof the Globalnaja Nawigazionnaja Sputnikowaja Sistema, Russian term for global nav-igation satellite system and abbreviated by GLONASS. The first satellite, together withtwo test satellites, was launched in 1982, see Hofmann-Wellenhof et al. 2008, Rothacher2005. Until 1993 the orbital constellation increased to twelve satellites and the initialsystem operation began. Since 1995 the system was fully operational [Federal SpaceAgency 2015]. Due to the collapse of the USSR, GLONASS was suspended and par-tially operated [Jin et al. 2014]. After an upgrade to the Russian owned system, it hasbeen fully operational again since 2010. GLONASS is managed by the Russian SpaceForces and the system is operated by the Coordination Scientific Information Center(KNITs) of the Ministry of Defense of the Russian Federation [Xu 2007].The GLONASS space segment is composed of 24 satellites distributed over three or-bital planes, separated by 120 degrees right ascension of the ascending node at analtitude of 19,140 km and 64.8 degrees inclination. Each satellite completes an orbitin approximately 11 hours 16 minutes. GLONASS satellites broadcast signals in L1and L2 bands, using the Frequency Division Multiple Access (FDMA) technique as achannel access method. To provide better accuracy, multipath resistance and betterinteroperability with other GNSS Systems, new GLONASS-K satellites, transmittingCDMA signals in addition to the system’s traditional FDMA, have been launched since


2011 [ESA 2015c]. The current status of the GLONASS constellation is available at:http://www.rssi.ru/SFCSIC/english.html. The GLONASS ground control centre inMoscow and the telemetry and tracking stations are all located within the RussianFederation borders.

2.2.3 Galileo

The Galileo navigation system is named after the Italian astronomer and physicist Ga-lileo Galilei [Hofmann-Wellenhof et al. 2008]. Due to political reasoning that encouragedEuropean countries to be independent in context of satellite navigation from the U.S.’sGPS and the Russian GLONASS system, the Galileo system was initiated. The Galileosystem was intended to provide a more precise navigation service than that providedby GPS or GLONASS since its beginning.In March 2002 the European Union (EU) and European Space Agency (ESA) agreed todevelop the Galileo positioning system. The system is expected to be fully operationalby 2020 and will be compatible with the modernised GPS system. The future receiverwill be able to combine the signals from both Galileo and GPS satellites for signific-antly improved accuracy. Currently a number of countries are involved in the projecte.g. China, Israel, Ukraine, India, Morocco and Saudi Arabia as well as South Korea.In 2007, the 27 members of the European Union collectively agreed to move forwardwith the project and planned bases in Germany and Italy.The two Galileo Test satellites GIOVE-A, launched in 2005, and GIOVE-B, launchedin 2008, were dedicated to take the first step of the In-Orbit Validation (IOV) phasetowards full deployment of Galileo, broadcasting on L1, E5 and E6 bands [ESA 2015a].After the launch of the first two Galileo satellites on October 2011, the experimentalGIOVE satellites were turned off in 2012. In 2012 a second pair of Galileo satelliteswere sent into orbit. After a wide variety of IOV tests across Europe to assess the per-formance of the system sub-set already deployed, Galileo achieved In-Orbit Validationin February 2014 [ESA 2015c].The Initial Operational Capability (IOC) phase will be the partial commissioning of theground and space infrastructure as from 2014/2015 and the provision of the Open Ser-vice, the Search And Rescue service and the Galileo Public Regulated Service (PRS).The procurement of the IOC phase includes the launch of 14 additional satellites tothe four IOV satellites, the launch services, the required mission and ground controlinfrastructure, the system support services and the corresponding operations.The current status of the Galileo constellation can be found at: http://www.gsc-europa.eu/system-status/Constellation-Information. The Full Operational Capability(FOC) phase involves the deployment of the full system, which will consist of 30 satel-lites, control centres located in Europe and a network of sensor stations and uplinkstations installed around the globe, see figure 2.2. Galileo’s Full Operational Capability(FOC) should be achieved in 2019-2020, in a staggered approach from the IOC phase.The full constellation will consist of 30 satellites (27 operational, three spares) distrib-uted over three orbital planes 56 degrees inclined and at an altitude of 29,600 km. Eachsatellite will revolve around the Earth at a rate of one revolution every 14 hours. Thethree spare satellites will be on stand-by mode. The signals will be broadcast in E1,E6, E5, E5a and E5b bands, supporting Open Service (OS), Safety-Of-Life (SOL) andCommercial and Public Regulated Services.

2.3. GNSS SIGNALS 9

2.2.4 BeiDou

Since the 1980s China has pursued the idea of a regional satellite Navigation system[Hofmann-Wellenhof et al. 2008]. The concept provides two geostationary satellites andwas successfully tested in 1989 under the Twin-Star program. In 1994 China’s decisionon the implementation of an independent navigation system called BeiDou was made.The name BeiDou denotes the seven-star constellation, which is also known as UrsaMajor.A three-step approach has been chosen for the development of BeiDou following thegeneral guidelines of commencing with regional services and then expanding to globalservices [China Satellite Navigation Office 2013].The first step is the ’BeiDou Navigation Satellite Demonstration System’ with a spaceconstellation of three geostationary satellites positioned at 80, 110.5 and 140 degreesEast respectively above the equator. The first two BeiDou navigation experiment satel-lites were launched in 2000, followed by the third in 2003 to further enhance the system.The second step, ’BeiDou Navigation Satellite System regional services’, initiated theconstruction of the BeiDou Navigation Satellite System in 2004. In 2012 the system con-sisted of 14 operational satellites in orbit, including five geostationary satellites (GEO),five inclined geosynchronous orbit (IGSO) satellites and four medium earth orbit satel-lites (MEO). The system possesses Full Operational Capability (FOC) for China andsurrounding areas.The third step followed in 2014 and focuses on the global services. Additional satelliteswill be launched until 2020 and a system with global coverage will be fully established.The full constellation consists of five GEO satellites and 30 non-GEO satellites. Thepositions of the GEO satellites are 58.75, 80, 110.5, 140 and 160 degrees East. Thenon-GEO satellites include 27 MEO (24 operational, three spares) and three IGSOsatellites. The MEO satellites are operating at an altitude of 21,528 km and 55 degreesinclined, evenly distributed in three orbital planes. The IGSO satellites are orbitingat an altitude of 35,786 km and 55 degrees inclined, evenly distributed in three IGSOplanes [China-Satellite-Navigation-Office 2013]. The global BeiDou system is expectedto be fully operational by 2020 [Ge et al. 2012].The two signals, I and Q , are broadcast in three bands B1, B2 and B3 [Jin et al. 2014].The ground control segment consists of a Master Control Station, Time Synchronisa-tion/Upload Stations and Monitor Stations.

2.3 GNSS Signals

The GNSS signal consists of three components: Carrier, ranging code and the nav-igation data, see Hofmann-Wellenhof et al. 2008, Misra et al. 2001. The three signalcomponents are derived coherently from one of the atomic standards aboard the satellite.

2.3.1 Carrier Frequency

Each satellite transmits continuously using radio frequencies in L-band. L-band coversfrequencies between 1 GHz and 2 GHz with a wavelength between 30 and 15 cm re-spectively. The carrier frequencies of the different Global Navigation Satellite Systemsare listed in the table 2.3.


Denotation Carrier Frequency [MHz] Wavelength [cm]L1 1575.420 19.0

GPS L2 1227.600 24.4L5 1176.450 25.5G1 1602.000 18.7

GLONASS G2 1246.000 24.1G3 1204.000 24.9

E1/L1 1575.420 19.0E5/E5a+E5b 1191.795 23.4

Galileo E5a/L5 1176.450 25.2E5b 1207.140 25.5E6 1278.750 24.8B1 1561.0908 19.2

BeiDou B2 1207.140 24.8B3 1268.520 23.6

Table 2.3: Carrier frequencies and wavelength of the Global Navigation Satellite SystemsGPS, GLONASS, Galileo and BeiDou [ESA 2015c, Hofmann-Wellenhof et al. 2008]

2.3.2 Ranging Code

The ranging code is a unique binary code assigned to each satellite, which enables thereceiver to determine the signal transmission time instantaneously. The binary codes,called pseudo random noise (PRN) codes are generated by mathematical algorithmsand have special properties that allow all satellites to transmit at the same frequencywithout interfering with each other. GPS and GLONASS are transmitting two differentcodes: A course acquisition (C/A) code and a precision (encrypted) (P) code. EachC/A- code is a unique sequence of chips, which is repeated each millisecond for GPS.For GPS the duration of each C/A-code chip is about 1 µs with a chip width of 300 m.The chipping rate is 1,023 MHz (megaschips/s). The P-code is a unique segment of along PRN sequence, around 1014, with a chipping rate of 10.23 Mcps and chip widthof 30 m. Due to the shorter chip width of the P-Code one obtains better precision forrange measurements than with C/A-code. The P-code is repeated after one week. Fora detailed description see Hofmann-Wellenhof et al. 2008, Chapter 9.5.2.The C/A- and P-code of the GLONASS ranging signal has a different code length andrate, see Hofmann-Wellenhof et al. 2008, Chapter 10.5.2.The signal structure of Galileo and BeiDou differs from GPS and GLONASS, for de-tails see Hofmann-Wellenhof et al. 2008, Chapter 11.5.2 and China Satellite NavigationOffice 2013.Each satellite transmits a distinct code pattern, which enables the receiver to identifythe satellites.

2.3.3 Navigation Data

The navigation data is a binary message consisting of data on the satellite health status,ephemeris (satellite position and velocity), clock bias parameters and almanac data,which contains less precise ephemeris data on all satellites of the constellation. Thenavigation message is transmitted at a rate of 50 bps for GPS and GLONASS.

2.4. GNSS OBSERVABLES 11

The ranging code is combined with the binary navigation data using the modulo-2addition technique.The combined binary signal is then impressed upon the carrier in a process calledmodulation. One modulation used in GPS signals is called Binary Phase Shift Keying(BPSK). For a detailed description see Hofmann-Wellenhof et al. 2008, chapter 4.2.2.Figure 2.3 shows the composition of the navigation satellite signal.

2.4 GNSS Observables

The basic GNSS observable is the travelling time ∆T = tr−ts of the signal to propagatefrom the phase centre of the satellite antenna at the time of emission ts to the phasecentre of the receiver antenna at the reception time tr [ESA 2015c]. Time of emissionts is transmitted in the navigation message via the PRN code. The receiver determines∆T correlating the received code from the satellite with a replica of it generated inthe receiver. This replica is moved in time ∆T until the maximum correlation of thereceived and receiver-generated signal is obtained. This value multiplied by the speedof light c results in the range ρ = c ·∆T . Since the ranges are biased by satellite and re-ceiver clock errors, they are denoted as pseudoranges [Hofmann-Wellenhof et al. 2008].

Figure 2.3 Composition of GNSS signal: The ranging and the binary navigationdata are combined using the the modulo-2 addition technique. The combined bin-ary signal is then impressed upon the carrier using modulation. Adapted fromHofmann-Wellenhof et al. 2008


2.4.1 Code Pseudorange

Thus the code pseudorange equation reads

P = ρ+ c · δr − c · δs (2.1)

with clock biases of the transmitting δs and receiving δt satellite

For a detailed derivation of the equation see Rothacher 2007, Hofmann-Wellenhof et al.2008.

2.4.2 Phase Pseudorange

Besides the code, the carrier phase itself is also used to obtain a measurement of theapparent distance between satellite and receiver. These carrier phase measurementsL are much more precise than the code measurements, but they are ambiguous by anunknown integer number of wavelengths N . Due to the receiver temporarily losing lockon the carrier of a GPS signal caused by e.g. signal blockage, the ambiguity changesarbitrarily, producing jumps or range discontinuities (cycle slips).

The phase observation equation reads

L = ρ+ c · δr − c · δs + λ · b (2.2)

where λ = cf denotes the carrier wavelength and the ambiguity term b = N + αr + αs

including the instrument errors of the transmitting αs and receiving αr satellite.

By means of the code and phase pseudorange observables the position can be determ-ined, for detailed information see Hofmann-Wellenhof et al. 2008, chapter 6.

Chapter 3

GNSS Reflectometry

GNSS Reflectometry (GNSS-R) is a Remote Sensing technique, which was introducedto densify Earth observations in a low cost effective manner [Jin et al. 2014].Surface multi-path is one of the main error sources for GNSS navigation and positioning[Kenyon et al. 2009]. It has been recognised that a special kind of GNSS multi-pathdelay reflected from the Earth’s surface could be used to sense the Earth’s surface en-vironments. In 1988 Hall and Cordey first addressed the bistatic radar using L-bandsignals transmitted by GPS, (originally proposed by ESA) as an ocean scatterometer.Rubashkin demonstrated in 1993 the concept of bistatic radar sensing of the oceansurface using two satellites with a transmitter in LEO and a receiver in GEO. In thesame year Martin-Neira [Martin-Neira 1993] proposed and described an altimeter sys-tem using ocean GPS reflections to measure sea surface heights. Katzberg and Garrisonproposed in 1996 using the reflection of the GPS signal from the ocean for ionosphericmeasurements by adding a GPS receiver and downward-pointing antenna to any satel-lites and evaluated the feasibility and effectiveness of this method [Katzberg et al. 1996].The GNSS signal reflections from low Earth orbit at very low grazing angles were occa-sionally observed during radio occultation experiments [Beyerle et al. 2002, Cardellachet al. 2004].Similar to traditional radar remote sensing, the GNSS reflectometry technique can beapplied to remote sensing of various types of natural cover such as ocean, land, ice, snowand vegetation. A number of experiments and missions using GNSS reflected signalsfrom ocean and land surfaces have been tested and applied, such as determining oceansurface height, tsunami detection, wind speed and direction, soil moisture, snow andice thickness, see e.g. Stosius et al. 2010, Zavorotny et al. 2000.The measurement of the delay between the direct and the reflected signal from theEarth’s surface and recalculating the temporal delay into the spatial intervals turnsGNSS bistatic radar into an altimeter [Zavorotny et al. 2014]. Conventional radar alti-metry is monostatic and therefore provides altimetric measurements only along a singleground track. With GNSS-R, altitude measurements along multiple widely spacedground tracks, acquiring signals simultaneously from several satellites are performed.Recent GNSS-R altimetry experiments with a Zeppelin and the German High AltitudeLong Range (HALO) research aircraft showed a potential in improvement of conven-tional altimetry measurements [Semmling et al. 2014, Semmling et al. 2013]. The futuremission GEROS-ISS focuses on GNSS altimetry from the ISS [Wickert et al. 2014b].In Chapter 4 the global reflection coverage of the GEROS-ISS mission is simulated andanalysed.

13

14 CHAPTER 3. GNSS REFLECTOMETRY

3.1 Method and Geometry

The method works as a bistatic radar, which means that transmitter and receiver areseparated by a significant distance, see Kostelecký et al. 2005. This definition can beextended to a system in which a single receiver can simultaneously track a variety of bi-statically scattered signals, from different transmitting sources, see Ruffini 2006. Thisis called a multi-static system as depicted in figure 3.1.

Figure 3.1 Multistatic GNSS Reflectometry System. From one individual receiver,a large number of GNSS signals can be received: Directly and reflected off theEarth’s surface. This set of bistatic observations occur at different azimuth andelevation angles, providing glistening zones, indicated in yellow. Adapted from Jinet al. 2014

The receiver receives signals from several GNSS satellites. Different GNSS transmitterscan be identified and separated. The received signals are signals propagated directlyfrom the source to the receiver, crossing the atmosphere, as well as signals that havepropagated down to the Earth surface, scattered off its surface and up to the receiversposition. The received signals are called rays. Two different types of signals can bereceived using two different antennas: One pointing towards the transmitter to gatherdirect rays and the other one pointing to the Earth surface, to catch scattered signals.Receivers can be mounted in satellites, aircraft, ground stations etc.. In case the receiveris at air-borne or higher altitudes, the delay and Doppler information can also be usedto separate both radio-links. For some applications it is desirable that both direct andreflected signals interfere with each other, being then gathered by a signal antennapointing towards the horizon, the Earth limb or at a certain slant orientation.The amount of reflected radio links can be as large as the amount of direct radio-links.By 2020 one expects to have four fully operational GNSS Systems, with at least 99operational satellites only taking into account the Walker constellations. In 2014 witharound 55 fully operational GPS and GLONASS transmitters it was possible to capturesignals from 15 to 25 GNSS sources simultaneously using a receiver on the Earth’ssurface [Jin et al. 2014]. The potential reflection coverage of a hypothetical GNSS-R aboard the LEO Orbiter ISS, with 107 GNSS transmitters in total, is analysed inchapter four.As a consequence of the large amount of potential simultaneously received signals,one expects a spatial coverage obtained with a nadir-looking antenna correspondingto a gapped and irregular sampled wide swath image of the surface beneath, depictedin figure 3.1. The obtained image is compounded by tessellation of glistening zonesproduced by the reflected GNSS signals. In contempt of the distance between glistening

3.2. SPECULAR AND DIFFUSE SCATTERING 15

zones, space-based GNSS-R receivers achieve a coverage that gives a general view ofmany hundreds of kilometres across-track.

3.2 Specular and Diffuse Scattering

Electromagnetic scattering is a complex process involving surface dielectric propertiesand topographic features as a whole system. Two different ways of reflection are typicallydistinguished and contrasted: Specular/mirror-like and diffuse Scattering, see figure 3.2.Generally, the scattering process contains both types of contribution.Specular reflection corresponds to scattering in which waves from a single direction arereflected into another single direction. In contrast, diffuse scattering describes when theincoming waves are reflected in a broad range of directions.The specular-to-diffuse trend is determined by the roughness structures of the surfacetopography. One way to define the roughness of a surface is the Rayleigh criterion[Hajnsek et al. 2005].Considering a plane monochromatic wave transmitted at angle θinc onto a rough surface,the phase difference ∆Φ between two rays scattered from separate points on the surfacecan be calculated by:

∆Φ = 2 · σ2 · πλ· cos θinc (3.1)

where σ is the standard deviation of the roughness height in relation to a referenceheight and θ the local incident angle. The Rayleigh criterion states that if t∆Φ < 2/π,then the surface may be considered as smooth and is defined by:

σ <λ

8 · cosθ(3.2)

Hence through the Rayleigh-Criterion, specular and diffuse reflection can be distin-guished. In smooth surfaces, scattering with a dominant specular component occurswhere the surface roughness has no significant features of spatial scales similar to theelectromagnetic wavelength. Therefore the roughness spectrum has contributions atmuch higher and/or much lower wavenumbers than the electromagnetic wave. Formore details about electromagnetic scattering, see Beckmann et al. 1987.

From the roughness information contained in the signal power of the scattered sig-nal (see figure 3.2 right column), local wind speed can be derived [Zavorotny et al.2000]. The scattering cross-chapter image is called Delay Doppler Map (DDM), withvariable lag correlation and the Doppler shift as the two coordinates [Ruf et al. 2012].The DDM resolves the spatial distribution of the scattering cross-chapter. For moredetails about Delay Doppler Mapping see Zavorotny et al. 2014 and Jin et al. 2014,Chapter 8.4.


Figure 3.2 Specular and diffuse reflection: 1.a) Specular reflection, energy fromone point is reflected to the receiver. The surface is mirror-like and there is noroughness σ = 0. 1.b) Waveform resulting from specular reflection, correspondingto a smooth surface 1.a). 2.a) Slight diffuse reflection, energy from a small glisteningzone reflected to the receiver. 2.b) Waveform resulting from slight diffuse scattering2.a). 3.a) Strong diffuse reflection, energy from a large glistening zone reflected tothe receiver and its resulting waveform 3.b). Adopted from Garrison 2013

3.3 The Concept of GNSS-R Altimetry

Conventional radar altimetry is monostatic and only measures the ocean height at sub-satellite (nadir) points. Both sender and receiver are tied to the same spacecraft andlimits the spectrum in time of the returns to a recurring pattern for most altimetry mis-sions [Wagner et al. 2003]. Thus radar altimetry is spatiotemporal limited [Zavorotnyet al. 2014]. Therefore the concept of using reflectometry for altimetry measurementswas proposed by Martin-Neira in 1993, see Martin-Neira 1993.The large number of synchronized GNSS transmitters yields various reflection tracksof GNSS signals observed simultaneously by a single spaceborne receiver [Semmlinget al. 2014]. The altitude measurements with GNSS-R are therefore along multiplewide spaced ground tracks. Ocean Remote Sensing using GNSS-R provides additionalmeasurements of the sea surface and increases spatial and temporal resolution of RadarAltimeters (RA) [Jin et al. 2014]. Using GNSS-R as a passive wide-swath altimeter,new applications such as detection of tsunamis, ocean eddies and other mesoscale fea-tures regarding ocean height can be derived. This is further contributed to researchtopics such as Geostrophic velocities and gravity anomalies, tides and physical-chemical-biological interactions. Improvements in ocean coverage with GNSS reflectometry havebeen shown in simulations studies [Stosius et al. 2010, Rius et al. 2010, Wagner et al.2003]. Chapter 4 also focuses on a simulation of the reflection coverage of a receiveronboard the LEO-orbiter ISS.Various airborne experiments on ocean altimetry have been conducted, e.g. Semmling

3.4. GNSS REFLECTOMETRY MISSIONS 17

et al. 2014, Semmling et al. 2013, and spaceborne missions recently launched, e.g.TechDemoSat-1 [Unwin 2015], and planned such as GEROS-ISS [Wickert et al. 2015b].A recent ground-based experiment shows that the mean sea surface level can be re-trieved with an accuracy of 4cm [Alonso-Arroyo et al. 2015].

The basic principle in GNSS-R altimetry is that the reflected signal will arrive laterthan the direct one, since it will travel a longer path to the receiver.Altimetry using GNSS-R can be carried out in two general ways, depending on the ran-ging principle used [Ruffini 2006]. Both code and phase altimetry study the differentialdelay between the direct and indirect signal. It is derived from GNSS measurementsusing cross correlation of the incoming signals from the direct and reflected components[Kostelecký et al. 2005].The differential delay consists of the total travelled distance as well as of atmosphericdelays, including ionospheric and tropospheric effects, instrumental components, as e.g.antenna offsets, and noise.

3.4 GNSS Reflectometry Missions

Whilst GNSS-R has established itself as a promising remote sensing technique throughsuccessful ground-based and air-borne experiments, e.g.Alonso-Arroyo et al. 2015, Semmlinget al. 2014, there is a demand for spaceborne missions, that conduct research on re-ceiving reflected signals with receivers in space. The U.K. mission TechDemoSat-1,focusing on altimetry and ocean remote sensing, commenced in October 2014 [Unwinet al. 2011]. The launch of the U.S. CYGNSS mission, addressing tropical cyclone innercore studies, is expected in October 2016 [Ruf et al. 2012]. The ESA GEROS-ISS mis-sion, emphasising remote sensing of the Earth’s System with a focus on climate changecharacterisation, is in currently in Phase A feasibility studies [Wickert et al. 2014b].

3.4.1 TechDemoSat-1

TechDemoSat-1 is a collaborative project between industry and academia to demon-strate the advanced capabilities of state-of-the-art small satellite technology for sci-entific and commercial applications [Unwin 2015, Unwin et al. 2011]. Surrey SatelliteTechnology Ltd (SSTL), as the project leader, cooperates with research and commercialpartners providing the payloads in building, testing and operating the satellite. Themission goal is to approach the demand of better temporal and spatial knowledge ofthe sea’s state. Therefore two payloads, flown on TechDemoSat-1, address these needs:The Sea State Payload (SSP) Altimeter and the Space GNSS Receiver - Remote SensingInstrument (SGR-ReSi). The SGR-ReSi is a space GNSS receiver primarily designedfor GNSS reflectometry and processes reflected GPS signals on-board into DDMs. Al-ternatively the remote sensing receiver can collect raw data for processing on ground.The TechDemo-Sat-1 satellite was launched in July 2014 and is operated by Sat AppsCatapult Center and SSTL. The satellite orbits in a sun-synchronous, near-circular or-bit at an altitude of about 825 km and with an inclination of 98◦. The payload testphase, commenced in October 2014 and in May 2015, made the transition to the datacollection phase. The expected lifetime of the satellite is three years. Initial results ofthe derivation of wind speed using GNSS-R were published by Foti et al. 2015.


3.4.2 CYGNSS

The Cyclone Global Navigation Satellite System (CYGNSS) is a spaceborne missionwith a focus on tropical cyclone (TC) inner core process studies [Ruf et al. 2012].CYGNSS consists of eight GPS bistatic radar receivers deployed on separate nanosatel-lites. The satellites will be deployed in one circular orbit plane at an altitude of 510km and 35◦ inclination. The primary scientific motive is rapid sampling of ocean sur-face winds in the inner core of tropical cyclones. Therefore four simultaneous real timeDDMs will be generated by each receiver using the GPS L1 C/A signal [Ruf et al.2015]. CYGNSS attempts to resolve the principle deficiencies with current TC intens-ity forecasts, which lies in inadequate observations and modelling of the inner core. Theinadequacy in observation results from obscuration of the inner core ocean surface forconventional remote sensing instruments and poorly sampled rapidly evolving stages oflife cycle from space. The mission’s specific design addresses these two limitations bycombining all-weather performance of GNSS bistatic ocean surface scatterometry withthe sampling properties of a constellation of satellites. Using a dense constellation ofnanosatellites results in spatial and temporal sampling properties which are remarkablydifferent from conventional imagers. The project commenced in December 2012. Aftercompletion of the system requirements review and preliminary design review in 2013and 2014, Phase C, the critical design review, was accomplished in spring 2015. Theexpected launch date is October 2016.

3.4.3 GEROS-ISS

GEROS-ISS stands for GNSS REflectometry, Radio Occultation and Scatterometry onboard the International Space Station (ISS). This scientific experiment was proposed tothe European Space Agency (ESA) in 2011. The emphasis of GEROS is the dedicateduse of signals from currently available GNSS signals for remote sensing of the Earthsystem with a focus on climate change characterisation, see Wickert et al. 2014b andWickert et al. 2014a.

3.4.3.1 Mission Idea

GEROS-ISS is a new ISS experiment, which primarily focuses on exploiting reflectedL-band signals from GNSS satellites to measure key parameters of ocean surfaces, whichare relevant for the characterisation of climate change. Global atmosphere and iono-sphere observations using the GNSS radio occultation technique and the monitoring ofland surface parameters utilising reflected GNSS signals are secondary mission goals.Figure 3.3 shows the schematic overview of the GEROS-ISS experiment to be installedaboard the International Space Station. Red lines indicate the scatterometry meas-urements for water, ice and land surface monitoring. Blue lines indicate GNSS-R andcoherent reflectometry observations and the green lines symbolise the GNSS signals,received from zenith for Precise Orbit Determination (POD) of the GEROS Payloadand 3D upside ionosphere monitoring.

Complementing the Earth System observations from other current satellite missions,GEROS-ISS will pioneer the exploitation of GNSS remote sensing signals from theEuropean Galileo system. This will also improve the accuracy as well as the spatio-temporal resolution of the derived geophysical properties compared to GPS standalonemeasurements. Additional signal use from GLONASS, BeiDou and the Japanese QZSSsatellite systems is also intended.


Figure 3.3 Schematic overview of the GEROS experiment: Red lines indicate scat-terometry measurements for water, ice and land surface monitoring. Blue lines in-dicate GNSS radio occultation and coherent reflectometry observations. The greenlines symbolise the GNSS signals, received from zenith for Precise Orbit Determ-ination (POD) of the GEROS-ISS payload and 3D upside ionospheric monitoring,from Wickert et al. 2014b.

GEROS will contribute to long-term and climate relevant observations of major compon-ents of the Earth System: Oceans/Hydrosphere, Gyrosphere/Snow, Atmosphere/Iono-sphere and solid Earth/Landcover.

The experiment will mainly provide mid- and low-latitude observations on submeso-scale or longer oceanic variability with a focus on coastal regions, surface ocean cur-rents, surface winds, wave heights and vertical atmospheric temperature, water vapourand electron density structure for a period of at least two years, depending on the life-time of the International Space Station. The GEROS-ISS observations will lead to abetter understanding of the climate system, e.g. ocean barotropic variability, Rossbywave large-scale structures, eddy-current systems, fronts and coastal upwelling. HerebyGEROS-ISS takes advantage of the capacious infrastructure aboard the ISS, which isa unique platform for the development of further advanced GNSS reflectometry tech-niques, despite minor limitations such as antenna size or appropriate electric poweravailability.

Figure 3.4 shows the oceanic observations carry signals with a wide range of relatedprocesses. The observed fingerprints of these processes have temporal time scales from1 hour to tens of thousands of years and spatial scales from ten to tens of thousandsof kilometres. The figure illustrates the spatial and temporal scales for these processesand indicates phenomena which can be investigated with GEROS data complementaryto and distinct from the planned NASA Surface Water Ocean Topography (SWOT)mission and ESA’s and NASA’s radar altimetry missions.

GEROS will also provide a sensor calibration/validation option for other upcomingsatellite missions including, e.g. the European twin platform ocean remote sensing


mission Sentinel-3, U.S./European SWOT (Surface Water Ocean Topography) and theU.S./Taiwan 12 satellite constellation FormoSAT-7/COSMIC-II for GNSS radio oc-cultation. The GNSS remote sensing data will also complement the innovative GNSSscatterometry measurements from the U.S. mission CYGNSS (CYclone Global Naviga-tion Satellite System).

Figure 3.4 Oceanic observations carry signals of a wide range of related processes.The observed fingerprints of these processes have temporal time scales from onehour to tens of thousands of years and spatial scales from ten to tens of thousandskilometres. The figure illustrates the spatial and temporal scales of these processesand indicates phenomena, which can be investigated with GEROS data comple-mentary to and distinct from the planned NASA SWOT mission and ESA’s andNASA’s radar altimetry missions, from Wickert et al. 2014b.

3.4.3.2 Mission Goals

Primary mission objectives of GEROS-ISS are:

The measurement of the altimetric sea surface height of the ocean using reflected GNSSsignals to allow methodology demonstration, establishment of error budget, resolutionsand comparison/synergy with results of satellite based nadir-pointing altimeters. Fur-thermore the scalar ocean surface mean square slope (MSS), which is related to searoughness, wind speed and direction, will be retrieved with a GNSS spaceborne receiverto allow methodology testing, establishment of error budget and resolutions. As a sec-ondary outcome, 2D MSS (directional MSS) will be desirable.


Secondary mission objectives, which increase the scientific value of the GEROS data,but do not influence the instrument developments, are:

Further exploitation of the potential of GNSS radio occultation data (vertical profilesof atmospheric bending angle, refractivity, temperature, pressure, humidity and elec-tron density), particularly in the Tropics, to detect changes in atmospheric temperatureand climate parameters (e.g. tropopause height) and to provide additional informationfor the analysis of the reflectometry data from GEROS. In addition, the potential ofGNSS scatterometry will be assessed for land applications and in particular to developproducts such as soil moisture, vegetation biomass, and midlatitude snow/ice propertiesto better understand anthropogenic climate change.

3.4.3.3 Status

In 2011 the European Space Agency Directorate of Human Space Flight and Opera-tions (HSO) in coordination with the Directorate of Earth Observation Programmes(EOP) released an announcement of opportunity for soliciting scientific experimentsfor the International Space Station relevant to global climate change studies. At theend of 2012, the GEROS-ISS proposal was accepted to Phase A feasibility studies aftera peer-review. An interdisciplinary and international Science Advisory Group (SAG)of acknowledged experts in Oceanography, Geodesy, Atmosphere and GNSS Sciencestarted to work in June 2013 on details of the preparation of the GEROS-ISS mission.This SAG consists of key experts from the GEROS-ISS proposing team and additionalexperts, nominated by ESA. The commencement of two competitive industrial phase Astudies for the GEROS-ISS mission implementation was foreseen for early 2014. Accord-ing to the current schedule and in case of successful preparative studies and provisionof appropriate funding, a launch of GEROS-ISS can be expected in 2018.

3.4.3.4 Scientific Studies

Part of the preparation of the GEROS-ISS mission and the work of the Science Ad-visory Group involves dedicated scientific studies and campaigns. One example is aninitial Observation System Simulation Experiment (OSSE) to investigate the GEROScapability for the observation of highly energetic mesoscale ocean currents (eddies) withchanges of <20 cm sea surface within regions of <100 km2 [Lee et al. 2013]. Know-ledge on these eddies is important for the characterisation of nutrients and/or pollutantswith many societal and scientific applications. Currently the tracking and forecastingof eddies is limited due to the capability of the present ocean altimetry missions. TheOSSE used artificial GEROS-ISS measurements (only GPS, 50 cm accuracy, 1 month)and a regional ocean model. Initial results indicate that GEROS-ISS data, even withmeasurements from only one GNSS and with conservative accuracy assumption, couldbe used to improve current regional ocean topography forecasting with a special focuson highly energetic mesoscale currents. The OSSE investigations will be continued withdata from additional GNSS satellites and from classical altimetry missions. Anotherpart of the Phase A activities is the scientific study GNSS-Reflectometry Assessmentof Requirements and Consolidation of Retrieval Algorithms (GARCA) [Wickert et al.2015a]. The objective of GARCA is to support the assessment and consolidation ofscientific requirements and the consolidation of retrieval algorithms for a spaceborneGNSS-R experiment, focusing on the GEROS-ISS concept and its primary and sec-ondary data products (sea surface height and ocean surface roughness). The mainwork is the development of an end-to-end-Simulator for the GEROS-ISS measurements


(GEROS-SIM), and the evaluation of the Level-1 observables and expected Level-2 geo-physical products. A GEROS-SIM version will be executable through a web-server,freely accessible to the interdisciplinary scientific GEROS-ISS community. Another aimis the study of compliance of different GEROS-ISS implementations with respect to themission requirements and optimisation of its geophysical data products and the studyof their impact on current global ocean observation systems and synergies with existingsatellite missions. GARCA also fosters a broad GEROS-ISS scientific community, as away to promote and advertise the concept and its potential.

Chapter 4

Numerical Simulation of expectedObservation Coverage ofGEROS-ISS

This chapter focuses on the geometrical simulation and visualisation of the expectedlocations of reflectometry measurements of GEROS-ISS. Firstly, in 4.1, the used MAT-LAB Simulation Software is briefly introduced. Subsequently, in 4.2, the global obser-vation coverage with respect to the different Global Navigation Satellites Systems GPS,GLONASS, Galileo and BeiDou were studied for different time intervals. The reflectionevents were simulated for a time period of one day and one week respectively. For theGPS system, reflection events for a longer period of one month were also computed.In Chapter 4.3 a visibility mask of the GNSS antennas aboard the ISS is taken intoaccount. The actual feasible global reflection coverage according to geometrical restric-tions on the ISS is visualised and analysed. In chapter 4.4 a case study on the oceansurrounding Southern Africa is addressed and the reflection coverage of this region isstudied.

4.1 Description of the Simulation Software

A algorithmic tool available in MATLAB was provided by the GNSS reflectometryworking group of GFZ in the Department of Geodesy and Remote Sensing. For thenumerical simulation of the expected observation coverage, the tool has been adaptedand the simulated data has been further processed. Thereby the two main challengesthat need to be solved are the calculation of the orbits and the computation of thespecular point.

4.1.1 Satellite Orbit Simulation

Firstly, for this calculation, orbit data is required for the GPS, GLONASS, Galileo andBeiDou satellites as well as for the ISS, see figure 4.1.

For GPS, broadcast ephemeris data were obtained from the GFZ server and MATLABcode for the orbit determination was provided from the GNSS Reflectometry workinggroup at GFZ. The orbits are propagated using the algorithm from Assistant Secretaryof Defense for Command, Control, Communications, Intelligence 1995 with a step sizeof one second. The orbit accuracy of the broadcast ephemeris is approximately 100 cm[IGS 2015]. The computation time for the propagation of one satellite for one day is

23

24 CHAPTER 4. NUMERICAL SIMULATION OF OBSERVATION COVERAGE

approximately 18 seconds1.

For the orbit determination of GLONASS, Galileo, BeiDou and the ISS, Two Line Ele-ment (TLE) data was used. TLE is a data format encoding orbital elements, providedby CelesTrak [Kelso 2015]. Since the structure of the GLONASS broadcast ephemerisvaries from GPS, easy implementation using TLEs was chosen. The GLONASS andISS TLEs were downloaded from the CelesTrak website. To simulate the Galileo andBeiDou orbits synthetic TLEs were used since the full Walker constellation and there-fore real orbit data is currently not available.

For given TLE orbit data the orbits are propagated using the SGP4 model for theISS and SDP4 model for GNSS. The SGP4 model is used for near-Earth satellites witha period less than 225 minutes and SDP4, an extension of SGP4, for a period longerthan or equal to 225 minutes. For more detailed information see Vallado et al. 2008and Hoots et al. 1980. The SGP4 orbital data, in form of TLE sets, does not provideany kind of accuracy information.

Figure 4.1 MATLAB Simulation Software Overview: Input Data of the simulation isthe orbit data of the ISS and the GNSS satellites in Two Line Element (TLE) formatand GPS in Broadcast Ephemeris format (BRC). First the orbits are propagated(4.1.1): The ISS orbit is propagated using the SGP4 method and the GNSS orbitsare propagated by applying the SDP4 model [Vallado et al. 2008, Hoots et al. 1980];GPS orbits are determined with an algorithm from Assistant Secretary of Defensefor Command, Control, Communications, Intelligence 1995. Following this in 4.1.2,the specular points are computed applying the geometric mirror equation andoutput in WGS84 [Martin-Neira 1993].1For all computations a PC with 3.7 GB working memory and a AMD Athlon(tm) 64 X2 Dual Core

Processor 5600+ was used.

4.1. DESCRIPTION OF THE SIMULATION SOFTWARE 25

Approaches of error estimations by comparing SGP4 ephemeris to precision ephemerishave been made and convey an idea of the expected radial, in-track and cross-trackerrors, which are in a range of kilometres [Muldoon et al. 2008, Kelso 2007]. Thereforethe accuracy is significantly poorer than the accuracy of broadcast ephemeris, but suf-ficient for our simulation. The computation time for the propagation of one satellite forone day is approximately 55 seconds and is significantly longer than the computationtime for broadcast ephemeris. The GNSS orbits were propagated with a step size ofone second. The LEO orbit of the ISS was propagated with a step size of one minuteand linear interpolated with a step size of one second.

4.1.2 Specular Point Computation

With the transmitter position (GNSS satellite) and the receiver position (ISS) possiblereflection events are calculated. For the computation two different approaches will beintroduced: The trigonometric approach and the computation of the specular pointusing the spherical mirror equation. Both methods presume a spherical model of theEarth’s surface and need to be adapted to a ellipsoidal model of the Earth for betteraccuracy. Both approaches reduce the three dimensional problem to a two dimensionalone, only considering the plane, within which the GNSS signal propagates.

4.1.2.1 Trigonometric approach

The coordinates of the point of specular reflection are computed for the geometry ofthe system shown in Figure 4.2, assuming a spherical earth [Semmling et al. 2015].The transmitter is at a higher altitude than the receiver. In case transmitter and re-ceiver were at the same altitude the solution would be trivial: The reflection point wouldbe halfway between the two satellite radials. The fact that one is higher than the othermeans that the reflection point moves from this mid-point towards the lower satellite.

Referring to figure 4.2, the coordinates of T (xT , yT ) and R(xR, yR) are given and thereflection point coordinates P (xP , yP ) are unknown. We assume hP to be the Earth’sradius and hT , hR are the distances from the Earth centre 0 to transmitter and receiver.The angle αT is the angle P-T-0 and αR is the angle P-R-0. The angle β is the angleT-0-P and βT and βR respectively T-0-P and P-0-R.

Five equations can be set up:

With the law of sine it reads

sin (90◦ + ε)

hT=

sinαT

hP(4.1)

sin (90◦ + ε)

hR=

sinαR

hP(4.2)

Compuation of the angular sum reads

αT + (90◦ + ε) + βT = 180◦ (4.3)

αR + (90◦ + ε) + βR = 180◦ (4.4)

And through the equation of the scalar product of the two position vectors of transmitterand receiver read

βT + βR = arccos

(T ∗R|T | · |R|

)(4.5)


Figure 4.2 Reflection geometry trigonometric approach: The angle ε describes theelevation angle of the reflection point P . The angles αT and αR describe theangle at the transmitter T and receiver R position between the specular pointand the Earth’s center 0 respectively. The height hP corresponds to the Earth’sradius and the heights hT and hR relate to the distances from the Earth’s centerto the transmitter and receiver. The angle β describes the angle at the Earth’scenter between transmitter and receiver and βT and βR the angles T-0-P and P-0-R respectively.

First the elevation ε needs to be determined. Therefore one first computes β:

β = βT + βR = arccos

(T ∗R|T | · |R|

)Then the equations (4.1) and (4.2) are substituted into (4.3) and (4.4):

arcsin

(sin (90◦ + ε) · hP

hT

)+ (90◦ + ε) + βT = 180◦ (4.6)

arcsin

(sin (90◦ + ε) · hP

hR

)+ (90◦ + ε) + βR = 180◦ (4.7)

Now the two equations (4.6) and (4.7) can be substituted into equation (4.5) and itreads

0 = 2 · ε+ arcsin

(sin (90◦ + ε) · hP

hT

)+ arcsin

(sin (90◦ + ε) · hP

hR

)+ β − 180◦ (4.8)

After solving the non-linear equation (4.8) for ε, one can compute αT and αR as

αT = arcsin

(sin (90◦ + ε) · hP

hT

)(4.9)


αR = arcsin

(sin (90◦ + ε) · hP

hR

)(4.10)

The angles βT and βR read

βT = 90◦ − ε− αT (4.11)

βR = 90◦ − ε− αR (4.12)

Now the coordinates of the reflection point xP and yP can be computed by solving thefollowing system of linear equations:

(xT · xP + yT · yPxR · xP + yR · yP

)=

(hT · hP · cosβThR · hP · cosβR

)(4.13)

4.1.2.2 Spherical Mirror Equation

The first approach for calculating the specular reflection point was introduced by Martin-Neira in 1993, see Martin-Neira 1993.The coordinates of the point of specular reflection are computed for the geometry ofthe system shown in Figure 4.3, assuming a spherical earth.

Let xy be the plane containing transmitter T (xT , yT ), receiver R(xR, yR) and reflec-tion point P (xP , yP ). Φ is the angular polar coordinate of P and hP the radius of theEarth. Let x′y′ be a system of coordinates that is obtained by rotating the xy coordin-ates and angle Φ counter clockwise and then translating it along the positive x-axis ata distance equal to the radius of the sphere hP . In that case the following relationshipbetween xy and x′y′ occurs:

(x′

y′

)=

(cos Φ sin Φ− sin Φ cos Φ

)·(xy

)−(hP0

)(4.14)

First the transmitter and receiver coordinates are transformed to the x′y′ system andit reads (

x′Ty′T

)=


)·(xTyT

)−(hP0

)(4.15)

(x′Ry′R

)=


)·(xRyR

)−(hP0

)(4.16)

Now the condition for specular reflection (Snell’s law) can be easily expressed in thex′y′ system and reads

x′Ty′T

= −x′Ry′R

(4.17)


Figure 4.3 Reflection geometry spherical mirror equation: The reference system xyis transformed into a reference system x′y′ at the specular point P . The distance hPdescribes the radius of the Earth and the angle Φ the angle between the referencedirection and the specular point P . The incidence angle of the reflection betweenthe transmitter T and the receiver R is denoted with θ. Adpated from Martin-Neira1993.

Substituting equations (4.15) and (4.16) into (4.17) leads to:

xT · cos Φ + yT · sin Φ− hP−xT · sin Φ + yT · cosΦ

=xR · cos Φ + yR · sin Φ− hP−xR · sin Φ + yR · cos Φ

(4.18)

rearranging this expression one obtains

2(xT · xR − YT · yR) sin Φ · cos Φ− (xT · yR + yT · xR)(cos Φ2 − sin Φ2)

−hP · sin Φ(xT + xR) + hP cos Φ(yT + yR) = 0(4.19)

Making the following change of variable

t = tanΦ

2(4.20)

Equation (4.19) becomes:

2(xT · xR − YT · yR) · 2t

1 + t2· 1− t2

1 + t2

−(xT · yR + yT · xR) ·

((1− t2

1 + t2

)2(2t

1 + t2

))

−hP ·2t

1 + t2· (xT + xR) + hP ·

1− t2

1 + t2· (yT + yR) = 0

(4.21)

Rearranging this expression, the equation of the specular point, spherical mirrorequation, can finally be written as:

c4 · t4 + c3 · t3 + c2 ·2 +c1 · t+ c0 = 0 (4.22)


where

t = tanΦ

2c0 = (xT · yR + yT · xR)− hP (yT + xR)

c1 = −4(xT · xR − yT · yR) + 2 · hP (xT + xR)

c2 = −6(xT · yR + yT · xR))

c3 = 4(xT · xR − yT · yR) + 2 · hP · (xT + xR)

c4 = (xT · yR + yT · xR) + hP (yT + yR)

After solving the spherical mirror equation (4.22) one obtains the reflection pointcoordinates P (Φ, hP ).

4.1.2.3 Specular Point Simulation

For the simulation of the GEROS-ISS reflection coverage, Martin-Neira’s sphericalmirror equation method is applied. The computation of the reflection events for onePRN for a simulation period of one day takes approximately 100 seconds. In contrastthe expected computation time for the sinus approach is significantly longer.

First an osculation sphere is iterated, assuming the reflection point to be at nadir of theISS, applying the WGS 84 for all computations. Then the specular point on the iteratedosculation sphere, using the spherical mirror equation, is computed. After checkingthe curvature bias, a second iteration of an osculation sphere in the prior determinedreflection point is performed. The specular point on the adjusted osculation sphere iscalculated a second time and saved. The bias between the osculation sphere and theellipsoid depends on the incidence angle and ranges of < 1 m up to 100 m. After afirst iteration the bias is negligible [Semmling et al. 2015]. The simulation focuses onthe specular points of the reflection rather than the entire reflection glistening zone.The computed specular point will thus be understood as the point where the reflectionwould occur if the surface were perfectly smooth, with no diffuse scattering component.The reflection events are determined with a step size of one second. No atmosphericeffects are considered in the computation.


4.2 Reflection Coverage

To visualise the reflection coverage, a grid with the same bin size of 1x1 degrees as inWagner et al. 2003, was created. The number of specular points were counted per bin.The actual bin size varies depending on the location on the Earth surface, due to thedefinition of the graticule. The side length of one bin at the equator measures approx.110 km and approx. 80 km at a latitude of 50◦. This leads to a bin size area of 12, 400km2 at the equator and 6, 900 km2 at a latitude of 50◦.

The computed specular points are converted to WGS 84. For all global plots the equir-ectangular Plate Carre Projection was applied. As specified in the mission requirementsfor sea surface height, the required spatial resolution of one observation is 10 km crosstrack and 100 km long track [GEROS-SAG 2013]. Since the average speed of the ISSis approximately 8 km/sec [ESA 2015b], the spacecraft is going to move about 100 kmin 12 seconds. To fullfill the long track requirements, the sampling rate is once every12 seconds for the global observation coverage.

4.2.1 Simulation Period - One Day

For the simulation of the time period of one day, the 9 th March 2015 was chosen, sinceorbital data for GPS, GLONASS and the ISS was available for that date. First the GPScoverage is described in detail. Following this, the similarities and differences betweenthe GPS coverage, the GLONASS, Galileo and BeiDou coverage plots are elaborated.The coverage of all GNSS satellites combined is studied subsequently.

The simulation of the reflection events originating form GPS satellites take into ac-count 32 satellites: The 24 satellites of the Walker constellation and 8 spare satellites.The spare GPS satellites were taken into account as well, because continuous orbit dataof these satellites was available.

Figure 4.4 shows the computed GPS reflection coverage for one day. The colour in-dicates the number of reflection points per bin. The maximum number of reflectionevents for the GPS constellation is 17. The pole areas north and south of 50◦ and −50◦

latitude feature only a small number of random reflection events and thin out towardsthe poles. At the areas north of 70◦ and south of −70◦ no reflection events occur. Adense accumulation of reflection events is found at a latitude of 50◦ and −50◦ for alllongitudes. In between 50◦N and 50◦S a line structure is distinguishable. This area alsofeatures a significant number of gaps with no reflection events. Between 150◦W and90◦W and 50◦N and 50◦S, an accumulation of reflection events along the line structureis visible. The reflection coverage appears to be mirrored along the equator.

To explain the coverage structure, the ground track of one GPS satellite, the ISS groundtrack and the occurring specular points are plotted. Figure 4.5 shows the ground trackof the GPS satellite PRN 1 and the ISS, as well as the resulting specular reflectionpoints. In the plot a time frame of 1.5 hours from 4:00 AM to 5:30 AM was utilised.Due to the reflection geometry and long distance between transmitter and receiver, thereflection occurs close to the ground track of the receiver and follows its shape.For a better understanding of the overall line structure of the coverage, the ISS groundtrack of a simulation period of one day is plotted. In figure 4.6 the ground track ofthe ISS overlays the reflection coverage of the GPS Constellation. Clearly recognisable

4.2. REFLECTION COVERAGE 31

is that the accumulation of reflection events between 150◦W and 90◦W and 50◦N and50◦S, occurs due to a revision of the ground track close to the ground track at thebeginning of the day. The dense accumulation of reflection events, found at a latitudeof 50◦ and −50◦ and at all longitudes, can be explained with the ISS ground track aswell: The maximum and minimum latitude of 51.6◦ is an accumulation point [NASA2015].

For the simulation of the GLONASS observation coverage, all 24 GLONASS satel-lites of the Walker constellation are considered. In figure 4.7 the simulated reflectioncover on the 9th of March 2015 is depicted. The observation coverage of the Galileo re-flection events was simulated with the full Walker Constellation of 27 satellites. Figure4.8 shows the observation coverage, simulated with synthetic Galileo orbit data. Forthe simulation of the BeiDou observation coverage with reflected signals from BeiDousatellites, only 24 MEOs are taken into account. Due to the differing reflection geometrywith IGSO and GEO satellites, they were not considered. In figure 4.9, one sees thereflection coverage plot of the BeiDou MEO-constellation.

The structure of the GLONASS, Galileo and BeiDou coverage plots is similar to thestructure of the GPS coverage. The ISS ground track is clearly distinguishable. Thecoverage of GPS and Galileo is distinctly denser compared to BeiDou and GLONASSdue to a higher number of satellites considered for the simulation. Noticeable is thatin the Galileo plot no reflection points occur for latitudes north and south of 67◦/−67◦

latitude. In contrast for GPS, GLONASS and BeiDou, infrequent specular points existnorth and south of 67◦/−67◦ latitude.

−180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180−90

−60

−30

0

30

60

90

Longitude [deg]

La

titu

de

[d

eg

]

GPS Reflection Coverage − 2015/03/09

Nu

mb

er

in b

in

0

5

10

15

20

25

30

Figure 4.4 GPS coverage - simulation period one day: The figure depicts the globalreflection coverage with a receiver onboard the ISS, receiving reflections from 32GPS satellites. The reflection events are simulated over a period of one day withorbit data from the 9th of March 2015. The colour indicates the number of reflectionpoints per bin, with a bin size of 1◦x1◦.


−180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180−90

−60

−30

0

30

60

90L

atitu

de

[d

eg

]

Longitude [deg]

GPS − PRN 1 − 2015/03/09

Tim

e [h

of d

ay]

4

4.5

5

5.5ISS OrbitGPS PRN 1 OrbitSpecular Point

Figure 4.5 Ground track plot of GPS PRN 1, the ISS and the resulting SpecularPoints in time dependency from 4:00 AM until 5:30 AM on 2015/03/09. Thereflection occurs close to the ground track of the ISS and follows its structure.

−180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180−90

−60

−30

0

30

60

90

Longitude [deg]

La

titu

de

[d

eg

]

GNSS Reflection Coverage − 2015/03/09

Nu

mb

er

in b

in

0

5

10

15

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Figure 4.6 GPS coverage and ground track of the ISS - simulation period one day.The figure shows the global reflection coverage with a receiver onboard the ISS,receiving reflections from 32 GPS satellites over a period of one day. The groundtrack correlates with the structure of the observation coverage.


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Figure 4.7 GLONASS coverage - simulation period one day: The figure shows thereflection coverage with a receiver onboard the ISS, receiving reflected signals from24 GLONASS satellites. The reflection events are simulated over a period of oneday with orbit data from the 9th of March 2015. The colour indicates the numberof counted specular points per bin, where the bin size is 1◦x1◦.

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Figure 4.8 Galileo coverage - simulation period one day: The figure depicts theglobal reflection coverage with a receiver onboard the ISS, receiving reflections from27 Galileo satellites. For the orbit simulation of the Galileo satellites, syntheticorbit data was used. The simulation was carried out over a period of one day withISS orbit data from the 9th of March 2015. The colour indicates the number ofreflection points per bin, with a bin size of 1◦x1◦.


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Figure 4.9 BeiDou coverage - simulation period one day: The figure shows theglobal reflection coverage with a receiver onboard the ISS, receiving reflected signalsfrom 24 BeiDou MEO satellites. For the orbit simulation of the BeiDou satellites,synthetic orbit data was used. The reflection events are simulated over a period ofone day with ISS orbit data from the 9th of March 2015. The colour indicates thenumber of reflection points per bin, with a bin size of 1◦x1◦.

The observation coverage of all GNSS systems, in total 107 satellites, is shown in figure4.10. The maximum number of reflection points per bin is 34. North and south of 70◦ noreflection points were counted. Between 65◦N and 55◦N as well as 65◦S and 55◦S a bandwith an average value of 5 reflection events per bin exists along all longitudes. The bandhas a small number of gaps with bins, where no reflection points were counted. Most re-flection events occur along 52◦N and 52◦S and along the line structure between 50◦ and−50◦ latitude. Along the ISS ground track an average of 15 reflection points per bin arecounted. At crossings of the line structure a high number of reflection events is clearlydistinguishable. The reflection coverage appears to be mirrored at the equator. Afterone day almost the whole Earth between 60◦ and −60◦ longitude and for all latitudes iscovered with reflection events. Only 114 bins with no specular points arise, see table 4.1.

Table 4.1 compares the reflection coverage of GPS, GLONASS, Galileo, BeiDou andthe four combined after a simulation period of one day. The total number of specularpoints varies distinctly for each global system. The largest number occurs for GPSwith 125, 766 followed by Galileo with 107, 216. GLONASS and BeiDou have a smallernumber of specular points with 95, 784 and 98, 207, because of the smaller number ofsatellites considered for the simulation. The maximum number of specular points perbin is similar for all systems and lies between 15 and 17. The number of blank bins,with no reflection points, between 50◦N-50◦S is inversely proportional to the total num-ber of reflection points. Therefore for GPS, the lowest number of blank bins is 4, 706and for GLONASS, the highest number of 8, 060 occurs. The minimum and maximumlatitude is similar for GPS, GLONASS and BeiDou around −71◦ and 71◦. For Galileothe minimum and maximum latitude is slightly lower at −67◦ and 67◦.


Considering all global systems, the total number of reflections increases up to 426,962after the simulation period of one day. The maximum number per bin is 34 and thenumber of blank bins between 50◦N-50◦S decreases down to 114. The minimum andmaximum latitudes thus align to the minimum and maximum of the four global systems.

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Figure 4.10 GNSS coverage - simulation period one day: The figure depicts theglobal reflection coverage with a receiver onboard the ISS, receiving reflected sig-nals from 107 GNSS satellites: 32 GPS, 24 GLONASS, 27 Galileo and 24 BeiDousatellites. The reflection events are simulated over a period of one day with orbitdata from the 9th of March 2015. The colour indicates the number of countedspecular points per bin, with a bin size of 1◦x1◦.

Number ofSpecularPoints

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GPS 125,755 17 4,706 -70 70GLONASS 95,784 16 8,060 -71 72Galileo 107,216 15 5,136 -67 67BeiDou 98,207 17 7,448 -71 71GNSS 426,962 34 114 -71 72

Table 4.1: A comparison of the reflection coverage of GPS, GLONASS, Galileo andBeiDou and all combined after a simulation period of one day.


4.2.2 Simulation Period - One Week

For the simulation duration of one week, a period from the 9th March 2015 to the 15thof March 2015 was selected. First the reflection coverage of the GPS system is describedin detail. Subsequently the differences and similarities with the coverage plots of theGLONASS, Galileo and BeiDou systems are described. Following this, the coverage,considering all 107 GNSS satellites, is outlined.

Figure 4.11 shows the GPS reflection coverage of the Earth after one week. The max-imum value of specular points per bin is 45. The pole areas north and south of 50◦

and −50◦ latitude feature a dense band of approximately 10 specular points per binafter a simulation of one week. The band thins out from 55◦ and −55◦ latitude to-wards the poles with the result that no reflection events occur from 72◦N and 72◦Sonwards. Reflection point maxima occur along the maximum and minimum latitude ofthe ISS ground track for all longitudes: At about 50◦N and 50◦S. Between 50◦ and −50◦

latitude, reflection point maxima exists along the ISS ground track, which is clearly dis-tinguishable. The chequered pattern of the ISS ground track is more finely woven afterone week, due to slightly shifted and barley overlaid tracks. The maximum is distincttowards the poles and merges slowly into the line structure towards the equator. Binswith an intersection of two lines have a high value of reflection events. The reflectioncoverage is dense between these latitudes, no bins with no reflection events occur. Thewhite bins occurring in the plot have a low, non-zero number of specular points, butappear white because of the fixed scale. The average value of points per bin betweenthe line structure is approximately 20. The equator appears to be a mirror axis forthe reflection coverage distribution. The number of reflection events decrease towards−180◦ and 180◦ longitude. This decrease in reflection points can be explained witha boundary value problem, which occurs during the MATLAB simulation. The linearinterpolation of the ISS Longitudes between −180◦ and 180◦ leads to unusable values.These values are eliminated and accordingly gaps in the orbit occur for the interval−180◦ and 180◦. Therefore no reflection events, for when the ISS crosses the boundarybetween −180◦ and 180◦ latitude, are determined.

In figure 4.12 the global coverage of the GLONASS constellation after one week is de-picted and figure 4.13 shows the Galileo reflection coverage after one week. The BeiDoureflection coverage is depicted in figure 4.14. In all three plots the distinguishableground track structure of the ISS is similar to the one described in the GPS coverageplot. For GLONASS, bins with a very low number of reflection points, indicated inwhite, are accumulated between 10◦N/S and 30◦N/S. The bins are located betweenthe ground track structure. A clear increase in reflection points in the equator area isnoticeable. For GPS, Galileo and BeiDou, bins with a low number of reflection pointsare accumulated in the equator regions. The Galileo coverage has a wider accumulationband of reflections around 50◦N/S which fades slowly into the line structure towardsthe equator. Remarkably the coverage is dense between 52◦N/S-67◦N/S with a distinctborder, whereas for GPS, GLONASS and BeiDou, the reflection points thin out towardsthe poles.

Figure 4.15 shows the reflection coverage including the GPS, GLONASS, Galileo andBeiDou constellation. The maximum number of specular points per bin after one weekis 135. A distinct maximum at 52◦N and 52◦S is recognisable. North and south ofthe maximum, the number of reflection events decreases rapidly to approximately 30reflection points per bin at a latitude of 60◦N and 60◦S. From 60◦ to 70◦N and 70◦S the


reflection events decrease more and thin out with the result that no reflection eventsoccur from 72◦N and 72◦S onwards. The maximum at 52◦N and 52◦S fades and de-creases slowly into the line structure of the ISS ground track between 50◦ and −50◦

latitude. The number of reflection events lies between 50 and 100. At some line in-tersections high values of reflection point per bin occur. The global coverage between60◦N and 60◦S is dense and no blank bins exist. The equator acts as the mirror axis ofthe reflection coverage distribution. The number of specular points decreases towards180◦E and 180◦EW.

Table 4.2 compares the reflection coverage of GPS, GLONASS, Galileo, BeiDou andthe combination of the four. The total number of specular points varies dependingon the system. The largest number occurs for GPS with 886, 023 followed by Galileowith 754, 702. GLONASS and BeiDou have a smaller number of specular points with669, 237 and 688, 179, due to the smaller number of considered satellites. After oneweek the maximum number of specular points per bin is distinctly higher for GPS, at54, compared to the other three systems. The maximum number per bin for GLONASSis 39, followed by Galileo and BeiDou with 41 and 42 points. The number of blank binsbetween 50◦N-50◦S is zero for GPS and Galileo, one for BeiDou and two for GLONASS.The minimum and maximum latitude is around −71◦ and 71◦ for all systems. Consid-ering all 107 GNSS satellites, the total number of specular points is 2,998,141 and theminimum and maximum latitude is −72◦ and 72◦.

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Figure 4.11 GPS coverage - simulation period one week: The figure shows the globalreflection coverage with a receiver onboard the ISS, receiving reflections from 32GPS satellites. The reflection events are simulated over a period of one week withorbit data from the 9th until the 15th of March 2015. The colour indicates thenumber of counted reflection points per bin, with a bin size of 1◦x1◦.


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Figure 4.12 GLONASS coverage - simulation period one week: The figure showsthe reflection coverage with a receiver onboard the ISS, receiving reflected signalsfrom 24 GLONASS satellites. The reflection events are simulated over a period ofone week with orbit data from the 9th until the 15th of March 2015. The colourindicates the number of counted specular points per bin, where the bin size is 1◦x1◦.

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Figure 4.13 Galileo coverage - simulation period one week: The figure depicts theglobal reflection coverage with a receiver onboard the ISS, receiving reflections from27 Galileo satellites. For the orbit simulation of the Galileo satellites, synthetic orbitdata was used. The simulation was carried out over a period of one week with ISSorbit data from the 9th until the 15th of March 2015. The colour indicates thenumber of reflection points per bin, with a bin size of 1◦x1◦.


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Figure 4.14 BeiDou coverage - simulation period one week: The figure shows theglobal reflection coverage with a receiver onboard the ISS, receiving reflected signalsfrom 24 BeiDou MEO satellites. For the orbit simulation of the BeiDou satellites,synthetic orbit data was used. The reflection events are simulated over a periodof one week with ISS orbit data from the 9th until the 15th of March 2015. Thecolour indicates the number of reflection points per bin, with a bin size of 1◦x1◦.

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Figure 4.15 GNSS coverage - simulation period one week: The figure depicts theglobal reflection coverage with a receiver onboard the ISS, receiving reflected sig-nals from 107 GNSS satellites: 32 GPS, 24 GLONASS, 27 Galileo and 24 BeiDousatellites. The reflection events are simulated over a period of one week with orbitdata from the 9th until the 15th of March 2015. The colour indicates the numberof counted specular points per bin, with a bin size of 1◦x1◦.





50◦N-50◦S



GPS 886,023 54 0 -72 72GLONASS 669,237 39 2 -71 72Galileo 754,702 41 0 -70 71BeiDou 688,179 43 1 -72 72GNSS 2,998,141 135 0 -72 72

Table 4.2: A comparison of the reflection coverage of GPS, GLONASS, Galileo andBeiDou and all combined after a simulation period of one week.

4.2.3 Simulation Period - One Month

To obtain an idea of how the reflection point coverage develops after a longer periodof one month, the reflection events of the GPS constellation were simulated from the9th of March 2015 until the 8th of April 2015. The GPS constellation was selectedbecause the orbit propagation for broadcast ephemeris is faster than the propagationusing TLEs. A simulation including the 107 GNSS satellites is time-consuming, sincethe simulation of one day takes approximetley 4.5 hours. Orbit data for PRN 26 wasnot available on the 18th-19th, 23rd-24th, 26th-29th of March.

The GPS coverage for the period of one month is depicted in figure 4.16. The totalnumber of specular points is 3,886,564, see table 4.3. The maximum value of reflectionpoints per bin is 171. The distinct maximum at 52◦N and 52◦S decreases rapidly to-wards the poles. At 60◦N and 60◦S it reaches a value of approximately 40 and beginsto thin out and decrease further. North and south of 72◦ and −72◦ latitude no morereflection events occur. Towards the equator, the maximum decreases more slowly andfades into the ISS ground track line structure between 50◦ and −50◦ latitude. Thenumber of reflection points varies between 60 and 120 per bin. After one month the linestructure is well defined and high values of reflection points occur at line intersections.The plot is dense and no blank bins exist between 65◦N and 65◦S. The reflection coveris symmetrical with the equator as the mirror axis. The number of specular pointsdecreases towards 180◦E and 180◦W more distinctly compared to the weekly plots.




50◦N-50◦S



GPS 3,886,564 171 0 -72 72

Table 4.3: The reflection coverage of GPS after a simulation period of one month.


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Figure 4.16 GPS coverage - simulation period one month: The figure shows theglobal reflection coverage with a receiver onboard the ISS, receiving reflectionsfrom 32 GPS satellites. The reflection events are simulated over a period of onemonth with orbit data from the 9th of March until the 8th of April 2015. Thecolour indicates the number of counted reflection points per bin, with a bin size of1◦x1◦.

4.2.4 Analysis of Observation Coverage

Firstly the coverage simulation periods are analysed and differences are taken into ac-count. The coverage variations in longitude and latitude are observed and finally, thetemporal observation density and the mean revisit time are discussed.

4.2.4.1 Comparison of Simulation Periods

The daily plots give a good idea of how many reflection events occur per day. It showsthat considering only one GNSS constellation does not give a dense global coverage afterone day of observation. In contrast, combining all Global Navigation Satellite Systemsprovides a dense coverage for the area between the maximum and minimum latitude ofthe ISS’ ground track with only a small number of gaps.

After one week of simulation a more distinct structure in the global reflection coverage isidentifiable for each system. The weekly plots of the different Global Navigation Satel-lite Systems already provide a nearly gapless coverage between 50◦N-50◦S . The plot,which considers all systems, shows a complete coverage of the region between 50◦N-50◦Sand no gaps occur.

The month-long simulation illustrates that the coverage becomes more dense towardsthe poles, up to 72◦N and 72◦S. Also the decrease in reflection events towards 180◦Eand 180◦W is highlighted in the monthly plot. The line structure of the ground trackof the ISS is still recognisable.


4.2.4.2 Latitude and Longitude Distribution

To get a better idea of the different latitude and longitude distributions of the variousGNSS systems over a time frame of 7 days, the longitude and latitude is plotted independency on time.

Figure 4.17 shows the number of specular points in dependency on the latitude fora simulation period of one week. The most reflection events occur for the GPS system,due to the largest number of satellites considered in the simulation. All four plots aresymmetrical with the equator as the mirror axis. All systems have peaks at −52◦ and52◦ latitude. The maximum of the GPS latitude distribution is approx. 11,800 andthe maximum of the GLONASS latitude distribution is approximately 10,000 reflectionpoints. For Galileo, the maximum of the latitude distribution is approximately 9,000specular points and for BeiDou, approx. 10,500. Noticeably, the Galileo system featureslower peaks than the GLONASS and BeiDou systems despite a higher number of satel-lites in the Walker constellation. This concludes, that divergent distribution in latitudeis reducible to the orbit constellation with four satellites in one plane and at a higheraltitude than GPS, GLONASS and BeiDou. Remarkably, at a latitude of −60◦ and 60◦,the Galileo system has a local maximum of approx. 4000 reflection points, where asfor GLONASS and BeiDou, the number of reflection points exponentially decreases to-wards the poles. For the GPS system the decrease towards the poles is also less smooththan for BeiDou and GLONASS. It is noted that the higher inclined GLONASS orbits,for a better coverage of the poles, have no influence on the reflection coverage of thepole areas, due to bounded reflection coverage by the ISS orbital inclination. Anotherremarkable feature of the latitude distribution is the two small peaks between −50◦

and 50◦. For the GPS system, the two peaks occur at approximately −20◦ and 20◦

latitude and are flat. The GLONASS plot features a plateau from −10◦ to 10◦ latitudeframed by two heightened peaks. This correlates with the described gaps between 10◦

and 30◦N and 30◦S in figure 4.12. For the Galileo system, the two peaks appear at alatitude of approximately −20◦ and 20◦. The BeiDou plot also features two peaks atapproximately −20◦ and 20◦. Besides the two remarkable peaks, two saddle points atapproximately −35◦ and 35◦ also occur. Since the peaks between −30◦ and 30◦ latitudeare similar for GPS, Galileo and BeiDou, only for GLONASS a distinct shift towardsthe equator is noticeable, one can conclude a correlation with the orbital inclination.The higher inclination, of approximately 10◦ or more, compared to GPS, Galileo andBeiDou, results in reflections occurring closer to the equator.The latitude distribution after one week considering all Global Navigation Satellite Sys-tems is depicted in 4.18. The peaks at −52◦ and 52◦ latitude have a maximum ofapproximately 38,000 reflection points. Considering all Systems leads to an exponentialdecay towards the poles with a small decrease of the negative slope at a latitude of −60◦

and 60◦. Between −50◦ and 50◦, the distribution features four small peaks at −20◦/20◦

and −10◦/10◦.

The different longitude distributions of the various Global Navigation Satellite Sys-tems are shown in figure 4.19. All four plots are more or less continuous without a slopebetween −150◦ and 150◦ longitude. This means there is no significant variation in thenumber of specular points with change in longitude. Small slumps in the coverge alongthe longitude are noticeable for GPS and Galileo. The slumps correlate with gaps inthe ground track coverage depicted in A.1 and A.3. The number of reflection points forthe GPS coverage is the highest at approximately 2,500 and is followed by the Galileosystem at approximately 2,100.


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Figure 4.17 Reflection coverage of GPS, GLONASS, Galileo and BeiDou depending onlatitude: Each plot shows the number of reflection points per bin as a function of latitudefor each global system starting with GPS and GLONASS and followed by Galileo andBeiDou. The reflection points are simulated for a period of one week, starting on the9th of March 2015.

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Figure 4.18 Latitude distribution of GNSS reflection coverage: The figure showsthe distribution of the reflection points, considering 107 GNSS satellites for thesimulation, as a function of latitude. The reflection coverage is simulated for aperiod of one week starting on the 9th of March 2015.


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Figure 4.19 Longitude distribution of GPS, GLONASS, Galileo and BeiDou: Each plotshows the number of reflection points per bin as a function of longitude for each globalsystem starting with GPS and GLONASS and followed up by Galileo and BeiDou. Thereflection points are simulated for a period of one week, starting on the 9th of March2015.

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Figure 4.20 Longitude distribution of GNSS coverage: The figure depicts the distri-bution of the reflection points, considering 107 GNSS satellites for the simulation,as a function of latitude. The reflection coverage is simulated for a period of oneweek starting on the 9th of March 2015.


The GLONASS and BeiDou systems have both a number of approximately 1,800 re-flection points for all longitudes between −150◦ and 150◦. This variation is due to thenumber of satellites considered for the simulation. All numbers decrease towards the−180◦ and 180◦ from −150◦ and 150◦ onwards. As explained in 4.2.2, the reason behindis a boundary value problem, which occurs through linear interpolation of longitudesbetween −180◦ and 180◦ during the MATLAB simulation.

Figure 4.20 shows the longitude distribution considering all GNSS systems. The dis-tribution is similar to those of the different Global Navigation Satellite Systems witha number of reflection points of approximately 8,500. Towards −180◦ and 180◦ thenumber of points decreases due to the boundary value problem.

4.2.4.3 Temporal Distribution

To analyse the temporal distribution of the reflection events, first the occurring specularpoints were counted for each sampling every 12 seconds. Futhermore the revisit time ofeach bin is studied.

The temporal observation density, depicted in figure 4.21, shows that at each sampling,an average of 60 reflection events occur. The maximum reflection events per samplingis approximately 70 and the minimum approximately 55. According to the MissionRequirements of GEROS-ISS only 4 observation samples can be taken at one time[GEROS-SAG 2013]. Therefore including all Global Navigation Satellite Systems providesa good temporal observation density.

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Figure 4.21 Temporal observation density of GNSS reflection coverage: This figureshows the number of reflection observations over time with a sampling rate of 12seconds. It takes into account the specular points of all 107 GNSS satellites for aperiod of one day, the 9th of March 2015.

Figure 4.22 depicts the mean revisit time of the GNSS reflection coverage. For each binthe occurring specular points and their time of occurrance were studied. The mean timelag between the occurring events over a period of one week is indicated by colour. The


mean revisit time for the bins near the pole regions increases up to 150 hours and arenot representable with the chosen scale. Therefore all bins with a revisit time equal to10 hours are negligible for the evaluation of the outcomes. Between 52◦N/S and 60◦N/Sthe mean revisit time increases from 4 up to about 8 hours towards the poles. At theminimum and maximum latitude of the ISS, 51.6◦N/S, the mean revisit time is less thanone hour. The revisit time increases towards the equator. In the region between 30◦Nand 30◦S, an average revisit time of 3 hours occurs. The mean revisit time correlateswith the coverage density in 4.15. According to the Mission Requirements Documentof the GEROS-ISS mission, the temporal revisit is 4 days or less for SSH observations[GEROS-SAG 2013]. Therefore the required temporal revisit is fullfilled.

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Figure 4.22 Mean revisit time of GNSS reflection coverage: This figure shows themean revisit time over a period of one week per bin. The bin size is 1◦x1◦. Ittakes into account the specular points of all 107 GNSS satellites from the 9th untilthe 15th of March 2015. The mean revisit time for the bins near the pole regionsincreases up to 150 hours and are not representable with the chosen scale. Thereforeall bins with a revisit time equal to 10 hours are negligible for the evaluation of theoutcomes.

4.3. VISIBILITY MASK 47

4.3 Visibility Mask

The antenna of the GEROS-ISS project is going to be positioned on the EuropeanColumbus module of the ISS. Due to the mounting of the Atmosphere-Space Interac-tions Monitor (ASIM) beneath the GEROS-ISS antenna, depicted in figure 4.23, theField of View (FoV) of the antenna is narrowed. Thus constraints regarding the verticalfield of view will occur.

Figure 4.23 GEROS-ISS Field of View: The FoV is narrowed by the ASIM payload.A semi-cone around nadir is blocked by ASIM and also the port side view [Wickertet al. 2015b].

The Visibility Mask, depicted in figure 4.25 applies. The left plot of the figure shows theview geometry in direction cosines. On the right side the field of view is illustrated. Theactual field of view is indicated in black. The limitations in port view, in consequence ofthe ASIM, are indicated with a chequered pattern. The narrowing can be implementedthrough a azimuth constraint.


Figure 4.24 Reflection geometry: Theangle αR is the nadir angle at the re-ceiver

The limited black areas in the forwardlooking vertical field of view can be quer-ied by a nadir angle constraint. Thenadir angle is the respective angle betweenthe reflection point ray and the directionpointing directly below the ISS, see figure4.24.

This section approaches the nadir angle andazimuth angle constraints separately and il-lustrates their influences on the reflection cov-erage in 4.3.1 and 4.3.2. subsequently all con-straints are combined and the impact of thevisibility mask on the reflection coverage is de-scribed and analysed in detail in 4.3.3.

Figure 4.25 Visibility Mask GEROS-ISS : The figure illustrates the potential fieldof view. The left plot shows the view geometry in direction cosines. The directionη indicates the flight direction of the ISS. The plot on the right depicts the differentfield of views: The FoV-1 is the around-nadir altimetry and scatterometry indicatedwith black and denoted with 1A, 1B and 1C. The FoV-2 corresponds to the grazingaltimetry also indicated with black and denoted with 2A and 2B. The third fieldof view, FoV-3, indicated with grey, is used for radio-occultation and precipitation.The chequered area is the port side and completely blocked by the ASIM payload[Wickert et al. 2015b].


4.3.1 Nadir Angle Constraints

Firstly one can look at the reflection point distribution as a function of the nadir angleαR. Figure 4.26 and 4.27 show the nadir angle distribution.

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Figure 4.26 Nadir angle distribution -simulation period one day: The figureshows the number of specular pointsas a function of the nadir angle. Thereflection points of 107 GNSS satel-lites are counted over a period of oneday, the 9th of March 2015.

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Figure 4.27 Nadir angle distribution- simulation period one week: Thefigure shows the number of specu-lar points as a function of the nadirangle. The reflection points of 107GNSS satellites are counted over aperiod of one week. The simulationlasts from the 9th until the 15th ofMarch 2015.

Both distributions follow a similar exponential curve. The exponentially increasingcurve ends at a nadir angle of 70◦. For 71◦ the number of reflection points comes downto one third of the maximum value at 70◦. The Earth’s limb is at approximately 70◦

nadir angle for the mean altitude of the ISS and denotes the nadir angle limit for re-flection points. Since the altitude of the ISS varies, variations in the limb angles occurand the simulation results in specular points at a nadir angle up to 71◦. To obtain thetwo different FoVs for altimetry measurements, two constraints for the nadir angle αR

occur. Since figure 4.26 and 4.27 show that a very low number of reflections pointsoccur around nadir, one considers the whole nadir view instead of the around-nadirview. The nadir altimetry and scatterometry, corresponds to a nadir angle αR between0◦ and 41.4◦. The long (optimal) range of nadir angles for grazing altimetry, FoV-2,corresponds to a nadir angle αR of 54.2◦ to 68.6◦. The angle ranges are provided bythe GEROS-ISS working group of ESTEC.

This leads to the following constraints:

0◦ ≤ αR ≤ 41.4◦ (4.23)

54.2◦ ≤ αR < 68.6◦ (4.24)

With these constraints concentric annuli are studied. The specific areas indicated withblack in figure 4.25 are obtained with a combination of the azimuth constraint. Inchapter 4.3.1 the nadir annulus and the grazing annulus are first studied separately andlater combined. They are denoted with near-nadir FoV and grazing FoV.


4.3.1.1 Near-Nadir Field of View

Figure 4.29 illustrates the GNSS reflection coverage only considering the near-nadir fieldof view after one day of simulation. No reflection events occur north and south of 54◦

and −53◦ latitude, see table 4.4. Between 54◦ and −53◦ latitude, only reflection eventsalong the ISS ground track occur and therefore the plot features a distinct grid shape.The maximum number per bin is 19. Significant gaps exist between the ground tracklines. An average of 5 reflection points per bin arise for non blank bins. The numberof blank bins between 50◦N-50◦S is 14,839 after one day. Since reflection points with asmall nadir angle occur close to the nadir point, the points appear near the ISS groundtrack for the nadir FoV by default. Figure 4.28 depicts the ground track of the ISS,the ground track of the GPS satellite as well as the occurring reflection points in thenear-nadir field of view for a period of 1.5 hours. The figure illustrates how close to theISS ground track the reflection points occur and proves the resulting coverage structureof figure 4.29.

Figure 4.30 shows the GNSS reflection coverage taking only the near-nadir field ofview into account after a simulation period of one week. North and south of 54◦ and−54◦, no reflection points exist, see table 4.4. The minimum and maximum latitude isnearly unchanged after the week-long simulation, since the occurring reflection pointsare bound through the near-nadir constraint to an area close to the ISS ground track.The maximum number of reflection points, approximately 65, occur along 50◦N and50◦S. Between 20◦N and 20◦S an accumulation of gaps exist. The gaps decrease towardsthe poles, due to the decrease in the grid width of the ISS ground track. The bound-ary value problem at 180◦ and −180◦ longitude is clearly noticeable with the nadir FoV.

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Figure 4.28 Ground track plot of GPS PRN 3, the ISS and the resulting SpecularPoints in time dependency from 4:00 AM until 5:30 AM on 2015/03/09 in nadirFoV. The reflection occurs very close to the ground track of the ISS and follows itsstructure.


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Figure 4.29 GNSS reflection coverage with near-nadir field of view - simulationperiod one day: The figure shows the simulated reflection coverage taking intoaccount the reflected signals of 107 GNSS satellites. The nadir angle constraint(4.23) is applied and thins out the reflection coverage. The simulation period is oneday, the 9th of March 2015.

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Figure 4.30 GNSS reflection coverage with near-nadir field of view - simulationperiod one week: The figure depicts the nadir field of view of simulated reflectioncoverage, taking into account the reflected signals of 107 GNSS satellites. Thenadir angle constraint (4.23) is applied and thins out the reflection coverage. Thesimulation period is one week beginning on the 9th of March 2015


The weekly plot is more dense compared to the day plot and the nadir FoV, sincethe repeating ISS ground track is slightly shifted and covers a greater area. The totalnumber of specular points after one day is 87,201 and increases to 619,665 after oneweek, see table 4.4. The weekly plot provides a dense reflection coverage between 30◦-52◦ and −30◦-−52◦ latitude and a fragmentary coverage near the equator with 76 blankbins.




50◦N-50◦S



GNSSOne Day 87,201 19 14,839 -53 54

GNSSOne Week 619,665 65 76 -54 54

Table 4.4: The GNSS reflection coverage for the near-nadir field of view of the GEROS-ISS antenna.

4.3.1.2 Grazing Field of View

The GNSS reflection coverage for one day from the grazing field of view is depictedin figure 4.32. The reflection events occur between a latitude of 65◦ and −66◦ degreesand no reflection points exist in the pole regions, see table 4.5. There is no distinctmaximum noticeable at around 52◦N and 52◦S . A cluttered line structure is visible,but the ground track of the ISS is not distinguishable. Figure 4.31 shows the Groundtrack plot of GPS PRN 8, the ISS and the resulting specular points in time dependencyfrom 4:00 AM until 5:30 AM on 2015/03/09 in grazing FoV.

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Figure 4.31 Ground track plot of GPS PRN 8, the ISS and the resulting SpecularPoints in time dependency from 4:00 AM until 5:30 AM on 2015/03/09 in grazingFoV. The nadir angle of the reflection geometry at the ISS lies between 65◦ and68.6◦. The reflection occurs far from the ground track of the ISS and follows itsstructure.


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Figure 4.32 GNSS reflection coverage with grazing field of view - simulation periodone day: The figure shows the grazing field of view of the reflection coverage simu-lation considering the reflected signals of 107 GNSS satellites. The nadir constraint(4.24) applies and leads to a thinning of the coverage. The simulation period is oneday, the 9th of March 2015.

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Figure 4.33 GNSS reflection coverage with grazing field of view - simulation periodone week: The figure depicts the grazing field of view of the reflection coveragesimulation considering the reflected signals of 107 GNSS satellites. The nadir con-straint (4.24) applies and leads to a thinning of the coverage. The simulation periodis one week, beginning on the 9th of March 2015.


It depicts an example of a grazing event for a nadir angle between 65◦ and 68.6◦ andgives an idea of how far from the ISS ground track the grazing events occur. There-fore the ISS ground track is not clearly distinguishable after a simulation period ofone day. On average approximately 5 specular points are counted for non blank bins.The coverage appears to be more dense at the areas between 40◦-60◦ and −40◦-−60◦

latitude as well along the equator area between 10◦ and −10◦ latitude. The bins withthe a maximal number of reflection points, 22, exist along a latitude approximately40◦N and 40◦S and along the equator. The one day plot provides a fragmentary reflec-tion point coverage with a number of 2,201 blank bins between 50◦N-50◦S, see table 4.5.

The reflection coverage of one week with the grazing FoV is depicted in figure 4.33.The minimum and maximum latitude is consistent at −66◦ and 65◦, see table 4.5.Between 60◦ and −60◦ latitude the weekly plot provides a dense reflection coveragecompared to the daily plot. The total number of specular points is 173,214 after oneday and increases to 1,209,177 after one week and no blank bins exist. A line structureis now distinguishable. The bins with the maximal number of reflection points, 64, areaccumulated at 35◦-45◦ and −35◦-−45◦ latitude as well as along the equator with awidth of 30◦. The accumulation of reflection events at 35◦-45◦ and −35◦-−45◦ latit-ude can be explained with the accumulation point of the ISS ground track at around52◦N and 52◦S: If the ISS is at 52◦N and 52◦S, signals reflected from this region arereceived due to the narrowing of the FoV. The boundary value problem at −180◦ and180◦ longitude is noticeable for the grazing reflection events.




50◦N-50◦S



GNSSOne Day 173,214 22 2,201 -66 65

GNSSOne Week 1,209,177 64 0 -66 65

Table 4.5: The GNSS reflection coverage of the grazing field of view of the GEROS-ISSantenna.

4.3.1.3 Near-Nadir and Grazing Field of View

The GNSS reflection coverage with a combination of the near-nadir and grazing FoVafter one day is shown in figure 4.34. The combination leads to a fragmentary coveragebetween 50◦N and 50◦S with a maximal number of reflection points along the groundtrack. A number of 787 blank bins occur between 50◦N-50◦S, see table 4.6. The min-imum and maximum latitude is at −66◦ and 66◦. The maximum number of reflectionpoints increases up to 26 per bin. The ground track is clearly distinguishable throughthe reflection points from the nadir FoV.

The weekly plot of the near-nadir and grazing FoV, depicted in figure 4.35, provides agapless coverage between 60◦N and 60◦S. The minimum and maximum latitude at −66◦

and 66◦ is unvaried after one week. Between 52◦-60◦ and −52◦-−60◦ latitude, an aver-age of 20 reflection points occur per bin. A distinct maximum, with up to 106 countedreflection points per bin, exists along 52◦/−52◦ latitude and fades slowly towards theequator.


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Figure 4.34 GNSS reflection coverage with near-nadir and grazing field of view -simulation period one day: The figure shows the reflection coverage considering107 GNSS satellites and applying both nadir constraints (4.23) and (4.24). Thesimulation period took place on the 9th of March 2015.

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Figure 4.35 GNSS reflection coverage with near-nadir and grazing field of view -simulation period one week: The figure shows the reflection coverage considering107 GNSS satellites and applying both nadir constraints (4.23) and (4.24). Thesimulation period is one week, starting on the 9th until the 15th of March 2015.


Another accumulation of reflection points exists along the equator. Between 40◦N and40◦S an average of 40 specular reflection points exist per bin. At −180◦ and 180◦ latit-ude, less reflection points exist because of the boundary value problem. Even with thenarrowing of the field of view through the nadir constraints, a gapless reflection coveragebetween 50◦N-50◦S is provided after one week compared to the daily plot. The totalnumber of specular points after one day is 267,355 and rises up to 1,877,427 within oneweek, see table 4.6.




50◦N-50◦S



GNSSOne Day 267,355 26 787 -66 66

GNSSOne Week 1,877,427 106 0 -66 66

Table 4.6: The GNSS reflection coverage combining the near-nadir and grazing field ofview of the GEROS-ISS antenna.

4.3.2 Azimuth Constraint

For the azimuth one assumes that the direction η, see figure 4.25, is equivalent to theflight direction of the ISS. To simplify the constraint, the azimuth of the velocity vectorof the ISS is assumed to be equal to the heading angle of the ISS. Also no rotationsof the ISS in pitch or roll are considered, since the elevation angle of the velocityis comparatively small. The heading vector is equated with the azimuth of the ISS.Therefore only the azimuth angle of the velocity vector of the ISS AzimuthVISS

andthe azimuth vector of the reflection geometry AzimuthReceiver at the receiver need tobe compared. This results in the constraint:

AzimuthReceiver ∈ [AzimuthVISS, AzimuthVISS

+ 180◦] (4.25)

The following figures 4.36 and 4.37 show the GNSS reflection coverage for one day andone week including the azimuth constraint.

After a simulation period of one day with the azimuth constraint, a distinct thinning ofthe reflection coverage is recognisable with an overall reflection point number of 214,716,see table 4.7. From 51.6◦ N no reflection points occur. A distinct accumulation of spec-ular points exists along −50◦ latitude. In contrast, a maximum of reflection points along52◦ N is not distinguishable. Between −52◦ and 60◦ latitude an average of 5 specularpoints per bin are counted. From 60◦ S towards the poles, the reflection points thin outand south of 70◦ latitude no reflection points exist. Through the azimuth constraintthe antenna is only pointing towards the right side of the flight direction. Therefore,the antenna is always looking in a south direction at a latitude of 52◦ and can notreceive reflected signals from GNSS satellites over the North Pole. Between 50◦ and−50◦ latitude the ISS ground track is clearly distinguishable through a high numberof reflection points occurring along the track. Conditioned by the constraint, the thin-ning of the observation coverage in this area leads to a number of 2,753 blank bins inthe coverage along the line structure. The number of gaps between the line structureincreased significantly compared to figure 4.10.


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Figure 4.36 GNSS reflection coverage with azimuth constraint - simulation periodone day: The figure shows the reflection coverage considering 107 GNSS satellitesand applying the azimuth constraint (4.25). Note that only on the starboard sideof the field of view can reflected signals be received. The simulation period is oneday, the 9th of March 2015.

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Figure 4.37 GNSS reflection coverage with azimuth constraint - simulation periodone week: The figure depicts the reflection coverage considering 107 GNSS satellitesand applying the azimuth constraint (4.25). Only on the starboard side of the fieldof view, reflected signals can be received. The simulation period is one week, the9th until the 15th of March 2015.


The Azimuth constraint has a noticeable impact on the observation coverage and leadsto a fragmentary reflection coverage after one day. The most conspicuous change dueto the side-facing antenna is the non existing reflection points north of 52◦ latitude andthe accumulation at −52◦ with a better coverage towards the South Pole.

The coverage after one week, depicted in figure 4.37, shows are a dense coverage com-pared to figure 4.36. As listed in table 4.7 the total number of Specular points increasesfrom 214,716 after one day up to 1,500,257 after one week. The areas between 52◦Nand 65◦S are completely covered with specular points. North of 52◦ no reflection eventsoccur. Between 30◦ and 50◦ latitude, a cluster with an average of 50 reflection eventsoccurs. From 30◦N to 52◦S, approximately 50 specular points per bin arise along theground track of the ISS. Along −52◦ latitude, a maximum of approximately 116 reflec-tions per bin exists. Between −52◦ and −65◦ the number of reflection points decreasesrapidly down to 20. South of −65◦ latitude the reflection events begin to thin outtowards the South Pole. The Azimuth constraint reduces the overall number of reflec-tion points, and provides a non-symmetric reflection coverage concentration at −52◦

latitude.




50◦N-50◦S



GNSSOne Day 214,716 26 2,753 -71 52

GNSSOne Week 1,500,257 116 0 -72 52

Table 4.7: The GNSS reflection coverage applying the azimuth angle constraint.

4.3.3 Azimuth and Nadir Angle Constraint

In figure 4.38 the azimuth and nadir constraints are combined and provide the actualpossible coverage with the narrowed FoV through the architecture of the ISS. North of52◦ no reflection events occur due to the azimuth constraint. Between −52◦ and −60◦,7,220 blank bins occur and an average of 5 reflection points per non blank bin exists.South of −66◦ latitude no reflection events occur towards the pole. The maximumnumber of reflection points, 21, exists along 52◦S and along the ISS ground track. Asmaller accumulation of specular points exists along 50◦N and 40◦N. Between 40◦N and40◦S a line structure with a thickening along the ground track of the ISS is noticeable.An average of 5 reflection points are counted per non blank bin. The GNSS reflectioncoverage with the full visibility mask does not provide a dense reflection coverage afterone day with no coverage north of 52◦ latitude. The total number of specular points is135,081, see table 4.8.

The reflection coverage after one week is depicted in figure 4.39. North of 52◦ latit-ude and south of approximately −66◦ latitude, no reflection events occur. Between−52◦-−60◦ the average number of reflection points is 20. Furthermore the reflectioncoverage is continuous. The blank gaps between 40◦ and −40◦ latitude have a valueclose to zero and appear white due to the fixed colour scale.


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Figure 4.38 GNSS reflection coverage applying visibility mask - simulation periodone week: The figure shows the reflection coverage, taking into account the reflectedsignals of 107 GNSS satellites. Nadir and Azimuth constraints are applied anddepict the impact of the visibility mask. The simulation period is one week startingon the 9th of March 2015.

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Figure 4.39 GNSS reflection coverage applying visibility mask - simulation periodone week: The figure depicts the reflection coverage, taking into account the re-flected signals of 107 GNSS satellites. Nadir and Azimuth constraints are appliedand illustrate the impact of the visibility mask. The simulation period is one week,beginning on the 9th of March 2015.


A distinct accumulation of reflection points exists along −52◦ latitude with up to 88reflection points per bin and a smaller, but still distinguishable, accumulation between40◦ and 50◦ with approximately 50 reflection points per bin. Between 40◦N and 40◦Sthe ISS ground track structure is noticeable. Compared to the daily plot, the weeklycoverage plot provides a dense coverage between 50◦N and 50◦S with a distinct maximaat −52◦ latitude. The total number of reflection points is 940,559.






GNSSOne Day 135,081 21 7,220 -66 52

GNSSOne Week 940,559 88 0 -66 52

Table 4.8: The GNSS reflection coverage applying the visibility mask.

The number of reflection points as a function of longitude and latitude is depicted infigure 4.40 and 4.41. The azimuth constraint has a significant impact on the latitudedistribution. In comparison to 4.18, its distribution is no longer mirrored along theequator. The maximum at −52◦ decreased from approximately 38,000 down to 23,000reflection points. A distinct accumulation appears at the equator through the grazingFoV, which does not exist without a non narrowed field of view. The maximum at −52◦

decreases by around 28,000 specular points. The structure of longitude distribution issimilar to the distribution considering no constraints. The number of specular pointsdecrease from 8,000 down to approximately 2,500 compared to figure 4.20.

The temporal observation density of the reflection events is also effected by the vis-ibility mask. The number of observations as a function of time is depicted in figure4.42. The average number of reflection points per sampling rate is 19, considering thereflected signals of 107 GNSS satellites. Compared to figure 4.21, the average num-ber of specular points per sampling rate decreased significantly from 60 down to 19.Nevertheless a minimum observation per sampling, highlighted in the GEROS missionrequirements, is still fulfilled.

The mean revisit time of the GNSS reflection coverage is depicted in figure 4.43. Foreach bin, the occurring specular points and their time of occurrance were studied. Themean time lag between the occurring events is indicated by colour. The mean revisittime for the bins near the South Pole region increases up to 150 hours and are notrepresentable with the chosen scale. Therefore all bins with a revisit time equal to 30hours are negligible for the evaluation of the outcomes. At 52◦N a band with a meanrevisit time varying between 5 and 18 hours occurs. Between 50◦N and 40◦N an averageof 5 hours of mean revisit time exists. In the region between 40◦N and 40◦S a strongvariation in the mean revisit time per bin is noticeable. It ranges from 5 to 30 hourswith a lower average mean revisit time in the equator region. Along 52◦S the revisittime is the lowest at around 1 hour. South of 52◦S the mean revisit time increasesrapidly. The mean revisit time correlates with the coverage density in 4.39. Accordingto the Mission Requirements Document of the GEROS mission, the acceptable revisittime is 4 days or less for SSH observations [GEROS-SAG 2013]. After the application ofthe visibility mask the required temporal revisit is still fullfilled for the region between


52◦N and 52◦S.

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Figure 4.40 GNSS latitude distribu-tion applying visibility mask - simu-altion period one week: The figureshows the distribution of the reflec-tion points, considering 107 GNSSsatellites for the simulation, as a func-tion of latitude. The plot takes intoaccount the nadir and azimuth con-straints as a consequence of narrowedfield of view due to the physique ofthe ISS. The reflection coverage issimulated for a period of one weekstarting on the 9th of March 2015.

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Figure 4.41 GNSS longitude distribu-tion applying visibility mask - simu-altion period one week: The figuredepicts the distribution of the spec-ular points as a function of longitude.The reflected signals of 107 GNSSsatellites are taken into account. Thenadir and azimuth constraints are ap-plied. The reflection coverage is simu-lated for a period of one week startingon the 9th of March 2015

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Figure 4.42 Temporal observation density of GNSS reflection coverage applyingvisibility mask: This figure shows the number of reflection points over time withsampling rate of 12 seconds whilst applying the visibility mask. It takes into accountthe specular points of all 107 GNSS satellites for a period of one day, the 9th ofMarch 2015.


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Figure 4.43 Mean revisit time of GNSS reflection coverage applying visibility mask:This figure shows the mean revisit time over a period of one week per bin. The binsize is 1◦x1◦. It takes into account the specular points of all 107 GNSS satellitesfrom the 9th until the 15th of March 2015. The mean revisit time for the bins nearthe pole regions increases up to 150 hours and is not representable with the chosenscale. Therefore all bins with a revisit time equal to 30 hours are negligible for theevaluation of the outcomes.

4.4. CASE STUDY SOUTHERN AFRICA 63

4.4 Case Study Southern Africa

Since GEROS-ISS capability for observing highly energetic mesoscale ocean currentshas been investigated [Wickert et al. 2014a] and following the case study for the South-ern African current system in Saynisch et al. 2015, the reflection coverage of the oceanssurrounding Southern Africa is studied. The oceans surrounding South Africa are dom-inated by the Agulhas current and the Agulhas Retroreflection. At the retroreflection,the Agulhas reverses its zonal direction and flows as the Agulhas Return current east-wards parallel to the Antarctic circumpolar current. The implications of the Agulhascurrent system range from ecological to meteorological and impact the southern regionof the African continent. Furthermore, large eddies are dispersed that leak heat and saltfrom the Indian Ocean into the Atlantic. Since the Agulhas current is a highly non-linearsystem, a rigorous combination of observations and models is necessary. This so calleddata assimilation is approached in Saynisch et al. 2015 by combining ocean models withprospective space-borne GNSS-R based SSH observations. To examine if the GEROS-ISS mission contributes reflectometry observations with a dense coverage of the oceanssurrounding South Africa, the reflection coverage of this region is subsequently analysed.

The figures 4.44 and 4.45 show the coverage of the oceanic region surrounding SouthernAfrica after a simulation period of one week.Figure 4.44 depicts the coverage without any limitations in field of view. Since theselected area is located near the ISS ground track accumulation point at −52◦ latitude,the area features a high number of specular points. The overall number of reflectionpoints is 107,608 for the whole region. An average of 71 specular points per bin occurwithin the region, including reflection over land. No blank bins exist. The ocean regionbetween Mozambique and Madagascar has a lower number of reflection points with anaverage of around 60. The maximum number per bin is 123, see table 4.9.Figure 4.45 shows the reflection coverage considering the visibility mask. The num-ber of reflection points decreases significantly down to 52,848. The average number ofreflection points counted per bin is 54 for the whole region. For the current regionsbetween the east coast of Mozambique and Madagascar the number of reflection pointsdecreases down to 5 per bin. With limitations in the field of view, GEROS-ISS providesa dense reflection coverage and no blank bins exist.The Agulhas region is located close to the maximum of reflections events at 51.6◦ andtherefore the GEROS-ISS simulations provide a dense reflection coverage with up to123 reflection points without any restrictions on the FoV. Applying the visibility maskdecreaes the overall number of reflection points, but provides a dense coverage of theregion after one week. On can conclude that even with a narrowed FoV through the vis-ibility mask, observations of the GEROS-ISS mission enhance studies on the SouthernAfrican current system and can be used for data assimilations.


Maximumnumber per

bin

Meannumber per

bin

Number ofblank bins

GNSSwithout visibility mask 107,608 123 71 0

GNSSwith visibility mask 52,848 54 22 0

Table 4.9: The GNSS reflection coverage of the South Africa region between 10◦S-50◦Sand 10◦W-50◦E with and without applying the visibility mask.


Longitude [deg]

La

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[d

eg

]GNSS Reflection Coverage − 2015/03/09−2015/03/15

−10 0 10 20 30 40 50−50

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Figure 4.44 Reflection coverage Southern Africa - simulation period one week: Thefigure shows the reflection coverage of the oceans surrounding Southern Africa fora simulation period of one week beginning on the 9th of March 2015. For thesimulation the reflected signals of 107 GNSS satellites are considered.

Longitude [deg]

La

titu

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[d

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]


−10 0 10 20 30 40 50−50

−40

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−20

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Figure 4.45 Reflection coverage Southern Africa applying the visibility mask - sim-ulation period one week: The figure shows the reflection coverage of the oceanssurrounding Southern Africa for a simulation period of one week beginning on the9th of March 2015. For the simulation the reflected signals of 107 GNSS satellitesare considered. The visibility mask, explained in chapter 4.3, is applied.

Chapter 5

Conclusions and Outlook

The different Global Navigation Satellite Systems GPS, GLONASS, Galileo and BeiDouprovide similar reflection coverage structures with some variation in latitude distributionand density. The variation in latitude exists because of the diverse satellite constella-tions. The number of satellites within the constellation considered in the simulations hasan obvious impact on the reflection density. For 32 GPS satellites, an overall number of125,755 specular points were counted after a simulation period of one day. Galileo, in-cluding 27 satellites, provides 107,216 reflection points. Whilst GLONASS and BeiDou,with 24 satellites each, result in 95,784 and 98,297 reflection events respectively.The coverage structure is aligned to the ground track structure of the ISS. The reflectioncoverage is bound to tropical and mid-latitudes by the ISS orbital inclination of 51.6◦.It is shown in chapter 4.2 that a relatively dense coverage of the tropical and mid-latitudes between 50◦N-50◦S with only 114 blank bins, is already provided after oneday, taking into account all 107 GNSS satellites. The defined bin size is 1◦x1◦. Themaximum number of reflection points per bin is 34. The observation density is approx-imately 60 observations per sampling.After a simulation period of one week the various individual Ground Navigation Satel-lite Systems provide dense coverage between 50◦N and 50◦S, with less than three blankbins. A gapless coverage between −60◦ and 60◦ latitude is obtained when all 107 GNSSsatellites are included within the simulation. The overall number of reflection pointsincreased up to 2,998,141 from 426,962 after one day. The maximum number of re-flection points per bin is 135. Remarkably, some areas, e.g. at −52◦ and 52◦ latitudeare better covered than other regions due to the accumulation points of the ISS groundtrack along these circles. Therefore the coverage shows a strong equator-symmetric vari-ation in latitude and a fairly consistent coverage in longitude dependency. For futuresimulations the boundary value problem at the −180◦/180◦ border will be bypassed byinterpolation of Cartesian coordinates. The slight differences in the coverage structuresof GPS, GLONASS, Galileo and BeiDou are clearly distinguishable after the simula-tion period of one week. The mean temporal revisit time ranges between one and 10hours depending on the latitude. The lowest mean revisit time occurs for the bins along50◦N/S and increases towards the equator.The month-long simulation of the GPS coverage shows consistency in the coverage struc-ture and an increase in the overall number of specular points, 3,886,564.

The visibility mask has a clear impact on the reflection coverage as shown in chapter4.3. The geometrical conditions at the ISS narrow down the possible reflectometry ob-servations in comparison to no limitations in the field of view, depicted in chapter 4.2.The overall number of reflection points of the week-long simulation decreases down to

65

66 CHAPTER 5. CONCLUSIONS AND OUTLOOK

940,559, which presents a loss of around 70%. A dense coverage between 50◦N and 50◦Sis still provided after one week. Since the portside view of the antenna is covered andonly reflected signals on the starboardside can be received, the non-symmetric latitudedistribution is more dense towards the minimum latitude of the ISS, at −51.6◦. Thecoverage towards the North Pole region is cut off at 52◦N.The observation density is approximetly 10 per sampling and with a mean revisit time,varying from one to 30 hours for a latitude between 52◦N and −60◦S, still satisfies theGEROS-ISS mission requirements.

Future simulation studies on reflection coverage should focus on long-term coverageof GPS GLONASS, Galileo, BeiDou and the combination of the four Ground Naviga-tion Satellite Systems. The outcome with a definition of a smaller grid size, would beof interest.

The simulation presented in this thesis considers a distinctly higher number of trans-mitting satellites than previous GNSS-R simulation studies. Stosius et al. 2010 showedthat tsunami detection using GNSS-R leads to better performance if various GlobalNavigation Satellite Systems are considered. A combination of 24 GPS, 24 GLONASSand 27 Galileo satellites was chosen for the tsunami detection simulation. The cover-age studies in Wagner et al. 2003 consider reflected signals of 24 GPS satellites anda receiver positioned on TOPEX/Poseidon. It was extended in Kostelecký et al. 2005with receivers located at the CHAllenging Minisatellite Payload (CHAMP) and the Sci-entific Application Satellite-C (SAC-C) as well. In Wagner et al. 2003 and Kosteleckýet al. 2005 a simulation period of 10 days and 180 days was chosen, respectively. Bothstudies defined a sampling rate of 50 seconds, a grid size of 1◦x1◦ and a horizon cutoffat 20◦. Jin et al. 2014 considered the constellation status in March 2012 with 32 GPSand 24 GLONASS transmitters with an assumed LEO receiver at 800 km altitude. Thelocations of the reflection points were simulated for one day with a sampling rate of10 seconds. Ulitmatley the coverage simulation study in this thesis is more extensivebecause it is the first time that coverages of GPS, GLONASS, Galileo and BeiDou werecompared and analysed individually and in combination.

This study has successfully analysed the coverage distribution with and without ap-plying a visibility mask. In conclusion, the coverage data obtained in this thesis is mostbeneficial in deciding on potential locations for future GEROS-ISS GNSS-R observa-tions, such as sea surface height and the ocean mean square slope, which are importantclimate change variables.

Appendix A

GNSS Ground Track Plots

The following figures depict the ground track coverage of GPS, GLONASS, Galileo andBeiDou. The satellite’s orbits are projected onto the surface of the Earth. The pro-jected satellite positions are counted in every bin. The bin size is 1◦x1◦. The colourindicates the number of projected points per bin. The ground track coverage is plottedover a period of one week, beginning on the 9th of March 2015.

The GPS ground track coverage is depicted in figure A.1. Broadcast ephemeris datawas used for the orbit propagation, taking 32 satellites into account.For the ground track coverage of GLONASS, depicted in figure A.2, TLE orbit data wasused, considering 24 satellites . The ground track coverage plots of Galileo,figure A.3,and BeiDou,A.4 , were generated by using synthetic TLEs. The Galileo constellationtakes 27 satellites into account and BeiDou considers 24.

−180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180−90

−60

−30

0

30

60

90

Longitude [deg]

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GPS Ground Track Coverage − 2015/03/09−2015/03/15

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Figure A.1 GPS ground track coverage: The figure shows the ground track coverageafter one week of simulation.

67

68 APPENDIX A. GNSS GROUND TRACK PLOTS

−180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180−90

−60

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Figure A.2 GLONASS ground track coverage: The figure shows the ground trackcoverage after one week of simulation.

−180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180−90

−60

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Figure A.3 Galileo ground track coverage: The figure shows the ground track cov-erage after one week of simulation.

69

−180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180−90

−60

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Figure A.4 BeiDou ground track coverage: The figure shows the ground trackcoverage after one week of simulation.

List of Abbreviations

BPSK Binary Phase Shift Keying

BRC Broadcast Ephemeris

CDMA Code Division Multiple Access

CHAMP CHAllenging Minisatellite Payload

CNES Centre National d’Etudes Spatiales

CYGNSS CYclone Global Navigation Satellite System

DDM Delay Doppler Map

DNSS Defence Navigation System

DOD Department of Defence

DOT Department of Transportation

EOP Earth Observation Programme

ESTEC European Space Research and Technology Centre

EU European Union

FDMA Frequency Division Multiple Access

FOC Full Operational Capability

FoV Field of View

GARCA GNSS-Reflectometry Assessment of Requirements and Consolidation of Re-trieval Algorithms

GEO Geostationary Orbit

GLONASS Globalnaja NAwigazionnaja Sputnikowaja Sistema

GNSS-R GNSS Reflectometry

GPS Global Positioning System

GSS Galileo Sensor Station

HALO High Altitude Long Range Research Aircraft

HSO Human Space Flight and Operations

71


IGS International GNSS Service

IGSO Inclined Geosynchronous Orbit

IOC Initial Operational Capability

IOV In-Orbit Validation

ISS International Space Station

KNITs Coordination Scientific Information Center of the Ministry of Defense ofthe Russian Federation

LEO Low Earth Orbit

MEO Medium Earth Orbit

MEOLUT Medium-Earth Orbit Local User Terminal

MSS Mean Square Slope

NASA National Aeronautics and Space Administration

NOAA National Oceanic and Atmospheric Administration

OS Open Service

OSSE Observation System Simulation Experiment

POD Precise Orbit Determintation

PRN Pseudo Random Noise

PRS Public Regulated Service

QZSS Quasi-Zenith Satellite System

RA Radar Altimeter

SAC-C Application Satellite-C

SAG Science Advisory Group

SGR-ReSi Space GNSS Receiver - Remote Sensing Instrument

SOL Safety-Of-Life

SSH Sea Surface Height

SSP Sea State Payload

SSTL Surrey Satellite Technology Ltd

SWOT Surface Water Ocean Topography

TC Tropical Cyclone

TEC Total Electron Content

TLE Two Line Element

73

TT&C Telemetry, Tracking and Command Station

ULS Uplink Station

USSR Union of Soviet Socialist Republics

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