Low Altitude Rocket Trackerbased on Monopulse Radar

Author:

JOAN MITJANS

Supervisor:

DR. ALBERT AGUASCA

Department of Signal Theory and Communications

UNIVERSITAT POLITÈCNICA DE CATALUNYA

A dissertation submitted to the Universitat Politècnica deCatalunya in accordance with the requirements of the de-gree of GRAU EN ENGINYERIA DE TECNOLOGIES I SERVEIS

DE TELECOMUNICACIÓ in the Faculty of the Escola TècnicaSuperior d’Enginyeria de Telecomunicació de Barcelona.

BARCELONA, JULY 2018

ABSTRACT

Tracking is one of the most critical subsystems in a sounding rocket as safety, security andrecovery of the payload are directly related with an accurate positioning of the spacecraft.There are some different techniques to track a spacecraft. This thesis is going about the

use of passive monopulse direction finfing (DF) techniques for tracking a low altitude rocket withan apogee of 15 Km at UHF open band.

Several methods of implementing this strategy have been described. The use of a phase detectorhas been examined in detail using interferometer techniques. A study of the system feasibility hasbeen done, as well as a global simulator build in MATLAB®. The modelling involved an analysisand measurements of the effect of changing the separation between the receiver antennas,varying both ground station (GS) positions and orientations, and varying the antennas beamshape.

The results of the modelling are presented and some ideas for future work are shown.

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RESUM

E l seguiment és un dels subsistemes més crítics en un coet, ja que tant la seguretat comla recuperació de la càrrega útil estan directament relacionades amb un posicionamentprecís de l’aeronau. Existeixen diferents tècniques per a fer el seguiment d’una aeronau.

Aquesta tesi estudia la utilització de tècniques passives de detecció d’angle d’arribada, basadesen la teoria del monopuls, per fer el seguiment d’un coet suborbital amb un apogeu de 15 km fentservir la banda ICM de 868 MHz.

En el projecte s’han descrit diversos mètodes per a implementar el sistema de seguiment fentservir tècniques de monupuls. S’ha examinat detalladament l’ús d’un detector de fase ambtècniques d’interferometria. S’ha realitzat un estudi de la viabilitat del sistema, així com eldesenvolupament d’un simulador complet fet amb MATLAB®. Per a dimensionar el sistema, s’hafet un anàlisi amb mesures de dels efectes de canviar la separació entre les antenes receptores ide variar tant les posicions de les estacions de terra com les orientacions.

Al final els resultats del dimensionament i especificacions obtingudes es mostren i se n’extreuenalgunes conclusions, així com millores que es poden fer i idees per a treballar en un futur.

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RESUMEN

E l seguimiento es uno de los subsistemas más críticos en un cohete, ya que tanto la seguri-dad como la recuperación de la carga útil están directamente relacionadas con un posi-cionamiento preciso de la aeronave. Existen diferentes técnicas para hacer el seguimiento

de una aeronave. Esta tesis estudia la utilización de técnicas pasivas de detección del ángulo dellegada, basadas en la teoría del monopulso, para hacer el seguimiento de un cohete suborbitalcon un apogeo de 15 km utilizando la banda ICM de 868 MHz.

En el proyecto se han descrito varios métodos para implementar el sistema de seguimientoutilizando técnicas de monupulso. Se ha examinado detalladamente el uso de un detector defase con técnicas de interferometría. Se ha realizado un estudio de la viabilidad del sistema, asícomo el desarrollo de un simulador completo hecho con MATLAB. Para dimensionar el sistema,se ha hecho un análisis con medidas de los efectos de cambiar la separación entre las antenasreceptoras y de variar tanto las posiciones de las estaciones de tierra como las orientaciones.

Al final los resultados del dimensionamiento y especificaciones obtenidas se muestran y se extraenalgunas conclusiones, así como mejoras que se pueden hacer e ideas para trabajar en un futuro.

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DEDICATION AND ACKNOWLEDGEMENTS

Several people have contributed to this thesis. I would firstly like to express my sinceregratitude to my supervisor Dr. A. Aguasca for the knowledge, guidance and unendingencouragement that I have enjoyed working with him.

I also would like to thank Professor Dr. S. Blanch for their in-valuable suggestions during thedesign of the various sub-systems of the receiver.

A lot of appreciation for all of the COSMIC RESEARCH colleagues for their support and for give,between all of us, the opportunity to work in such an amazing project.

I would like to extend my thanks to Universitat Politècnica de Catalunya for all their facilitiesgiven during my study.

Finally, I am thankful to all members of my family and friends for their support and en-couragement. Specially to Gerard and Natàlia for being every day next to me during the thesisdevelopment.

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LIST OF TERMS AND ACRONYMS

Glossary

apogee Is the farthest or highest point of the flight.

CoCom limits In GPS technology, the term "CoCom Limits" refers to a limit placed on GPStracking devices that disables tracking when the device calculates that it is moving fasterthan 1,000 knots (1,900 km/h; 1,200 mph) at an altitude higher than 18,000 m (59,000ft). This was intended to prevent the use of GPS in intercontinental ballistic missile-likeapplications. The term CoCom cames from the Coordinating Committee for MultilateralExport Controls.

Kálmán line The space is considered to begin at 100Km. That heigh is known as the Kármánline where the atmosphere around this altitude becomes too thin to support aeronauticalflight, since a vehicle at this altitude would have to travel faster than orbital velocity toderive sufficient aerodynamic lift to support itself.

sounding rocket A sounding rocket is an instrument-carrying rocket designed to take mea-surements and perform scientific experiments during its sub-orbital flight.

Acronyms

Σ−∆ sum and difference.

AOA angle of arrival.

AWGN additive white gaussian noise.

DF direction finfing.

FOV field of view.

GNSS Global Navigation Satellite System.

GPS Global Positioning System.

GS ground station.

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ACRONYMS

RF radio frequency.

RTT round trip delay time.

SNR signal to noise ratio.

TT&C Telemetry, Tracking and Command system.

UHF Ultra High Frequency (300MHz−3GHz).

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AUTHOR’S DECLARATION

I declare that the work in this dissertation was carried out in accordance withthe requirements of the University’s Regulations and Code of Practice and thatit has not been submitted for any other academic award. Except where indicated

by specific reference in the text, the work is the candidate’s own work. Work done incollaboration with, or with the assistance of, others, is indicated as such. Any viewsexpressed in the dissertation are those of the author.

SIGNED: .................................................... DATE: ..........................................

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REVISION HISTORY AND APPROVAL RECORD

Name mail

Joan Mitjans (Author) jmitjansblasco@gmail.com

Albert Aguasca (Supervisor) aguasca@tsc.upc.edu

Revision Date Purpose

0 30/05/2018 Dissertation structure discussion

1 07/06/2018 Start of the dissertation

2 20/06/2018 First Revision

3 29/06/2018 Final Revision

Written by:

Date July 2, 2018

Name Joan Mitjans

Position Author

Reviewed and approved by:

Date July 2, 2018

Name Albert Aguasca

Position Supervisor

xiii

TABLE OF CONTENTS

Page

List of Tables xvii

List of Figures xix

1 Introduction 11.1 Project Overview and Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Project Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 Project Requirements and Specifications . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3.1 Project Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3.2 Project Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 State of the art and the technology used 52.1 Radar Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 Tracking radars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Monopulse Angle Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 Angle Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1.1 Amplitude Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1.2 Phase Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.2 Ratio Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.3 Angle Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Methodology and project development 113.1 Target Trajectory Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Signal Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.2.1 Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2.2 Angle Processor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2.3 Accuracy in Phase Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.3 Tracker Deployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3.1 Trigonometric Relations for Rocket Positioning . . . . . . . . . . . . . . . . . 18

3.3.2 Ground Stations Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

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TABLE OF CONTENTS

3.3.3 Antenna Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.4 Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4 Results 254.1 Theoretical Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 Phase Monopulse Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3 Server Timings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5 Budget 31

6 Conclusions and future development 33

A Appendix 35

Bibliography 39

xvi

LIST OF TABLES

TABLE Page

1.1 CoCom limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Project specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Monopulse relations for DF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1 Parameters to optimize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4.1 Selected values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 Transmitter and receiver specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3 Mobile networks RTT characterization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.1 Salaries budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.2 Hardware budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.3 Overall budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

xvii

LIST OF FIGURES

FIGURE Page

2.1 Amplitude monopulse response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Phase monopulse response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.1 General scheme of the tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.2 Target trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.3 Unambiguous zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.4 Phase monopulse angle processor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.5 Altitude and positioning trigonometric relations . . . . . . . . . . . . . . . . . . . . . . . 20

3.6 Behaviour of the tracker depending on the GS distance . . . . . . . . . . . . . . . . . . 20

3.7 GS location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.8 Azimuth and elevation angles from GS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.1 Measured phase difference for different AOA and antenna separation . . . . . . . . . . 27

4.2 Estimated AOA from empirical measurements for different antenna separation . . . 28

4.3 Error when estimating the AOA for different antenna separation . . . . . . . . . . . . 28

A.1 Bondar rocket scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

A.2 Two antenna interferometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

A.3 SNR required in function of the AOA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

A.4 AOA derivative seen from GS1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

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1INTRODUCTION

1.1 Project Overview and Goals

This final thesis is carried out at the Escola Tècnica Superior d’Enginyeria de Telecomunicacions

de Barcelona (ETSETB), UPC, within the Signal Theory and Communications department, but

not related in.

The main purpose of the project is study and design a low altitude spacecraft tracker taking

advantage of the telemetry signal that the rocket radiates during the flight. The tracking system

will be based on microwave passive DF techniques, interferometry and monopulse methods.

The main goals of the project are:

• Demonstrate that high position accuracies can be achieved using passive DF techniques.

• Design a complete tracker system able to determine the space position of a supersonic-

stratospheric sounding rocket that transmits telemetry signals at 27dBm in 868MHz UHF

band.

1.2 Project Background

The rocketry world is something very uncommon outside big companies or organizations. Since

few years ago there was only a reduced number of companies were able to put in orbit some

pyloads/satellites. With the birth and succes of SpaceX a new world had oppened tho the private

companies. Nowadays it seems that there is a huge market in putting payloads not only in orbit

but also in microgravity conditions and other situations that can only be achieved with rockets.

1

CHAPTER 1. INTRODUCTION

Limitations GNSS max values Rexus rocket

Dynamics 4 g 20 g

Altitude 50 Km 85-95Km

Velocity 500 m/s Around 1500 m/s

Table 1.1: CoCom limits

That is why new launcher-companies are growing in what they say the new space era [6] , but

the technology and theory are still difficult to find and achieve.

Nowadays while big companies are fighting to reach Mars [2], there is a new space race, but

between students. The fact is that some amateur-rocketry teams have already reached the space

(cross the Kálmán line) but no student team has sent anything beyond 100km. The author of this

thesis is part of the COSMIC RESEARCH1 team, which is a multidisciplinary student organization

linked to the UPC with the aim of become the first in reaching the space.

One of the most critical subsystems in any spacecraft mission is the Telemetry, Tracking and

Command system (TT&C) and is the part of tracking which this project is going to focus on.

The most used system for tracking applications is the GNSS one, both for terrestial and space

tracking. As the GNSS can be used aswell for guidance applications, there are some hardware

security limitations in the receivers (in GPS are called CoCom limits). When a spacecraft is

exceeding this limitations the GNSS module automatically detects that it is a threat and stops

working. It means that for a sounding rocket tracking purpose the GNSS can not be used as

a tracking system during the ascension period, as it is surpassing the dynamic and velocity

maximum values. This values are shown in Table 1.1 and compared with the well-known Rexus

rocket (from Rexus/Bexus ESA & DLR programme).

The aim of this project is to develop a low-altitude rocket tracking system using passive monopulse

radar techniques in order to determine the rocket position during either it’s ascension and descend

period. The idea is to take advantage that the rocket is transmitting a telemetry signal to a GS

and apply DF techniques in order to determine the spacecraft position by triangulation. This

system will be a possible way to track sounding rockets without having to acquire expensive and

high-restricted GNSS receivers without the CoCom limits.

1See www.cosmicresearch.org

2

1.3. PROJECT REQUIREMENTS AND SPECIFICATIONS

1.3 Project Requirements and Specifications

The tracker Requirements and specifications are adapted to guarantee the tracking of a specific

rocket. For other targets or purpose, all the DF techniques will remain the same but other

requirements will be needed and some calculus and optimizations recomputed.

The target that this system is designed to track is a supersonic rocket called Bondar (FIGURE A.1)

that is being build by the students from COSMIC RESEARCH and expected to be launched by the

end of 2018. The rocket is expected to radiate a UHF telemetry signal through an omnidirectional

antenna (as it is expected that the rocket will have some spin during the ascension and a kind of

pseudo-random attitude when descending with the parachute) fixed in the nosecone, and this

signal will be the one used for passive tracking.

1.3.1 Project Requirements

The requirements are set in order to full fill some needs :

• Be able to locate the spacecraft in a relatively small uncertainty volume.

• Be able to track the rocket without ambiguities during all the flight.

• Be able to detect when the rocket reaches the apogee.

• Use passive techniques, taking advantage of the rocket telemetry signal.

• The tracker must be movable and easy to deploy.

1.3.2 Project Specifications

Desired specifications Values

Heigh accuracy < 200 m

Horizontal accuracy < 250 m

Max. information delay 0.5 s

Min. refresh frequency 2 Hz

Max. distance launchpad-GS 25 km

Table 1.2: Project specifications

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2STATE OF THE ART AND THE TECHNOLOGY USED

Monopulse or simultaneous lobing, is a method used for determining the angular location

of a source of radiation or of the energy reflected by a target when it is illuminated.

Monopulse is used in certain types of radars, and the same or analogous techniques

(not limited to pulsed operation or to electromagnetic radiation) are also applied in fields such as

DF, communications, missile guidance, and sonar [9].

Donald R. Rhodes [8], in 1959, was one of the first to publish a unified theory of monopulse after

the declassification of some specific World War II documentation. This publication became the

basis of much of the technology now in present use, and set the 3 postulates of monopulse:

Postulate 2.1. The monopulse angle information appears in the form of a ratio. The angle infor-

mation is obtained by comparing pairs of received signals. The requirement that the comparison

be in the form of a ratio implies that the angle output of a monopulse system will be a function

only of the angle of arrival (AOA), and thus independent of the signal and any common noise or

modulation present in it.

Postulate 2.2. The ratio of a positive angle is the inverse of the ratio of the negative angle. This

postulate requires that the patterns be symmetrical about the boresight axis and when coupled

with the requirement for a ratio. Being Γm(Φ) and Γa(Φ) the multiplicative and additive rates in

function of the AOA, we find that:

Γm(Φ)= 1Γm(−Φ)

(2.1)

Γa(Φ)=−Γa(−Φ) (2.2)

5

CHAPTER 2. STATE OF THE ART AND THE TECHNOLOGY USED

Postulate 2.3. The angle-output function is an odd real function of the angle of arrival. The

output of the monopulse system is considered by Rhodes to be a sensing ratio Γ(Φ). This postulate

indicates that the real output of the detection process is the negative angle measured from the

boresight. This is a general-case definition of odd or skew symmetry for complex numbers:

Re(F[Γ(Φ)])=−Re(F[Γ(−Φ)]) (2.3)

2.1 Radar Principles

The basic functions of radar are to detect the presence of electromagnetic scatterers (radar

targets) in the antenna beam and to determine their positions. In a typical radar system there is

a transmitter that generates electromagnetic radiation and sends in through a high-directional

antenna, which can be used as well for receiving incoming signals (monostatic radar) or which

can be placed in a different place than the receiving part (bistatic radar).

When there is a target in the antenna pattern, some of the radiated energy is intercepted and

reradiated in many directions. Part of this echo is received by the radar antenna and the signal

is processed in order to get information about ranging, radial velocity, angular direction, size and

shape.

The direction of a target can be found from the direction in which the rotating antenna is pointing

when the received echo is at a maximum but this method it is not adequate in applications

requiring much finer precision. Also, it is not suitable for closed-loop angle tracking because when

the beam axis deviates from the target, the echo power decreases and there is no information to

tell the servo which way to drive the antenna to bring it back to the target.

The need for continuous, accurate angle and range measurements on a specific target led to the

development of tracking radars. The most important single improvement in angle tracking was

the introduction of monopulse, which is now used also for nontracking angle measurements

2.1.1 Tracking radars

A tracking radar is a radar that automatically keeps the antenna beam axis aligned with a

selected target. Any deviation of the target from the beam axis produces a correction signal that

is approximately proportional to the angular deviation and is used to drive the axis toward the

target.

The tracking radars are classified in three major categories according to the techniques employed.

These techniques are conical scan, sequentially lobed and monopulse (which was developed for

precision target tracking and the only technique that is explained. For further information the

Radar Handbook of Skolnik [10] is a recommended read).

6

2.2. MONOPULSE ANGLE DETERMINATION

FIGURE 2.1. Amplitude monopulse response of two physically squinted antennas.

2.2 Monopulse Angle Determination

The problems of pulse-to-pulse variations in echo amplitudes, common in sequential measure-

ments, can be overcome by using more than one beam simultaneously to measure the angular

position of the target on a single pulse. This technique, known as monopulse tracking or simulta-

neous lobing, makes use of amplitude, phase or even both informations of the incoming signal

to give much better precision than sequential conical scan techniques [4]. Another advantage is

that a target can be located from a single pulse measurement, being the radar more difficult to

be jammed. Furthermore, as mentioned in the postulate 2.1, the monopulse angle information

appears in the form of a ratio, meaning that no matter the modulation and coding used, the

signal will be able to be tracked if there is signal to noise ratio (SNR) enough.

Most tracking radars in use today are of the monopulse type. Throughout the world thousands of

monopulse radars have been built and installed on land, at sea, on aircraft and guided missiles,

and in space. However, this techniques can be employed for nontracking radar applications too,

like surveillance or a simple DF system with no auto-pointing antennas, which is our case.

In the unified concept of monopulse, three basic functions are performed: angle sensing by the

antennas, ratio conversion, and angle detection [5].

2.2.1 Angle Sensing

Although there are two different ways to sense the angle information, one can be readily converted

to the other mathematically by adding a 90 degree phase shift [8] or interchanging I & Q

components, so it is often convenient to substitute one for the other when there are processing

advantages.

2.2.1.1 Amplitude Sensing

Amplitude monopulse is the one in which the angular deviation of the target from the antenna

axis is measured as the amplitude ratio of the target as received by two antenna patterns at a

common phase center origin. The two beams are physically displaced, squinted, or overlapped to

provide a displacement of the patterns about boresight as shown in FIGURE 2.1.

7

CHAPTER 2. STATE OF THE ART AND THE TECHNOLOGY USED

FIGURE 2.2. Phase monopulse response due to time difference of arrival of signal intwo parallel beam antennas.

2.2.1.2 Phase Sensing

Phase monopulse is form of monopulse employing receiving beams with different phase centers,

as obtained, for example, from side-by-side antennas or separate portions of an array. The

information on target displacement from the antenna axis appears as a relative phase between

the signals received at the two phase centers. This makes their patterns appear essentially

parallel or overlapped in the far field as shown in FIGURE 2.2. An input signal arriving off

boresight will arrive at the beam A before the B representing a time or phase angle difference.

The difference in the phase angle as measured in each antenna of an arriving phase front of

a signal is Ψ from which is possible to calculate the estimated AOA Φ taking into account the

distance between the antennas L and the wave number k = 2πλ

:

Ψ = − kL = − 2πLλ

= − 2πD sinΦ

λ(2.4)

So, seeing the FIGURE 2.2 and being R the distance between the target and the closest antenna,

the RF voltage that the antennas A and B will receive respectively are:

EA = E0 e− jkR

EB = E0 e− jk(R+L) = E0 e− jkR e jΨ = EA e− j2π D sinΦλ

(2.5)

2.2.2 Ratio Conversion

There are three possible outputs from the ratio conversion function. The first is amplitude, where

angle information is contained in the detected voltages of the squinted overlapped beams. The

second is phase representing the time delay of a signal received by two parallel beams (both of

them are already explained). The third is a set of sum and difference (Σ−∆) signals received

8

2.2. MONOPULSE ANGLE DETERMINATION

Amplitude Phase Σ−∆Evaluation of magnitude Evaluation of angular Evaluation of both magnitude

ratio difference ratio and angular difference

Ψ = |EA ||EB| = VA

VBΨ = ∠ EA − ∠ EB Ψ = ∆

Σ = EA−EBEA+EB

FIGURE 2.1 FIGURE 2.2 FIGURE 2.1 & 2.2

Table 2.1: Monopulse relations for DF

by two beams that may be used with either of the two angle-sensing methods by combining

the signals in an RF comparator or hybrid network [5]. In this case, the angle information is

contained in both the amplitude (as a magnitude) and phase (as a sign) of the resulting signals.

So using the FIGURE 2.2 antenna distribution:

Σ = EA +EB = 2E0 e− jkR (1+ e jΨ) = − 2E0 e− jkR e jΨ2 (e− jΨ2 + e jΨ2 )

= 4E0 e− jkR e− jk D2 sinΦ cos(k D

2 sinΦ)(2.6)

∆ = EA −EB = j4E0 e− jkR e− jk D2 sinΦ sin(k D

2 sinΦ) (2.7)

2.2.3 Angle Detection

The angle-processing circuitry is designed to form the ratio (TABLE 2.1) stated in postulate 2.1

and to extract the magnitude and, if necessary, the sign of the AOA. As might be expected, since

there are three types of monopulse angle determination methods there will be three types, or

classes, of angle processors for radar systems. The angle detection function in the monopulse

theory can be fitted in one of this three categories: amplitude, phase and Σ−∆, which is a radio

frequency (RF) combination.

The development of a phase detector is explained in Chapter 3, as is the one used in the spacecraft

tracker. For further information other mnopulse detectors, Microwave Passive Direction Finding

[5], section 2.2 from Lipsky is a recommended read.

9

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3METHODOLOGY AND PROJECT DEVELOPMENT

Several parts are involved in the low altitude rocket tracker development. Not only the

monopulse DF techniques used are described but a wide overview of all the system are

exposed with all decisions duly justified.

The first step in a tracker design is to know the target specifications. As mentioned in section 1.3,

it is going to be a sounding rocket (The name of the rocket, Bondar, is the one used in the thesis

for target references) with an apogee of 15 km, and the idea is to take advantage of the rocket

telemetry signal for a tracking purpose. In other words, use passive DF techniques as there is no

need to illuminate the spacecraft. That means that the tracker has no information about ranging

neither Doppler (the telemetry signal sent by the rocket is unknown in the GS and will not be

processed. So there is no way for the GS to know when the package has been sent neither carrier

frequency shifts).

For a properly tracking in space, there are three degrees of freedom that need to be specified [1].

As only 2 AOA can be sensed (azimuth and elevation) in a single GS, at least 2 GS are needed.

For symmetry reasons and a final accuracy improvement, both GS are supposed to sense azimuth

and elevation angles, meaning that there is a redundant dimension that will help to reduce the

uncertainty volume.

In our system, shown in FIGURE 3.1, once the GS has both AOA, this information with a GNSS

time reference is sent to a MySQL database through a RESTful API hosted in a remote server.

The communication between the GS and the server is done trough the mobile network, so some

significant delay is expected. It means that, although the tracking is not done using the GNSS

technology, it is used by GS in order to have a common time reference.

11

CHAPTER 3. METHODOLOGY AND PROJECT DEVELOPMENT

Then, once the server gets the AOA packages of both GS corresponding to the same time, it

computes the latitude, longitude and heigh of the target (section 3.3.1). Notice that a previous

knowledge of GS position is needed, so they must be fixed or take advantage that they have a

GNSS receiver and send their position as well.

Finally any logged user should be able to display the tracking information on its own device with

internet connection just making a HTTP request to the API.

3.1 Target Trajectory Simulation

As the rocket is a known target, with a know trajectory, a more accurate tracking system can be

designed if advantage is taken of the "a priori" information about the target position. For doing

that, an accurate trajectory simulator has to be build. In this project it is used the positioning

(FIGURE 3.2) data from the simulator that COSMIC RESEARCH build for Bondar rocket.

3.2 Signal Sensing

With minor exceptions, like some surveillance systems, monopulse radars designed in the recently

years have used microwave comparators to Σ and ∆ patterns, and subsequent circuits form a

normalized difference signal ∆Σ rather than pure amplitude or phase comparators.

However, for a specific tracking with "a priori" information the other configurations may be more

advantageous, as they are less complex and could be more accurate in some cases. In this tracking

system some aspcets has been taken into account for choosing the optimal solution:

• The rocket will follow with some error the predicted trajectory, so a specific non-ambiguous

"narrow" field of view (FOV) is needed in the GS instead of the 360º needed for unknown

target detection.

• As it is mentioned in section 3.3, in order to full fill the tracker specifications (Table 1.2) a

very little angular error is tolerated.

• The GS should be portable and easy to mount, so big antennas can not be used.

Taking into account the previous points some decisions has been taken. First of all, due to

the high precision that the tracker has to have, the idea of mounting a tracking radar with

auto-pointing antennas has been discarded, since extremely accurate rotors and calibration are

needed. Instead of that, fixed GS with 4 non-directional antennas (since they are not pointing to

the target but they need to cover a specific zone and they should be easily mounted in a plane)

are used. So, as the antennas are not very directional, the amplitude information, for this specific

purpose, is practically useless. Thus, monopulse phase sensing followed by a phase detector using

interferometer techniques is the one used and explained.

12

3.2. SIGNAL SENSING

FIGURE 3.1. General scheme of the designed low altitude rocket tracker.

13

CHAPTER 3. METHODOLOGY AND PROJECT DEVELOPMENT

(a)

0 10 20 30 40 50 60

Time s

0

2

4

6

8

10

12

14

16

18

Altitude K

m

Bondar simulated height

(b)

0 10 20 30 40 50 60

Time s

0

100

200

300

400

500

600

700

800

900

Speed m

/s

Bondar simulated speed

Rocket speed

Speed of sound

FIGURE 3.2. (a) Instantaneous rocket height during the rocket ascension. (b) Instanta-neous spacecraft speed.

The phase sensing part is already described in section 2.2.1.2. So only the other parts are

summarized in this chapter.

3.2.1 Interferometry

Interferometers can be considered specific cases of array antennas. While linear arrays have all

the antenna elements center in a straight line at equal spacings and the beam forming is done by

phase shift networks. In an interferometer, the elements can also lie in a straight line but are

usually at different spacings to obtain time-of-arrival relationships that can be transposed into

measurable phase differences for determination of AOA information.

In FIGURE 2.2, the used interferometer antenna system was described as a DF measurement

technique based upon the difference of the time of arrival of a signal detected by two identical

collocated antennas in space separated a distance D. It was shown that the output of the antennas

differed in phase from each other in proportion to the extra time it took a plane wave signal to

travel a greater distance to the further antenna. FIGURE A.2 is a zoomed and clearer scheme.

Taking the equations (2.5) and setting the phase origin to the nearer antenna (A) we have:

EA = E0

EB = E0 e− jkL = E0 e jΨ = EA e− j2π D sinΦλ

(3.1)

Substracting the natural logartithm of both voltages and making it real (Table 2.1) we get the

phase difference.:

14

3.2. SIGNAL SENSING

Ψ = j [LnEB − LnEA] = − 2πDλ

sinΦ (3.2)

Where the negative sign indicates a time lag. Solving equation (3.2):

sinΦ = λ Ψ

2π D(3.3)

Where:

Φ = AOA in radians.

λ = wavelength in meters.

D = Distance between antennas in meters.

Ψ = Phase difference between antennas in radians.

So from equation (3.2) can be seen that the greater the distance between antennas, the more

difference between phases (Ψ), so the more accurate will be the AOA estimation. However, there

is a trade-off since for unambiguous resolution, Ψ must be between [0, −2π) and |sinΦ| ≤ 1. So

for a given unambiguous FOV, set by Φmax, there is a Dmax (FIGURE 3.3).

It is important to notice that there is always a 180º of ambiguity if only a phase detector is used

(there is no way to know from which hemisphere the signal is coming), so it makes no sense to

approach the antennas closer than D = λ2 . At D = λ there is a discontinuity since for distances

further than this one, Ψ can take values grater than 2π, something that does not happen for

closer distances. Finally, in section 3.3, where the tracker sizing is done, a optimal D is chosen.

3.2.2 Angle Processor

The monopulse processor is that portion of a monopulse radar that operates on the voltages

derived from the simultaneous antenna patterns to produce the monopulse outputs.

FIGURE 3.4 shows an idea of phase monopulse angle processor. Where is necessary to remark that

both lines have to work in perfect synchronization since the AOA information is given by a delay

between signals, so it has to work coherently. The output angle is a voltage that is a sinusoidal

function of the AOA, form often found in instantaneous frequency encoders.

The phase detector block can be achieved using different methods as displacement between both

FFT peaks, cross-correlating the signals or using a PM or FM phase-shift discriminator [3].

3.2.3 Accuracy in Phase Measurements

Monopulse, along with all other angle-measuring systems, is subject to errors from various source.

As noise is the dominant one for relatively long ranges, is the one who will set our final angular

accuracy, as it is directly dependent upon the SNR.

15

CHAPTER 3. METHODOLOGY AND PROJECT DEVELOPMENT

0 1 2 3 4 5 6 7 8 9 10

D / lambda

0

20

40

60

80

100

120

140

160

180

Un

am

big

uo

us a

ng

ula

r zo

ne

in

de

gre

es

Unambiguous angular zone

FIGURE 3.3. Unambiguous zone

FIGURE 3.4. Phase monopulse angle processor

16

3.2. SIGNAL SENSING

Random noise, assumed AWGN here, can be split in two components: ni, which is in phase with

the amplitude of the signal and nq, which is in quadrature. While ni adds to the signal E varying

its amplitude, nq adds a phase angle γ that is random:

E = E0 e jφ

Er = (E0 +ni) e j(φ+γ)(3.4)

Where:

γ = tan−1 nq

E0 +ni(3.5)

Making a first order approximation for SNR >> 1 :

tan γ ≈ γ

γ ≈ nq

E0

(3.6)

Being the noise RMS power N and solving for nq:

N = (ni)2 + (nq)2 = 2(nq)2 → nq =√

N2

(3.7)

Substituting (3.7) to (3.6) and assuming S = (E0)2 the signal power:

γ ≈ nq

E0=

√N

2 (E0)2 =√

12 SNR

(3.8)

As the monopulse compares the phase between two uncorrelated signals (the antennas are

separated more than D > λ2 ), and assuming equal SNR in both antennas. The total phase error

is:

γT =√

12 SNR

+ 12 SNR

=√

1SNR

(3.9)

In order to relate the received phase error to an AOA error we have to compute the variation

of AOA (Φ) for a Ψ (3.2) change. If we define ΨA and ΨB as the phase diference between each

antenna and the boresight we found that:

δΨA

δΦ= −δΨB

δΦ= π

Dλ

cos Φ → δΦ = λ

π D cos ΦδΨA = −λ

π D cos ΦδΨB (3.10)

So the RMS AOA error is:

∆Φ = λ

π D cos Φ

√(∆ΨA)2 + (∆ΨB)2 = λ

π D cos ΦγT = λ

π D cos Φp

SNR(3.11)

17

CHAPTER 3. METHODOLOGY AND PROJECT DEVELOPMENT

Action Consequences

Increase Dλ

. Better angular accuracy (3.11) but narrowerunambiguous FOV (FIGURE 3.3).

Separate the GS from the rocket. Less unambiguous FOV needed but worseSNR thus worse angular accuracy.

Change the relative positions between bothGS and the target, keeping the distancerocket-GS constant.

As the target is located by crossing the GSuncertainty cones (FIGURE 3.1), there is an op-timal β1 and β2 (FIGURE 3.5) which minimizesthe horizontal accuracy.

Table 3.1: Parameters to optimize

It is important to notice that, for achieving high resolutions with a fixed SNR, the relation Dλ

should be as high as possible. So, theoretically huge resolutions can be achieved using monopulse

techniques but you must have an almost-ideal tracking system because, as seen in section 3.2.1,

there is a trade-off between accuracy and ambiguities. For this project, an intermediated value is

found in the system sizing (section 3.3). Also, the further the target is from the boresight, the

more angular error, so the initial antennas orientation is very important if they are fixed.

3.3 Tracker Deployment

In this section, the dimensioning of the monopulse tracker is done. The main idea is to deploy a

system like the one shown in FIGURE 3.1, so, in order to find the optimal configuration a MATLAB®

based simulator and optimizer has been build. As there are so many parameters that can be

configured, and most of them are correlated ones each others, some iterations have had to be done

in order to find a optimal solution that satisfies the required specifications. The main parameters

that can be modified are listed on the Table 3.1 with some of their consequences.

3.3.1 Trigonometric Relations for Rocket Positioning

After sensing the DF in both antenna planes and in both GS, the 4 AOA have to be converted in

real elevation (α1, α2) and azimuth angles taking into account the antennas orientation. Then,

as the GS are fixed in a known position, the angle β1 ans β2 from FIGURE 3.5 can be found.

Being h the instantaneous height of the rocket and M its trajectory ground projection:

h = x1 tan α1 = x2 tan α2 → x1

x2= tan α2

tan α1

M = x1 sin β1 = x2 sin β2 → x1

x2= sin β2

sin β1

(3.12)

18

3.3. TRACKER DEPLOYMENT

From (3.12), it can be proved that only 3 angles are needed, since all of the are related:

tan α2

tan α1= sin β2

sin β1(3.13)

Now, defining L as the distance between the 2 GS:

L = x1 cos β1 + x2 cos β2 = h cos β1

tan α1+ h cos β2

tan α2(3.14)

Solving for h in order to find the rocket altitude:

h = Ltan α1 tan α2

cos β1 tan α2 + cos β2 tan α1(3.15)

Replacing one of the angles using (3.13) we can found multiples solutions:

h = Ltan α1 tan β2

cos β1 (tan β1 + tan β2)= L

tan α1 sin β2

sin (β1 + β2)

= Ltan β1 tan α2

cos β2 (tan β1 + tan β2)= L

tan α2 sin β1

sin (β1 + β2)

(3.16)

The latitude and longitude coordinates of the target can be computed as a displacement x1 or x2

from the GS1 or GS2 respectively, where:

x1 = htan α1

; x2 = htan α2

(3.17)

3.3.2 Ground Stations Location

The rocket is expected to be launched from the Instituto Nacional de Técnica Aeroespacial (INTA)

arenosillo (Huelva) installations and with a very specific orientation in order to guarantee that

the spacecraft is always inside a safe zone on the sea. That means that the sea is one of the

biggest limitations in order to place the GS.

Using the formulas (3.16) and (3.11) and taking into account the AOA error found in (3.11), a

script that converts the desired vertical and horizontal accuracy in meters (set in Table 1.2) to an

angular accuracy and then to a required SNR has been done. As a non-linear equation has to be

solved, the trust-region dogleg algorithm is used. The algorithm is a variant of the Powell dogleg

method described in [7] and integrated in MATLAB® with the function fsolve.

Seeing the FIGURE 3.6 (a) it can be seen that for sensing the azimuth angle less angular accuracy

is needed than the elevation one. That is because the rocket displacement in the ground is, by

far, smaller than the vertical one so an angular error in the elevation AOA will be more critical.

Also, both curves have an optimal distance that maximizes the error tolerated, which are more or

19

CHAPTER 3. METHODOLOGY AND PROJECT DEVELOPMENT

FIGURE 3.5. Relation between the angular information and space positioning of therocket.

(a)

0 10 20 30 40 50 60 70 80 90

Distance launch pad - GS (Km)

0

0.5

1

1.5

2

2.5

Degre

es

AOA Accuracy needed

Athimuth

Elevation

(b)

0 10 20 30 40 50 60 70 80 90

Distance launch pad - GS (Km)

20

25

30

35

40

45

50

SN

R (

dB

)

SNR needed

D = 0.5 lambda

D = 1 lambda

D = 1.5 lambda

D = 2 lambda

D = 5 lambda

FIGURE 3.6. (a) Maximum angular error tolerated in azimuth and elevation dimensionsin order to guarantee the spatial accuracy set in Table 1.2 during all the flight. (b)SNR needed in the GS for achieve the resolutions shown in graphic (a)

20

3.3. TRACKER DEPLOYMENT

less the ground displacement and altitude respectively. Notice that for achieving not extreme

spatial resolutions, accuracies of less than half a degree are needed so that is why, as mentioned

in section 3.2, mounting the antennas on a rotor for pointing the target is not a feasible option

due to the mechanical error of the not very expensive devices.

FIGURE 3.6 (b) has been obtained applying (3.11) to the most critical AOA. Here, the existence of

an optimal distance is more clear. We should separate the GS from the launch pad more or less

the same distance as the rocket apogee.

3.3.3 Antenna Separation

Once found the distance between the GS and launch pad where less SNR is required, different

antenna separations should be simulated. The desired result is the maximum separation (best

accuracy with the same SNR) that has no ambiguities when the rocket tracking is done. In this

thesis, the GS are supposed to have 4 low gain antennas distributed with a North, South, East

and West disposition.

There are only two different zones that are near the sea and meet the condition of distance found

in section 3.3.2. The former condition is important for better triangulation and permanent line

of sight between the target and the GS. This regions found are near Matalascañas and Punta

Umbría (FIGURE 3.7).

Then, for every time step, the theoretical DF angles has been computed in both GS, as well

as the relative angles (taking into account the antennas orientation). The simulator takes the

instantaneous rocket and GS geodetic coordinates and makes the conversion to East-North-Up

(ENU) frame before finding the DF angles. Then, in order to find the relative angles, another

conversion from ENU frame to GS-Body frame has been done through the predefined GS attitude

quaternion.

The most critical point is when the rocket reaches the apogee, which is the furthest point from

GS, so the point with less SNR and also when the maximum angular resolution is needed. The

fixed antennas should be pointing to the target apogee for 2 reasons: The former is to minimize

the propagation losses with the antenna gain. The latter, and most important, is the fact that the

angular error increases with the target deviation from the antenna boresight Φ (3.11), clearly

seen in FIGURE A.3.

FIGURE 3.8 shows that, once placed and oriented both GS, they are expected to sense variations

of 46º in elevation and 11º in azimuth so we must guarantee that, if the target is in those regions,

it can be tracked with no ambiguities. The maximum antenna separation is D = 1.4λ for the

vertical antenna pair and D = 5λ for the horizontal one (FIGURE 3.3). A separation of D = 1.2λ,

that allows unambiguous variations of 55º were chosen for both dimensions in order to have some

21

CHAPTER 3. METHODOLOGY AND PROJECT DEVELOPMENT

FIGURE 3.7. GS location.

0 10 20 30 40 50

Time (s)

-50

-40

-30

-20

-10

0

10

20

30

40

50

Degre

es

Azimuth & Elevation from GS1

Athimuth

Relat. Ath.

Elevation

Relat. elev

FIGURE 3.8. Azimuth and elevation anglesfrom GS1.

margin in elevation. As azimuth measurements do not need better resolution than elevation,

keeping the same D is a good idea to increase the unambiguous FOV.

3.4 Network

The DF information of both GS need to be centred in a common node (server) in order to compute

the geodetic coordinates of the target. A possible solution is described here and illustrated in

FIGURE 3.1.

A RESTful API is an application program interface (API) that uses HTTP requests to GET, PUT,

POST and DELETE data. This means that developers have no need to install additional software

or libraries when creating a RESTful API. One of the key advantages of RESTful APIs is that

they provide a great deal of flexibility. Data is not tied to resources or methods, so REST can

handle multiple types of calls and return different data formats. So, seen from the users, which

are the GS and all the electronic devices that want see the rocket position, they only have to

POST the AOA and time values through and HTTP request and GET the data respectively.

Internally, the API is expected to store all the incoming data in a MySQL database, which is

an open-source relational database management system (RDBMS), multi-user, that uses the

structured query language (SQL). The main benefits are its scalability and easy treatment of

data.

The channel used to send the information of both GS is using the mobile network. As they are

located near Matalascañas and Huelva populations, GSM EDGE or GPRS and UMTS HSPA

coverages are expected but not LTE (although it has been studied as well as a real option). The

22

3.4. NETWORK

most important parameter that should be taken into account is the round trip delay time (RTT)

of the packages. So, if it full fills the specification of maximum information delay of 0.5 s (Table

1.2), it should be easy to connect both GS to the server with an Arduino or RaspberryPi with

modules like SIM808 (GSM+GPRS+GPS), Adafruit FONA 3G Cellular + GPS or some 4G Shield.

Finally, a simple interface that constantly makes HTTP GET requests to the server and refreshes

the rocket position can be done. However, only the RESTful API using the PYTHON Flask

framework and hosted on a RaspberryPi 3 with an Apache web server has been done. Then,

with the server running the average RTT for every mobile network generation can be found if

some petitions to the server are done from a mobile terminal connected to GSM, UMTS and LTE

respectively.

23

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4RESULTS

Once the overall monopulse radar tracker system has been designed, some proofs-of-

concept where done in order to check the design feasibility. First of all, after iterating

several times the simulator some optimal values are shown and also the results of a link

budget using realistic receiver specifications. Then, serveral measurements were done in order to

proof the feasibility of a passive phase monopulse DF processor. Finally some delays in the GS

connection system are calculated for guarantee that the data is displayed in almost real-time.

4.1 Theoretical Study

Values Optimal Chosen Limitation

Elevation D 1.4 λ 1.2 λ Some unambiguous FOV margin is needed

Azimuth D 5 λ 1.2 λ No such precision is needed, more FOV instead

Dist. GS1-Launchpad 17 km 16.8 km -

Dist. GS2-Launchpad 17 km 20.1 km At 17 km there is the mouth of the Odiel river.

Table 4.1: Selected values

Table 4.1 shows the values chosen for the tracker. A link-budget in the worst case scenario (at the

rocket apogee) has to be done and the check if the SNR at the receiver is enough to achieve the

angular accuracy needed. The transmitter and receiver specifications are shown in Table 4.2.

So taking into account the free-space loss, defined as:

L f s = 20 log4π Rλ

= 119.1 dB (4.1)

25

CHAPTER 4. RESULTS

And the total temperature defined by the Friis formula:

Tt = Ta

L f eeder+ T f eeder

L f eeder − 1L f eeder

+ T0 (NF − 1) = 339k (4.2)

The final SNR at the receiver is:

SNR = Ptx + G tx − L f ,tx − L f s + Grx − L f ,rx − Lpol − 10 log (Kb Tt Bw) = 34.7 dB (4.3)

At the apogee, the AOA = 0 due to the antenna orientation chosen, so the required SNR to achieve

the 200x250m resolution set in the specifications table is 33.4 dB (FIGURE A.3 b). That means

that the system designed would have SNR enough but with a margin of only 1.3 dB.

Transmitter Receiver

Tx Power 27 dBm Rx Gain 7 dB

Tx Gain 1.5 dB Feeder Loss 0.5 dB

Feeder Loss 0.5 dB Polarization Loss 1 dB

Carrier frequency 869.525 MHz Bw 200 KHz

Propagation distance 24.8 Km Noise Figure (LNA) 3 dB

Ant. Temperature (sky) 20 K

Rx physical Temperature 290 K

Table 4.2: Transmitter and receiver specifications

4.2 Phase Monopulse Measurements

A proof-of-concept of passive phase DF monopulse processor has been done in an anechoic chamber

because, as the delay between 2 signals is measured, the presence of multipath would corrupt

the measurements.

The transmitter was a mobile dipole, excited by a signal generator and was radiating a pure

868 MHz tone. The receiver antennas were 2 folded dipoles separated 0.5λ, λ, 1.5λ and 2λ.

The receiver was similar that the one shown in FIGURE 3.4. First of all the signal was amplified

17dB through a LNA, then filtered at 868 MHz before down converting to 30 MHz. Finally the

signal was low pass filtered and recorded in a oscilloscope with time windows of 500 samples.

The measures was taken for every 5º angular displacement of the transmitter from the re-

ceiver boresight and repeated for every antenna separation. Then all the samples were digitally

processed in order to find the phase difference between antennas anth then the estimated AOA.

26

4.3. SERVER TIMINGS

0 10 20 30 40 50 60

Angle of arrival (º)

0

50

100

150

200

250

300

350

Phase d

iffe

rence (

º)

Antenna Separation 0.5 lambda

0 10 20 30 40 50 60

Angle of arrival (º)

0

50

100

150

200

250

300

350

Phase d

iffe

rence (

º)

Antenna Separation 1 lambda

0 10 20 30 40 50 60

Angle of arrival (º)

0

50

100

150

200

250

300

350

Phase d

iffe

rence (

º)

Antenna Separation 1.5 lambda

0 10 20 30 40 50 60

Angle of arrival (º)

0

50

100

150

200

250

300

350

Phase d

iffe

rence (

º)

Antenna Separation 2 lambda

FIGURE 4.1. Measured phase difference for different AOA and antenna separation

First of all the continuous part of the signal was filtered and then normalized in amplitude. The

method for detecting the phase difference was using the complex FFT that consists on searching

the absolute maximum (peak) of both FFTs and computing the phase difference between this

complex maximum FFT values. The values obtained are shown in FIGURE 4.1 and two important

things can be seen: One is that the phase difference increase the slope as the antenna separation.

That is the reason why the accuracy is increased with the antenna separation. The other is, as

seen in FIGURE 3.3, when the separation is 1.5λ and 2λ there are ambiguities at around 42º and

30º respectively, represented by phase differences higher than 2π and easily identifiable.

Finally, making use of the equation (3.2) the estimated AOA is computed and compared with the

real one (FIGURE 4.2). That comparison allows us to get an approximation of the squared angular

error and its root mean square error. The results of FIGURE 4.3 corroborates what we said in the

previous paragraph. However, the accuracies reached are worse than the desired ones. That is

due to the manually movement of the transmitter inside the anechoic chamber. Furthermore, the

SNR where less and the LNA a little bit noisier than the needed for the real rocket tracker.

4.3 Server Timings

In order to make an estimation of the RTT, as mentioned in section 3.4, an Apache server was

mounted in a RaspberryPi model 3B connected to the home router through a CAT 6 etehrnet

27

CHAPTER 4. RESULTS

0 10 20 30 40 50 60

Angle of arrival (º)

0

10

20

30

40

50

60

70

Com

pute

d A

OA

(º)

Antenna Separation 0.5 lambda

0 10 20 30 40 50 60

Angle of arrival (º)

0

10

20

30

40

50

60

70

Com

pute

d A

OA

(º)

Antenna Separation 1 lambda

0 10 20 30 40 50 60

Angle of arrival (º)

0

10

20

30

40

50

60

Com

pute

d A

OA

(º)

Antenna Separation 1.5 lambda

0 10 20 30 40 50 60

Angle of arrival (º)

0

10

20

30

40

50

60

Com

pute

d A

OA

(º)

Antenna Separation 2 lambda

FIGURE 4.2. Estimated AOA from empirical measurements for different antenna sepa-ration

0 10 20 30 40 50 60

Angle of arrival (º)

0

5

10

15

AO

A e

rror

(º)

Antenna Separation 0.5 lambda

Squared error

RMS error

0 10 20 30 40 50 60

Angle of arrival (º)

0

1

2

3

4

5

6

7

AO

A e

rror

(º)

Antenna Separation 1 lambda

Squared error

RMS error

0 10 20 30 40 50 60

Angle of arrival (º)

0

0.5

1

1.5

2

AO

A e

rror

(º)

Antenna Separation 1.5 lambda

Squared error

RMS error

0 10 20 30 40 50 60

Angle of arrival (º)

0

0.5

1

1.5

2

2.5

AO

A e

rror

(º)

Antenna Separation 2 lambda

Squared error

RMS error

FIGURE 4.3. Error when estimating the AOA for different antenna separation

28

4.3. SERVER TIMINGS

cable. The server was hosting the mentioned RESTful API and the client used was a mobile

phone.

For the test, several hundreds of petitions to the server has been done using GSM, UMTS and

LTE mobile networks. The final RTT as well as the minimum and maximum values are shown in

in Table 4.3.

Minimum RTT (ms) Average RTT (ms) Maximum RTT (ms)

GSM EDGE 181.151 612.685 2779.165

UMTS HSPA/HSPA+ 48.742 147.080 955.003

LTE 47.563 88.33 209.221

Table 4.3: Mobile networks RTT characterization.

As the packages has to travel, first from the GS to the server, and then from the server to

the electronic device were the information is displayed and processed, the total delay of the

information will be, at least, twice the RTT. As the requirements said that only a delay of 0.5s

was tolerated, only the UMTS (in average) and LTE (always) will be a good option.

29

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TE

R

5BUDGET

This project involves research, design and test, but non the implementation of the tracking

system. That means that the biggest part of the budget is destined to cover salaries of

the people involved in the project.

Considering the salary of an undergraduate engineer as 8C per hour and the supervisor salary as

senior engineer as 20C per hour. The gross salary is used (assuming the social security charges +

IRPF of 10% ). Te total salaries cost, calculated with 400 hours of dedication from the student

and 1 hour/week from the supervisor:

Worker Salary (C/h) Hours Total (C)

Student 8.89 450 4000.5

Supervisor 22.22 22 488.84

Total 4489.34 C

Table 5.1: Salaries budget

For the testing and different proofs-of-concept just a few components were purchased, since

almost all of te hardware and equipments were borrowed by the university during the test. The

following table contains the material purchased. The personal laptop used for making simulations

is not considered in the table.

31

CHAPTER 5. BUDGET

Part Unit cost (C) Units Total (C)

RaspberryPi model B 39.99 1 39.99

microSD card 12 1 12

Cable CAT 6 6.5 1 6.5

Dipole Antenna 8.75 1 8.75

SMA cables 7 2 14

Total 81.24 C

Table 5.2: Hardware budget

So the overall cost of the project is:

Part Total (C)

Salaries 4489.34

Hardware 81.24

Total 4570.58 C

Table 5.3: Overall budget

.

32

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6CONCLUSIONS AND FUTURE DEVELOPMENT

In this thesis a brief introduction to monopulse techniques has been done, as well as an

explanation of the advantages with respect to other techniques when they are applied for

tracking purposes. It has also explained the different monopulse ratios that can be sensed

and the pure phase processor in further detail.

The main goal of the thesis was to find a way to track a low-altitude spacecraft that surpass the

CoCom limits of common GNSS receivers. There are several ways to implement a tracker, and one

of them, the implemented in this project, is using DF based on monopulse techniques, in a limited

number of GS located in a very specific place, and applying some trigonometric operations.

One of the main differences between the common tracking radars is that the proposed tracking

system is passive, taking advantage of the telemetry signal that the target radiates to the ground.

The other one is that, due to an unnecessary increase of complexity and cost, the decision of

leaving the antennas fixed (instead of auto-pointing the target) has been taken. That decision

made that the taker must have a relatively wide non-ambiguous FOV, so not very directive

antennas where able to be used. Since the antennas used where not very directive, there where

very poor amplitude variations between both antennas. That made almost useless all of the

monopulse information coming from amplitude relations and was the main reason why only

phase monopulse processor has been studied.

After several simulations and some tests, the results obtained shows us that, if the overall

system is well-dimensioned, it is possible to achieve the accuracy and other specifications set in

the Table 1.2. However, a very little SNR margin has been obtained. In order to improve this

results and keeping the antennas fixed, and array of antennas with different and increasingly

33

CHAPTER 6. CONCLUSIONS AND FUTURE DEVELOPMENT

separation between each others can be build instead of only one pair per plane. With more

antennas, more monopulse combinations can be done. That means that, we can have in the same

array separations of 0.5 λ for resolving ambiguities and separations of 5 λ or more to increase

the accuracy. Other possible solutions is to implement a common tracking radar with moving

antennas. For doing that the AOA derivative from every GS should be taken into account (FIGURE

A.4) as the rotor must be powerful enough to rotate the antenna array at the angular speed

required.

The phase monopulse angular processor was not designed during the thesis, but can be done

using non expensive SDR dongles working as a multiple channel coherent receiver but a perfect

synchronization between channels is needed. Nowadays there are companies like Coherent

Receiver that are using the RTL-SDR v3 20$ dongle connected to a common external clock and

combined with a RF switch that switches between the antenna and a noise generator. That switch

allows to calibrate the different channels, just doing the FFTs and aligning them (as all the

inputs are the same AWGN noise, the crosscorralation must be a delta centred in the origin).

The GS communication part using the mobile networks and a RESTful API + MySQL database

seems to be a good solution for our purpose. It has been proved that GSM EDGE connection is

not feasible due to the big RTT that the packages have but can be done with UMT HSPA and

LTE networks. An improvement of this system would be communicate the GS by a RF link and

make the overall tracker by far much accurate, since an almost real-time data refresh can be

achieved (IP protocol is to slow and random).

To sum up, extremely precise trackers can be done using monopulse techniques (you can always

increase the antenna separation, thus increase the resolution). The main idea was to develop a

complete tracking system and keep it the simplest as possible. This way to think was present in

every decision taken during all the thesis development. The final results obtained, shows that

the proposed tracker is feasible, relatively cheap to build (depending on the phase processor used)

and highly movable and scalable. However, for targets that are going higher than 15 km with the

same power transmitted, auto-tracking high directive antennas are needed (known as tracking

radar). And then, would be reasonable to use both phase and amplitude informations, building

what is said a complex monopulse processor and working with the Σ−∆ signals [9].

34

AP

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IX

AAPPENDIX

In this appendix several figures, that were not relevant enough to be fitted in the chapters

but they may be of interest to the reader, are attached. Also some plots for further knowledge

can be fond here. All of the figures are referenced during the thesis.

FIGURE A.1. Bondar rocket scheme yielded by COSMIC RESEARCH team.

35

APPENDIX A. APPENDIX

FIGURE A.2. Two antenna interferometer.

(a)

0 10 20 30 40 50 60 70 80 90

AOA (degrees)

20

30

40

50

60

70

80

S/N

(dB

)

S/N needed for 250 m horizontal and 200 m vertical resolution

D = 0.5 lambda

D = 1 lambda

D = 1.5 lambda

D = 2 lambda

D = 5 lambda

(b)

0 5 10 15 20 25 30 35 40 45

AOA (degrees)

33

33.5

34

34.5

35

35.5

36

36.5

S/N

(dB

)

S/N needed for 250 m horizontal and 200 m vertical resolution

D = 1.2 lambda

FIGURE A.3. (a)SNR required in function of the AOA in order to guarantee the sameresolution. (b) The specific case of D = 1.2λ which is the one chosen in the tracker.

36

0 10 20 30 40 50

Time (s)

-1

-0.5

0

0.5

1

1.5

2

2.5

Degre

es/s

Athimuth & Elevation derivative

Athimuth

Relat. Ath.

Elevation

Relat. elev

FIGURE A.4. AOA derivative seen from GS1.

BIBLIOGRAPHY

[1] T. BENSON, Guide to rockets.

https://spaceflightsystems.grc.nasa.gov/education/rocket/shortr.html, 2015.

Last accessed: 2018-06-05.

[2] J. CONDLIFFE, The 21st-century space race: Will boeing or spacex be first to mars?, MIT

Technology Review, (2016).

[3] P. CRILLY AND A. CARLSON, Communication Systems, McGraw-Hill Education, 2009.

[4] S. KINGSLEY AND S. QUEGAN, Understanding radar systems, vol. 2, SciTech Publishing,

1999.

[5] S. E. LIPSKY, Microwave passive direction finding, SciTech Publishing, 2004.

[6] J. M. LÓPEZ-URDIALES AND E. DIEZ, New space unconference, in Space Up Barcelona,

2018.

[7] M. POWELL, A fortran subroutine for solving systems of nonlinear algebraic equations,

Numerical methods for nonlinear algebraic equations, (1970), pp. 150–166.

[8] D. R. RHODES, Introduction to monopulse, McGraw-Hill, 1959.

[9] S. M. SHERMAN AND D. K. BARTON, Monopulse principles and techniques, Artech House,

2011.

[10] M. I. SKOLNIK, Radar handbook, McGraw-Hill Education, 1970.

39