Orbit Determination Analysis for SSAPurposes

DEGREE PROJECT, IN AEROSPACE ENGINEERING , SECOND LEVEL STOCKHOLM, SWEDEN 2015

Orbit Determination Analysis for SSA Purposes

MATTEO CRIMELLA

www.kth.se

Kungliga Tekniska H¨ ogskolan Totalf¨ orsvarets Forskningsinstitut

Master’s Thesis Project

Orbit Determination Analysis for SSA Purposes

Author:

Matteo Crimella

Supervisors:

Dr. Nickolay Ivchenko

Dr. Lisa Rosenqvist

Matteo Crimella - Orbit Determination Analysis for SSA Purposes

Abstract

Space Situational Awareness (SSA) is the characterization of the space environment and of space activities. The fundament of SSA is the access to information about the orbit of space objects. There exist several techniques to determine the orbit of objects in space, both from space-based and from ground-based observations. This Master’s Thesis project aims at investigating orbit determinations from ground-based radar observations.

In particular, the use of the EISCAT Ultra-High-Frequency (UHF) incoherent scatter

radar for orbit determination purposes is investigated. The radar data necessary for

this work were acquired during the “EISCAT Prisma Odin Experiments” (EPO-1 and

2) in July 2014 and March 2015. During the experiments, the Swedish satellites Odin

and Mango were tracked with the EISCAT system and their known GPS data were

used to validate the radar accuracy. The results of the analysis show that the EISCAT

UHF radar is affected by systematic errors in the range calculation: a constant offset

and an error that increases when the target moves west from the radar. There is no

evidence of systematic errors in the range rate calculation. However, the analysis shows

that between two different calculation methods, one seems to be more accurate. The

second part of this project analyzes the initial orbit determination problem (OD) based

on synthetic EISCAT data. The tool for this part of the thesis is the software Systems

Tool Kit (STK). STK is used to simulate the observation of a satellite with EISCAT

and to propagate the orbit of the radar target from an initial state. The initial state

(r,v) is derived via Lambert’s initial orbit determination method based on the synthetic

EISCAT observation of the satellite. The computed initial state from Lambert’s method

differs by several kilometers from the true initial state. This is a consequence of the fact

that the method relies on the analytical solution of the Two-Body problem and can not

be expected to be more precise. Furthermore, the sensitivity of the Lambert’s solver

to perturbations of the initial radar observations is investigated. Based on expected

errors of the EISCAT radar observations, it is shown that the in-track range difference

quickly approaches several thousands of kilometers and several hundreds of kilometers

in cross-track range difference between the estimated orbit and the true orbit. Thus,

the EISCAT UHF radar is not suitable for precise orbit determination but can only be

used for initial orbit determination purposes of a previously known object to provide

crude estimates of its initial state. Multiple target position and velocity measurements

are needed to improve the initial orbit determination.

Matteo Crimella - Orbit Determination Analysis for SSA Purposes

Acknowledgement

Foremost, I would like to express my sincere gratitude to my supervisors, Dr. Lisa Rosen- qvist and Dr. Nickolay Ivchenko for the continuous support during the development of my Master’s Thesis, for their patience, motivation, enthusiasm, and knowledge. Their guidance helped me in all the time of research and writing of this thesis.

I gratefully acknowledge the EISCAT and IRF staff, in particular Dr. Johan Kero and Dr. Jussi Markkanen, for their assistance during the experiments. EISCAT is an in- ternational association supported by research organisations in Norway (NFR), Sweden (VR), Finland (SA), Japan (NIPR and STEL), China (CRIPR) and the United King- dom (NERC).

My sincere thanks also goes to my family and my girlfriend Lorenza. To my parents,

Cristina and Roberto, because they supported me throughout my life and made possible

my studies, in Italy and in Sweden. To Lorenza, my life partner, that brings joy to my

life and, during my thesis work, let me use her computer when mine got broken. To my

brother Francesco, because life in Sweden was easier knowing that he was home taking

care of my family. To my grandparents Lidia and Roberto, because they always hoped

that one of their grandchildren would have been an engineer.

Matteo Crimella - Orbit Determination Analysis for SSA Purposes

Contents

Abstract v

Acknowledgement vii

List of Figures xi

List of Tables xiii

Acronyms xv

1. Introduction 1

1.1. Space Situational Awareness - SSA . . . . 1

1.2. SSA - The International Context . . . . 4

1.3. Objectives Of The Study . . . . 6

2. Experiments 9 2.1. The EISCAT UHF Radar . . . . 9

2.2. Odin Satellite . . . . 11

2.3. Mango Satellite . . . . 12

2.4. EPO-1 2014-07-23 . . . . 13

2.5. EPO-2 2015-03-20-21 . . . . 15

3. EPO Data Analysis 17 3.1. Systems Tool Kit . . . . 17

3.2. Methods For Range And Range Rate Calculation From EISCAT Data . . 18

3.3. EPO-1 . . . . 20

3.4. EPO-2 . . . . 26

3.5. Results Summary . . . . 30

4. Initial Orbit Determination 33 4.1. Lambert’s Method . . . . 34

4.2. High-Precision Orbit Propagator . . . . 36

4.3. Initial Orbit Determination . . . . 37

5. Sensitivity Analysis 41 5.1. Perturbed Initial State . . . . 41

5.2. Propagation Of Perturbed States And Error Analysis . . . . 42

Contents

6. Conclusions 47

6.1. EPO Analysis . . . . 47

6.2. Initial Orbit Determination . . . . 47

6.3. Sensitivity Analysis . . . . 48

6.4. Final Considerations . . . . 48

Bibliography 49

A. EPO Experiments Results 51

B. MATLAB Function “rv from observe.m” 57

C. Range Comparison Algorithm 61

D. MATLAB Script “OD HPOP.m” 63

E. STK Support: External Ephemeris. 69

F. STK Support: HPOP. 73

x

Matteo Crimella - Orbit Determination Analysis for SSA Purposes

List of Figures

1.1. SSA Context . . . . 2

1.2. US Space Surveillance Network . . . . 3

1.3. American, European and International SSA sensors . . . . 4

2.1. The EISCAT UHF Radar . . . . 10

2.2. Odin Satellite . . . . 11

2.3. Mango Satellite . . . . 12

2.4. EISCAT Facilities . . . . 13

2.5. EPO-2 Scan . . . . 16

3.1. STK Scenario . . . . 18

3.2. Doppler shift and SNR . . . . 20

3.3. Range . . . . 22

3.4. Range Comparison . . . . 23

3.5. Range Rate Calculation . . . . 25

3.6. Range Rate Comparison . . . . 26

3.7. Range Comparison . . . . 27

3.8. Range Rate Comparison . . . . 28

3.9. Range Comparison . . . . 29

3.10. Range Rate Comparison . . . . 29

3.11. Range Comparison Summary . . . . 30

3.12. Range Rate Comparison Summary . . . . 30

4.1. Tristatic EISCAT . . . . 34

4.2. State Vectors . . . . 35

4.3. Initial Position Difference . . . . 38

4.4. STK Range Difference . . . . 38

4.5. Input Parameters . . . . 39

5.1. STK Initial Perturbed Scenario . . . . 43

5.2. STK Perturbed Scenario . . . . 43

5.3. STK Range Comparison . . . . 44

5.4. In-Track Range Comparison . . . . 44

5.5. Cross-Track Range Comparison . . . . 45

Matteo Crimella - Orbit Determination Analysis for SSA Purposes

List of Tables

2.1. EISCAT UHF specifications . . . . 10

2.2. EISCAT UHF position . . . . 10

2.3. Odin orbital parameters . . . . 11

2.4. Mango orbital parameters . . . . 12

2.5. EPO-1 outcome. . . . 14

2.6. EPO-2 outcome. . . . 16

4.1. X, Y, Z difference at the initial time. . . . 39

5.1. Perturbation sets 1-4 . . . . 41

5.2. Perturbation sets 5-8 . . . . 42

A.1. Range difference, SNR max, Odin, EPO-1 . . . . 51

A.2. Range rate difference, SNR max, Odin, EPO-1 . . . . 51

A.3. Range difference, GPS fit, Odin, EPO-2 . . . . 52

A.4. Range difference, SNR max, Odin, EPO-2 . . . . 52

A.5. Range rate difference, GPS fit, Odin, EPO-2 . . . . 52

A.6. Range rate difference, SNR max, Odin, EPO-2 . . . . 52

A.7. Range difference, GPS fit, Mango, EPO-2 . . . . 53

A.8. Range difference, SNR max, Mango, EPO-2 . . . . 54

A.9. Range rate difference, GPS fit, Mango, EPO-2 . . . . 55

A.10.Range rate difference, SNR max, Mango, EPO-2 . . . . 56

Matteo Crimella - Orbit Determination Analysis for SSA Purposes

Acronyms

CNES Centre National d’ ´ Etudes Spatiales, National Centre for Space Studies CRIPR Chinese Research Institute of Radio Wave Propagation

CSSS Chinese Space Surveillance System

DLR Deutsches Zentrum f¨ ur Luft- Und Raumfahrt, German Aerospace Center ECEF Earth-Centered-Earth-Fixed

ECI Earth-Centered-Inertial

EISCAT European Incoherent Scatter Organization EPO EISCAT Prisma Odin Experiment

FOI Totalf¨ orsvarets Forskningsinstitut, Swedish Defence Research Agency GEO Geostationary Orbit

GPS Global Positioning System HPOP High-Precision Orbit Propagator ICRF International Celestial Reference Frame

IRF Institutet F¨ or Rymdfysik, Swedish Institute of Space Physics ISON International Scientific Optical Network

KTH Kungliga Tekniska H¨ ogskolan, Royal Institute of Technology LEO Low Earth Orbit

LoS Line of Sight NEO Near-Earth Objects

NERC Natural Environment Research Council, United Kingdom

NFR Norges Forskningsr˚ ad, Research Council of Norway

NIPR National Institute of Polar Research, Japan

List of Tables

RSSS Russian Space Surveillance System SA Suomen Akatemia, Academy of Finland SGP4 Simplified General Perturbations SLR Satellite Laser Ranging

SNR Signal to Noise Ratio

SSA Space Situational Awareness SSC Swedish Space Corporation SST Space Surveillance and Tracking

STEL Japanese Solar-Terrestrial Environment Laboratory STK Systems Tool Kit

SWE Space Weather TLE Two-Line Element UHF Ultra High Frequency UK United Kingdom US United States

USA United States of America VHF Very High Frequency

VR Vetenskapsr˚ adet, Swedish Research Council

xvi

Matteo Crimella - Orbit Determination Analysis for SSA Purposes

Chapter 1.

Introduction

1.1. Space Situational Awareness - SSA

Space Situational Awareness (SSA) is the ability to characterize the space environment and the activities in space [1]. This broad definition includes four main activities related to the security of space operations:

• 1) the ability to view, understand and predict the physical location of natural and manmade objects in orbit around the Earth [2].

• 2) the ability to predict and differentiate potential attacks to space assets and space weather environment effects.

• 3) the ability to characterize the observed targets in terms of performance and function.

• 4) the ability to create and maintain a catalog of the tracked objects and to inte- grate multi-source data into a single common operational picture of space opera- tions [3].

According to its definition, SSA is the basis for conducting safe space operations and it

is clear that the importance of the SSA programs will increase with the amount of space

objects that orbit the Earth. An overview of the framework of SSA is shown in Figure 1.1.

CHAPTER 1. INTRODUCTION

High dependency on space operations for navigation,

communications, military operations

Need of global collaboration, regulatory framework,

Space Situational Awareness (SSA)

Risks related to extreme environment, space debris,

several satellites

Figure 1.1. – SSA Context

Nowadays the primary method for tracking objects in space entails the use of the radar. This is especially true for the objects that orbit in the Low Earth Orbit (LEO) region, located between 150 km and 2000 km form the surface of the Earth. Ground- based radar and optical telescopes forms the hardware of the US Space Surveillance Network (SSN) illustrated in Figure 1.2, that is able to track and catalog over 20000 orbiting space objects, in different orbit regimes. The metric measurements provided by this sensors in this network are the input for an orbit determination process that determines and constantly updates the state vectors of Earth-orbiting satellites and to predict their location in space [4]. It is necessary to update the satellite path because they are influenced by the environmental perturbing accelerations, like air drag, solar wind and gravitational influences and their orbit varies with time. The US SSN is an example of how the radar fulfills the primary scope of the SSA programs of tracking objects in space. In particular, the radar metric data, range, azimuth, range rate of the target, are at the base of the orbit determination phase of the actual SSA programs.

On the other hand, when the tracked object is a satellite, the radar alone is not able to offer any information about the function of the detected target [5]. The characteri- zation of objects in space, of their capabilities and limitations, is a typical military and national security SSA application [1]. The understanding of the function of the target is not the object of this Master’s Thesis project even if there are methods to infer function information from the knowledge of the position of the satellite. One way of doing so is to track a satellite in different phases of its mission, from the launch to the final orbit and to relate location information with data from other intelligence sources. In addition to this, images of target satellites, obtained with optical sensors, can show instruments and antennas associated with known devices and functions [5].

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CHAPTER 1. INTRODUCTION

Figure 1.2. – US Space Surveillance Network (http://unbonmotgroundswell.

blogspot.se/2014/01/us-lab-developing-technology-for-space.html, Friday

21

August, 2015).

The main concerns for safe space operations are the large amount of space debris and the high number of satellites that, as concomitant factors, aggravate the risk of colli- sions. The number of artificial objects larger than 10 centimeters in diameter, in Earth orbit, has gone from zero in 1956 to more than 21000 as of today. These objects are currently tracked, while several hundred thousand additional pieces of smaller dimen- sions are largely untracked. Approximately 1000 of these objects are active satellites and they represent billions of dollars in investment and revenue [6]. This overcrowding problem is particularly acute in the LEO region, that is the physical area of interest of this work, and in the Geostationary Orbit (GEO) region. In the LEO area, impor- tant assets such as reconnaissance, Earth-observing and communication satellites, orbit together with objects that move on highly elliptical orbits that have their perigee in the LEO region. These satellites share the LEO altitude range with a large amount of space debris, composed, among the rest, by uncontrolled satellites, remains of rockets and remains of intentional or accidental satellite disintegration. The orbital parameters of space objects can be calculated from metric measurements acquired by SSA sensors and, in this sense, Space Situational Awareness contributes to determine if an object is a threat for space assets and, eventually, to stimulate defensive actions [5].

There is another aspect of the space situation that rises the need of a SSA program. It

is the fact that the orbiting satellites belong to many different Countries, different “play-

ers”, and represent, for them, strategic assets and possible threats. Since the launch of

Sputnik 1 in 1957, ten nations gained the capability to place artificial satellites into orbit

and more than seventy nations, together with international organizations and agencies,

currently operate space assets. The US military’s SSN is now the most advanced source

of SSA in the world but it is not able to provide a level of SSA adequate enough to

CHAPTER 1. INTRODUCTION

For these reasons, it is not possible to rely on the existing database, like the US Space Surveillance Network catalog, that, eventually, needs to be checked and completed with supplementary data. As a consequence, different international associations and research agencies started to develop independent SSA programs.

1.2. SSA - The International Context

SSA activities started when the US tracked the first artificial satellite, the russian Sput- nik 1, after its launch in 1957 [4]. As of today, USA and Russia have the most advanced capability in the SSA sector. The European Space Agency, ESA, undertook an indepen- dent SSA program in 2009 [7]. The Chinese Space Surveillance System, CSSS, features more than 10 sensors, radars and optical sensors, in both national and international territory. Canada, India, Japan, Kazakhstan, Korea and Ukraine have sensors that can be used for SSA activities. Finally, between 2001 and 2005, the International Scientific Optical Network (ISON) was created with the Keldysh Institute of Applied Mathemat- ics in the Russian Academy of Sciences as the principal scientific and organizational coordinator. The ISON network entails the use of only optical sensors and by 2010, 90 researchers were operating 33 telescopes at 23 observatories in 11 countries [8]. The american (SSN), European (ESA) and ISON sensor system locations are illustrated in Figure 1.3.

Figure 1.3. – American (green), European (red) and International (magenta) SSA ground-based sensors (Vallado & Griesbach [8], 2011).

This international scenario is under continuous development. As already mentioned in Section 1.1, the US SSN system, despite of its level of development, is not anymore able to satisfy the increasing need of space surveillance. This is the reason why it is being

4

CHAPTER 1. INTRODUCTION

replaced by the newer american SSA network, the Space Fence program, scheduled to be operative in 2018. This program will use S-band ground-based radars, more than 400 arrays deployed worldwide, capable of high accuracy in tracking space objects, primarily in the LEO region [9].

The Russian Space Surveillance System (RSSS) was founded in 1962 and evolved similar to the US SSN. Both the programs began as missile warning systems and were gradually transformed in SSA networks; the RSSS catalog now contains more than 5000 objects larger than 10 centimeters in size. Starting from 2015 and for the near future, the russian space monitoring system will install 10 laser-optical and radio systems to expand the range of tracked orbits and to lower the minimum detectable size of space objects [10].

In Europe, ESA is developing a SSA program with the focus on three main areas: 1) Space Weather, SWE, 2) Near-Earth Objects, NEO, 3) Space Surveillance and Tracking (SST). For what concerns the SST program, its core is to produce and maintain a space objects catalog with an orbit determination process based on data produced by the SST sensors. The Preparatory Phase of the ESA’s SSA program took the years form 2009 to 2012. During this phase the techniques and algorithms needed for the SST system together with the performances of the system, in terms of design and distribution of the sensors, were investigated. From November 2010 to February 2011, the staff of the ESA SST segment conducted an experimental tracking campaign using European facilities to test how existing radars and telescopes can serve as SST sensors. Throughout a collab- oration with european satellite operators, the candidate sensors were used to observe a dozen of target satellites to investigate the sensor’s tracking capabilities. Together with facilities in UK, Switzerland, Spain and Cyprus, the EISCAT UHF radar was tested as SSA sensor [11]. Currently, the last task of the Preparatory Phase, the development of the framework for the data processing, from the sensors to the catalog, has been com- pleted. ESA is now in the second phase of the SST development. The main activities of this phase, scheduled to be completed in 2016, include the enhancements required to improve the systems developed in the Preparatory Phase, the research in the area of satellite laser ranging (SLR) and the improvement of the optical surveillance [7].

During the SST sensors test campaign, ESA identified two main types of tracking sys- tems: Surveillance Sensors and Tracking Sensors. It follows a summary of the outcome of the SST test campaign.

• Surveillance Sensors. ESA considers the surveillance sensors as the primary

hardware of the european SST system. This sensor provides data for the production

and for the maintenance of the space objects database. It sees a large area of the

sky at one time, in a fixed position, passively looking for objects to pass over. It

is also possible to actively look at the sky with a radar system that scans across a

path at a frequency that ensures nothing is missed, with the same effectiveness of

the passive sensor. When the sensor tracks space debris or satellites, the related

CHAPTER 1. INTRODUCTION

objects can trigger the “fence” created by the surveillance sensors and no prior information about the targets is required: the system does not need to be tasked to look out for any object in the sky. The accuracy of the catalog created with the surveillance sensors data is not very high initially, but, according to ESA, it should be enough to generate a reliable warning of potential collisions with active space assets. At this point, once the warning is triggered, it comes the turn of the tracking sensor to refine the orbit of the target object, in order to provide more accurate information needed to make decisions on the situation [7].

• Tracking Sensors. This type of sensors improve the initial orbit determination performed with the surveillance sensors. They have a very small field of view, allowing, given a fixed detector performance, a location of the target that is more precise than the one available in the initial catalog. This because the smaller the field of view, the more accurate the location of the object within the field of view of the sensor. This characteristic of the tracking sensors requires that the rough orbital data of the target are already available, before the observation. This limitation of the tracking sensors comes from the fact that since their field of view is small, it is nearly impossible to observe an object if the prediction of its position is too rough or completely unknown. As a consequence, ESA concludes that the tracking sensors, that include the EISCAT UHF radar, are really inefficient in the initial orbit determination, while they perform at the best when used to refine an initial orbit determination process and to maintain an existing space objects catalog [7].

Sweden has no independent SSA program. However, Sweden is a nation with a broad spectrum of space activities and participates in the SST part of the ESA SSA program.

The Swedish Defence Research Agency (FOI) has investigated the importance of a na- tional SSA capability and how Sweden can take advantage of the opportunities that SSA offers [12], [13]. Such a national SSA activity would serve not only to protect the national space assets but also to initiate international collaborations in the area of SSA, which is of global concern.

1.3. Objectives Of The Study

As the foundation of all SSA capabilities is the information about the orbit of space objects, it is natural to first study national sensor assets for orbit determination. The objective of this Master’s Thesis is to investigate how it is possible to use an existing radar system, the EISCAT radar, in the purpose of detecting and determining the orbit of space objects.

From early measurements with the EISCAT radar system it was understood that ob- servations of short-lived signals, interpreted as echoes from satellites, space debris or meteors passing through the lobe of the radar beam, contained useful information about these targets [14]. During the first investigations of the capabilities of the EISCAT UHF

6

CHAPTER 1. INTRODUCTION

radar for the calculation of range and range rate of the targets, the system was used to detect meteors [15]. However, it was clear from the beginning that, in order to determine the orbit of the target, tristatic measurements were needed. The latest development of the EISCAT system concern the methods for the calculation of the range and range rate of the radar target [16]. The work done on the EISCAT system for tracking meteors and space debris demonstrates the capabilities of the EISCAT system in monitoring space objects [14]. The future EISCAT 3D system will enhance the EISCAT ability to mon- itor space objects. First of all, EISCAT 3D will cover a wide area of the spatial area, about 60 degrees. Then, the multi-static nature of EISCAT 3D will permit to obtain full orbital parameters that now can only be acquired with tristatic measurements from the adapted EISCAT UHF/VHF (Very-High-Frequency) system. EISCAT 3D, with a wide spatial range and multi-static measurements capacity, will be an important asset in the future of international SSA networks [14].

To further investigate the capabilities of the EISCAT radar as SSA sensor and espe- cially to build knowledge in preparation for EISCAT 3D, two tracking campaigns have been performed with the EISCAT radar. Two Swedish scientific satellites, Odin and Mango, were tracked during the EISCAT-Prisma-Odin experiments (EPO). The posi- tion of the satellites, in terms of GPS data, was acquired in order to validate the EISCAT radar accuracy. The EPO experiments were performed in July 2014 (EPO-1) and March 2015 (EPO-2) at the EISCAT scientific association facility in Tromsø, Norway.

This thesis project aims at analyzing the data from these two experiments and to further investigate the initial orbit determination problem based on EISCAT data. The thesis consists of three main activities:

• Analysis of EPO experiments: the focus of the analysis of the EPO experiments is to evaluate both the hardware and software of the EISCAT radar system, in particular the EISCAT UHF radar. This first part of the thesis is divided in two sub-analyses:

– evaluation of range and Line-of-Sight velocity calculation methods by com- paring the results to GPS data

– investigation of possible systematic errors in the EISCAT system

• Initial Orbit Determination: tristatic radar data are required for initial orbit deter- mination purposes. Out of the EPO experiments, at the time when this analysis is carried out, only monostatic radar data are available. The initial state (r,v) is derived via Lambert’s initial orbit determination method based on synthetic EISCAT observation simulated with the Systems Tool Kit (STK) software by An- alytical Graphics Inc. (AGI).

• Sensitivity analysis: the third and last section of this thesis investigates the sensi-

tivity of the Lambert’s solver to perturbations of the initial radar observations.

Matteo Crimella - Orbit Determination Analysis for SSA Purposes

Chapter 2.

Experiments

2.1. The EISCAT UHF Radar

The main tool for the analysis performed in this thesis is the UHF radar of the EISCAT Scientific Association (Figure 2.1). It is designed for the observation of the ionosphere and operative since the 1980s. EISCAT is a scientific association that conducts research on the atmosphere and the ionosphere by means of the incoherent scatter radar tech- nique. The experimental facilities of the association are located in the Scandinavian sector and they consist of three radar systems, two on the mainland and one on the island of Spitzbergen in the Svalbard archipelago.

The EISCAT UHF radar operates in the 931 MHz band with a peak transmitter power of more than 2.0 MW and its antenna is a 32 m, fully steerable parabolic dish.

The transmitter and the UHF receiver are in Tromsø (Norway). VHF receivers are also

located near Kiruna (Sweden) and Sodankyl¨ a (Finland), allowing continuous tristatic

measurements [17]. The characteristics of the radar, especially its large antenna gain

due to relative high frequency, the large antenna diameter and the coherent integration

used in the signal processing, make it capable of observing particles with diameters down

to 2 centimeters at a distance of 1000 km [16]. Details of the specifications and position

of the UHF radar are shown in Table 2.1 and Table 2.2.

CHAPTER 2. EXPERIMENTS

Figure 2.1. – The EISCAT UHF Radar (http://kaira.sgo.fi/2013/11/

eiscat-uhf.html, Friday 21^st

August, 2015).

Table 2.1. – EISCAT UHF specifications

Band UHF

Transmit frequency band 926.6-930.5 MHz

Transmitter 2 klystrons

Peak Power 2 MW

Pulse Duration 1 µs-2.0 ms

Min Interpulse 1.0 ms

Coding binary phase shift (BPSK)

UHF Receiver Frequency Band 925 ± 7.5M Hz Receiver analog double superheterodyne

Antenna 32 m parabolic dish

Feed Cassegrain

Table 2.2. – EISCAT UHF position

Location Tromsø

Geographic latitude 69 ° 58’ N Geographic longitude 19 ° 22’ E

Altitude 86.5 m

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CHAPTER 2. EXPERIMENTS

2.2. Odin Satellite

One of the two targets for the EISCAT tracking campaign is the Swedish satellite Odin, illustrated in Figure 2.2. Odin is a scientific satellite that works on astrophysics and aeronomy. It was launched on February 20, 2001 from Svobodny (Russia) developed by OHB Sweden and operated by the Swedish Space Corporation, SSC. In the field of astrophysics, it is used in the study of star formation while, when used in aeronomical observations, it explores the depletion of the ozone layer [18]. The orbital parameters of Odin are listed in Table 2.3.

Table 2.3. – Odin orbital parameters

Regime Low Earth

Orbit Type Sun-synchronous polar

Perigee 622 km

Apogee 622 km

Inclination 97.83 °

Period 97.6 minutes

Figure 2.2. – Odin Satellite (https://directory.eoportal.org/web/eoportal/

satellite-missions/o/odin, Friday 21^st

August, 2015).

CHAPTER 2. EXPERIMENTS

2.3. Mango Satellite

The second target for the EISCAT tracking campaign is the satellite Mango. Mango, together with Tango, is one of the two Swedish satellites that form the satellite forma- tion Prisma. The Prisma mission is led by SSC and its primary objective is to test the satellite autonomous formation flight. The secondary objective of the mission is to test a new thruster propelled by Ammonium DiNitramide (ADN).

Mango was manufactured by Saab Ericsson Space, Omnisys Instruments and ECAPS and it was launched on June 15, 2010 on a Dnepr-1 launcher from Dombarovskiy, Russia.

The orbital parameters of Mango [19] are listed in Table 2.4 while a representation of the satellite is shown in Figure 2.3.

Table 2.4. – Mango orbital parameters

Regime Low Earth

Orbit Type Sun-synchronous polar

Perigee 668 km

Apogee 749 km

Inclination 98.4°

Period 99 minutes

Figure 2.3. – Mango Satellite (http://missions-scientifiques.cnes.fr/

PRISMA/GP_satellites.htm, Friday 21^st

August, 2015).

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CHAPTER 2. EXPERIMENTS

2.4. EPO-1 2014-07-23

On July 23, 2014, FOI, together with EISCAT and the Swedish Institute of Space Physics (Institutet F¨ or Rymdfysik, IRF), conducted the first Swedish SSA experiment; it con- sisted of in-orbit radar observation of satellites by means of the EISCAT UHF radar located in Tromsø. Together with Odin and Mango, the Picard satellite was observed during the campaign. The task of the experiment was to investigate the possibility of using the EISCAT radar as SST sensor for the initial orbit determination problem.

The outline of the experiment consisted in:

• Hardware (see Figure 2.4):

– UHF transmitter and receiver in Tromsø – VHF transmitter in Tromsø

– VHF receivers in Tromsø (N), Kiruna (S) and Sodankyl¨ a (FIN)

Figure 2.4. – EISCAT Sites (http://kaira.sgo.fi/2011_03_01_archive.html, Friday 21

August, 2015)

• Target satellites:

– Prisma/Mango

CHAPTER 2. EXPERIMENTS

– Odin

• GPS data:

– 30 seconds time step data for Odin – 10 seconds time step data for Mango

The outcome of the EPO-1 experiment resulted in a partial failure because of the loss of the GPS data of Mango and because of the malfunction of the VHF radar. For these reasons it was not possible to analyse the tristatic VHF data and only Odin was con- sidered for the comparison between the satellite position calculated by EISCAT and the GPS position.

A summary of the outcome of EPO-1 experiment is listed as follows:

• Odin and Mango were fully visible from Tromsø.

• VHF radar did not work. The reason of the failure is that one panel of the radar stuck due to a blown fuse, which resulted in significant loss of transmit power and receiver gain. In remote receivers, an experiment programming error brought a wrong receiver tuning frequency.

• GPS data of Mango not available - the comparison between the position of Mango calculated by EISCAT and the GPS position was not possible.

• Analysis performed for Odin.

• Odin GPS position and velocity data not synchronized with the EISCAT data - a numerical interpolation was need for the data analysis.

• Range and range rate velocity of the satellite evaluated from EISCAT data with two methods: Combined method and High-Resolution method.

Details of the tracked objects are shown in Table 2.5:

Table 2.5. – EPO-1 outcome.

Scan Satellite UHF VHF GPS Date Time Interval Access

1 Picard X - - 2014-07-23 02:05 - 02:10 10

2 Mango X - - 2014-07-23 02:35 - 02:40 5

3 Odin X - 30 s time step 2014-07-23 06:03 - 06:07 6 4 Odin X - 30 s time step 2014-07-23 15:28 - 15:33 5

14

CHAPTER 2. EXPERIMENTS

2.5. EPO-2 2015-03-20-21

EPO-2 experiment was conducted by FOI, EISCAT and IRF on March 20-21, 2015.

Differences with respect to the first EPO experiment concerned the hardware and the experiment procedures; they are summarized in the following list:

• Hardware (see Figure 2.4):

– UHF transmitter and receiver in Tromsø – VHF transmitter in Tromsø

– VHF receivers in Tromsø (N), Kiruna (S) and Sodankyl¨ a (FIN) – UHF transmitter in Longyearbyen (Svalbard)

– hardware test on VHF radar, 11-13 March 2015

• Target satellites:

– Prisma/Mango – Odin

• GPS data:

– 30 seconds time step data for Odin – 10 seconds time step data for Mango

Whilst the EPO-1 experiment suffered from some problems, EPO-2 resulted in a suc- cessful experiment. The hardware performed as expected and the analysis of the data led to conclusive and satisfactory results.

As for EPO-1, it follows a summary of the outcome of the second EPO experiment:

• Odin and Mango were fully visible from Tromsø - 3 passes of Mango and 1 pass of Odin were tracked by the EISCAT system. Two passes were observed with the tristatic system.

• Full functionality of the EISCAT system.

• GPS data of Mango and Odin synchronized with the EISCAT accesses.

• EISCAT data calculated at GPS time and maximum signal-to-noise ratio (SNR max).

• Analysis performed for Odin and Mango.

• Range and range rate velocity of the satellite evaluated from EISCAT data with two methods: Combined method and High-Resolution method.

Details of the outcome are shown in Table 2.6. Figure 2.5 shows one scan during EPO-2.

CHAPTER 2. EXPERIMENTS

Table 2.6. – EPO-2 outcome.

Scan Satellite UHF VHF GPS Date Time Interval Access

1 Mango X - 10 s time step 2015-03-20 17:36 - 17:40 7 2 Mango X X 10 s time step 2015-03-20 19:14 - 19:18 8 3 Mango X - 10 s time step 2015-03-20 20:53 - 20:55 7 1 Odin X X 30 s time step 2015-03-21 06:45 - 06:49 5

Figure 2.5. – EPO-2 Scan: Odin, 2015-03-21. The satellite moves along the North-East to South-West direction.

16

Matteo Crimella - Orbit Determination Analysis for SSA Purposes

Chapter 3.

EPO Data Analysis

This thesis project, as a feasibility study, wants to investigate the performances of the EISCAT UHF radar when used for orbit determination purposes. Therefore, the first analysis to be carried out, following the EPO data acquisition campaigns, is the investi- gation of the accuracy of the acquired range and range rate of the radar target.

This chapter describes the analysis of the data obtained from the EPO experiments.

First, the method to acquire orbital information like range and range rate of the radar target, from the EISCAT observations, is described. The acquired range and range rate values are then compared to the corresponding GPS values, made available by the satellites operators (Deutsches Zentrum f¨ ur Luft- und Raumfahrt, DLR and SSC). Based on this comparison, it is finally possible to draw conclusions about the performances of the EISCAT system. The tools for this analysis are MATLAB and the software Systems Tool Kit (STK), described in Section 3.1.

3.1. Systems Tool Kit

STK, developed by Analytical Graphics Inc., plays an important role in this work. It

is a modeling environment that can be used, among the rest, to analyze complex space

systems and scenarios. In this thesis project, it is used to interpolate the satellite GPS

data to correspond to the EISCAT access times and to propagate the satellite orbits in

time. Figure 3.1 shows as an example a frame of the Odin STK scenario during a radar

access (EPO-2).

CHAPTER 3. EPO DATA ANALYSIS

Figure 3.1. – STK scenario - Odin moves in the NorthEast-to-SouthWest direction.

The STK scenario is created once the EISCAT geographic position and the satellites GPS data, in the form of ephemeris, are imported in the software as input data. STK then calculates the position of the satellites through an interpolation of the ephemeris values. In this way, starting from position and velocity values given with a time step of 10 seconds (Mango) or 30 seconds (Odin), it is possible to generate the required infor- mation at any instant of time, like the EISCAT reports time.

The interpolation of the ephemeris with STK is performed in the same reference frame that the data are defined in. The default interpolation method is the Lagrange method.

The order is 5 and the number of points used in the interpolation corresponds to the order plus one [20]. The AGI support documentation about the interpolation of external ephemeris files is reported in Appendix E.

3.2. Methods For Range And Range Rate Calculation From EISCAT Data

The UHF radar raw data are processed using the methods described in reference [21]:

the Combined method and the High-Resolution method. One part of this analysis of the EISCAT system consists in the investigation of the performances of these methods.

The Combined method and the High-Resolution method are algorithms that determine orbital information of a satellite from radar pulses obtained during a pass of the target in the radar beam. They were developed using the radar raw data acquired during the European SSA Preparatory Phase of 2010-2011.

If a tristatic measurement of the passing object would be available, a set of the mini-

18

CHAPTER 3. EPO DATA ANALYSIS

mum six orbital elements needed for the orbit determination problem would be obtained.

This measurement can not be performed with the single UHF radar, therefore the radar system computes the position of the satellite as distance from the antenna (range) while the line-of-sight velocity, i.e., the range rate, is calculated considering the Doppler shift of the target [16].

The High-Resolution method computes the satellite range and beam-aligned velocity separately. The method is based on the individual per-pulse range and range range estimates R

, for times t

, and V

, for very slightly different times t

. This means that a second-order polynomial fit to the V

data is done to get an estimated velocity value and an independent third order polynomial fit to the R

data is done to get an estimated range value. The final estimates can be calculated for any desired particular instant of time, once the polynomial coefficients a

and b

are known.

R

= X

k

a

× t

, k = 0...3 (3.1) V

= X

k

b

× t

, k = 0...2 (3.2) The accuracy of the results obtained with this method is prone to the characteristics of the target. The orientation of the space object and its dimensions have an influence of the range and range rate values calculated with the High-Resolution method. If for a satellite the standard deviations of the velocity are below 1 cm

, it is not possible to obtain such good results with the low SNR values of small space debris [16].

In the Combined method, the final range and range rate are based precisely the same input data R

and V

as in the High-Resolution method. The Combined method makes, on the other hand, only a single fit, for fewer (hence more constrained) parameters a

. In this method the known exact relation V (t) =

R(t) is used to derive equation 3.2 from equation 3.1. Because equation 3.2 is computed from equation 3.1 by derivation, the four unknown parameters to be fitted are only the four a

.

The range calculation is affected by an uncertainty on the position of the transmission point that is larger than the standard deviation of the calculated range. In addition to this, it is not possible to determine precisely the direction of the satellite as it is not possible to determine the position of the object within the 0.5 ° wide radar beam. Finally, the radar pulse travels across the ionosphere and the signal can be affected by refraction resulting in a signal path different from a straight line between the radar and the target.

This effect is larger at low elevations of the radar [22].

An additional comment on the EISCAT system is about the time at which the data

are processed. It is indeed possible to extract, out of the radar raw data, the values of

interest at any desired time instant. For the purposes of this work, but only for the EPO-

2 experiment, two sets of data were calculated, at two different time sets. The first time

set contains the range and range rate values calculated at the maximum signal-to-noise

CHAPTER 3. EPO DATA ANALYSIS

ratio (SNR max ), providing the best accuracy from the radar point of view. Figure 3.2 shows the “peaks” of the curve that correspond to the local maximum SNR value: the time that corresponds to these spikes is the time of the best computed range and range rate values. The second time set contains, on the other hand, the data calculated at the exact same time as the GPS data are given (GPS fit ). In this way, it is possible to get rid of the numerical error introduced by the interpolation, performed with the STK software, that is needed to compare the results of EISCAT with the GPS values. For the EPO-1 experiment, only the SNR max EISCAT data are available.

Figure 3.2. – Doppler shift (bottom) and SNR (top) values for a single satellite pass (Nygr´ en et al. [16], 2012).

3.3. EPO-1

STK is a powerful tool that is able to generate all the different properties needed for the OD problem, such as range, range rate, azimuth, elevation, and so on. However, STK works as a “black box” and there is no access to the algorithms that is implemented.

Thus, it is necessary to check that STK produces the same values of range and range rate as if they were calculated directly from the GPS data.

To do so, the range calculated with MATLAB from the GPS and EISCAT position data is compared to the range produced by STK. In MATLAB, the range is computed as the geometric distance from the satellite and the EISCAT facility as:

R

= p

(∆X

) + (∆Y

) + (∆Z

) (3.3)

20

CHAPTER 3. EPO DATA ANALYSIS

where,

∆X = X

− X

(3.4a)

∆Y = Y

− Y

(3.4b)

∆Z = Z

− Z

(3.4c)

The GPS data acquired during EPO-1 for Odin are used for this analysis while the STK range values are produced with 0.01 seconds sample time.

It is necessary to unpick the “Light Time Delay” option in the STK settings, when the STK report is generated. The option accounts for the signal delay from the radar to the target and back, when the software calculates the range. This delay is not considered in the GPS range calculation and it is therefore necessary to not consider it in STK when the comparison between the two ranges is done.

The difference in range calculated with STK and MATLAB varies between 10

and 10

meters during the duration of the GPS data set. The difference would be expected to be zero if the STK range was calculated at the exact same time as the GPS data time. However, the 0.01 seconds sampling time of STK does not correspond to the Odin GPS data time resolution (30 seconds) and this might be the cause of the difference.

Another possible source of error might lie in the difference between the methods used to calculate the ranges with MATLAB and STK. According to the magnitude of the difference between STK and GPS data, it is possible to conclude that STK features the required accuracy for the interpolation of the GPS values.

3.3.1. Range Comparison

In this section, the range values obtained by the EISCAT system during the observation campaign EPO-1 are compared to the equivalent GPS data. The EISCAT results are calculated over two accesses but only one of these matches with the GPS data. As a consequence, there is only one radar access that can be used for the current analysis.

The EISCAT range and range rate values for this experiment are given at the time that corresponds to the maximum SNR of the radar.

The algorithm for this analysis is presented in Appendix C and its main passages are:

• Analytically calculate the range from the STK coordinates:

R

= p

(∆X

) + (∆Y

) + (∆Z

) (3.5)

∆X = X

− X

(3.6a)

∆Y = Y

− Y

(3.6b)

∆Z = Z − Z (3.6c)

CHAPTER 3. EPO DATA ANALYSIS

• Calculate the range difference as the difference of the range values taken at the same epoch:

∆R = R

− R

(3.7)

Figure 3.3 shows a comparison of the range values while Figure 3.4 shows the range difference for the radar accesses considered in this case, for both the Combined method and High-Resolution method (“CMB” and “HR” respectively). For Odin, the GPS error is available: it represents the uncertainty of the coordinates of the satellite computed with the GPS. For details of the range differences for each radar time, see Appendix A, Table A.1.

15:28:00 15:29:00 15:30:00 15:31:00 15:32:00 15:33:00 15:34:00 400

600 800 1000 1200 1400 1600

Time 23−Jul−2014 [UTC]

Range [km]

EISCAT vs GPS RANGE, ODIN, EPO−1

CMB HR GPS

Figure 3.3. – Comparison between the range calculated from EISCAT observation and the range obtained from the GPS data interpolated in STK. The values are calculated for both the Combined method (blue) and High-Resolution method (red) at each radar access, in this case, five times.

22

CHAPTER 3. EPO DATA ANALYSIS

Time 23-Jul-2014 [UTC]

15:28:00 15:29:00 15:30:00 15:31:00 15:32:00 15:33:00 15:34:00

Difference [m]

0 10 20 30 40 50 60

EISCAT Vs GPS RANGE, ODIN, EPO1

CMB HR GPS error

Figure 3.4. – Difference between the range calculated from EISCAT observation and the range obtained from the GPS data interpolated in STK. The values are calculated for both the Combined method (blue) and High-Resolution method (red) at each radar access, in this case, five times. The uncertainty on the GPS (green bars) values is also showed. It is possible to infer that, since the range error exceeds the GPS uncertainty, it is attributable to EISCAT.

3.3.2. Range Rate Comparison

In this section, equivalentelly to the range comparison above, the range rate obtained by the EISCAT system during the observation campaign EPO-1 is compared to the equivalent GPS data.

The following algorithm describes the range rate analysis:

• Import the GPS data in MATLAB.

• Extract the X, Y, Z velocity components calculated by STK from the STK report:

the components are in ECEF reference frame.

• Analytically calculate the range rate from the STK coordinates:

CHAPTER 3. EPO DATA ANALYSIS

– Define the position vector of Odin in ECEF:

Odin =



 X

Y

Z



 (3.8)

– Define the position vector of EISCAT in ECEF:

EISCAT =





X

Y

Z



 (3.9)

– Calculate the range between Odin and EISCAT as the difference of (3.8) and (3.9):

R = Odin − EISCAT (3.10)

– Calculate the unit vector of the range vector:

ˆ u = R

||R|| (3.11)

– Define the velocity vector of Odin in ECEF, from the STK report

V =



 V x

V y

V z



 (3.12)

– Calculate the projection of the velocity vector of Odin in the direction of the range vector:

R = V · ˆ ˙ u (3.13)

The range rate obtained in (3.13) is calculated as the scalar product of the velocity of Odin with the unit vector of the range between EISCAT and Odin:

in this way it is possible to obtain the projection of the velocity along the range direction, Figure 3.5.

24

CHAPTER 3. EPO DATA ANALYSIS

Earth

EISCAT Odin

Range Velocity

Velocity*UnitVector

I

J K

UnitVector

Figure 3.5. – Range Rate Calculation

• Extract the range rate calculated by EISCAT from the EISCAT report.

• Calculate the range rate difference as the difference of the range rate values taken at the same time.

The algorithm is repeated for each EISCAT access, in this case, five times.

Figure 3.6 shows the range rate difference for the radar accesses considered in this

case, for both the EISCAT analysis methods (the legend notation of the MATLAB plot

is the same as for the range difference plot), together with the GPS and the EISCAT

estimated errors. The EISCAT error is available for the range rate estimated values only,

for both the Combined method and the High-Resolution method. The detailed range rate

differences for each radar time are shown in Appendix A, Table A.2.

CHAPTER 3. EPO DATA ANALYSIS

Time 23-Jul-2014 [UTC]

15:28:00 15:29:00 15:30:00 15:31:00 15:32:00 15:33:00 15:34:00

Difference [m/s]

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

1.4 EISCAT Vs GPS LoS VELOCITY, ODIN, EPO1 CMBHR

GPS error EISCAT CMB error EISCAT HR error

Figure 3.6. – Difference between the range rate (“Line-of-Sight”, LoS, velocity) calculated by the EISCAT system and the range rate obtained from the GPS data interpolated in STK. As for the range, the values are calculated for both the Com- bined method (blue) and High-Resolution method (red) at each radar access. The uncertainty on the GPS values is showed (green bars).

3.4. EPO-2

3.4.1. Range And Range Rate Comparison

The analysis of the data obtained during the EPO-2 experiment follows the same prod- cedures described in Sections 3.3.1 and 3.3.2. The differences with respect to EPO-1, as described in Chapter 2, are the availability of data for both Odin and Mango. These data are both synchronized with the GPS time, GPS fit data, and calculated at the maximum signal-to-noise ratio of the radar, SNR max data.

Odin. The results are presented considering first the range difference and then the range rate difference. Figure 3.7 shows the difference between the range calculated by the EISCAT system and the range calculated from the STK-interpolated GPS coordi- nates of Odin. As for EPO-1, the GPS error is reported. The legend notation is the same as the one used for EPO-1 with the addition of the notation for the GPS fit and

26

CHAPTER 3. EPO DATA ANALYSIS

SNR max data (for EPO-1 there are only the SNR max data). In Appendix A, Table A.3 reports the range difference, for each radar time, for the GPS fit EISCAT data set, while Table A.4 reports the same data but for the SNR max case.

The comparison of the range rate is shown in Figure 3.8 while, in Appendix A, Tables A.5 and A.6 report the range rate differences for the different radar times, for the GPS fit and SNR max cases.

Time 21-Mar-2015 [UTC]

06:45:00 06:46:00 06:47:00 06:48:00 06:49:00 06:50:00

Difference [m]

0 10 20 30 40 50 60 70

EISCAT Vs GPS RANGE, ODIN, EPO2

CMB, GPS

fit

HR, GPS

fit

CMB, SNR

max

HR, SNR

max

GPS error

Figure 3.7. – Range Comparison

CHAPTER 3. EPO DATA ANALYSIS

Time 23-Jul-2014 [UTC]

06:45:00 06:46:00 06:47:00 06:48:00 06:49:00 06:50:00

Difference [m/s]

-1 -0.5 0 0.5 1

1.5 EISCAT Vs GPS LoS VELOCITY, ODIN, EPO2

CMB, GPS_fit HR, GPS_fit CMB, SNR_max HR, SNR_max GPS error

EISCAT HR error, GPS_fit

Figure 3.8. – Range Rate Comparison

Mango. Three measurements, performed during EPO-2 experiment, are shown to- gether in Figure 3.9. The figure shows the range comparison for the different cases, Combined method and High-Resolution method for GPS fit and SNR max data sets.

It is relevant to notice the fact that all the range difference values are positive except for the second value of the second access, computed with the Combined method, for the GPS fit data. This is the only case in which the GPS range is larger than the range calculated by EISCAT. Tables A.7 and A.8, of Appendix A, report the calculated range differences. Unlike the case of Odin, the GPS error is not available for Mango, for either the coordinates or the velocity data.

For the range rate, the difference between EISCAT observation and GPS is shown, for the three scans, in Figure 3.10 and it is reported, in details, in Appendix A, Table A.9 and Table A.10. Figure 3.10 is a zoom-in of the original MATLAB plot that shows the range rate difference for Mango. It is necessary to report the zoom-in of the plot because the range rate difference values calculated from the High-Resolution method data, for both the GPS fit and SNR max sets, differ of orders of magnitude, in some cases, with respect to the same values calculated from the Combined method data. To see the Combined

28

CHAPTER 3. EPO DATA ANALYSIS

method results, it is necessary to cut off the bad High-Resolution method results.

Access

2 4 6 8 10 12 14 16 18 20 22

Difference [m]

-10 0 10 20 30 40 50 60 70

EISCAT Vs GPS RANGE, MANGO, EPO2

CMB, GPS_fit HR, GPS_fit CMB, SNR_max HR, SNR_max

Figure 3.9. – Following the standards of the EPO-1 analysis, the figure reports the comparison of the range values computed by EISCAT and from the GPS data. For EPO-2, the range values computed for the GPS fit and SNR max data are available.

The three radar scans of EPO-2, with all the accesses, are reported.

Access

0 5 10 15 20

Difference [m/s]

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

EISCAT Vs GPS LoS VELOCITY, MANGO, EPO2

CMB, GPS fit HR, GPS_fit CMB, SNR max HR, SNR_max

Figure 3.10. – According to the Mango EPO-2 range rate analysis, the figure shows the LoS velocity differences computed on the base of the GPS data and the Combined method and High-Resolution method EISCAT data, GPS fit and SNR max sets.

Again, the radar scans of EPO-2 and the accesses are reported.

CHAPTER 3. EPO DATA ANALYSIS

3.5. Results Summary

The results presented in Section 3.3 and Section 3.4 are summarized in Figure 3.11, for the range, and in Figure 3.12, for the range rate.

Figure 3.11. – Range Comparison Summary. Above each plot, one STK frame shows the corresponding radar scan. In all the cases, the satellite moves from East to West.

Figure 3.12. – Range Rate Comparison Summary

3.5.1. Range

Figure 3.11 shows the results for both EPO-1 and EPO-2. The results of the analysis of the evaluation of the EISCAT radar as a SSA sensor, for the range case, are listed as

30

CHAPTER 3. EPO DATA ANALYSIS

follows:

• The difference between the EISCAT-calculated range and the range from the GPS data varies between 7 and 65 meters.

• The range difference ∆R = R

− R

is always positive, except for one value of the Mango analysis. This implies that the EISCAT system overestimates the range.

• There are evidences of systematic errors in the EISCAT calculations:

– Constant offset of 15 meters, on average. This error is bigger than the GPS estimated error (Figure 3.11, Odin), so it is induced by the EISCAT system.

It might be caused by the fact that the backscattered radar signal follows a path, before the sampling in the EISCAT hardware, that is longer than expected.

– Increasing error when the satellites move west from the radar. Considering that Odin and Mango, for both EPO-1 and EPO-2, fly from East to West, the origin of this error trend might lie in a wrong estimated position of the EIS- CAT UHF radar; in particular, the radar would be considered to be located east with respect to its real position.

• There is no relevant difference between the Combined method and the High-Resolution method results.

• The range values calculated at the maximum signal-to-noise ratio (SNR max set) are slightly more accurate than the same values obtained at the GPS time (GPS fit set). The difference between the two data sets increases with the time lapse between the GPS time and the maximum signal-to-noise ratio time.

• When the time lapse exceeds fractions of a second, see Tables A.7 and A.8, the High-Resolution method fails in the calculation of the range; it follows that, in this case, the difference between the GPS fit and SNR max data becomes very large too.

3.5.2. Range rate

With reference to Figure 3.12, it is possible to present the results of the analysis of the range rate calculation.

• The difference between the range rate computed by EISCAT and the GPS range

rate varies, in terms of magnitude, between 10

m/s and 3 · 10

m/s. This is the

best result of the range rate analysis and it is valid for the SNR max data processed

with the Combined method. This difference is comparable (with the exception of

two values) to the GPS uncertainty and it is therefore not possible to account for

this error as a systematic error of the EISCAT system.

CHAPTER 3. EPO DATA ANALYSIS

• The sign of the range rate difference is uniformly distributed between positive and negative values, for all the cases.

• The High-Resolution method provides poor results with respect to the Combined method, for both the GPS fit and SNR max data. The range rate difference com- puted on the basis of the High-Resolution method data differs, in most of the cases, of different orders of magnitude from the Combined method results.

• When the time lapse exceeds fractions of a second, see Tables A.9 and A.10, the Combined method fails in the calculation of the range rate. The High-Resolution method, in this case, provides range rate differences in the order of magnitude of thousands of meters per second.

32

Matteo Crimella - Orbit Determination Analysis for SSA Purposes

Chapter 4.

Initial Orbit Determination

Following the analysis of the range and range rate of the targets from EISCAT observa- tions, in this chapter the initial orbit determination is stuided more closely.

To univocally determine the orbit of an object in space, a set of minimum six inde- pendent parameters is needed. The parameters can be the classical Keplerian elements, Eccentricity, Semimajor axis, Inclination, Longitude of the ascending node, Argument of periapsis and Mean anomaly or the six components of the state vectors Position (r) and Velocity (v). To aquire this from the EISCAT system, tristatic measurements are needed, see Figure 4.1. Out of the EPO experiments, at the time when this analysis is carried out, only results from the monostatic radar data were available.

Monostatic measurements performed without interferometry, i.e., in-beam determina- tion of the target, like those available from the EPO experiments, are not able to provide accurate values of azimuth and elevation of the observed object as the object could be anywhere in the antenna beam pattern. Monostatic measurements can only provide ac- curate values of range and range rate, together with time. One way of improving such measurements, a method that was applied during the EPO experiments, is to repoint the antenna in order to get several independent values of range, range rate and time;

the different monostatic measurements are then combined in an equations system whose solution is the determination of the orbit of the radar target.

During a tristatic measurement, three sensors perform a monostatic measurement each

at the same time instant. This allows the acquisition of three independent values of range

and three independent values of range rate. The result is that tristatic measurements

allow the determination of the full velocity and position vectors of the target and, to a

final extent, the calculation of its orbit [23].

CHAPTER 4. INITIAL ORBIT DETERMINATION

Figure 4.1. – Example of EISCAT tristatic measurement (Kero J. “High resolution meteor exploration with tristatic radar methods”. PhD Thesis. Ume˚ a University, Faculty of Science and Technology, Physics. IRF Scientific Report 293 (2008)).

In the lack of tristatic EISCAT measurements, STK is used to simulate the EISCAT observation of the target and to produce the synthetic data necessary for the OD anal- ysis. Without loss of generality, only Mango is considered for this analysis.

The initial state (r,v) is derived via Lambert’s preliminary orbit determination method [24], described in Section 4.1, based on the synthetic EISCAT observation of the satellite.

The solutions of the Lambert’s problem, the initial state vectors, are propagated with the High-Precision Orbit Propagator (HPOP), described in Section 4.2.

4.1. Lambert’s Method

The Lambert’s method allows to compute the trajectory of an orbiting object given the position vectors r

and r

of two points P

and P

on its trajectory and the flight time between P

and P

[24].

Once the state vectors of an object are known at a certain instant of time and with respect to a geocentric reference frame, its orbit around the Earth is determined. Because of this, given a satellite observation from a ground station, see Figure 4.2, it is necessary to convert the ground-based position and velocity data into geocentric state vectors.

34

CHAPTER 4. INITIAL ORBIT DETERMINATION

Figure 4.2. – State Vector (Position r) from ground-based observation (Howard D. Curtis [24], 2005).

The synthetic data produced by STK are converted into initial state vectors r and v with the MATLAB function “rv from observe.m” written by Howard D. Curtis and described in his “Orbital Mechanics For Engineering Students” [24]. The function is reported in Appendix B and the script that develops the calculation of r and v is available in Appendix D. The function generates the state vectors at the desired time instant in the Earth-Centered-Inertial (ECI) reference frame according to the following algorithm [24] that reports the main equations of the process:

• Take as inputs Range ρ, Azimuth A, Elevation a, and corresponding rates ˙ρ, ˙ A and ˙a of the target.

• Calculate the geocentric position vector R of the ground-based observer from its altitude H, latitude Φ and sidereal time θ:

R =





R

q

1 − 2f − f

sin (Φ)

+ H



 cos (Φ) 

cos (θ) ˆ I + sin (θ) ˆ J 

+





R

(1 − f)

q

1 − 2f − f

sin (Φ)

+ H



 sin (Φ) ˆ K

(4.1)

where ˆ I, ˆ J and ˆ K are the directions of the geocentric reference frame (ECI), R

is the radius of the Earth and f is the Earth’s flattering factor.

• Calculate the topocentric declination δ of the target.