Collaborative UAS Control to Increase
Deconfliction Ability in the NAS
Except where reference is made to the work of others, the work described in this
thesis is my own or was done in collaboration with my advisory committee. This
thesis does not include proprietary or classi ed information.
Brian C. Reitz
Certi cate of Approval:
John E. Cochran Jr.
Professor and Head
Aerospace Engineering
Gilbert L. Crouse Jr., Chair
Associate Professor
Aerospace Engineering
Andrew J. Sinclair
Assistant Professor
Aerospace Engineering
George T. Flowers
Dean
Graduate School
Collaborative UAS Control to Increase
Deconfliction Ability in the NAS
Brian C. Reitz
A Thesis
Submitted to
the Graduate Faculty of
Auburn University
in Partial Ful llment of the
Requirements for the
Degree of
Master of Science
Auburn, Alabama
August 10, 2009
Collaborative UAS Control to Increase
Deconfliction Ability in the NAS
Brian C. Reitz
Permission is granted to Auburn University to make copies of this thesis at its
discretion, upon the request of individuals or institutions and at
their expense. The author reserves all publication rights.
Signature of Author
Date of Graduation
iii
Vita
Brian Christopher Reitz, son of Steven L. Reitz, Linda Ellen Cowall, and Debra
Ann Reitz, was born August 14, 1985 in Columbus, Georgia. He graduated with
honors from Russell County High School in Seale, AL, and entered Chattahoochee
Valley Community College in the summer of 2003. After receiving his Associate of
Science degree, he entered Auburn University in the spring of 2005. He graduated
cum laude with a Bachelor of Aerospace Engineering degree in May of 2007, and
entered Graduate School, Auburn University, the following semester.
iv
Thesis Abstract
Collaborative UAS Control to Increase
Deconfliction Ability in the NAS
Brian C. Reitz
Master of Science, August 10, 2009
(B.A.E., Auburn University, 2007)
(A.S., Chattahoochee Valley Community College, 2004)
111 Typed Pages
Directed by Gilbert L. Crouse Jr.
The progression of aviation has led to the strong desire to integrate unmanned
aerial systems (UASs) into the national airspace system (NAS). In order for UASs to
occupy the NAS concurrently with other aircraft, the Federal Aviation Administration
(FAA) regulations require that UASs \see and avoid" (SAA) other air tra c to the
same extent as a human pilot. The focus of this research is to explore the use of two
collaborating unmanned aircraft working together to ensure separation from other air
tra c using measurement data obtained from optical sensors. The system is designed
for use with small, light-weight aircraft that are operated below 10,000 feet mean sea
level. Computer simulation was used to explore the implementation of a control
strategy for positioning the collaborating aircraft to maximize the accuracy of their
estimates of interfering tra c locations and minimize the potential for con icts while
 ying to a speci ed location. The performance of the range estimation algorithm was
explored while subject to multiple interfering aircraft and operational constraints such
as ownship maneuverability. A comparison with two other possible formations was
v
conducted to determine how the proposed method performed in both range estimate
and miss distance of con icting air tra c. The system reliability was also examined
when faced with multiple types of target scenarios.
vi
Acknowledgments
The author would like to thank Dr. Gilbert L. Crouse Jr. for the opportunity to
work on this research as well as his knowledge and invaluable support throughout the
project. The author is appreciative of Dr. Crouse?s belief in his abilities and guidance
to become a young professional.
The author would also like to thank the Aerospace Engineering Department
for its  nancial assistance and the Aerospace Engineering faculty for providing the
knowledge to initially understand such a task. Dr. Andrew J. Sinclair was of great
assistance in the acquisition of reference materials. The author also wishes to thank
his colleague and friend, Jason Welstead, for his moral support and help with LATEX.
The author is perpetually thankful to his parents for their support and steadfast
encouragement.
Finally, the author would like to dedicate this thesis to the memory of his grand-
father, Mr. George Miller Reitz (March 19, 1931 - August 27, 1997.) Without this
gentleman, the author?s interest in aviation may have never been sparked. As the
author continues his education, he will forever value the lessons learned from his
grandfather.
vii
Style manual or journal used American Institute of Aeronautics and Astronautics
(AIAA)
Computer software used MATLAB 2007a, Microsoft O ce Word 2007, Microsoft
O ce Excel 2007, Microsoft Paint, WinEdt, LATEX
viii
Table of Contents
List of Figures xi
List of Tables xiii
1 Introduction 1
1.1 Performance Requirements . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 SAA System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Review of Literature 7
2.1 SAA Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Sensor Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Range Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 SAA System Decision . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3 System Comparison and Discussion 11
4 Platform Positioning and Target Localization 14
4.1 Range Estimation Positioning . . . . . . . . . . . . . . . . . . . . . . 14
4.2 Measurement Platform Dynamics . . . . . . . . . . . . . . . . . . . . 17
4.3 Target Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.4 Iterative EKF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.5 Area of Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.6 Time to Closest Approach . . . . . . . . . . . . . . . . . . . . . . . . 25
4.7 Platform Positioning Controller . . . . . . . . . . . . . . . . . . . . . 26
5 Conflict Resolution 31
5.1 Con ict Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
5.2 Resolution Heading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.3 Return to Initial Flight Path . . . . . . . . . . . . . . . . . . . . . . . 37
5.4 Resolution Heading Maneuvering . . . . . . . . . . . . . . . . . . . . 38
6 System Implementation 40
6.1 Optical Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.2 Target Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.3 Computational Processing . . . . . . . . . . . . . . . . . . . . . . . . 41
6.4 Weight Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
ix
7 Results 44
7.1 Alternative Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
7.2 Comparison Target Scenario . . . . . . . . . . . . . . . . . . . . . . . 47
7.3 Comparison Without Con ict Resolution . . . . . . . . . . . . . . . . 48
7.3.1 Range Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
7.3.2 Excess Distance Traveled . . . . . . . . . . . . . . . . . . . . . 54
7.4 Con ict Resolution Algorithm Veri cation . . . . . . . . . . . . . . . 56
7.5 Comparison With Con ict Resolution . . . . . . . . . . . . . . . . . . 61
7.5.1 Range Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
7.5.2 Excess Distance Traveled and Miss Distance . . . . . . . . . . 68
7.6 A ect of Platform Separation Distance . . . . . . . . . . . . . . . . . 70
7.6.1 Range Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7.6.2 Excess Distance Traveled and Miss Distance . . . . . . . . . . 74
7.7 A ect of UAS Performance Parameters . . . . . . . . . . . . . . . . . 77
7.7.1 Range Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
7.7.2 Excess Distance Traveled and Miss Distance . . . . . . . . . . 80
7.8 Accuracy of Error Bounds . . . . . . . . . . . . . . . . . . . . . . . . 83
7.9 System Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
8 Conclusions 89
8.1 Comparison of Platform Separation Distances . . . . . . . . . . . . . 89
8.2 Comparison of Performance Parameters . . . . . . . . . . . . . . . . . 90
8.3 Error Bound Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . 90
8.4 System Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
9 Future Work 93
Bibliography 95
x
List of Figures
1.1 Measurement Platform UAS with Sensors (Top, Front, and Side View). 5
2.1 TCAS System Diagram. . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 ADS-B Broadcast Service Architecture. . . . . . . . . . . . . . . . . . 9
3.1 Researched SAA System Architecture. . . . . . . . . . . . . . . . . . 12
3.2 Measurement UAS Maneuvering. . . . . . . . . . . . . . . . . . . . . 13
4.1 Optimal and Worst-case UAS Positioning for Range Estimation. . . . 15
4.2 UAS Formation Description. . . . . . . . . . . . . . . . . . . . . . . . 16
4.3 Gaussian PDF With 90% Con dence Region. . . . . . . . . . . . . . 25
4.4 Block Diagram of Measurement Platform Controller. . . . . . . . . . 27
4.5 Block Diagram of PID Controller. . . . . . . . . . . . . . . . . . . . . 27
5.1 Geometry for Level Con ict Scenario. . . . . . . . . . . . . . . . . . . 32
5.2 Heading Changes to Resolve Con ict (VA >VB). . . . . . . . . . . . . 34
5.3 Heading Changes to Resolve Con ict (VA <VB). . . . . . . . . . . . . 35
5.4 Limiting Case for Two Solutions (VA <VB). . . . . . . . . . . . . . . 36
7.1 Three Platform Formation. . . . . . . . . . . . . . . . . . . . . . . . . 46
7.2 Constantly Rotating Two Platform Formation. . . . . . . . . . . . . . 47
7.3 Comparison Scenario; Y-Axis Points North. . . . . . . . . . . . . . . 48
7.4 Average Range Error (Blue Line) and Standard Deviation (Red Line)
for System 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
xi
7.5 Average Range Error (Blue Line) and Standard Deviation (Red Line)
for System 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
7.6 Average Range Error (Blue Line) and Standard Deviation (Red Line)
for System 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
7.7 Average Range Error Comparison. . . . . . . . . . . . . . . . . . . . . 55
7.8 First Four Veri cation Target Positions Traveling at 75 knots. . . . . 57
7.9 Last Four Veri cation Target Positions Traveling at 75 knots. . . . . 58
7.10 First Four Veri cation Target Positions Traveling at 125 knots. . . . . 59
7.11 Last Four Veri cation Target Positions Traveling at 125 knots. . . . . 60
7.12 Average Range Error (Blue Line) and Standard Deviation (Red Line)
with Con ict Resolution for System 1. . . . . . . . . . . . . . . . . . 63
7.13 Average Range Error (Blue Line) and Standard Deviation (Red Line)
with Con ict Resolution for System 2. . . . . . . . . . . . . . . . . . 64
7.14 Average Range Error (Blue Line) and Standard Deviation (Red Line)
with Con ict Resolution for System 3. . . . . . . . . . . . . . . . . . 65
7.15 Average Range Error Comparison with Con ict Resolution. . . . . . . 67
7.16 Average Range Error with 500 ft. Separation Distance. . . . . . . . . 71
7.17 Average Range Error with 1000 ft. Separation Distance. . . . . . . . 72
7.18 Average Range Error with 1500 ft. Separation Distance. . . . . . . . 73
7.19 Average Range Error Comparison with Varying Separation Distances. 75
7.20 Average Range Error with SEP of 500; ROT of 90 deg/min. . . . . . 78
7.21 Average Range Error with SEP of 1500; ROT of 270 deg/min. . . . . 79
7.22 Average Range Error Comparison with Varying Performance Parameters. 81
7.23 Estimated Target Positions with Associated Area of Uncertainty. . . . 83
7.24 Initial Estimated Target Position with Associated Area of Uncertainty
for Target 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
7.25 Range Estimate Histograms. . . . . . . . . . . . . . . . . . . . . . . . 85
7.26 Multiple Target Near Miss Scenario. . . . . . . . . . . . . . . . . . . . 88
xii
List of Tables
6.1 Hardware Component Speci cations. . . . . . . . . . . . . . . . . . . 42
6.2 Total System Weight and Power Required. . . . . . . . . . . . . . . . 43
7.1 Speci c Simulation Parameters. . . . . . . . . . . . . . . . . . . . . . 45
7.2 Summary of Range Error Plots without Con ict Resolution. . . . . . 53
7.3 Average Excess Distance Traveled and Standard Deviation for System 1. 54
7.4 Average Excess Distance Traveled and Standard Deviation for System 3. 56
7.5 Miss Distances for Veri cation Targets. . . . . . . . . . . . . . . . . . 61
7.6 Summary of Range Error Plots with Con ict Resolution. . . . . . . . 66
7.7 Average Excess Distance Traveled and Standard Deviation for System
1 with Con ict Resolution. . . . . . . . . . . . . . . . . . . . . . . . . 68
7.8 Average and Minimum Miss Distances and Standard Deviations for
System 1 with Con ict Resolution. . . . . . . . . . . . . . . . . . . . 68
7.9 Average and Minimum Miss Distances and Standard Deviations for
System 2 with Con ict Resolution. . . . . . . . . . . . . . . . . . . . 69
7.10 Average Excess Distance Traveled and Standard Deviation for System
3 with Con ict Resolution. . . . . . . . . . . . . . . . . . . . . . . . . 69
7.11 Average and Minimum Miss Distances and Standard Deviations for
System 3 with Con ict Resolution. . . . . . . . . . . . . . . . . . . . 70
7.12 Summary of Range Error Plots for Varying Separation Distances. . . 74
7.13 Average Excess Distance Traveled and Standard Deviation with a Sep-
aration Distance of 500 ft. . . . . . . . . . . . . . . . . . . . . . . . . 75
xiii
7.14 Average and Minimum Miss Distances and Standard Deviations with
a Separation Distance of 500 ft. . . . . . . . . . . . . . . . . . . . . . 76
7.15 Average Excess Distance Traveled and Standard Deviation with a Sep-
aration Distance of 1500 ft. . . . . . . . . . . . . . . . . . . . . . . . 76
7.16 Average and Minimum Miss Distances and Standard Deviations with
a Separation Distance of 1500 ft. . . . . . . . . . . . . . . . . . . . . 76
7.17 Summary of Range Error Plots for Varying UAS Performance Param-
eters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.18 Average Excess Distance Traveled and Standard Deviation; SEP of
500, ROT of 90 deg/min. . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.19 Average and Minimum Miss Distances and Standard Deviations; SEP
of 500, ROT of 90 deg/min. . . . . . . . . . . . . . . . . . . . . . . . 81
7.20 Average Excess Distance Traveled and Standard Deviation; SEP of
1500, ROT of 270 deg/min. . . . . . . . . . . . . . . . . . . . . . . . 82
7.21 Average and Minimum Miss Distances and Standard Deviations; SEP
of 1500, ROT of 270 deg/min. . . . . . . . . . . . . . . . . . . . . . . 82
xiv
Chapter 1
Introduction
In the national airspace system (NAS), civil unmanned aerial systems (UASs)
could perform tasks such as aerial geophysical surveys, low-level pipeline inspections,
disaster monitoring, and forest- re mapping [1]. Border surveillance, telecommuni-
cations relay services, and environmental monitoring are also missions that could be
performed by civil UASs [2]. UASs could perform tasks in the NAS related to both
military and commercial applications that would be infeasible or even impossible for
manned aircraft. This is due in-part to their ability to stay aloft for long periods
of time without concern for pilot fatigue as well as lower operating costs in some
instances when compared to manned aircraft. Pilot safety is also a concern. UASs
can do jobs that a human pilot cannot do safely.
Integrating UASs into the NAS comes with the challenge of avoiding midair
collisions with other aircraft including non-cooperative piloted and non-piloted air
vehicles. The Federal Aviation Administration?s (FAA) Aeronautical Information
Manual (AIM) describes a near midair collision as: \an incident associated with
the operation of an aircraft in which a possibility of collision occurs as a result of
proximity of less than 500 feet to another aircraft" [3]. Non-cooperative aircraft would
include aircraft without a transponder and ones operating without communicating
with air tra c control. Federal Aviation Regulations (FARs) require that pilots
\see and avoid" other aircraft when operating under visual  ight rules (VFR) or
when operating under instrument  ight rules (IFR) in visual meteorological conditions
(VMC) [4]. In congressional testimony the FAA?s Nick Sabatini said, \The extremely
1
broad range of unmanned aircraft make their successful integration into the national
airspace system a challenge, but certainly one worth meeting" [5]. The O ce of the
Secretary of Defense (OSD) UAS Roadmap identi es the development of see and
avoid (SAA) and collision avoidance systems as a critical technology goal [6].
Since UASs currently lack the ability to \see and avoid" other air tra c au-
tonomously, military and government agency UAS operations in non-segregated airspace
are limited under the Certi cate of Waiver or Authorization (COA) process that re-
quires operational restrictions to ensure that con icts with other NAS users are lim-
ited. Civil unmanned aircraft have to go through a more di cult process to enter the
NAS. Civil UAS users must obtain a Special Airworthiness Certi cate in the Experi-
mental Category and even then still face severe limitations on when, where, and how
they can operate [7].
In order to operate freely in the NAS, unmanned aircraft must meet an \equiva-
lent level of safety" (ELOS) to manned aircraft regarding the ability to see and avoid
other aircraft [8]. The goal of the research described herein is to develop and simulate
a system of two collaborating aircraft in which optical sensors are used to detect con-
 icting air tra c. By using two aircraft, a triangulated estimate of the tra c?s range
is obtained. A control strategy is developed to maneuver the aircraft to optimize the
range estimate. Successive range estimates and estimates of the tra c?s velocity are
used to determine if the tra c is a collision hazard. If a hazard exists the controller
maneuvers the aircraft to avoid any near midair collisions. Once the collision hazard
is cleared the controller maneuvers the aircraft back to the original  ight path and
heading.
2
1.1 Performance Requirements
Performance requirements for SAA systems depend greatly on the size of the
applicable UAS as well as the type of missions it is to accomplish while operating in
the NAS. Smaller UASs have a substantially lower payload capability than their larger
counterparts. Therefore, if a small UAS is to complete a mission in the NAS, the
SAA system must be light-weight to allow for the addition of a payload. While larger
UASs might e ectively implement radar or other active scanning system to meet the
requirements for operating UASs in the NAS, such a solution is problematic for smaller
UASs because of their weight and power [9]. Solutions such as the Tra c alert and
Collision Avoidance System (TCAS) and automatic dependent surveillance-broadcast
(ADS-B) provide a method of sensing transponder equipped aircraft, however, due to
weight and power constraints, most small UASs are not out tted with such equipment.
One solution to this size and weight constraint is through the use of optical sensors
to sense interfering air tra c. Optical sensors are small, light-weight, and require
little electrical power. On the other hand, optical sensors require processing power.
With small, light-weight, optical sensors care has to be taken in the image resolution
to e ciently detect tra c as early as possible to allow for ownship avoidance if the
need arises. Title 14 Code of Federal Regulations (14 CFR) Part 91, section 91.117
dictates the maximum speed at which aircraft may be operated below 10,000 feet
mean sea level as 250 knots [4]. With this speed restriction, research has shown that
resolution requirements become less stringent [9]. A recommended instantaneous
 eld of view per pixel for an avoidance maneuver with a 25 bank angle at 120
knots is 1.34 milliradians [9]. The instantaneous  eld of view per pixel is the camera
 eld of view divided by the number of linear pixels in the focal plane [9]. Previous
research has also determined that an appropriate Field of Regard (FOR) for the SAA
3
system should include airspace that lies within  110 of the longitudinal axis of the
aircraft and  15 with respect to the vertical  ight path [10]. With this FOR, a
camera with at least 955 pixels in the horizontal plane is needed. 14 CFR Part 91,
sections 91.111(a) and 91.113(b) are also important in the design of an SAA system
because they describe how to operate near other aircraft as well as the right-of-way
rules except water operations respectively [4]. The performance requirements for the
designed system are to be light-weight and compact, have a FOR of at least  110 
in azimuth and  15 in elevation, as well as follow all FARs.
1.2 SAA System Overview
The SAA approach presented here involves the use of two aircraft  ying in for-
mation nominally 1000 feet apart at the same altitude and heading. Each aircraft is
equipped with three  xed optical sensors for tra c detection. The three sensors are
placed on the airframe such that each sensor has a coverage area of  40 degrees in
azimuth and  30 degrees in elevation. This is to ensure that the monitored azimuth
covers  120 of the longitudinal axis of each platform. With this coverage area, the
FOR requirement mentioned in Section 1.1 will be exceeded. Figure 1.1 shows an
example of the UAS and the  eld of view for each of the sensors.
Methods to detect a target in a digital image have been demonstrated by previous
researchers [11, 12, 13, 14, 15]. Therefore, this research started with the assumption
that a detection algorithm which provided azimuth and elevation measurements of
the line of sight vector to the target was already available. It was also assumed that
the sensors could detect the target perfectly. Another assumption made includes that
of computational power. It was assumed that at least one of the UASs in the SAA
system would either possess the equipment necessary to run the control algorithms
4
Figure 1.1: Measurement Platform UAS with Sensors (Top, Front, and Side View).
or it would possess the wireless capability to transmit and receive data at a rate high
enough to use the output from algorithms implemented on a ground station. Also, the
assumption that the UASs in the system could communicate with each other to relay
information was made. With this foundation, the present research focused solely on
the control algorithms along with the target position and velocity estimation.
Including the above assumptions, the system of UASs was simulated in a MAT-
LAB environment. Various con icting tra c  ight paths were modeled with the
target?s motion assumed to follow a constant velocity trajectory. Simulated measure-
ments at each time step (30 Hz) were generated based on the assumed trajectories.
Zero-mean, Gaussian pseudorandom noise was then added to each of the measure-
ments to simulate measurement uncertainty. Control of each of the measurement
platforms was accomplished through the use of a proportional, integral, derivative
5
(PID) controller. The controller maneuvered the platform UASs to take more accu-
rate measurements while also maneuvering them to avoid tra c con icts.
6
Chapter 2
Review of Literature
Research in the area of collision avoidance has been occurring since the mid 1950s
when the FAA got involved after several mid-air collisions occurred where numerous
people were killed [16]. With the modernization of the air tra c control system, the
term con ict resolution, or decon iction, has come about. The di erence between col-
lision avoidance and con ict resolution may  rst seem minuscule. In practice though
the di erence is quite important. Collision avoidance is an extreme maneuver per-
formed at the last possible moment to avoid a collision. Con ict resolution, however,
involves the careful planning of multiple  ight tracks to avoid a collision avoidance
situation.
2.1 SAA Systems
Many solutions to the collision avoidance and con ict resolution problem exist.
Solutions such as various versions of the TCAS have been employed since the early
1980s. TCAS is an airborne system developed by the FAA that operates indepen-
dently from the ground-based Air Tra c Control (ATC) system. It was designed
to increase cockpit awareness of proximate aircraft and to serve as a \last line of
defense" for the prevention of mid-air collisions [17]. Figure 2.1 shows a diagram of
the TCAS system. More recently, the FAA, with the development of ADS-B, has
o ered another solution to the detection of con icting air tra c. With ADS-B, both
pilots and controllers can see radar-like displays with highly accurate tra c data that
7
update in real time and do not degrade with distance or terrain. The ADS-B system
provides air-to-air surveillance as well as surveillance to remote or inhospitable areas
that do not currently have coverage with radar [18]. Figure 2.2 shows a diagram of
the ADS-B system architecture.
Figure 2.1: TCAS System Diagram [19].
Airborne radar has been in military use since World War II, when it was intro-
duced to help night  ghters locate bombers [16]. While the TCAS and ADS-B are
both viable solutions for large transponder equipped aircraft, they are unable to de-
tect non-cooperative aircraft. Radar, electro-optical, and infrared sensor systems are
appealing solutions for detecting tra c because they do not require that other aircraft
have special equipment. Passive systems such as electro-optical and infrared systems
are attractive for unmanned aircraft since their power requirements and payload sizes
would not accomodate radar systems [21].
8
Figure 2.2: ADS-B Broadcast Service Architecture [20].
2.2 Sensor Description
Radar sensors work by emitting short pulses of radio waves created with a mag-
netron from an antenna. As the radio waves bounce o of other objects, they return
to the antenna which doubles as a receiver when it is not transmitting. With the
known direction of the antenna when the microwave was emitted and the time for the
microwave to return, the range as well as direction to the target can be computed.
A passive sensor is a sensor designed to detect energy radiated or re ected from
other objects. Passive sensors, unlike radar, do not emit energy themselves. Two
types of common passive sensors are optical and infrared. An optical sensor detects
light rays and converts them to an electric signal. An infrared sensor detects infrared
radiation emitted from all objects in relation to their temperature. Both sensors
compare the received energy with the previous, or standard, level of energy to detect
an object. Since the sensors do not transmit energy themselves, the only information
available is the direction from which the energy arrived.
9
2.3 Range Detection
Passive sensors work well for the detection of a collision hazard, but do not
give very much information on where the target actually is or where it is going. O.
Shakernia et al. employed the use of a small self maneuver to triangulate the position
of the target after it has been detected [8]. Others have combined multiple types
of sensors to detect and gather information on a collision hazard. G. Fasano et al.
employed infrared sensors combined with radar to detect non-cooperative tra c [22].
The infrared sensors were used to detect con icting tra c, and radar was used to
gather information on the tra c?s location and approximate velocity.
2.4 SAA System Decision
The main consideration as to the type of SAA system to incorporate on a par-
ticular UAS depends on its size, weight, mission, and payload capability. Currently
there are no laws or FARs governing the type of SAA system UASs must use. The
FAA?s main concern with UASs operating in the NAS is safety. The FAA, in 2005,
asked the Radio Technical Commission for Aeronautics (RTCA), a group that fre-
quently advises the agency on technical issues, to help develop standards for UAS
SAA systems [23]. The RTCA committee for UASs, SC-203, has been asked to pro-
duce Minimum Aviation System Performance Standards (MASPS) for SAA systems
to be employed on UASs operating in the NAS by  scal year 2011 [24].
10
Chapter 3
System Comparison and Discussion
Until recently, most of the SAA solutions available were extremely heavy or bulky.
This is in part due to the fact that most of the systems available were developed for
large manned aircraft. With UASs becoming a more viable solution for some missions,
a compact and light-weight solution is needed. Systems with multiple sensor types
are satisfactory for some applications, but the complexity of these systems make them
unsuitable for use on small UASs.
A diagram of the proposed SAA system can be seen in Figure 3.1. As can be seen
in the illustration, the SAA system includes the use of two UASs each equipped with
optical sensors for target detection. Since the system only employs the use of one
type of sensor, there is an advantageous decrease in the system weight carried by the
UASs. Optical sensors are incorporated to decrease the system size and complexity as
opposed to carrying radar sensing equipment. Two UASs are employed to triangulate
the position of the target to address the range detection problem with optical sensors
mentioned previously. Using two UASs to triangulate the position also addresses the
issue of time with respect to an accurate estimation in target location. In the method
mentioned in Section 2.3 where a small self maneuver is used to triangulate the
target?s position, an increase in the time required to accurately estimate the target?s
position is incurred. This time is important because the aircraft has to detect the
tra c with enough time remaining before collision to execute an avoidance maneuver
and maintain the required separation distance.
11
Figure 3.1: Researched SAA System Architecture.
Measurements from the sensors on-board each UAS are used in conjunction with
an iterative extended Kalman  lter (EKF) to estimate the state for each of the observ-
able targets. After each target?s state is estimated, the area of uncertainty associated
with the estimate is calculated from the estimated covariance. The time to closest
approach, tca, for each of the targets is also calculated from the state estimate. Based
on this tca, the system determines which target needs to have more accurate mea-
surements. A PID controller then aligns the UASs to take those measurements. The
more accurate measurements are obtained by aligning the UASs perpendicular to the
line of sight vector to the tra c. Using the estimated target position and velocity, the
system determines if there will be a tra c con ict. If so, a PID controller maneuvers
the UASs to avoid that con ict. If no con ict exists, the UASs continue on their
assigned  ight path.
12
The orientation of the measurement UASs is based o of a circle. During maneu-
vering, the UASs are held at a  xed distance apart. To maneuver, the UASs simply
rotate about the center point of the formation. Figure 3.2 depicts how the UASs
maneuvere to provide more accurate measurements to the target state estimator.
Figure 3.2: Measurement UAS Maneuvering.
Since the UAS system geometry is based o of a circle it is easy to control the
system to maneuver away from con icting tra c. The heading of the center point
for the circle is simply commanded to change. This system geometry coupled with
the target estimator simpli es con icting tra c position estimation as well as con ict
resolution.
13
Chapter 4
Platform Positioning and Target Localization
In the previous chapter, methods for positioning the UAS platforms for target
localization were introduced. Presented now is an in-depth description of the math-
ematical method for performing those tasks.
4.1 Range Estimation Positioning
Since the optical sensors provide only azimuth and elevation to the target, range
cannot be directly measured by a single measurement platform UAS. However, by
working collaboratively, the two UASs are able to triangulate the position of the
tra c. The accuracy of that position estimate depends on the relative position of the
target to the measurement aircraft. To obtain an optimal range estimate or the best
range estimate for the formation, the two aircraft are positioned perpendicular to
the line joining the tra c and the mean of the two aircraft?s positions. On the other
hand, if they are positioned parallel to that line, no range information can be deduced
as illustrated in Figure 4.1. In the  gure, and for the remainder of this thesis, the
word optimal is used to refer to the position of the aircraft in the de ned formation
in which the best range estimate is obtained.
Initially, and anytime there are no targets in the FOR of the measurement air-
craft, the UASs are con gured to  y abreast at the same altitude. The angle of the
platforms, aop, and the separation distance, sepdist, are the two parameters that
describe the aircraft formation. Figure 4.2 illustrates these parameters. The angle of
14
Figure 4.1: Optimal and Worst-case UAS Positioning for Range Estimation.
the platforms is calculated using Equation (4.1) and is based o of the target location
as well as the center location of the measurement aircraft system. Equation (4.2)
describes how the position of each measurement aircraft is found from the angle of
the platforms.
aopopt = tan 1
 y
t yc
xt xc
 
(4.1)
x1 = xc + sepdist2 sin (aopopt)
y1 = yc + sepdist2 cos (aopopt)
x2 = xc sepdist2 sin (aopopt)
y2 = yc sepdist2 cos (aopopt)
(4.2)
15
Figure 4.2: UAS Formation Description.
16
4.2 Measurement Platform Dynamics
Each UAS, or measurement platform, was modeled as a point mass that traveled
with constant acceleration. Equation (4.3) describes the dynamics of the measurement
platforms.
_X = AX +BU (4.3)
Equation (4.4) describes the state of the measurement platforms and Equation (4.5)
describes the state matrix.
X =
2
66
66
66
66
66
66
66
4
x
_x
y
_y
z
_z
3
77
77
77
77
77
77
77
5
(4.4)
A =
2
66
66
66
66
66
66
66
4
0 1 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0
0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 1 0
0 0 0 0 0 0 0 0 1
3
77
77
77
77
77
77
77
5
(4.5)
17
Equations (4.6) describe B and U from Equation (4.3).
B =
2
66
66
66
66
66
66
66
4
0 0 0
1 0 0
0 0 0
0 1 0
0 0 0
0 0 1
3
77
77
77
77
77
77
77
5
U =
2
66
66
4
 x
 y
 z
3
77
77
5
(4.6)
Here, the x, y, and z directions correspond with a East, North, and Up coordinate
system.
4.3 Target Dynamics
In the present research, the target?s motion was assumed to follow a constant
velocity trajectory. The  lter state, X, includes the three-dimensional vector location
and velocity for the target in world coordinates as shown in Equation (4.7).
X =
2
66
66
66
66
66
66
66
4
x
_x
y
_y
z
_z
3
77
77
77
77
77
77
77
5
(4.7)
18
The state transition matrix for the target?s motion is shown in Equation (4.8).
 =
2
66
66
66
66
66
66
66
4
1 dt 0 0 0 0
0 1 0 0 0 0
0 0 1 dt 0 0
0 0 0 1 0 0
0 0 0 0 1 dt
0 0 0 0 0 1
3
77
77
77
77
77
77
77
5
(4.8)
4.4 Iterative EKF
To estimate the position of potentially con icting tra c, a Kalman  lter based
state estimator was developed. The Kalman  lter is a set of mathematical equations
that provide an e cient computational (recursive) means to estimate the state of
a process, in a way that minimizes the mean of the squared error [25]. Since a
Kalman  lter addresses the general problem of estimating the state of a discrete-time
controlled process that is governed by a linear stochastic di erence equation and our
measurements are non-linear some modi cations had to be made. A Kalman  lter
that linearizes about the current mean and covariance is referred to as an extended
Kalman  lter or EKF [25].
For this work, an iterative EKF was developed to accept the azimuth and ele-
vation measurements generated and estimate the state of the target from those mea-
surements. The iterated EKF is the same as the EKF with the addition of a tolerance
on the state estimation. The  lter iterates the state estimate until the speci ed error
tolerance between the projected estimate of the state and the  lter state estimate is
reached.
19
The measurements are generated each time step by  rst calculating the true
azimuth and elevation from the known position of both the measurement platforms
and the true  ight track of the target. Zero-mean, Gaussian pseudorandom noise
with a standard deviation, r, of 14 was then added to each of the measurements
to simulate measurement uncertainty. This value corresponds to an error in target
detection of three pixels in the camera FOV. Equations (4.9) show how the azimuth
and elevation measurements, Azmeas and Elmeas, for each platform are calculated. For
the performed simulations presented later, the FOV for each sensor was unlimited.
Azmeasmp1 = Aztruemp1 +r randn
Elmeasmp1 = Eltruemp1 +r randn
Azmeasmp2 = Aztruemp2 +r randn
Elmeasmp2 = Eltruemp2 +r randn
(4.9)
Estimating the state with a Kalman  lter occurs in two steps. First, the  lter
projects the current state and error covariance forward in time. This is known as
the \time update." Equations (4.10) are the time update equations for the state and
error covariance.
X k =  Xk 1
P k =  Pk 1 T +Q
(4.10)
Next, feedback on the estimate is obtained through measurements. The previously
correlated measurements of azimuth and elevation from each platform are incorpo-
rated into the projected state estimate to obtain an improved estimate. This second
portion of the  lter is known as the \measurement update." Equations (4.11) are the
20
measurement update equations.
K = P k HT  HP k HT +R  1
Pk = (I KH)P k
Xk = X k +PkHTR 1 (zk h)
(4.11)
Process or plant noise, Q, was added to the error covariance, P k , to allow for
minor disturbances in position and velocity as well as to allow the estimator to adapt
to target maneuvers. The amount of process noise needed depends on the convergence
rate of the estimated state to the value of the true state. The process noise can be
increased slightly to speed up the convergence rate. There is a limit, however, on the
amount of noise added. Too much process noise can cause oscillations in the state
estimate and the estimate will never fully converge to the actual value.
The updated state estimate and error covariance in Equation (4.11) include the
Kalman gain, K, as well as H which relates the state to the measurement, z. For the
EKF, H is the Jacobian matrix of partial derivatives of h with respect to the state
as shown in Equation (4.12).
H[i;j] = @h[i]@x
[j]
( ~xk;0) (4.12)
Equation (4.13) represents h, or the measurements of azimuth, Az, and elevation, El,
from each of the two measurement platforms.
h =
2
66
66
66
64
Azmp1
Elmp1
Azmp2
Elmp2
3
77
77
77
75
(4.13)
21
where
Azmp1 = tan 1 x xpltfm1y y
pltfm1
Elmp1 = tan 1 z zpltfm1Rg1
Azmp1 = tan 1 x xpltfm2y y
pltfm2
Elmp1 = tan 1 z zpltfm2Rg2
(4.14)
and
Rg1 =
q
(x xpltfm1) + (y ypltfm1)
Rg2 =
q
(x xpltfm2) + (y ypltfm2)
(4.15)
R in the measurement update equations is the measurement noise covariance
matrix derived from the estimated position and orientation uncertainty of the mea-
surement platforms used in the measurement model. Equation (4.16) represents the
measurement noise covariance matrix, R where r is the same as in Equations (4.9)
above.
R =
2
66
66
66
64
r2 0 0 0
0 r2 0 0
0 0 r2 0
0 0 0 r2
3
77
77
77
75
(4.16)
In the SAA system, each target in the FOR of the measurement platforms was
assigned a separate  lter. Each  lter was initialized based on the measurements of
azimuth and elevation to that target as well as the known location of both measure-
ment UASs. Each target?s  lter received the same initial conditions for velocity and
error covariance. The initial velocity estimate was set to zero and the initial error
22
covariance was set high so that the  lter would rely more on the measurements than
the initial state estimate for the  rst  lter iteration.
4.5 Area of Uncertainty
In addition to the state estimate for each target in the UAS?s FOR, the area of
uncertainty for the estimate was calculated along the target?s estimated  ight track.
This was accomplished through the error covariance matrix that was calculated in
the EKF. The error covariance matrix that was output by the EKF was a 6 6
matrix that described how the state variables in uenced each other. Equation (4.17)
represents the error covariance matrix.
P =
2
66
66
66
66
66
66
66
4
 2x  x_x  xy  x_y  xz  x_z
 _xx  2_x  _xy  _x_y  _xz  _x_z
 yx  y_x  2y  y_y  yz  y_z
 _yx  _y_x  _yy  2_y  _yz  _y_z
 zx  z_x  zy  z_y  2z  z_z
 _zx  _z_x  _zy  _z_y  _zz  2_z
3
77
77
77
77
77
77
77
5
(4.17)
The error covariance matrix can be broken up into three 2 2 matrices, rep-
resented by Equations (4.18), where each one describes the area of uncertainty in a
23
separate two-dimensional coordinate frame.
Pxy =
2
64  2x  xy
 yx  2y
3
75
Pxz =
2
64  2x  xz
 zx  2z
3
75
Pyz =
2
64  2y  yz
 zy  2z
3
75
(4.18)
The area of uncertainty is the area inside an error ellipse that is centered at
the target location estimate. Therefore, to calculate the area of uncertainty, the
composition of an ellipse must be understood. Every ellipse is de ned by two axes, a
semi-major axis and a semi-minor axis. The two things that are needed to determine
the size of an ellipse are the magnitude and direction of each axis. To obtain these
values, the eigenvectors and eigenvalues for each of the 2 2 error covariance matrices
in Equations (4.18) were calculated. The eigenvectors specify the direction of the
ellipse axes while the square roots of the eigenvalues give the magnitude.
All error ellipses have an associated con dence factor. The con dence bound for
the area of uncertainty in the SAA system was set to 74% due to the two variables
with which each ellipse was plotted. This con dence bound describes the probability
that the true position of the target will be located in the con dence area and was
used for visualization of the  lter estimate. Since the measurements are assumed to
contain Gaussian noise with zero-mean, the con dence factor for the error ellipses
was determined by using a standard normal distribution table. Figure 4.3 illustrates
24
a Gaussian probability density function (PDF) for a single variable with a 90% con-
 dence region and the con dence factor of 1.645. For two variables, this con dence
factor relates to a 74% con dence region.
Figure 4.3: Gaussian PDF With 90% Con dence Region.
4.6 Time to Closest Approach
For each target being tracked, their time to closest approach, tca, was calculated.
The time to closest approach is the time at which the tra c would be within min-
imum range if the speed and heading of both the platforms and the target remain
constant. The  rst step in this calculation is to  nd the relative position vector from
the measurement UASs to each target at an arbitrary time, t. The relative position
vector,  !r , is de ned as the di erence between the position vector to the measure-
ment platform UASs in world coordinates,  !rp, and the position vector to the target
in world coordinates,  !rt , and is shown in Equation (4.19).
 !r = !rp   !rt (4.19)
25
Equations (4.20) and (4.21) describe the position vector to the measurement plat-
forms and the position vector to the target respectively.
 !rp = !rp0 + !vpt (4.20)
 !rt = !rt0 + !vtt (4.21)
To solve for the time to closest approach, the magnitude of the relative position
vector, j !rj, must be di erentiated with respect to time, t, and set equal to zero as
in Equation (4.22). With the magnitude of the relative position vector, the time
to closest approach is represented as a function of measurement platform position
and velocity as well as the position and velocity of the target as can be seen in
Equation (4.23).
@j !rj
@t = 0 (4.22)
tca =  (
 !vp  !vt ) ( !rp   !rt )
j !vp  !vtj2 (4.23)
4.7 Platform Positioning Controller
Once the optimal location of each aircraft for taking measurements is known from
Equation (4.2) as well as a con ict resolution heading discussed in the next chapter,
a PID controller is used to maneuver the aircraft to that location. The two aircraft in
the system are each assigned a controller. A block diagram of the platform controller
is shown in Figure 4.4
A PID controller corrects errors between a measured process variable, in this
case the location of the aircraft, and a desired variable, where the aircraft needs to
26
Figure 4.4: Block Diagram of Measurement Platform Controller.
be to take optimal measurements, by outputting a corrective action. The controller
has three elements that determine the corrective action. A block diagram of a PID
controller is shown in Figure 4.5 where t here represents time. A brief description
of each element, or block in the illustration, of the controller accompanies the  gure
[26].
Figure 4.5: Block Diagram of PID Controller.
(P) Proportional Block: The proportional block of the controller determines the
reaction of the process to the current error, e. In this case, the error is the dis-
tance between where the aircraft is and where it needs to be. Kp in Figure 4.5 is
the proportional gain. The proportional block makes a change to the controller
output that is proportional to the current error value.
27
(I) Integral Block: The integral block of the controller determines the process? re-
action based on the summation of recent errors. The integral block is used to
add long-term precision to the controller. Ki in Figure 4.5 is the integral gain.
The integral term, when added to the proportional term, eliminates the residual
steady-state error associated with a proportional only controller. The output
from the integral block is proportional to both the magnitude of the error and
the duration of the error.
(D) Derivative Block: The derivative block determines the reaction of the process
based on the rate at which the error has been changing. The derivative term
accelerates the rate of change of the controller output. Kd in Figure 4.5 is the
derivative gain.
The corrective output from the PID controller for each aircraft is a sequence
of acceleration commands that should maneuver the aircraft to the desired location.
The controller up-date rate was 30 Hertz. Each time step, the current position as
well as the desired position from Equation (4.2) was known. The di erence between
the two values was the error in the controller.
The acceleration values in the controller were limited by maximum and mini-
mum values to simulate the desired  ight characteristics of the measurement aircraft.
Assuming the platforms are traveling East, the longitudinal acceleration limits, in the
direction of the velocity, were determined by the speci c excess power, SEP, which
is the di erence between the power available and the power required for the aircraft.
The lateral acceleration limits, in the Y direction assuming an Easterly heading, were
determined by the maximum rate of turn for the aircraft, ROTmax, as well as the sep-
aration distance, sepdist, between the two measurement aircraft. Equations (4.24)
show how each of these limits were calculated. Vc is the measurement platform cruise
28
speed and g is the acceleration of gravity.
 xmax = SEP gV
c
 xmin = Xaccmax
 ymax = sepdist2 ROT2max
 ymin = Yaccmax
(4.24)
Another limit in the controller was on the integrator state. To keep the inte-
grator state from growing or shrinking to very large values, maximum and minimum
bounds on the error summation were incorporated. When the integrator state, the
error summation, gets large it results in integrator windup. In an integrator windup
situation, the controller plant would have reached the target, but the integrator value
would still be large. The integral block would then cause the output to go beyond
the desired value while the integrator unwinds and the process reverses.
In order to insure that the controller would give a stable output, the controller
gains, Kp, Ki, and Kd, had to be \tuned." There are several methods for tuning a PID
controller. The method chosen is known as the Ziegler-Nichols method introduced by
John G. Ziegler and Nathaniel B. Nichols [26]. This method was chosen because it is
a proven and accurate means for determining controller gains. First, the integral and
derivative gains are set to zero so that the controller only consists of the proportional
block. Then, through iterations with the  lter, the proportional gain is increased
until it reaches the critical gain, Kc. With this gain in the proportional block only,
the output of the controller causes the aircraft?s position to oscillate. The method
then describes the controller gains as functions of the critical gain and the oscillation
period, Pc. Equation (4.25) shows how the controller gains are functions of the critical
29
gain and the oscillation period.
Kp = 0:6Kc
Ki = 2KpP
c
Kd = KpPc8
(4.25)
For this system the critical gain was found to be two and the corresponding oscillation
period was 100 seconds. With these values the gains were set to 1.2, 0.024, and 15
for the proportional gain, Kp, the integral gain, Ki, and the derivative gain, Kd
respectively.
30
Chapter 5
Conflict Resolution
The purpose for this SAA system is to give UASs decon iction ability while
operating in the NAS. For UASs, one problem comes with their interaction with
human pilots. A collision avoidance algorithm, while it may meet certain separation
criteria, could give human pilots uncertainty as to when, how, or even if the UAS
is going to respond to a tra c con ict. With a con ict resolution algorithm, that
uncertainty can be minimized by performing a resolution maneuver well before the
con icting tra c is at it?s minimum separation distance.
For this system, a geometric approach to con ict resolution was employed. Pa-
pers by K. Bilimoria and R. Paielli review the literature on this topic and present
useful results [27, 28]. The method described by R. Bach et al. for level aircraft
con ict resolution was incorporated for con ict detection and resolution [29]. The
decon iction algorithm makes adjustments to the measurement platform?s heading
to resolve con icts with other air tra c as they are detected. The algorithm cre-
ated di ers from the one mentioned above in the method used to determine if the
tra c is no longer a con ict. In Bach?s paper a distance and time to turn back are
calculated. For this work, the geometry was used to determine if the tra c was no
longer a con ict. Once it was determined that the tra c was no longer a con ict, the
measurement platforms were commanded to return to their original  ight path and
heading by an intercept angle that was determined from the distance the platforms
deviated.
31
5.1 Con ict Geometry
To de ne the con ict geometry, a circle with radius equal to that of the minimum
allowable separation distance is  rst created around the tra c in question. For this
work the minimum allowable separation distance was set to 1000 feet which exceeds
the AIM?s de nition of avoiding a near midair collision. This radius, Rms, along with
the speed and heading for each aircraft and the range to the tra c, S0, describe the
geometry as shown in Figure 5.1 where A is the center of the measurement platforms
and B is the tra c. C in the  gure depicts the corner of the velocity triangle of the
measurement platforms and the con icting tra c. In the world coordinate system in
the  gure, the x-axis is de ned as East and the y-axis is North.
Figure 5.1: Geometry for Level Con ict Scenario [29].
From the EKF mentioned in Section (4.4) the estimated position and velocity
of the tra c is known. This information gives the range to the target as well as
the target heading. The angle  between the dashed lines tangent to the minimum
32
separation circle and the range vector was calculated from Equation (5.1) [29].
 = sin 1
 R
ms
S0
 
(5.1)
The angle  between the range vector and the relative velocity vector was calculated
using Equation (5.2)
 =  r  0 (5.2)
where  r was the relative heading of the tra c found from Equation (5.3) and  0
was the bearing to the tra c found from Equation (5.4).
 r = tan 1
 V
Ax VBx
VAy  VBy
 
(5.3)
 0 = tan 1
 Pos
Bx PosAx
PosBy  PosAy
 
(5.4)
A con ict exists if j j is less than  . This condition means that the relative
velocity vector is inside of the con ict zone as de ned by the dashed lines. If a
con ict exists, a new heading for the platforms was calculated to move the relative
velocity vector outside of the con ict zone. Every time-step through the simulation,
this new heading was adjusted to compensate for any changes in the tra c velocity.
5.2 Resolution Heading
A resolution heading for the platforms is one that would rotate the relative
velocity vector by an angle  outside of the con ict zone. Equation (5.5) was used
to calculate the needed rotation angle [29]. To  nd this new heading, a comparison
between the speed of the platforms and the speed of the tra c was needed. If the
33
speed of the platforms is greater than that of the tra c, then there will be two
possibilities for a resolution heading. Figure 5.2 depicts the two solutions as a counter
clockwise rotation of VA about point C to point c and a clockwise rotation of VA about
point C to point e by angles  c and  e respectively.
 =    (5.5)
Figure 5.2: Heading Changes to Resolve Con ict (VA >VB) [29].
If the speed of the platforms is less than that of the tra c, then there will be
four possibilities for a resolution heading. There will be two solutions that correspond
to the upper dashed tangent line and two that correspond to the lower tangent line.
Figure 5.3 depicts the four solutions as a counter clockwise rotation of VA about point
C to point c1 or point c2 by angles  c1 and  c2 respectively and a clockwise rotation
of VA about point C to point e1 or point e2 by angles  e1 and  e2 respectively.
34
Figure 5.3: Heading Changes to Resolve Con ict (VA <VB) [29].
In the case where the speed of the platforms is less than the speed of the traf-
 c, a limiting condition exists on the rotation angle of the relative velocity vector
 . Figure 5.4 shows the limit for two solutions to occur. Since both resolution vec-
tors are tangent to the circle of radius jVAj, trigonometry can be used to determine
the maximum and minimum rotation angles that will allow two solutions to occur.
Equation (5.6) describes the maximum and minimum possible rotation angles [29].
 max =  B  R +  sin 1
 V
A
VB
 
 min =  B  R  + sin 1
 V
A
VB
 (5.6)
35
Figure 5.4: Limiting Case for Two Solutions (VA <VB) [29].
36
Once the possible rotation angles are obtained the resolved relative heading,   R,
is calculated using Equation (5.7) for n number of possible angles.
  R (n) =  R + (n) (5.7)
The resolved heading for the platforms is then determined by the minimum heading
change needed. The possible headings to resolve the con ict are given by Equa-
tion (5.8) for n number of possible angles [29].
  A (n) =   R (n) + sin 1
  V
B
VA
 
sin ( B   R (n))
 
(5.8)
For the case when the platform speed is less than the tra c two solutions will exist
for each rotation angle  . The  rst solution is given by Equation (5.8) and the second
is given by Equation (5.9) for each  [29].
  A (n) =   R (n) sin 1
  V
B
VA
 
sin ( B   R (n))
 
+ (5.9)
Once all of the possible resolved headings were calculated, the heading that
required the least amount of maneuvering was selected.
5.3 Return to Initial Flight Path
If it was determined that no tra c con ict existed and the platform UASs were
both on their original  ight paths, no heading change occurred. If the UASs had
changed their heading to avoid a tra c con ict, but no con ict currently existed the
platforms needed to maneuver themselves back to their original paths. A function was
created to generate the heading needed to return to the initial  ight path assuming the
37
measurement platforms were traveling East. Equation (5.10) determined the heading
in degrees for the turn-back maneuver if the platforms maneuvered North to resolve
the con ict. Equation (5.11) determined the heading in degrees for the turn-back
maneuver if the platforms maneuvered South to resolve the con ict. Both equations
are functions of the center position of the platforms as well as the initial heading.
In the equations, Centery0 is the Y location in world coordinates of the center of
the platform formation before the resolution maneuver and Centery is the current Y
location of the formation center.
 TBmN =  initial + min(Centery Centery0;2nm)2nm 30 (5.10)
 TBmS =  initial + max(Centery Centery0; 2nm)2nm 30 (5.11)
The equations above both allow for a 30 intercept angle if the platform UASs
have traversed more than two nautical miles (nm) in the North or South direction to
resolve the con ict. If they did not move more than two nautical miles away from
their original  ight path a smaller intercept angle is applied.
5.4 Resolution Heading Maneuvering
The platform heading was changed using the same PID controller as described in
Section (4.7) while simultaneously changing the aop described in Section (4.1). The
corrective output from the PID controller for each aircraft was the acceleration values
that would maneuver the aircraft to the desired heading as well as the desired angle
for measurement acquisition. The up-date rate for the platform heading controller
was also 30 Hertz. Each time step, the position based o of the current velocity was
38
known as well as the position based o of the desired velocity. The di erence between
the two values was incorporated into the error in the controller.
39
Chapter 6
System Implementation
To implement the SAA system described in this thesis, three main components
would be needed. The  rst piece of hardware needed to implement the system on a
UAS is optical sensors. Along with sensors, a target recognition algorithm to detect
a target from a digital image is needed. Finally, to run all of the computations, an
onboard computer and the wireless capability to transmit and receive data at a high
rate is needed.
6.1 Optical Sensors
The sensor selection for the application should begin with the resolution require-
ments as well as the video capture rate. Given the size of likely threats, approximately
four feet across for head-on cases, the range of three nautical miles when a target needs
to be detected, and the size of the  eld of view described in Section (1.2), a camera
with at least 1042 pixels in the horizontal plane and a capture rate of 30 frames
per second is needed for this application. Equation (6.1) illustrates how the num-
ber of pixels, NoP, was determined. The recommended instantaneous  eld of view
per pixel, IFOVPP, from Section (1.1) of 1.34 milliradians and a horizontal  eld of
regard, HFOR, of 240 or 43 rad was used.
NoP = HFOR3 1IFOVPP (6.1)
40
Optical cameras such as the Creative Live Cam Notebook Ultra and the Microsoft
LifeCam VX-6000 would provide adequate resolution and capture rate at a low cost.
Both of these cameras have USB interfaces for connectivity to a computer.
6.2 Target Recognition
The SAA system needs a target recognition algorithm to detect a target in the
digital image taken by the sensors. The algorithm must compute azimuth and ele-
vation measurements to the target once it is detected. These measurements must be
corrected for the bank and pitch angles of the measurement platform. A few examples
of vision based tracking and target estimation methods accomplished by others are
available in the literature [11, 12, 13, 14, 15].
6.3 Computational Processing
The SAA method described requires moderate computational power. The air-
craft in the system must be able to communicate with each other as well as run the
system algorithms. The computational process for the system could be handled by
an onboard computer or a land based computer that communicates with the air-
craft through wireless transmission. Dennis et al. employed a custom computation
engine based on  eld-programmable gate array technology for onboard vision process-
ing [11]. The problem with land based computers comes from the data transfer rate
capabilities as well as communication range. Many UASs currently being operated
are commanded from a land based computer, so there is a possibility the SAA system
algorithms could be implemented on a ground station.
For onboard processing the Gumstix Verdex Pro XM4 could be used in combi-
nation with the ConsoleLCD-vx for connectivity. This processing board is equipped
41
with a Marvelltm processor and 64 megabytes of random access memory. It also has
16 megabytes of  ash memory and a micro SD card adapter. To handle communica-
tions, a Maxstream XT09-SI radio modem with interface board could be used. This
modem has an outdoor line of sight range capability of 40 miles and operates at a
frequency of 900 megahertz.
6.4 Weight Analysis
Weight considerations need to be made when deciding on the sensors to incorpo-
rate as well as the computational processing method chosen to increase the payload
capability of the UAS the system is implemented on. Large onboard computers add
signi cant weight to the SAA system total. The Helios board used in the onboard
system mentioned above only weighs 36 grams or approximately 1.3 ounces. Both
of the camera types mentioned as possible optical sensors weigh approximately 3.2
ounces each. Table 6.1 is a list of needed hardware and the component weights as
well as the size and power required for each. Table 6.2 is a list of the total weight
and total power required for the system.
Table 6.1: Hardware Component Speci cations.
42
Table 6.2: Total System Weight and Power Required.
43
Chapter 7
Results
Each of the twelve simulation cases presented were run on Dell Optiplex 755
machines equipped with Intel Core 2 Duo processors operating at 2.2 gigahertz with
two gigabytes of random access memory. Monte Carlo simulations consisting of 1000
iterations were used for each scenario that simulated six minutes in time. Monte Carlo
simulations were used to account for the random measurement noise associated with
the measurement model. System comparisons were made with and without con ict
resolution to show the advantages of the optimal measurement controller. Two main
alternative systems were generated to determine di erences in the range estimate, the
distance with which the platforms avoided the tra c, in the case when the con ict
resolution controller was activated, and the total distance traveled by each UAS in the
system. In the comparison simulations for each system the  lter was initialized based
on the true range to the target. The e ect of platform separation distance was also
determined by varying the measurement platform spacing in two simulations by 500
feet. Also, the UAS performance parameters of speci c excess power and maximum
rate of turn were varied to determine their e ect on the con ict resolution controller
and the range estimate. For all of the varying parameter simulations, the  lter was
initialized based on the initial measurements. Lastly, two simulations were run with
varying target scenarios to determine the reliability of the system. Table 7.1 lists the
speci c parameters for each simulation.
44
Table 7.1: Speci c Simulation Parameters.
45
7.1 Alternative Systems
The  rst alternative considered was of three measurement platforms  ying in a
 xed formation. Three platforms were used in order to ensure at least two platforms
would be able to take measurements on the tra c at all convergence angles. Mea-
surements from two platforms are needed so that some sort of range information can
be deduced. Figure 7.1 illustrates the three platform formation.
Figure 7.1: Three Platform Formation.
The second alternative considered was of two measurement platforms  ying in
a formation that rotated constantly about it?s center at an angular velocity of 90
deg/min. Rotating constantly allowed the two UASs to gather range information on
46
tra c at all convergence angles at various time intervals. Figure 7.2 illustrates the
constantly rotating two platform formation.
Figure 7.2: Constantly Rotating Two Platform Formation.
7.2 Comparison Target Scenario
To keep the comparison between systems equivalent, the same number of targets
and the same target  ight tracks were used for each scenario simulated. Figure 7.3
illustrates a top view of the scenario. Similar to several  gures in the remainder of the
chapter, the platforms are depicted in blue and the tra c is in red. The platforms
had a heading of 090 and a speed of 100 knots. Air tra c approached the  ight
path of the platforms at various angles. The  rst target started 500 feet East of the
platforms and  ve miles North at a speed of 140 knots with a heading of 135 . The
second target originated 10 miles East of the platforms and 12 miles North at a speed
47
of 145 knots with a heading of 225 . The third target originated 17 miles East of
the platforms and nine miles South at a speed of 120 knots with a heading of 315 .
The  nal target originated 500 feet West of the platforms and seven miles South at
a speed of 145 knots with a heading of 045 .
Figure 7.3: Comparison Scenario; Y-Axis Points North.
7.3 Comparison Without Con ict Resolution
A comparison was made between the three formation types without con ict reso-
lution to determine the penalty for maneuvering to take optimal measurements. The
average percent error in the estimated range was calculated after all of the Monte
Carlo iterations. The average percent di erence in excess distance traveled was also
computed for each of the cases. For each of the systems, the error starts at zero
48
because it is initialized with the true range. The velocity however, is initialized to
zero so the range error grows until the  lter is able to estimate velocity accurately.
7.3.1 Range Error
For the system with two measurement platforms maneuvering to take optimal
measurements, Figure 7.4 depicts the averages and standard deviations of the es-
timated range error for each of the four targets after 1000 Monte Carlo iterations.
The maximum average error for targets one and four occurred within the  rst few
seconds of simulation. Targets one and four were the two targets that the controller
was maneuvering toward to take optimal measurements. After the  rst spike in error
for both of these targets, the range estimate error decreased rapidly. The location of
minimum range error for targets one and four reveal the time of closest approach for
each of the respective targets.
For the system with three measurement platforms  ying in a  xed formation to
take measurements, Figure 7.5 depicts the averages and standard deviations of the
estimated range error for each of the four targets. The maximum average error for
target one again occurred during  lter initialization. The maximum error for target
four resembled that from target one. This was due to the formation being symmetrical
and the two target tracks closely resembling each other at di erent headings. Again,
the location of minimum range error for targets one and four reveal the time of closest
approach for each of the respective targets.
For the system with two measurement platforms constantly orbiting the center of
their formation to take optimal measurements, Figure 7.6 depicts the averages of the
estimated range error for each of the targets. For each of the targets the oscillation
in the range estimate from the orbiting platforms was exhibited. The error then
gradually decreased throughout the simulation. The range error plots of target one
49
Figure 7.4: Average Range Error (Blue Line) and Standard Deviation (Red Line) for
System 1.
50
Figure 7.5: Average Range Error (Blue Line) and Standard Deviation (Red Line) for
System 2.
51
and four again reveal the time of closest approach of 180 and 250 seconds respectively.
Figure 7.6: Average Range Error (Blue Line) and Standard Deviation (Red Line) for
System 3.
Table 7.2 summarizes the range error comparison without con ict resolution. The
optimal maneuvering formation and the orbiting formation had comparable estimates
for each of the targets.
The range error plots for the  rst two cases, optimal measurement maneuver-
ing and three platforms, are similar after the  lter is initialized and the platforms
52
Table 7.2: Summary of Range Error Plots without Con ict Resolution.
maneuver to obtain the best measurements. The only di erence in range error for
these two cases comes from the maximum error. With the three platform case there
is no convergence angle in the FOR to prevent the platforms from obtaining range
information. Therefore, as soon as a target is detected accurate range information
can be obtained. With the optimal maneuvering case however, there is a time lag
between when the target is detected and when accurate range information can be
deduced. This time lag comes from the maneuvering time for the UASs to reposition
themselves. For each of the targets, it was during this maneuvering time that the
error peaked. Once repositioned, the range estimates decreased.
With the orbiting formation, the range error throughout the simulation varies
greatly. Since the orbiting platforms are unable to obtain optimal measurements for
more than a short period of time, an oscillation in the range error occurs. As the
platforms orbit into a position to take optimal measurements, the range error becomes
less. As they orbit away from this position, the range error grows. This happens with
each half orbit of the platforms. The overall divergence in the range error for the
53
orbiting case comes from the time history of measurements and position estimates
from the EKF.
Figure 7.7 depicts the averages of the estimated range error for each of the targets.
The di erences from system one, the optimal maneuvering formation, from the other
systems comes from the initial  lter estimate in each of the simulations. For target
one, the time range of concern is from 75 to 175 seconds. For target two, the time
of concern is between 175 and 325 seconds. For targets three and four the time of
concern is between 225 and 360 seconds.
7.3.2 Excess Distance Traveled
For the system with two measurement platforms maneuvering to take optimal
measurements, Table 7.3 summarizes the average percent di erence in distance trav-
eled for both measurement platforms as well as the corresponding standard deviations.
Table 7.3: Average Excess Distance Traveled and Standard Deviation for System 1.
For the system with three measurement platforms  ying in a  xed formation to
take measurements, the average percent di erence in distance traveled for all three
measurement platforms as well as the corresponding standard deviations was zero.
This is because with this system the UASs only travel from their initial position to
their  nal position. Since the formation contains three aircraft, the UASs do not have
to maneuver to take measurements.
54
(a) Target 1. (b) Target 2.
(c) Target 3. (d) Target 4.
Figure 7.7: Average Range Error Comparison.
55
For the system with two measurement platforms constantly orbiting the center
of their formation to take optimal measurements, Table 7.4 summarizes the average
percent di erence in distance traveled for both measurement platforms as well as the
corresponding standard deviations. On average, platform one traveled 0.24% farther
than the straight line distance between its initial and  nal positions. Platform two
traveled an average of 0.25% farther.
Table 7.4: Average Excess Distance Traveled and Standard Deviation for System 3.
After examining the excess-distance data from the comparison without con ict
resolution it was determined that the penalty for maneuvering to take optimal mea-
surements was minuscule. The excess distance traveled was around 0.2%. The excess
distance incurred when the platforms constantly orbit the center of the formation was
slightly higher at around 0.25%. While the three platform formation had no excess
distance, the required use of another aircraft eliminates any gain from a decrease in
excess distance. It could be argued that the excess distance for this formation was
actually the entire distance traveled by the third aircraft.
7.4 Con ict Resolution Algorithm Veri cation
Before a comparison was made using con ict resolution, the resolution heading
algorithm was veri ed. This was done by running the optimal measurement maneu-
vering formation in 16 di erent simulations. For each simulation, the collision point
was set to occur three nautical miles from the platform starting location. For the
56
 rst eight simulations, the target speed was held constant at 75 knots and the target
heading was varied from 0 to 315 by 45 increments. The target speed was set to 75
knots to verify the part of the con ict resolution algorithm used when the con icting
tra c is traveling slower than the platforms. Figure 7.8 and Figure 7.9 show the
top view of each target scenario. The con icting tra c is depicted in red and the
measurement platforms are blue. The green in each image is the area of uncertainty.
(a) 0 Target Heading. (b) 45 Target Heading.
(c) 90 Target Heading. (d) 135 Target Heading.
Figure 7.8: First Four Veri cation Target Positions Traveling at 75 knots.
For the last eight simulations, the target speed was held constant at 125 knots
and the target heading was again varied from 0 to 315 by 45 increments. The faster
57
(a) 180 Target Heading. (b) 225 Target Heading.
(c) 270 Target Heading. (d) 315 Target Heading.
Figure 7.9: Last Four Veri cation Target Positions Traveling at 75 knots.
58
target speed was used to verify the second part of the con ict resolution algorithm
used when the con icting tra c is traveling faster than the platforms. Figure 7.10
and Figure 7.11 show the top view of each target scenario. The con icting tra c is
depicted in red and the measurement platforms are blue.
(a) 0 Target Heading. (b) 45 Target Heading.
(c) 90 Target Heading. (d) 135 Target Heading.
Figure 7.10: First Four Veri cation Target Positions Traveling at 125 knots.
Table 7.5 summarizes the miss distances for each target scenario shown above.
Since all of the miss distances were near the speci ed distance of 2000 feet, it was
concluded the con ict resolution algorithm was working properly.
59
(a) 180 Target Heading. (b) 225 Target Heading.
(c) 270 Target Heading. (d) 315 Target Heading.
Figure 7.11: Last Four Veri cation Target Positions Traveling at 125 knots.
60
Table 7.5: Miss Distances for Veri cation Targets.
7.5 Comparison With Con ict Resolution
A comparison was made between the three systems with con ict resolution to
determine how the proposed method of maneuvering to take optimal measurements
performs. The average percent error in the estimated range was calculated after all of
the Monte Carlo simulations. The average miss distance, the distance with which the
platforms avoided the tra c, was also calculated along with the standard deviation.
The miss distance was measured from the formation center. In order to prevent a near
midair collision, the miss distance must be greater than half of the separation distance
plus 500 feet. For the proposed system, this means the miss distance must be greater
than 1000 feet. To compensate for measurement noise and to ensure a near miss did
not occur, the minimum miss distance used by the con ict resolution algorithm was
set to 2000 feet for each of the simulations. The average percent di erence of excess
distance traveled was also computed for each of the cases.
61
7.5.1 Range Error
For the system with two measurement platforms maneuvering to take optimal
measurements, Figure 7.12 depicts the averages and standard deviations of the esti-
mated range error for each of the four targets. The maximum average error for targets
one and four again occurred within the  rst few seconds of the simulation while the
 lter was unable to accurately estimate the target velocity. After the  rst minute of
simulation, the error in the range estimate for targets one and four, the closer of the
four targets, decreased.
For the system with three measurement platforms  ying in a  xed formation
to take measurements, Figure 7.13 depicts the averages of the estimated range error
for each target. The relation in error for targets one and four is again due to the
formation being symmetrical and the two target tracks closely resembling each other
at di erent headings. After the  rst spike in error for targets two and three, the range
estimates gradually decreased as time progressed in the simulation.
For the system with two measurement platforms constantly orbiting the center
of their formation to take optimal measurements, Figure 7.14 depicts the averages
of the estimated range error for each target. The error for target one has two other
peaks aside from the maximum value. This is from the platforms orbiting and the
quality of the measurements changing with time. The average error for target two
gradually decreased as the time history going into the  lter increased. With each of
the targets, the oscillating measurement quality due to the orbiting of the platforms
is exhibited.
Table 7.6 summarizes the range error comparison with con ict resolution. Both
the optimal maneuvering and orbiting formations had similar minimum estimated
range error for targets one and four.
62
Figure 7.12: Average Range Error (Blue Line) and Standard Deviation (Red Line)
with Con ict Resolution for System 1.
63
Figure 7.13: Average Range Error (Blue Line) and Standard Deviation (Red Line)
with Con ict Resolution for System 2.
64
Figure 7.14: Average Range Error (Blue Line) and Standard Deviation (Red Line)
with Con ict Resolution for System 3.
65
Table 7.6: Summary of Range Error Plots with Con ict Resolution.
The range error plots for each of the comparison formation types with con ict
resolution capability look similar to the range error plots obtained when the forma-
tions did not posses the ability to resolve tra c con icts. This suggests the con ict
resolution controller does not a ect the ability to obtain an accurate range estimate.
The three platform formation still provided a better range estimate initially, but,
given the time to maneuver, the optimal maneuvering formation produced range er-
ror values that closely compared for targets one and four. The increased error for the
orbiting formation again suggests that this formation is not the optimal solution.
Figure 7.15 depicts the averages of the estimated range error for each of the
targets. The di erences from system one, the optimal maneuvering formation, from
the three platform formation again comes from the better initial  lter estimate in
each of the simulations. For target one, the time range of concern is from 75 to 175
seconds. For target two, the time of concern is between 175 and 325 seconds. For
targets three and four the time of concern is between 225 and 360 seconds.
66
(a) Target 1. (b) Target 2.
(c) Target 3. (d) Target 4.
Figure 7.15: Average Range Error Comparison with Con ict Resolution.
67
7.5.2 Excess Distance Traveled and Miss Distance
For the system with two measurement platforms maneuvering to take optimal
measurements, Table 7.7 summarizes the average percent di erence in distance trav-
eled for both measurement platforms as well as the corresponding standard deviations.
Table 7.8 lists the average miss distance for each target along with the correspond-
ing standard deviations. On average, platform one traveled 1.5% farther than the
straight line distance between its initial and  nal positions. Platform two traveled an
average of 1.09% farther. Approximately 45 of the excess distance traveled was from
the con ict resolution.
Table 7.7: Average Excess Distance Traveled and Standard Deviation for System 1
with Con ict Resolution.
Table 7.8: Average and Minimum Miss Distances and Standard Deviations for System
1 with Con ict Resolution.
For the system with three measurement platforms  ying in a  xed formation to
take measurements, the average percent di erence in distance traveled for all three
measurement platforms was 0.258%. This is because with this system the UASs travel
in the same formation throughout the  ight. The excess distance only comes from
68
the con ict resolution maneuver. Table 7.9 lists the average miss distance for each
target along with the corresponding standard deviations.
Table 7.9: Average and Minimum Miss Distances and Standard Deviations for System
2 with Con ict Resolution.
For the system with two measurement platforms constantly orbiting the center
of their formation to take optimal measurements, Table 7.10 lists the average per-
cent di erence in distance traveled for both measurement platforms as well as the
corresponding standard deviations. Table 7.11 lists the average miss distance for
each target along with the corresponding standard deviations. On average, platform
one traveled 1.8% farther than the straight line distance between its initial and  nal
positions. Platform two traveled an average of 1.6% farther.
Table 7.10: Average Excess Distance Traveled and Standard Deviation for System 3
with Con ict Resolution.
When the excess distances traveled were compared the three platform formation
again had the lowest excess distance with the penalty of the added aircraft to the
formation. Comparing the miss distances for each of the formations reveals an in-
teresting discovery. The miss distances for the optimal maneuvering formation, even
69
Table 7.11: Average and Minimum Miss Distances and Standard Deviations for Sys-
tem 3 with Con ict Resolution.
with the initial spike in error, were comparable to the miss distances for the three
platform formation. For targets one and two, the optimal maneuvering formation
had the highest average miss distances of 1799 and 5340 feet as well as the highest
minimum miss distances of 1759 and 5281 feet. For targets three and four, the three
platform formation had the highest average miss distances of 7963 and 2108 feet. The
di erence in miss distance between the optimal maneuvering formation and the three
platform formation was 60 feet for target two and 20 feet for target four. The miss
distances for the orbiting formation were all comparable to the other two formations
even with the range error  uctuation.
7.6 A ect of Platform Separation Distance
To determine the a ect of separation distance on the range estimate, miss dis-
tance, and excess distance traveled, three simulations were run with the separation
distance varied by  500 feet. The only system tested was that of the one proposed
in this research with two measurement platforms maneuvering to take optimal mea-
surements. For each of these simulations, the  lter was initialized based on the initial
measurements to the target.
70
7.6.1 Range Error
For the  rst simulation the platform separation distance was set to 500 feet.
Figure 7.16 depicts the averages of the estimated range error for each target. After
the maximum average error for target one occurred, the error decreased dramatically
to less than 2.5%. The average error for target four decreased below 5% after the
 rst two minutes of the simulation.
(a) Target 1. (b) Target 2.
(c) Target 3. (d) Target 4.
Figure 7.16: Average Range Error with 500 ft. Separation Distance.
71
For the second comparison simulation (Figure 7.17), the platform separation
distance was set to 1000 feet which corresponds to the nominal value.
(a) Target 1. (b) Target 2.
(c) Target 3. (d) Target 4.
Figure 7.17: Average Range Error with 1000 ft. Separation Distance.
For the next simulation the platform separation distance was set to 1500 feet.
Figure 7.18 depicts the averages of the estimated range error for each target. For
targets one and four, the error dropped below 1% within the  rst minute of simulation.
72
(a) Target 1. (b) Target 2.
(c) Target 3. (d) Target 4.
Figure 7.18: Average Range Error with 1500 ft. Separation Distance.
73
Table 7.12 summarizes the range error comparison for varying separation dis-
tances. The formation with the smaller separation distance had larger range error
due to the degraded overall measurements when the targets were farther away. The
formation with the larger separation distance had lower maximum range error values
for each of the four targets.
Table 7.12: Summary of Range Error Plots for Varying Separation Distances.
Figure 7.19 depicts the averages of the estimated range error for each of the
separation distances. A change in the separation distance had more a ect on the
range error for targets two and three that are farther away from the platforms.
7.6.2 Excess Distance Traveled and Miss Distance
For the system with a separation distance of 500 feet, Table 7.13 summarizes
the average percent di erence in distance traveled for both measurement platforms
as well as the corresponding standard deviations. Table 7.14 lists the average miss
distance for each target along with the corresponding standard deviations. On aver-
age, platform one traveled 0.18% farther than the straight line distance between its
initial and  nal positions. Platform two traveled an average of 0.14% farther.
For the system with a separation distance of 1500 feet, Table 7.15 summarizes
the average percent di erence in distance traveled for both measurement platforms
74
(a) Target 1. (b) Target 2.
(c) Target 3. (d) Target 4.
Figure 7.19: Average Range Error Comparison with Varying Separation Distances.
Table 7.13: Average Excess Distance Traveled and Standard Deviation with a Sepa-
ration Distance of 500 ft.
75
Table 7.14: Average and Minimum Miss Distances and Standard Deviations with a
Separation Distance of 500 ft.
as well as the corresponding standard deviations. Table 7.16 lists the average miss
distance for each target along with the corresponding standard deviations. On aver-
age, platform one traveled 0.44% farther than the straight line distance between its
initial and  nal positions. Platform two traveled an average of 0.82% farther.
Table 7.15: Average Excess Distance Traveled and Standard Deviation with a Sepa-
ration Distance of 1500 ft.
Table 7.16: Average and Minimum Miss Distances and Standard Deviations with a
Separation Distance of 1500 ft.
With a 500 foot increase in separation distance, from 1000 to 1500 feet, the
minimum miss distances for targets two and three decreased by more than 2000 feet.
76
This was more than likely due to a change in the resolution heading caused by the
decrease in range error for each of the respective targets. With a 500 foot decrease in
separation distance, from 1000 to 500 feet, the excess distance traveled decreased. The
downside to this scenario was that the average miss distance also decreased except
for target three.
7.7 A ect of UAS Performance Parameters
To determine the a ect the UAS performance parameters have on the range esti-
mate, miss distance, and excess distance traveled, two simulations were run. The  rst
with a speci c excess power (SEP) of 500 and a maximum rate of turn (ROT) of 90
deg/min. The second with a SEP of 1500 and a maximum ROT of 270 deg/min. The
only system tested was that of the one proposed in this research with two measure-
ment platforms maneuvering to take optimal measurements. A platform separation
distance of 1000 feet and a miss distance of 2000 feet were used for each simulation.
For each of these simulations, the  lter was initialized based on the initial measure-
ments to the target.
7.7.1 Range Error
For the  rst simulation, Figure 7.20 depicts the averages of the estimated range
error for each target. For targets one and four, after the maximum average range
error occurred, the error dropped below 5% within the  rst minute of simulation.
The simulation with the SEP and maximum ROT set to 1000 ft/min and 180
deg/min respectively, was previously presented in Figure 7.17 and represents the
nominal performance parameters. For the next simulation the SEP and maximum
ROT was set to 1500 ft/min and 270 deg/min respectively. Figure 7.21 depicts the
77
(a) Target 1. (b) Target 2.
(c) Target 3. (d) Target 4.
Figure 7.20: Average Range Error with SEP of 500; ROT of 90 deg/min.
78
averages of the estimated range error for each target. For targets one and four, the
range error promptly dropped below 5% within the  rst 50 seconds of simulation.
(a) Target 1. (b) Target 2.
(c) Target 3. (d) Target 4.
Figure 7.21: Average Range Error with SEP of 1500; ROT of 270 deg/min.
Table 7.17 summarizes the range error comparison for varying UAS performance
parameters. Surprisingly, the performance parameters had little e ect on the overall
range estimates.
79
Table 7.17: Summary of Range Error Plots for Varying UAS Performance Parameters.
Figure 7.22 depicts the averages of the estimated range error for each of the
separation distances. A change in the performance parameters had little a ect on the
range error.
7.7.2 Excess Distance Traveled and Miss Distance
For the system with the SEP and maximum ROT set at 500 and 90 deg/min
respectively, Table 7.18 summarizes the average percent di erence in distance traveled
for both measurement platforms as well as the corresponding standard deviations.
Table 7.19 lists the average miss distance for each target along with the corresponding
standard deviations. On average, both platforms traveled 0.29% farther than the
straight line distance between their initial and  nal positions.
Table 7.18: Average Excess Distance Traveled and Standard Deviation; SEP of 500,
ROT of 90 deg/min.
80
(a) Target 1. (b) Target 2.
(c) Target 3. (d) Target 4.
Figure 7.22: Average Range Error Comparison with Varying Performance Parame-
ters.
Table 7.19: Average and Minimum Miss Distances and Standard Deviations; SEP of
500, ROT of 90 deg/min.
81
For the system with the SEP and maximum ROT set at 1500 and 270 deg/min re-
spectively, Table 7.20 summarizes the average percent di erence in distance traveled
for both measurement platforms as well as the corresponding standard deviations.
Table 7.21 lists the average miss distance for each target along with the correspond-
ing standard deviations. On average, platform one traveled 0.41% farther than the
straight line distance between its initial and  nal positions. Platform two traveled an
average of 0.58% farther.
Table 7.20: Average Excess Distance Traveled and Standard Deviation; SEP of 1500,
ROT of 270 deg/min.
Table 7.21: Average and Minimum Miss Distances and Standard Deviations; SEP of
1500, ROT of 270 deg/min.
With a decrease in performance parameters, the average miss distance for targets
one and four decreased. For the other two targets, the miss distances increased
slightly. With an increase in performance parameters, the average miss distances
for targets two, three, and four decreased. The average miss distance for target one
increased approximately 120 feet after the increase in performance.
82
7.8 Accuracy of Error Bounds
Each target position and velocity estimate from the EKF has an associated area
of uncertainty or error bound. To test the accuracy of this error bound, during the
simulation in Section 7.2, data was collected on the area of uncertainty to produce
a histogram for each target in the simulation. Each histogram shows the number
of range estimates that had a certain normalized deviation. Figure 7.23 illustrates
a top view of the estimated target positions, in red, as well as the associated error
bound on the estimate in green. The blue lines are the two measurement platforms.
To illustrate the error bounds, Figure 7.24 depicts a zoomed view of the initial error
Figure 7.23: Estimated Target Positions with Associated Area of Uncertainty.
bounds for target three, from the lower right corner of Figure 7.23.
83
Figure 7.24: Initial Estimated Target Position with Associated Area of Uncertainty
for Target 3.
84
Each range estimate from the EKF has an associated variance. From this vari-
ance, the standard deviation for the estimate can be determined. The normal cumula-
tive density function (NCDF) for each value of standard deviation is plotted over the
histogram plots to represent a normal distribution. Figure 7.25 depicts the histogram
plots for each target.
(a) Target 1. (b) Target 2.
(c) Target 3. (d) Target 4.
Figure 7.25: Range Estimate Histograms.
The histograms for targets one and four closely follow the normal distribution rep-
resented by the NCDF except for a few values of standard deviation. The histogram
for target two closely follows the normal distribution represented by the NCDF except
85
for standard deviation values between two and three. The histogram for target three
closely follows the normal distribution represented by the NCDF except for standard
deviation values between two and 2.5. The range estimates that do not correspond
to a normal distribution are believed to be caused from the error in the  lter ini-
tialization. Initially, the covariance matrix is set to assumed values. This may be
inconsistent with the true error value and would result in errors outside the expected
bounds.
7.9 System Reliability
To determine the reliability of the system a random target generator was incor-
porated into the simulation. For comparison, two simulations of 1000 Monte Carlo
iterations each were run. For the  rst simulation, the number of con icting air tra c
 ight paths was randomly selected each iteration having a value of one, two, or three.
For the second simulation, the number of con icting  ight paths was held constant
at one. For both simulations, the miss distance for con icting tra c was set to 2000
feet to allow for any inaccurate measurements and to try to ensure a near miss did
not occur.
For the  rst simulation, each iteration contained a random number of targets with
random headings and  ight speeds. The  ight speed was restricted to a minimum of
80 and a maximum of 250 knots. The intercept points for each of the targets was
also chosen at random and uniformly distributed along the predicted  ight path of
the measurement UASs. It was assumed that each target would maintain separation
from all other targets at all times. The reliability of the system was determined from
the number of near misses that occurred during the simulation. In the end, 128 near
86
misses had been experienced. This equates to approximately one near miss every
eight di erent target scenarios or a near miss rate of 12.8%.
To determine what scenarios were causing problems for the system, the simula-
tions were set up to store the target geometry in the case of a near miss. In most of
the instances when a near miss occurred, it was after two successive targets were ap-
proaching the  ight path of the platforms approximately 180 apart. This resulted in
the platforms being boxed in. As the platforms maneuvered around the  rst con ict,
they had in-turn maneuvered themselves into a worse situation with the second tra c
con ict. Once this time had passed, there simply was not enough time remaining for
the platforms to maneuver back before the distance between the tra c and platforms
was less than 500 feet. Figure 7.26 depicts one such situation where the platforms
maneuvered around the  rst target only to intercept the second. For some of the
target scenarios, the error in the estimated range, resulting from the targets being in
excess of 10 nautical miles away, caused a delay in determining if the tra c was a
con ict. This delay usually resulted in the occurrence of a near miss.
For the last simulation, each iteration contained a new and random target sce-
nario with random headings and  ight speeds just as before only with a single target.
During this simulation, 37 near misses occurred. This means the simulation had a
near miss rate of 3.7%.
After reviewing some of the near miss data from the simulation, it appears the
error in range estimate for some of the cases was higher than usual. This high range
error made it di cult for the con ict resolution controller to determine an accurate
avoidance heading.
87
Figure 7.26: Multiple Target Near Miss Scenario.
88
Chapter 8
Conclusions
Overall, a small, light weight SAA system was simulated. The proposed optimal
maneuvering formation was able to perform just as well or better than the comparison
formations in terms of average miss distance and minimum miss distance as well
as minimum range error for the closest of the four targets. During the time when
the targets were closest to the platforms, the optimal maneuvering formation had
a lower range error than the orbiting formation. The excess distance traveled for
maneuvering caused very little expense in overall distance traveled. The con ict
resolution algorithm caused very little degradation in the range estimate.
8.1 Comparison of Platform Separation Distances
When the range error for each of the three separation distances was compared,
it was determined that an increase in separation distance provided better range es-
timates especially for targets that are more than a few miles away. The penalty for
this better range estimate however was a decrease in average miss distance for targets
two, three, and four.
With a 500 foot decrease in separation distance, the maximum error for each of
the targets increased signi cantly. This was likely due to the degraded overall azimuth
measurement as the platforms became closer together. The minimum average error
however, was close to the same for each of the di erent platform separation distances.
With the smaller separation distance, the time that the maximum error occurred for
89
targets two and three, the targets that are the farthest away, also changed. This result
indicates the angle of the platforms had di erent e ects for each of the formations.
8.2 Comparison of Performance Parameters
Comparing the range error and excess distance traveled for each of the three
sets of UAS performance parameters, it was found that a change in performance
parameters changed the range error and excess distance traveled very little. The
performance parameters did however a ect the average and minimum miss distances.
The major change noticed with a change in performance parameters was in the
UAS?s ability to maintain their formation size. When the performance parameters
were decreased and the formation was commanded to move, a few instances resulted
in the platform separation distance growing momentarily. This was caused by the
platforms being commanded to a new heading from the con ict resolution controller
as well as the angle of the platforms changing to take measurements. The acceleration
limits in the controller had been reached and it became a matter of time before the
platforms moved to their desired location.
8.3 Error Bound Accuracy
After reviewing the histograms for the range estimates, it was determined that
the estimates closely follow a normal distribution except for a few occasions. For
targets one and four there are only a few values of standard deviation where the
number of range estimates did not follow a normal distribution. This was more
than likely associated with the peak in the range error noticed in the beginning
of the simulation for each target. This peak in error caused by the error in  lter
initialization results in range estimates that are not normally distributed for a short
90
period of time. The remaining range estimates being normally distributed suggests
the estimated variance from the EKF and hence the error bounds are accurate after
 lter initialization.
For targets two and three however standard deviations greater than two have
a higher number of range estimates than expected. This is more than likely due
to the fact that targets two and three start more than twelve nautical miles away
from the platforms. At that distance, the platform?s measurement accuracy was
degraded. When this measurement degradation was coupled with the initial error
from  lter initialization mentioned above, a larger number of range estimates become
abnormally distributed.
For each target, even those with a larger number of abnormally distributed es-
timates, the majority of the range estimates were normally distributed. This meant
for the majority of the simulation the actual target location was in the predicted area
of uncertainty with a 74% con dence with multiple variables considered.
8.4 System Reliability
During the  rst simulation to determine the system reliability, 128 near misses
occurred. For the second simulation, when the platforms were only faced with one
tra c con ict each iteration, the near miss rate was decreased by approximately 9%
resulting in a total of 37 near misses throughout 1000 di erent target scenarios. This
simulation showed a dramatic improvement in the near miss ratio from the multiple
target simulation. It was likely that this was due to the con ict resolution algorithm.
The algorithm was originally intended for single target scenarios so adapting it to
work with multiple targets proved to be troublesome.
91
The simulation results proved that indeed the proposed SAA system is a viable
solution for the incorporation of UASs into the NAS. Since SAA system requirements
are not currently available, the accuracy of the system in terms of reliability is un-
known exactly. While the system reliability is not as well as the author would have
liked, it is believed that the process described is a good start to a SAA system for
implementation on small unmanned aircraft that perform missions at fairly low alti-
tudes during VMC in the NAS. Where the system struggles, is with air tra c that
is greater than  ve nautical miles away. The  lter has a di cult time accurately
predicting the location of the tra c at this range.
92
Chapter 9
Future Work
Using the work presented herein as a foundation, the author would like to make
several suggestions for future research on using collaborative control for SAA systems.
The  rst would be instead of using multiple sensors on each platform to implement the
use of a single gimballed camera to detect and take measurements on con icting tra c.
Another suggestion would be to investigate the use of a third measurement aircraft
maneuvering in the system. Also, altitude changes for the measurement aircraft
could be added to the control algorithm for con ict resolution as well as the ability to
handle multiple targets simultaneously. Lastly, the issue of system reliability should
be investigated further to try to increase the reliability of the system by decreasing
the number of near misses with other air tra c.
A single gimballed camera could be used in place of the three  xed cameras
to monitor the same  eld of view with the possibility of a weight savings. Instead
of each camera covering a speci c area around the circumference of the aircraft the
single camera would simply scan the FOR from side to side looking for a target.
One possible problem with this arises when there are multiple targets in the FOR.
This is because as the aircraft maneuver, measurements for all of the targets would
not be available at every time step. The measurement values would be intermittent
depending on the orientation of the scanning camera. One would need to incorporate
this loss of measurement into the EKF and determine the e ects on the  lter as well
as the con ict resolution algorithm.
93
The addition of a third measurement platform maneuvering in the formation
would decrease the time it takes to maneuver the aircraft to take more accurate
measurements. This could possibly be used in combination with the gimballed camera
to solve the problem with multiple targets. To accomplish this task, modi cations
to the control algorithm would need to be made to ensure the three UASs did not
interfere with each other. This would allow two aircraft to take measurements on one
target while the third aircraft took measurements on a separate target.
Altitude changes in the con ict resolution piece of the system could possibly
decrease the course deviations necessary for the measurement platforms to remain
\well clear" of other air tra c. Included with altitude changes is the ability for the
formation to rotate from the aircraft  ying abreast to  ying over each other at di erent
altitudes. This too could decrease course deviations by decreasing the diameter of
the formation. The varying types of formation maneuvers could be applied depending
on the predicted  ight paths for each target. With the con ict resolution algorithm,
the main piece of future work would be to incorporate the ability to simultaneously
resolve con icts with multiple targets. This would possibly decrease the near miss
rate for multiple target scenarios.
94
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