The Pennsylvania State University. The Graduate School. Department of Electrical Engineering TRILATERATION-BASED LOCALIZATION ALGORITHM

Transcription

1 The Pennsylvania State University The Graduate School Department of Electrical Engineering TRILATERATION-BASED LOCALIZATION ALGORITHM FOR ADS-B RADAR SYSTEMS A Dissertation in Electrical Engineering by Ming-Shih Huang 2013 Ming-Shih Huang Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy May 2013

2 The dissertation of Ming-Shih Huang was reviewed and approved* by the following: Ram M. Narayanan Professor of Electrical Engineering Dissertation Advisor Chair of Committee James K. Breakall Professor of Electrical Engineering Julio Urbina Associate Professor of Electrical Engineering Dennis K. McLaughlin Professor of Aerospace Engineering Kultegin Aydin Professor of Electrical Engineering Head of the Department of Electrical Engineering *Signatures are on file in the Graduate School

3 iii ABSTRACT Rapidly increasing growth and demand in various unmanned aerial vehicles (UAV) have pushed governmental regulation development and numerous technology research advances toward integrating unmanned and manned aircraft into the same civil airspace. Safety of other airspace users is the primary concern; thus, with the introduction of UAV into the National Airspace System (NAS), a key issue to overcome is the risk of a collision with manned aircraft. The challenge of UAV integration is global. As automatic dependent surveillance-broadcast (ADS-B) system has gained wide acceptance, additional exploitations of the radioed satellitebased information are topics of current interest. One such opportunity includes the augmentation of the communication ADS-B signal with a random bi-phase modulation for concurrent use as a radar signal for detecting other aircraft in the vicinity. This dissertation provides detailed discussion about the ADS-B radar system, as well as the formulation and analysis of a suitable non-cooperative multi-target tracking method for the ADS-B radar system using radar ranging techniques and particle filter algorithms. In order to deal with specific challenges faced by the ADS-B radar system, several estimation algorithms are studied. Trilateration-based localization algorithms are proposed due to their easy implementation and their ability to work with coherent signal sources. The centroid of three most closely spaced intersections of constant-range loci is conventionally used as trilateration estimate without rigorous justification. In this dissertation, we address the quality of trilateration intersections through range scaling factors. A number of well-known triangle centers, including centroid, incenter, Lemoine point (LP), and Fermat point (FP), are discussed in detail. To the author s best knowledge, LP was never associated with trilateration techniques. According our study, LP is proposed as the best trilateration estimator thanks to the desirable property that the total distance to three triangle edges is minimized. It is demonstrated through simulation that

4 iv LP outperforms centroid localization without additional computational load. In addition, severe trilateration scenarios such as two-intersection cases are considered in this dissertation, and enhanced trilateration algorithms are proposed. Particle filter (PF) is also discussed in this dissertation, and a simplified resampling mechanism is proposed. In addition, the low-update-rate measurement due to the ADS-B system specification is addressed in order to provide acceptable estimation results. Supplementary particle filter (SPF) is proposed to takes advantage of the waiting time before the next measurement is available and improves the estimation convergence rate and estimation accuracy. While PF suffers from sample impoverishment, especially when the number of particles is not sufficiently large, SPF allows the particles to redistribute to high likelihood areas over iterations using the same measurement information, thereby improving the estimation performance.

5 v TABLE OF CONTENTS LIST OF FIGURES... vii LIST OF TABLES... xi LIST OF ACRONYMS... xii ACKNOWLEDGEMENTS... xiv Chapter 1 Introduction Background Motivation Organization of the dissertation... 5 Chapter 2 Evolution of Surveillance Technologies Ground-based air surveillance system Primary surveillance radar Secondary surveillance radar Traffic alerting and collision avoidance system Automatic dependent surveillance - broadcast (ADS-B) Principal operation ADS-B signal format Remaining issues Other ADS-B related systems Hybrid surveillance Wide-area multilateration Chapter 3 ADS-B Radar Systems Overview System design Signal waveform System configuration Interference analysis Link budget analysis Signal specification comparison Chapter 4 Estimation and Tracking Algorithm for ADS-B Radar Systems Overview Signal coherence problem Trilateration-based localization algorithms Time of arrival Trilateration modes Triangle center approaches Centroid... 43

6 vi Incenter Lemoine Fermat Range-based weighted centroid Performance comparisons Enhanced algorithms for severe trilateration scenario Weighted trilateration Range-adjusted weighted trilateration Estimation error over range Particle filter algorithm Simplified resampling mechanism Supplementary particle filter algorithm Performance comparisons Chapter 5 Conclusions and Future Work Conclusions Future work Bibliography... 81

7 vii LIST OF FIGURES Figure 2-1: Principle of PSR operation Figure 2-2: Increased uncertainty over distance Figure 2-3: SSR relies on onboard transponder, which receives interrogation from ATC and transmits replied message Figure 2-4: Principle of operation for the ADS-B systems in an air traffic network Figure 2-5: ADS-B Mode-S Extended Squitter message format Figure 2-6: Illustration of WAM Figure 3-1: Comparison of surveillance principles between ADS-B and ADS-B radar systems Figure 3-2: Illustration of random phase modulation added onto ADS-B messages Figure 3-3: Illustration of the ADS-B waveform (blue) versus the ADS-B radar waveform (red) Figure 3-4: Conceptual architecture of the proposed ADS-B radar system Figure 3-5: Autocorrelation of standard ADS-B signal and autocorrelation of phase modulated ADS-B signal Figure 3-6: Cross-correlation of one phase modulated ADS-B signal with another standard ADS-B signal and another phase-modulated ADS-B signal

8 viii Figure 3-7: A simulated range profile based on autocorrelation of a randomly bi-phase modulated ADS-B signal Figure 4-1: Using trilateration to determine target location Figure 4-2: Illustration of trilateration modes Figure 4-3: Illustration of the error due to arc-line approximation Figure 4-4: Occurrence probability of each mode under various noise variances Figure 4-5: The distances between dashed and solid lines are equivalent to RSFs Figure 4-6: E 1, the difference of the first element of normalized FP and LP barycentric coordinates Figure 4-7: E 2, the difference of the second element of normalized FP and LP barycentric coordinates Figure 4-8: E 3, the difference of the last element of normalized FP and LP barycentric coordinates Figure 4-9: Distance between FP and LP in Cartesian coordinate. Green triangles are two fixed triangle vertices, with edge length as 1 m, and the third vertex moves in FOV Figure 4-10: Comparison between centroid and RWC. Numerical values are the computed weights for each intersection Figure 4-11: Average errors of 1000 Monte Carlo simulations with random noise variance and fixed target location

9 ix Figure 4-12: RMSE of 1000 Monte Carlo simulations with random noise variance and fixed target location Figure 4-13: Average errors of 1000 Monte Carlo simulations with random noise variance and random target location Figure 4-14: RMSE of 1000 Monte Carlo simulations with random noise variance and random target location Figure 4-15: The extended intersections define an overlapping area Figure 4-16: Average errors of WT and RAWT for mode 4 and mode Figure 4-17: RMSE of WT and RAWT for mode 4 and mode Figure 4-18: Average errors of all trilateration techniques under different map sizes Figure 4-19: RMSE of all trilateration techniques under different map sizes Figure 4-20: Resampling mechanism for multiple targets Figure 4-21: Transmitted ADS-B radar signal waveform Figure 4-22: Transmitted ADS-B radar signal and received signals from four sensors Figure 4-23: Tracking trajectories of PF and SPF methods against true target (20 MC trials) Figure 4-24: Range errors during each iteration (one trial) Figure 4-25: RMSE for a target with constant velocity, as well as Gaussian distributed acceleration and heading direction (20 MC trials)

10 x Figure 4-26: Tracking performance for a maneuvering target (20 MC trials) Figure 4-27: Range errors during each iteration (one trial) Figure 4-28: RMSE for a maneuvering target (20 MC trials) Figure 4-29: Tracking performance for multiple targets (20 MC trials)

11 xi LIST OF TABLES Table 3-1: Effects of random bi-phase modulation on correlation results Table 3-2: Link budget analysis Table 3-3: Comparison of signal specification for various air surveillance technologies Table 4-1: Comparison of various triangle center approaches for fixed target and standard deviation = 5 m Table 4-2: Comparison of various triangle center approaches for random target and standard deviation = 5 m Table 4-3: Estimation error comparison

12 xii LIST OF ACRONYMS ADS-B ATC ATM C2 CARATS CL DF DOP FAA FOV FP FRUIT GNSS ICAO LP MC MUSIC NAS NexGen PF PM PPM PSR Automatic dependent surveillance - broadcast Air traffic controller Air traffic management Command and control Collaborative actions for renovation of air traffic systems Centroid localization Direction finding Dilution of precision Federal aviation administration Field of view Fermat point False replies unsynchronized with interrogation transmissions Global navigation satellite systems International civil aviation organization Lemoine point Monte Carlo simulations Multiple signal classification National airspace systems Next generation air transportation system Particle filter Phase modulation Pulse position modulation Primary surveillance radar

13 xiii RAWT RCS RF RMSE RWC SAA SESAR SPF SSR SWAP TOA TDOA UAT UAV WAM WSN WT Range-adjusted weighted trilateration Radar cross section Radio frequency Root mean squared error Range-based weighted centroid Sense and avoid Single European sky air traffic research system Supplementary particle filter Secondary surveillance radar Size, weight, and power Time of arrival Time difference of arrival Universal access transceiver Unmanned aerial vehicle Wide-area multilateration Wireless sensing network Weighted trilateration

14 xiv ACKNOWLEDGEMENTS First and foremost, I am extremely grateful and thankful to my advisor, Dr. Ram M. Narayanan, for his guidance and patience throughout my entire course of my life at Penn State. Dr. Narayanan has inspired me with his enthusiasm, positive attitude, and hard-working nature. I would also like to thank my committee members, including Dr. Dennis K. McLaughlin, Dr. James K. Breakall, and Dr. Julio Urbina, for their insightful comments and suggestions that are incredibly helpful for my research work. Special thanks are due to Dr. Yan Zhang of University of Oklahoma and Dr. Randy Haupt of the Colorado School of Mines for numerous discussions that helped shape my research work. I would like to acknowledge the constant support from my fellow labmates and friends Chieh-Ping Lai, Jack Chuang, Shrawan Surender, Zhixi Li, Wei-Jen Chen, Pin-Heng Chen, Mahesh Shastry, Surendra Bhat, Russ Vela, Yangsoo Kwon, and many others. I thank Dr. Chujen Lin and Dr. Alexander Davydov from Intelligent Automation Inc. for the research internship opportunity. I would also like to thank Dr. Stefan Schwarzer, Dr. Sebastian Kunkel, Dr. Ulrich Loewen and Carolin Haussner in Corporate Research and Technologies in Siemens AG for giving me hands-on industrial experience. Last, but definitely not the least, I would like to express my personal appreciation to my parents, my loving wife, and my joyous daughter. Without their support and encouragement, my Happy Valley journey would not have been nearly as rewarding as it was. I thank you from the bottom of my heart for always being there for me.

15 xv DEDICATION To Hsin-Ling and Abigail.

16 Chapter 1 Introduction 1.1 Background Over the past few decades, the continuous expansion in air traffic volume and demand has created substantial problems in terms of capacity and safety for the air traffic management (ATM) system. In the very near future, we will soon face more increasing aviation challenges, out of which possibility of aircraft mid-air collisions needs special attention, especially in busy airport areas. In addition, rapidly increasing growth in various UAVs have pushed governmental regulation development and numerous technology research activities toward integrating unmanned and manned aircraft into the same civil airspace. To enable the transformation of the ATM to a new paradigm that can meet the demand for the next 20 years and beyond, several developmental programs are underway, such as Single European sky air traffic research system (SESAR) in Europe [1], next generation air transportation system (NextGen) in U.S.A. [2] [4], and collaborative actions for renovation of air traffic systems (CARATS) in Japan [5]. The philosophy is to move away from legacy ground based technologies to a new and more dynamic satellite based technology. A key element of SESAR and NextGen is automatic dependent surveillance - broadcast (ADS-B), which uses the global navigation satellite system (GNSS) signals to provide air traffic controllers and pilots with precise position information in space, in contrast to the traditional surveillance radar derived data. Aircraft transponders receive GNSS signals and use them to determine the aircraft s precise location in the sky, which is combined with other relevant data and broadcast out via a digital data link to other aircraft and air traffic control facilities. Besides ADS-B s wide acceptance in

17 2 Europe and U.S.A, NAV CANADA commenced operational application of ADS-B as a means of providing aircraft surveillance information to air traffic controllers (ATC) [6], and AirServices Australia commissioned the ADS-B Upper Airspace Project (UAP), providing ADS-B coverage across the whole continent [7]. In addition, ADS-B is being used as the key solution for UAV integration in the National Airspace System (NAS). When properly equipped with ADS-B, both pilots and controllers will see the same real-time displays of air traffic, substantially improving safety and minimizing collision probability. There has been much discussion regarding the concept of equivalent level of safety and whether UAVs can be shown to achieve a collision avoidance performance equivalent to that of manned aircraft. In accordance with Federal Aviation Administration (FAA) regulations, all pilots are responsible for seeing and avoiding other aircraft. As the UAV operator is physically removed from the cockpit, airborne sense and avoid (SAA) capability becomes the focus of technological efforts for UAV [8]. In addition, UAV mid-air collision avoidance capabilities must be interoperable and compatible with existing collision avoidance and separation assurance. Small UAV are difficult to see visually and sense electronically owing to the small size and/or the diversity of the platform size, weight, and power (SWAP). Many approaches, including camerabased sensing [9], [10], traffic alerting and collision avoidance system (TCAS), and ADS-B have been considered; however, none of the proposed techniques is convincing enough to be adopted by FAA. A few major drawbacks are highlighted below. Centralized flight control system, e.g. ATC, will soon reach its limit for high capacity of manned aircraft, let alone the airspace comprising manned and unmanned aircraft. Moreover, the command and control (C2) link between ATC and the flight system introduces a number of significant issues to aircraft in a fly-by-wireless system, such as link vulnerabilities due to radio frequency (RF) interference and potential latency of flight control messages. Without the onboard

18 3 pilot to make a spontaneous decision, the delay in the control message delivery from ATC to UAV is a very severe problem. Safety analysis of TCAS on medium to large sized UAV has been carried out [11], despite its cost and system requirement. Because aircraft are required to be equipped with altitude-reporting transponder in Class A, B, C airspace and Class E airspace above 10,000 feet, in low-altitude Class E and uncontrolled airspace through which UAV may fly, TCAS would not work. In addition, the safety studies conducted to certify TCAS assumed that aircraft would have a pilot onboard. Due to the bearing error and update rate of TCAS, the FAA and International Civil Aviation Organization (ICAO) have stated that TCAS display alone is not sufficient to provide the operator with enough situational awareness to avoid the threat. In order to reduce the risk of collision, it is essential to make UAV more conspicuous to other aircraft, and one simple way is through the electronic broadcast of the aircraft s state vector data (i.e. position, velocity, aircraft type, etc.). With the proposed rulemaking by FAA that would mandate ADS-B out equipage by 2020, it appears that ADS-B transceivers will most likely become critical pieces of an airborne SAA system for UAV operating in the NAS. The ITT Corporation, chosen in 2007 as the prime contractor for ADS-B ground stations, will implement the infrastructure covering the entire nation by Certainly some modifications would be required to successfully adapt the ADS-B system into UAV due to its high cost, the differences in aircraft characteristics, and the nature of possible collisions. A lightweight, low-cost and lowpower ADS-B beacon radio developed by The MITRE Corporation [12], [13], and a radio data system (RDS) proposed in [14] makes it promising to deem ADS-B technology as a key enabler to integrate UAV into NAS. A flight test of UAV utilizing the ADS-B transceiver [15] was tested in 2009, and it demonstrated the possibility to use an ADS-B transceiver for UAV as an entry into NAS.

19 4 In the environment covered by both ADS-B and radar stations, the fusion of radar and radio communication fusion provides improved tracking accuracy and system integrity [16], [17] at a costly expense. However, similar to the first issue to employ TCAS on UAV, many UAVs operate in airspace not covered by radar. 1.2 Motivation Before the ADS-B implementation and operation is fully complete, there will be a transition period involving coexistence of ADS-B equipped and non-equipped aircraft. In addition, ADS-B systems have several remaining concerns, such as vulnerability to spoofing, backup system needed at loss of satellite signals, and inability to see non-cooperative targets. It has been pointed out that the limited use of ADS-B as the sole means of surveillance may lead to a reduction of the integrity of the entire ATC system [16], [17]. Localized problems, such as less than the required four visible satellites, will confuse not only aircraft pilots but also ATC [18], [19]. Hence, it is desired to find a way to cope with the non-cooperative targets while retaining the benefits of the ADS-B system. Since the emergence of ADS-B concept, some researchers have considered the utilization of existing and installed infrastructure of the surveillance radar to combine with the satellitebased ADS-B system within the perspective of ATC. More interestingly, the use of the ADS-B signal itself to detect non-cooperative targets from the ADS-B message and from the radar processing, as an onboard collision avoidance system was first described in a patent disclosure [20] and the concept subsequently developed further [21] [26]. The novelty of the ADS-B radar system lies in that the system insightfully exploits the ADS-B out signal, which is primarily designed for communication purposes, as a radar signal to perform multiple target estimation and tracking, thereby creating a multifunctional waveform. With the affordable Universal Access

20 5 Transceiver (UAT) Beacon Radio developed by The MITRE Corporation [12], [13] and the hybrid estimation approach for resource-limited UAVs, the ADS-B radar concept appears to be an economically viable solution to facilitate integration of UAV into NAS. As a communication system, the ADS-B system has fundamental drawbacks, such as vulnerability to signal interception and spoofing and inability to see non-cooperative targets. There has been ongoing research collaboration between The Pennsylvania State University and Intelligent Automation, Inc. to develop a radar system, named the ADS-B radar, based on the original ADS-B system to go beyond the natural limitation of the communication system. 1.3 Organization of the dissertation This dissertation is organized as follows: Chapter 2 renders a general understanding the evolution of air surveillance technologies over the past few decades. Existing surveillance techniques are reviewed with a focus on their limitation in order to serve the future ATM. New air surveillance technologies are introduced in details, and potential issues are pointed out and discussed. Chapter 3 describes the ADS-B radar system in terms of system configuration and signal modulation technique. The feasibility of augmenting the communication ADS-B signals with a random bi-phase modulation to enhance radar capability is investigated. In addition, the link budget is analyzed in order to understand the system capability in terms of operational range. Chapter 4 presents the estimation and tracking algorithms proposed for the ADS-B radar system. Details of such radar-communication system specifications and problems of low-updaterate measurement due to the ADS-B system requirement are discussed. Trilateration-based localization algorithms are studied for resource-limited platforms, such as UAV. Particle filter algorithm is applied for multi-target estimation and tracking with a simplified resampling

21 6 mechanism presented. SPF is proposed to improve the estimation accuracy using the waiting time for the next observation. Chapter 5 draws the conclusions of the dissertation. A few suggested research directions for future work are also presented.

22 Chapter 2 Evolution of Surveillance Technologies It is foreseen that with rapid expansion of in air traffic volume and demand, the groundbased technology will face its limitation in the near future. The transition of the surveillance technologies that ATM is shifting from centralized systems to decentralized systems as the density of the air traffic continues to increase. Although in its early stage of implementation, the ADS-B system may soon replace and decommission the conventional radar stations and the delegation of specific separation responsibilities and associated tasks may need to be transferred to the flight crew to offer instantaneous situation awareness in airspace. A brief and comparative review of the existing and new surveillance technologies is provided in this Chapter. The major advantages and disadvantages for each approach are pointed out with an emphasis on the non-cooperative surveillance capability. Two traditional groundbased surveillance radar systems, primary surveillance radar (PSR) and secondary surveillance radar (SSR) will be covered describing their fundamental operational principles and their limitations [27]. The signal format and system specification of the ADS-B system will be provided and the remaining concerns for the new concept are presented. At the end of the Chapter, two ADS-B related systems, including a hybrid surveillance technique using TCAS and ADS-B and wide-area multilateration (WAM), are described. 2.1 Ground-based air surveillance system PSR and SSR are the main two components of an ATC station and are widely used for the past few decades. PSR has the capability to detect large metal objects, including cooperative

23 8 and non-cooperative targets, while SSR works only for transponder-equipped aircraft. SSR relies on aircraft with corresponding transponder, but the report provides aircraft identification. Both PSR and SSR were designed for low and medium traffic situations Primary surveillance radar PSR detects and reports the position of anything that reflects the transmitted radio signals. However, PSR only finds the aircraft within operational range without being able to identify them. In addition, the returned signal strength decays as the fourth power of distance from the radar station to the target. Figure 2-1 shows how PSR detects targets using reflected microwave bounced from the metal objects and the signal power after the round trip decreases dramatically. Moreover, the antenna beam gets wider as the target moves farther away from the antenna, thus making the measured position information less accurate, as illustrated in Figure 2-2. Although its coverage and information is more limited, PSR is still used by ATC today as a backup/complementary system for surveillance purpose. Signal strength decays as Figure 2-1: Principle of PSR operation.

24 9 uncertainty 2 uncertainty Figure 2-2: Increased uncertainty over distance Secondary surveillance radar The need to be able to identify aircraft and the impetus to reduce power decay led to the invention of SSR. SSR relies on a piece of onboard device known as transponder, which receives interrogation at the frequency of 1030 MHz and replies at 1090 MHz, as shown in Figure 2-3. With the aid of transponder, identification can be inserted in the replied message, and in the meantime, the signal power decays only to the second power of the distance and uncertainty issue is also alleviated due to half of the travelling distance compared to PSR technique. When there are a number of aircraft in close vicinity in terms of distance or direction, their SSR replies can overlap, the ground decoder is confused and finally their information is lost. This situation is known as Garbling, and it makes SSR unsuitable in dense aircraft areas. Moreover, when there are many SSR stations around the aircraft, replies received by other SSR stations that did not ask for these replies result in confusion and finally rejection due to errors. This phenomenon is known as False Replies Unsynchronized with Interrogation

25 10 interrogation interrogation response response Figure 2-3: SSR relies on onboard transponder, which receives interrogation from ATC and transmits replied message. Transmissions (FRUIT) [28], resulting from the fact that an aircraft SSR reply is received not only by the SSR that triggered it but by all the others around. The unexpected replies thus arriving at these other SSR stations in the area result in inconsistent position measurements. Within NAS, most of the airspace is under coverage of multiple SSR stations, and FRUIT results in loss of the aircraft position and inaccurate surveillance information. 2.2 Traffic alerting and collision avoidance system Due to continuing growth in air traffic, TCAS or other similar devices have been in various stages of research and development since the early to mid 1950s to serve as a last resort collision avoidance safety-net. TCAS operates similarly to the ground-based SSR but independently interrogates surrounding aircraft on a 1030-MHz radio channel. The pilot will be alerted to the presence of the intruding aircraft replying to the interrogation via 1090-MHz radio frequency. Current generation TCAS II, jointly developed by the US Radio Technical Commission for Aeronautics (DO-185B) and European Organization for Civil Aviation

26 11 Equipment (ED-143), issues two types of advisories: the resolution advisory (RA), which identifies an intruder that is considered a collision threat, and the traffic advisory (TA), which identifies an intruder that may soon cause an RA. According to the predicted closest point of approach (CPA), TCAS produces a TA at approximately 45 seconds and an RA at 35 seconds to CPA. TCAS is designed to reduce the incidence of mid-air collisions and has been very successful since its introduction. However, the major concern with regard to either TCAS or ADS-B is that they are not required all the time, and ADS-B Out is not yet mandated in most of the countries. Aircraft equipped with TCAS and/or ADS-B are still exposed to danger of collisions in low altitude of Class E and uncontrolled airspace owing to their inability to detect non-cooperative targets and unawareness of any illegal intruder in transponder-required airspace. 2.3 Automatic dependent surveillance broadcast (ADS-B) ADS-B is automatic in the sense that it transmits signals automatically without requiring controller action; it is dependent surveillance because the surveillance-type information depends on onboard navigation sources and onboard broadcast transmission systems to provide surveillance information. The system constantly broadcasts the signal at the rate of once every second. ADS-B is redefining the paradigm of communication, navigation, and surveillance in ATM. An ADS-B equipped aircraft determines its own position using GNSS and periodically broadcasts its four dimensional position (latitude, longitude, altitude, and time), track and ground speed, aircraft or vehicle identification and other additional relevant data as appropriate, e.g. intended trajectories [29], to nearby aircraft also equipped with the ADS-B system and potential ground stations without expectation of an acknowledgement or reply. One of the most significant advantage of the ADS-B system is that it minimizes radio frequency (RF) spectral congestion as would be generated by TCAS. Any user, either aircraft or ground stations

27 12 within broadcasting range, may receive and process ADS-B surveillance information. ADS-B system provides accurate information and improves situational awareness. Moreover, ADS-B enables a shift from a centralized, ground-based ATM system to a decentralized network involving pilots and aeronautical operational control centers. ADS-B also provides greater coverage, since ADS-B ground stations are so much easier to place than radar. Remote areas without radar coverage, like the Gulf of Mexico and parts of Alaska, are now covered by ADS-B. According to the ADS-B implementation timetable in USA, by 2020, the ADS-B Out is mandatory for all aircraft operating in any airspace that currently requires a transponder, and the ADS-B In equipment will be based on user perceived benefit. The ADS-B system might eventually allow pilots to use onboard instruments and electronics to maintain a safe separation and to reduce their reliance on ground controllers Principle of operation Figure 2-4 shows the role of ADS-B in an air traffic network, including ground station and surrounding airplanes. It is not difficult to envision that once all flying objects within the National Airspace System (NAS) are equipped with the ADS-B system, the airspace will be as clear as transparent for the aircraft to see and avoid imminent collisions, which is the ultimate goal of extreme aviation safety.

28 13 GPS Air to Air Link Air to Ground Link Figure 2-4: Principle of operation for the ADS-B systems in an air traffic network ADS-B signal format There are three different types of link technology suitable for ADS-B technology: Mode- S Extended Squitter (ES), VHF Data Link (VDL) Mode 4, and Universal Access Transceiver (UAT). A VDL Mode 4 system has the longest operational range among these three candidates, but the low bandwidth of the signal renders poor resolution to distinguish multiple targets. While UAT and Mode S ES both work on L-band, the latter has a larger bandwidth of 6 MHz, which provides many benefits especially in radar application. In the dissertation, only the Mode S ES will be discussed in our radar system design. Mode-S ES is agreed to be the first global datalink for international commercial flight, and the transponder emits periodically with a frequency up to 6 Hz. The uplink operates at 1030 MHz and the downlink at 1090 MHz. The ADS-B message information is encoded in the time

29 14 delay between pulses in a sequence of signal pulses, known as Pulse-Position Modulation (PPM). A pulse transmitted in the first half of the bit interval represents 1 while a pulse transmitted in the second half represents 0. A complete Mode-S ES is 120 s, including 8 s preamble, followed by 112 data block in 112 s. Each message contains 56 bits of information inserted between the 24 bit aircraft address and the parity information, as can be seen in Figure 2-5. Figure 2-5: ADS-B Mode-S Extended Squitter message format Remaining issues Ever since FAA released ADS-B technology, there has been an ongoing debate about its advantages and disadvantages. It is clearly desired from the pilots to be aware of all the nearby aircraft by the broadcasting techniques, but experts worry about the negative effects when the broadcast information is used by third parties, e.g. terrorists. In addition, it is very important that ADS-B is resistant to intentional interference or noisy environment. Furthermore, what is the

30 15 alternative procedure when GPS signal is lost and how does ADS-B deal with airplanes not equipped with the ADS-B system? Transparency The ADS-B system broadcasts in one message both the aircraft identification (ID) and location, which are the very information that could be misused by adversaries. A good encryption mechanism for ADS-B has not yet been proposed, and it needs to be developed and tested to upgrade the ADS-B system before any unwanted incidents happen. Vulnerability to spoofing Whenever an incoming ADS-B signal is received, the aircraft ID and location embedded in the message will be updated on the cockpit display. Even if it is a spoofed message, the receiving end has no way to find out that the information is not correct. The scenario can be worse if the aircraft that received a spoofed message makes maneuver to avoid the nonexistent collision and causes a real collision danger to other aircraft. Without additional support, the ADS- B system is vulnerable to spoofing. Backup system at the loss of GPS signals In the case of lost or incorrect GPS information, possibly caused by localized problem or device malfunction, a fallback solution is necessary before ADS-B has been extensively proven through operational experience. A few seconds of lost signals for a car GPS may not cause a big harm because the driver still visually sees the traffic even though he/she loses road guidance.

31 16 Nevertheless, a flight pilot is dependent upon accurate location information of nearby aircraft to avoid imminent collision. While en route airplanes fly at the speed of around 500 miles per hour, or equivalently 224 meters per second, a short period of lost GPS signal could make collision avoidance even more difficult. Therefore, a certain level of redundancy for aviation surveillance is needed to prevent casualty in the event the primary system shuts down. Blind to non-cooperative targets As described in the beginning of this chapter, the ADS-B systems allow the surrounding airplanes to be aware of each other and provide a safe airspace. However, a fundamental lack of capability is about non-cooperative targets, which include the aircraft not equipped with the ADS- B system, flying objects, and UAVs. It is certainly desirable, or necessary to some extent, for the ADS-B system to be able to see and avoid not only ADS-B equipped aircraft but also noncooperative targets. 2.4 Other ADS-B related systems The ADS-B system is a promising technology and in May 2010, FAA issued a final ruling mandating ADS-B equipage. A couple of surveillance systems are incorporating ADS-B to expand function capability or developing techniques to take advantage of the free broadcast ADS- B Out signals. For the sake of a complete background study on ADS-B, the hybrid surveillance and WAM are described in this Section.

32 Hybrid surveillance TCAS is an aircraft collision avoidance system designed to reduce the incidence of midair collisions between aircraft. Aircraft over 5700 kg or carrying more than 19 passengers are mandated by ICAO to be equipped with TCAS. The operational principal of the TCAS system is based on SSR transponder which operates independently of ground-based equipment to provide advice to the pilot on potential conflicting aircraft that are equipped with SSR transponders. Each TCAS-equipped aircraft interrogates all other aircraft in a determined range about their position and all other craft reply to other interrogations. This interrogation-and-response cycle may occur several times per second. Through this constant back-and-forth communication, the TCAS system builds a three dimensional map of aircraft in the airspace, incorporating their bearing, altitude and range. Then, by extrapolating current range and altitude difference to anticipated future values, it determines if a potential collision threat exists. The collaboration of TCAS and ADS-B signals, known as hybrid surveillance, has been implemented. TCAS hybrid surveillance makes use of both active surveillance data from interrogation reply sequence and passive position estimates from ADS-B so that at the presence of reception of ADS-B messages from an aircraft the rate at which TCAS interrogates that aircraft is reduced. When ADS-B and TCAS are both working in the operational range, the surrounding airspace is under satisfactory surveillance control and the probability of having a collision is minimized. Hence, it is considered as a safe measure to reduce the TCAS interrogation rate during hybrid surveillance. Furthermore, with reduced interrogation rate, there will be less microwave interference in the airspace and the operational life of TCAS system will be extended over time. In the future, prediction capabilities may be improved by using the state vector information present in ADS-B messages. Also, since ADS-B messages can be received at greater

33 18 range than TCAS normally operates, aircraft can be acquired earlier by the TCAS tracking algorithms Wide-area multilateration Multilateration techniques have been deployed for airport surveillance for a number of years, and nowadays, the same techniques are used for larger areas, hence the name wide-area multilateration (WAM) such as en route or approach areas thanks to many types of aircraft transmissions [30] [32]. The concept of WAM is illustrated in Figure 2-6. Figure 2-6: Illustration of WAM. WAM can be considered an a form of cooperative surveillance technique, and a WAM system consists of a number of antennas receiving a signal from an aircraft and a central

34 19 processing unit calculating the aircraft s position from the time difference of arrival (TDOA) of the signal at the different antennas. WAM systems can be deployed without any changes to the airborne infrastructure because the systems make use of currently existing aircraft transmissions and passively receive the transmissions in multiple locations to estimate the location of the source. In the event that the received signals contain identification, the estimated location can be associated with that aircraft, and the combined information is valuable for surveillance purpose. It is not hard to imagine that how ADS-B signals could be extremely beneficial to WAM systems. The fact that an aircraft broadcasts messages, including aircraft tail number and GPS-based location information, makes the ADS-B signal very suitable for a WAM system [32]. In light of a complete coverage of ADS-B signal in Australia, a large number of WAM surveillance applications have been developed at Sydney airport.

35 20 Chapter 3 ADS-B Radar Systems 3.1 Overview The ADS-B system has the goal of significantly increasing capacity within NAS, while maintaining or improving safety, but it can be only considered as a cooperative surveillance ATM technique. Non-cooperative targets, such as UAVs and private jets, are blind to the ADS-B systems when not equipped with the ADS-B system, but they pose equal collision danger if not being detected. ADS-B radar [20] [25] is intelligently introduced as a modification to the standard ADS-B system in the interests of a safe backup service without significantly enlarging the volume of ADS-B equipment. In addition, the radar report from ADS-B radar system could be also used to compare with the incoming ADS-B message to reject any spoofed information. The basic idea is that since the ADS-B systems constantly broadcast signals, the reflective ADS-B electromagnetic energy could be exploited and extended for use as radar echoes. Figure 3-1 illustrates the operational principal of the original ADS-B system and the ADS-B radar system. In Figure 3-1 (b), four links in an aviation network include the followings: o o o Link 1: Communication between aircraft and ATC through ADS-B signals Link 2 & 3: Communication between aircraft equipped with ADS-B systems Link 4: Detecting non-cooperative targets through reflected microwave Nevertheless, in order to utilize of the reflected signals as radar echoes, many challenges need to be overcome and modification to the original ADS-B system will be required. The ADS- B signal can be viewed as a narrow-band communication signal, but however a large bandwidth is generally desired for radar application in order to have high range resolution to distinguish targets in close vicinity. Furthermore, such radar system needs to work under the interference

36 21 from many other ADS-B signals transmitted at the same frequency. The key adaptation lies on the phase modulation added onto the standard ADS-B waveform, and it will be discussed in detail in the second section of this chapter. The location of the non-cooperative targets can be estimated using the reflected signals bounced off the targets, and techniques and design concerns will be mentioned in Chapter 4. It is interesting to note that the uncertainty, i.e. poor accuracy at long ranges, in the measured radar reports on the aircraft, will no longer be as a major issue as it is for the groundbased radar because the distance between a target and own aircraft is much smaller than that between a target and the ground station. Another significant advantage of exploiting the ADS-B signal is that it minimizes radio frequency (RF) spectral congestion as would be generated by introducing other interrogation techniques. ADS-B radar system provides pilots with a system independent of air traffic control to detect the presence of other aircraft, including both cooperative and non-cooperative aircraft and anomalous aerial objects, which may present a threat of collision. The location information of the targets can be estimated from the returned ADS-B radar signals. Both of the ADS-B In information and the estimated locations for the noncooperative targets will be fused and then combined fed into Cockpit Display of Traffic Information (CDTI) [33].

37 22 (a) ADS-B: communication between equipped aircraft and ATC ADS-B Out (Blind to ADS-B) ADS-B Out (b) ADS-B radar: able to detect both equipped and non-equipped aircraft ADS-B Out Detectable through reflected microwave (link 4) ADS-B Out Figure 3-1: Comparison of surveillance principles between ADS-B and ADS-B radar systems. 3.2 System design Before a communication signal can be utilized and treated as a radar signal, many issues need to be addressed first and a proper amount of modification to the system may be necessary. The transmitted signal must be suitably modulated so that the returned signals could be exploited

38 23 to detect targets and estimate their locations. The modification to the original ADS-B system should be minimized. The constraints from the ADS-B system include long pulse duration, maximum of peak transmit power, insufficient signal bandwidth, and coherent returned signals, which all degrade the radar performance. Therefore, one of the primary tasks for ADS-B radar design is to exam the feasibility of treating ADS-B signal as radar signal and it will be discussed in a later section with theoretical analysis and simulation results. Then the needed modification to the system will be described, followed by the link budget analysis Signal waveform Random bi-phase modulation for radar applications is depicted in Figure 3-2. Within the 112 μs message period, 180 phase shift is added pulse-by-pulse in a random manner, and the random phase keying code is memorized during each message transmission. The bi-phase modulation will not affect the ability for the ADS-B-in system to interpret the information because only the envelope of the received signal and the pulse position in the waveform will be use to decode the ADS-B message. Hence, the aircraft that receives the added phase modulated signals will still be able to decode the message correctly. This added phase modulation however provides the modulated signal the radar capability without affecting the decoding of the original ADS-B message. Figure 3-3 shows the simulated ADS-B waveform and the proposed ADS-B radar waveform. Both signals are of the same duration and have identical digital messages, except that the ADS-B radar signal has a random 180 phase shift. By randomizing the transmit signal, the matched filtering operation can be performed by cross-correlating the reflected signal with a time-delayed replica of the transmit waveform. The bi-phase modulation renders both positive and negative products, forcing the autocorrelation to be statistically zero except for zero time-lag. The effect of the sum of the products in the autocorrelation function is provided in Table 3-1.

39 24 Figure 3-2: Illustration of random phase modulation added onto ADS-B messages. Figure 3-3: Illustration of the ADS-B waveform (blue) versus the ADS-B radar waveform (red).

40 25 Table 3-1: Effects of random bi-phase modulation on correlation results. messages modulation PPM PPM with random bi-phase PM same phase (no phase shift) inverted phase (180 phase shift) (1, 1) or (0, 0) positive sum-product (1, 0) or (0, 1) zero sum-product positive sum-product zero sum-product negative sum-product zero sum-product System configuration A conceptual architecture of the proposed ADS-B radar system is depicted in Figure 3-4. The ADS-B radar system includes the following sub-systems: (a) ADS-B transceiver, (b) ADS-B encoder/decoder, (c) RF electronics with up and down frequency conversion, crosstalk cancellation, and filtering capabilities, (d) a phase modulator, and (e) four omni-directional antennas. Components (d) and (e) are particularly necessary to process the reflected radar signals and to estimate target locations in real-time. Both of the ADS-B In message and the estimated target location after processing the reflected signals from the antenna array will be fed into the CDTI so that the pilot is aware of all surrounding aircraft and more importantly any imminent collision.

41 26 TCAS receiving circular array antenna RF Radar processing coherent transceiver CDTI Standard ADS-B transceiver GPS ADS-B codec Figure 3-4: Conceptual architecture of the proposed ADS-B radar system. 3.3 Interference analysis As mentioned earlier in this chapter, one important task of the ADS-B radar system design is to validate the feasibility to use the bi-phase modulated ADS-B signal as radar signal through interference analysis. In radar applications, when a known signal is sent out, the reflected signal is examined for common elements of the out-going signal. With the signature of randomly added phase change, the match filter is capable of determining the received signal that share the same template as the transmitted signal. The significance of the random bi-phase modulation (0 or 180 ) can be seen clearly in the autocorrelation of the ADS-B radar signal and the ADS-B signal, as depicted in Figure 3-5. It is clear that the autocorrelation of the ADS-B radar signal outperforms that of the original modulation-free ADS-B signal and shows an improved

42 27 correlation peak to noise ratio. In addition, the ADS-B radar signal has to be resistant to other ADS-B signals coming from nearby aircraft. The cross-correlation between ADS-B radar signal and other ADS-B signal, as depicted in Figure 3-6, shows that a typical ADS-B radar signal is uncorrelated with both a standard ADS-B signal as well as another independent ADS-B radar signal, thereby indicating that the on-board ADS-B radar receiver will not be affected by standard ADS-B or ADS-B radar transmissions from other aircraft in the vicinity. With the introduced bi-phase modulation onto the original ADS-B signal, the modulated signal has wider bandwidth, the range resolution is improved and the range side lobes are also further suppressed [34]. The autocorrelation is acceptable to detect the existence of targets, and a range resolution of 75 meters can be achieved, as shown in Figure 3-7. Figure 3-5: Autocorrelation of standard ADS-B signal and autocorrelation of phase modulated ADS-B signal.

43 28 Figure 3-6: Cross-correlation of one phase modulated ADS-B signal with another standard ADS- B signal and another phase-modulated ADS-B signal. Figure 3-7: A simulated range profile based on autocorrelation of a randomly bi-phase modulated ADS-B signal.

44 Link budget analysis The link power budget can be calculated based on the radar range equation 2 t t r 3 4 PG G Pr (3.1) (4 ) R where P r and P t are the received and transmitted power, respectively; G t and G r are the receiving and transmitting antenna gain, respectively; is the signal wavelength; is the target s radar cross section (RCS); and R is the range to the target. We neglect atmospheric losses since ADS-B operates at a low enough frequency where losses in clear air and precipitation are negligible. As shown in Table 3-2, for a target having a RCS of 0 dbsm (1 square meter) at a distance of 4.5 km, the signal-to-noise ratio (SNR) is 5.0 db, a desirable value. For a large airliner with a higher RCS of 20 dbsm (100 square meters), the operational range for the same SNR value could extend to 14 km, which allows more than one minute of reaction time. The link budget calculation shown in Table 3-2 and does not consider any reduction in reception range that will result from the presence of interference and clutter as well as actual line-of-sight limitations. 3.5 Signal specification comparison For the sake of completeness, the signal specification for PSR, SSR, TCAS, ADS-B, and ADS-B radar is tabulated in Table 3-3.

45 30 Table 3-2: Link budget analysis. Receiver Noise Floor = dbm Received Signal Power = dbm Noise figure 3 db Peak transmit power +57 dbm Bandwidth 1 MHz baseband Processing gain (545 samples coherently integrated) 27.4 db Antenna gain (omni-directional) 0 dbsm Assumed RCS 0 dbsm 1/(4π) db 1/(Range) 4 (@3 km) dbm - 4 Square of wavelength 11.2 dbsm SNR = 5.0 db Table 3-3: Comparison of signal specification for various air surveillance technologies. Carrier Frequency Carrier Wavelength Peak Transmit Power Coverage Range Signal Repetition Period PSR (ASR-11) MHz 10 cm 25 kw 60 NM 12 RPM SSR (ASR-11) 1030 / 1090 MHz 30 cm W 60 NM 12 RPM TCAS (Honeywell 1030 / 1090 MHz 30 cm 400 W 30 NM Once per second. CAS 100) ADS-B 1090 MHz 30 cm 500 W 200 NM Once per second. ADS-B radar 1090 MHz 30 cm 500 W 7.5 NM Once per second.

46 31 Chapter 4 Estimation and Tracking for ADS-B Radar Systems 4.1 Overview Due to the limited resources aboard an aircraft, the detection and estimation technique for ADS-B radar system needs to be computationally efficient. In addition, as the number of targets within detection range is not known as prior knowledge, it is important for the ADS-B radar localization algorithm to have the capability to adapt to a sudden increase in the number of surrounding aircraft under the constraint of fixed number of antennas mounted. Moreover, the signal coherence problem, as discussed in the next Section, will need to be properly addressed in the estimation algorithm for the ADS-B radar system. 4.2 Signal coherence problem The Multiple Signal Classification (MUSIC) technique [35], which has been widely adopted in many applications, was the first candidate to be employed for ADS-B radar to perform detection and estimation. However, although MUSIC works well for multiple independent source signals, it encounters problems when the returned signals from multiple targets are highly correlated. The returned signals bounced off from different targets are highly correlated because all the reflected radar echoes are simply the transmitted signal with a slight Doppler shift, i.e. less than 1 khz for the speed of 300 m/s. Moreover, MUSIC has the constraint that the total number of antennas must be larger than the number of targets. In another word, the number of detectable targets is limited. To further elaborate the signal coherence problem and limitation of the number of detectable target,

47 let us assume there are L receivers and m signal sources (1m L) and the system model can be formulated as: 32 y1 ( t) s1 ( t) v1 ( t) [ ( 1, 1),..., ( m, m)] a a yl ( t) s m( t) vl( t) or Y = AS + V, (4.1) where 2 d exp{ j sinmcos( m 1 )} a( m, m) 2 d exp{ j sinm cos( m L )}, (4.2) yl () t is the received signal from the L-th sensor, sm() t is the signal from the m-th source, v () t is additive white noise with zero mean and standard deviation, d is the distance between sensors, is the signal wavelength, m is the arrival elevation angle of the m-th signal, L m is the arrival azimuth angle of the m-th signal, L is the angle according to the position relative to the origin of the coordinate system of the circular array, and a(, ) is the m-th steering vector. It is important to note that the steering vector is a known function of the signal arrival angles and the array element locations. The element a ij in matrix A is dependent on the i-th array element and m m

48 33 its response to a signal incident from the direction of the j-th signal. The L Lcovariance matrix of the Y vector is 2 C = YY = ASS A + VV = ASS A + σi, (4.3) where I is the identity matrix of size L L. If the elements of the vector S are uncorrelated, then the term SS will be positive definite. The angles of steering vectors can be possibly extracted from the eigenvalues and eigenvectors of the covariance matrix C [35]. The location estimation function can be formulated as follows: 1 ENENa PMUSIC (, ) [ a (, ) (, )], (4.4) where E N is defined to be the matrix whose columns are composed of the noise eigenvectors. P MUSIC will be large when and are both equal to the arrival elevation and azimuth angles of the targets, respectively. Hence, the peak of this estimation function may be used to estimate the location of the signal sources. However, if the signal sources are coherent, the received signals from each sensor will not be independent and hence the rank of the covariance matrix C will be reduced. Under this circumstance, it is not possible for MUSIC algorithm to obtain the arrival azimuth and elevation angles of the desired targets. Although there has been research dealing with correlated signals, such as constrained MUSIC [36], cumulant-based coherent signal subspace method [37], and focussing matrix for coherent signal subspace processing (for wideband signals) [38], these approaches do not apply to ADS-B radar system owing to either unavailable prior information or limited signal bandwidth. Therefore, for the ADS-B radar

49 34 system, MUSIC unfortunately cannot be a good candidate for detection and estimation for multiple targets. 4.3 Trilateration-based localization algorithms Similar to MUSIC, most Direction Finding (DF) methods have the constraint that the number of the antennas has to be larger than the number of the targets, thereby not suitable for the ADS-B radar system. Other methods, like the least squares and the unscented Kalman filter approaches, require prior information of the motion model. With thorough exploration, we propose to use trilateration-based localization algorithms for the ADS-B radar system, which no longer has the constraint on the number of detectable targets using fixed number of antennas. Trilateration is a method to determine absolute or relative position of an object based on simultaneous range measurements received from multiple stations located at known locations. Due to its ease of implementation, it is extensively used in applications as diverse as robotics, radar, aerospace surveillance, wireless sensing network (WSN), and automotive applications to provide location-aware services. However, trilateration-based localization approaches are facing many challenges since error is inevitably introduced in all ranging techniques [39], including, but not limited to, Received Signal Strength (RSS), Time of Arrival (TOA), and Time Difference of Arrival (TDOA). Although vision-based localization techniques are possible [40] [43], camera images are sensitive to weather conditions. In a dynamic system where range measurements are noisy and fluctuating, the trilateration problem becomes difficult. A computationally efficient closed-form trilateration solution has been derived in [44], [45]. However, because of the non-linearity between range and target location, the relationship between measurement noise and estimation error is also non-linear in the algebraic solution. The

50 35 ranging error, as well as the sensor placement, caused the Dilution of Precision (DOP) effect, i.e. the ranging error amplification when the position vector is computed. Moreover, it has been shown in [44], [45] that the position estimate is biased even under the assumption that the noise distribution is zero-mean. In the literature, several hybrid methods [46] [49] have been proposed. Localization is done through two phases of estimation processes: in the first phase, a rough location is obtained; subsequently, the second phase involves an iterative implementation that refines the output from the first phase. However, the required computational cost for hybrid methods is high. The motivation of this dissertation is to find a suitable trilateration algorithm that can be adopted by resource-limited UAVs, and hence computational load is a key factor to consider. As a simple and commonly used trilateration technique, centroid localization (CL) [50] exploits the most closely spaced three intersections of constant range loci from three sensors, out of possible six trilateration intersections. Nevertheless, to the author s best knowledge, no research papers have explicitly explained via rigorous analysis why the centroid has been selected, except by empirical evaluation. Similarly, other triangle centers, e.g. incenter [51] and Fermat point (FP) [52], have also been explored, but no clear justification has been provided either. Because position error is most likely embedded in all of the range measurements, which further results in inaccurate intersections, it is the authors belief that the intersections need to be prudently used. In addition to the locations of the intersections, their associated quality needs to be taken into consideration since each of the intersections includes different level of location offset. For example, in an optimistic case when two range measurements are error-free and one of the intersections happens to be the target location, the other intersections are incorrect. Rather than finding the location itself, it is interesting to look for the range errors that would allow the scaled range circles to meet at one point, which indirectly provides the estimated target location. Then the trilateration problem can be considered as searching the most possible

51 36 range scaling factors (RSF) based on the measurement noise statistics. Subsequently, the authors show that RSF can be well represented by the distances from the predicted location to the edges of the triangle with acceptable approximation error. Therefore, the optimal trilateration estimate should be related to the distance to the sidelines, instead of the intersections as conventional thinking. This dissertation investigates several triangle centers, including centroid, incenter, Lemoine point (LP), and FP, and their associated properties that can be useful to the trilateration problem. Finally, enhanced trilateration algorithms, i.e. weighted trilateration (WT) and rangeadjusted weighted trilateration (RAWT), are proposed to deal with sever trilateration scenarios, such as two-intersection case, which triangle center approaches do not work Time of arrival Let us denote the transmitted signal as st (). The distance between the target and the own aircraft can be obtained by cross-correlating the delayed transmitted signal, st ( d ), with the received signal, st ( r ), where d is the internal delay and r 2Rcis the round-trip time to the target. The target range is R and the speed of light is c. In theory, the cross-correlation peak occurs when d, from which the range can be determined. In our simulation experiment, the r peak location may vary a little due to the measurement noise and phase coding scheme. The actual target location is determined after trilateration of the signals received by different receive antennas, as shown in Figure 4-1.

52 37 Figure 4-1: Using trilateration to determine target location. Ideally, the intersection of the trilateration result should indicate the location of the target. However, due to noisy measurements, a blurred area, instead of a point, results, which may be bounded by the circular arcs, or possibly these circular arcs may not even overlap Trilateration modes The challenge encountered by the trilateration problem is the determination of the best estimate of the target position given the noisy range measurements. For the sake of simplicity, the trilateration problem is formulated in 2-D, but it can be extended to higher dimension using the same framework. The equations representing the target location with its distances from each sensor can be expressed as

53 ( x x ) ( y y ) r (4.5a) ( x x ) ( y y ) r (4.5b) ( x x ) ( y y ) r (4.5c) where ( xy, ) is the target location, S ( x, y ), i 1,2,3 the coordinates of sensor station i, and i i i r i the distance from the target to each sensor. All ranging techniques are subject to additive noise. For example, RSS is sensitive to the channel noise and device variation, and TOA and TDOA can be affected by time synchronization or temperature or humidity changes. To incorporate the ranging inaccuracy, the observed ranges are r r, i 1,2,3 (4.6) measurement true i i i where the error i has zero-mean but not necessarily having a Gaussian distribution. Let us define range circle as 3-tuple ( xi, yi, r i) and the coordinates of the intersections from range circles as I x y intersection intersection (, ). The number of intersections from three range circles can be six, four, two, or zero. Let us further define mode 6, mode 4, mode 2, and mode 0 according to the number of intersections, as illustrated in Figure 4-2. The triangle PQ 1 1R1 formed by the most closely spaced three intersections I ( x, y ), i 1,2,3 has closest intersection intersection i i i the smallest circumcircle radius in the Delaunay triangulation of the set of six range intersections. The smallest area of the triangle is not used because the far three intersections can sometimes be co-linear, which renders the triangle area to be nearly zero, as is the case in Figure 1.

54 39 Figure 4-2: Illustration of trilateration modes. As the trilateration problem is viewed in this dissertation as finding the target location through scaling range circles, some preparation work is provided here to facilitate proper analysis. Without loss of generality (WLOG), let us assume ' ' SPis 2 1 the true distance between target and sensor 2 and the measurement noise PP, as shown in Figure 4-3. When the measurement range circle ( x2, y2, S2P 1) is scaled exactly with negative 2, the target should reside on the scaled range circle ' ( x, y, S P ). In the event that all three range circles are scaled with RSFs as negative, i 1,2,3, the three scaled range circles should intersect at the exact i target location. Although the actual values of measurement noise are not known, the prior knowledge of measurement noise distribution can be used in estimation algorithm.

55 40 Figure 4-3: Illustration of the error due to arc-line approximation. The last piece to complete the analysis tool is line-arc approximation. The relationship between RSF, which is ' PP 1 1 in Figure 4-3, and the parallel distance, d( PQ, PQ ) is simply ' ' ' ' d( PQ 1 1, P1 Q1 ) sin( S2PQ 1 1) (4.7) PP ' 1 1 S2PQ 1 1 is an isosceles triangle, and therefore P1 and Q1 must lie between 0 and 90. Since PQ 1 1R1 is formed by the most closely spaced points, Q 1 and R 1 should be located close to each other, therebysin( S2PQ 1 1) 1. As a result, the approximation error of using d( PQ, PQ ) to describe RSF, is small, usually less than 2%. For the sake of brevity, RSF will ' '

56 be considered equivalently as the parallel shift from edges of PQ 1 1R since the concept of RSF 1 will be used extensively in the analysis. In order to understand the occurrence probability of each mode under various noise variances, a simple simulation is set up and the result is shown in Figure ,000 iterations of trilateration using random target locations are executed under noise standard deviation up to 10 m. According to the probability distribution in the simulation result, mode 6 is the most common trilateration scenario, especially when the noise variance is small. However, as the noise variance becomes large, the occurrence probability of mode 4 and mode 2 increases. Specifically, the chance of having four intersections increases from 4% to 22% when the noise standard deviation increases from 0.2 m to 10 m. The probability of seeing mode 2 is about 2% under large noise variance. Finally, the probability of mode 0 is insignificant as none of 10,000 iterations experiences mode Figure 4-4: Occurrence probability of each mode under various noise variances.

57 Triangle center approaches Because of the geometric meaning of its vertices, the triangle PQ 1 1R is a good starting 1 point to estimate the target location. The characteristics of a few triangle centers are discussed in detail. While no single triangle center can always render the best estimate of target location under various types of noise, it is nevertheless interesting to study how the properties of each triangle center correspond to the noise statistical characteristics. To further elaborate this point, let us look at the trilateration problem from a reverse direction and assume that the range measurements are given and the intersections are already determined. The target can still reside at any location as long as the measurement errors satisfy the conditions: measurement r r true, i 1,2,3 (4.8) i i i While follows a certain probability distribution, it is stochastic and its realization can i take any value. As long as i provides appropriate compensation, the target can appear at random location with the intersection locations unaltered. No deterministic methods, to which triangle center approaches belong, can guarantee success in all probabilistic cases. At the end, it is important to note that the computational load to find triangle centers is nearly the same, and hence the best triangle center approach is solely based on the estimation accuracy. Several well-known triangle centers will be discussed in this Section. Note that all triangle center approaches work only for mode 6, and an additional step to identify the correct triangle is critical to the estimation performance.

58 Centroid As the geometric center of the triangle PQ 1 1R, the centroid location in Cartesian 1 coordinate can be found as x x x y y y, 3 3 P1 Q1 R1 P1 Q1 R1, and its barycentric coordinate is B C : : (4.9) Using PQ 1 1R as an example, the translation between barycentric coordinate, [ a : b : c ], 1 and Cartesian coordinates, Cartesian Cartesian (, ) x y, has explicit relationship as follows: Cartesian Cartesian P1 Q1 R1 P1 Q1 R1 ( x, y ) ( ax bx cx, ay by cy ) (4.10) It is straightforward to prove that, given the location of three vertices, the centroid minimizes the summed norm: e ( xˆ, yˆ ) ( xˆ, yˆ ), P ( xˆ, yˆ ), Q ( xˆ, yˆ ), R, ( xˆ, yˆ ) (4.11) vertex As a matter of fact, centroid is the least squares estimator, which finds the estimation result such that the sum of the squares of the difference between the possible location and the three vertices is minimized. However, since the vertices may be off from the true target, the distance from a point to vertices is not always a meaningful metric to the estimation algorithm.

59 Incenter Incenter is the point of concurrence of the interior angle bisectors of a triangle, and the distances from incenter to three edges are equal. In [51], Ahammed et. al. discussed the potential to use incenter of PQ 1 1R as estimate of target location, but proper reasoning was not provided. 1 Recall that RSF is equivalent to the distance of the parallel shift from the triangle edges. Equal distances from incenter to three edges imply three identical RSFs. Stated differently, incenter is a good candidate of the predicted location if all of the sensors have the same magnitude of measurement noise. While identical measurement noises are unlikely, it can be statistically true that, for certain noise distribution, the measurement noises have similar magnitude, especially when the noise variance is very small. However, the estimation accuracy deteriorates quickly if noise variance is large or if different levels of systematic errors exist among measurements. The authors observe through abundant simulation results that the incenter renders acceptable estimation error, in general better than the centroid, when measurement noise variances are equal among all sensors Lemoine Bearing in mind that the distance of the parallel edge shift, as illustrated in Figure 4-5, is a more meaningful indicator than the distance from a point to vertices, one can easily see that the optimal estimator minimizes the sum of the squares of RSFs. Let us denote r ( xˆ, yˆ), i 1,2,3 as i the distances from a predicted location to three sensors. Then, in the sense of statistics, the optimal solution needs to minimize

60 3 2 2 ˆ ˆ edge i i1 e ( x, y) d ( xˆ, yˆ ) (4.12) 45 where d r xˆ yˆ r i measurement i i, ) i 1,2,3 P 1 Q 1 R 1 Figure 4-5: The distances between dashed and solid lines are equivalent to RSFs. Lemoine point, also known as symmedian point, has the property that the total distance to three edges is minimal, and, by its own triangle center definition, LP achieves the minimum of Eq. (4.12). Therefore, the authors propose to use LP as the trilateration estimator, and LP is expected to be the optimal solution among all triangle center approaches. The barycentric coordinate of LP is: LP : : (4.13) B a b c where a, b, and c are the sideline lengths of QR 1 1, PR 1 1, and PQ 1 1, respectively.

61 Fermat In [52], Huang et. al proposed to use FP as the estimation location, and the justification mentioned in [52] is that FP minimizes the total distance from a point in a triangle to three vertices. An interesting question arises: why does FP outperform centroid as the former minimizes the sum of the total distance to three vertices and the latter minimizes the sum of the squared distances? Moreover, one of the FP s properties is that when a triangle has an angle greater than 120, FP is always sited at the obtuse-angled vertex regardless. This property prohibits FP to well reflect the dynamics of the trilateration model. Surprisingly, FP is in general close to LP, especially when all of the angles are smaller than or equal to 120. We will show in the barycentric and Cartesian coordinates the distance between FP and LP is bounded for nearly all forms of triangles. The barycentric coordinate for PF of PQ 1 1R1 can be found as: BFP a1 p u sec P1 : b 1 q u sec Q1 : c 1 r u sec R (4.14) where p, q, and r respectively denote the Boolean variables p boolean( P1 120, q boolean( Q1 120, and r R1 boolean( 120, and u pq r. where To reduce the analysis dimension, let us use the normalized lengths m, 1 m 2, and m 3, a (4.15a) m1 a b c

62 m 2 47 b (4.15b) a b c c m 1 m m a b c (4.15c) As triangle centers are invariant under similarity, the triangle properties are preserved under the normalization process. By replacing the variables in Eq. (4.13) and Eq. (4.14) with m 1 and m, the barycentric coordinates for LP and FP are dependent only on 2 m and 1 m : LP m1 : m2 : (1 m1 m2 ) (4.16a) FP f ( m, m ) : f ( m, m ) : f ( m, m ) (4.16b) We then normalize Eq. (4.16) to obtain the normalized barycentric coordinates for LP and FP: LP LP : LP : LP normalized normalized normalized normalized m m (1 m m ) m m m m m m m m m m m m : : (1 1 2) 1 2 (1 1 2) 1 2 (1 1 2) (4.17a)

63 48 normalized normalized normalized normalized FP FP1 : FP2 : FP 3 f1( m1, m2 ) f2( m1, m2 ) : f1( m1, m2 ) f2( m1, m2 ) f3( m1, m2 ) f1( m1, m2 ) f2( m1, m2) f3( m1, m2 ) f3( m1, m2 ) : f1( m1, m2 ) f2( m1, m2 ) f3( m1, m2 ) (4.17b) After two normalization processes, all of the elements in Eq. (4.17) are functions of m 1 and m 2, and hence it is relatively straightforward to see in simulation how close FP and LP are located. Let us denote the difference between these two normalized barycentric coordinates: normalized normalized E FP LP FP LP, FP LP, FP LP E, E, E normalized normalized normalized normalized normalized normalized (4.18) The simulation results in Figure 4-6, Figure 4-7, and Figure 4-8 show that the elements in (14) are smaller than , and about 70% of various shapes of triangles are smaller than 0.1. Another simulation is performed to show the actual distance between FP and LP in Cartesian coordinate. Two triangle vertices are located at ( 0.5, 0) and (0.5, 0), and the third vertex moves in the field of view (FOV), from (-5, 0) to (5, 5), to create nearly all forms of triangles. Barycentric coordinates for FP and LP are calculated using Eq. (4.13) and (4.14), respectively, and their Cartesian coordinates are obtained through coordinate conversion in Eq. (4.10). The distance between FP and LP is plotted in Figure 4-9. It is shown that the difference of FP and LP locations in Cartesian coordinates is small, especially when the triangle has no angle

64 49 Figure 4-6: E 1, the difference of the first element of normalized FP and LP barycentric coordinates. Figure 4-7: 2 E, the difference of the second element of normalized FP and LP barycentric coordinates.

65 50 Figure 4-8: E 3, the difference of the last element of normalized FP and LP barycentric coordinates. greater than 120. When the third vertex moves further away from the initial two vertices, a slightly increased distance difference is expected. Note that the notch appears when the triangle has an angle equal to 120, and it serves as a good indicator that when the triangle has an angle greater than 120, the fixed FP position makes the estimation location obsolete.

66 51 Figure 4-9: Distance between FP and LP in Cartesian coordinate. Green triangles are two fixed triangle vertices, with edge length as 1 m, and the third vertex moves in FOV Range-based weighted centroid (RWC) Similar to the idea in [53] that each trilateration estimates obtained from different set of beacons have different quality of confidence, each of the intersections represents different probability of being target location. In [54], [55], the assigned weight is a function of RSS values of the access points whose corresponding circles intersect at that point. In another word, smaller range measurements are trusted with higher confidence. This is valid for RSS-based techniques because channel noise varies tremendously over distance. Nevertheless, when such type of weightage is used, the estimated location will inherently favor the closer access point locations.

67 52 Alternative likelihood quantification is sought in this dissertation. The relationship of the intersection of two range circles with respect to the third circle provides a good indication of the quality of the intersection because the true target location should not be far from any of the circles. Therefore, the weighting function is dependent on the range difference between distance from a triangle vertex to sensor i whose range circle does not cross this vertex, and measurement r i. Assuming the distance between two points possesses a normal distribution, vertex r i, representing the probability of one point being the other, the quality of each vertex can then be evaluated using the weighting function described as follows: w vertex i vertex 2 1 ( d ) i exp, v 1, 2, (4.19) where is the variance of the distribution and d r r. The normalized weight, vertex vertex measurement i i i i.e., w w w 3 vertex vertex vertex i i i i1, represents the likelihood of the triangle vertex being the target location. Instead of a fixed variance for the weighting function, a dynamic is chosen as one half of the radius of the circumcircle of the triangle PQ 1 1R1 such that weighting function can adjust properly on the fly. The final estimated location is the weighted-sum of the triangle vertices given by 3 RWC RWC vertex closest, ˆ i i i1 xˆ y w I (4.20)

68 53 Figure 4-10 shows an example of a head-to-head comparison between centroid localization and RWC. The number next to each vertex is the calculated weight using Eq. (4.20), and it can be seen clearly that the top vertex is far away from the true target and has small weight. It is not wise to treat all three vertices equally, like centroid localization essentially does. As a result, RWC outperforms centroid by taking into account the likelihood of each vertex in the final estimation. It is demonstrated that blind usage of intersections may result in poor estimation performance, and in addition, RSF is a useful metric in trilateration analysis. Figure 4-10: Comparison between centroid and RWC. Numerical values are the computed weights for each intersection Performance comparisons To compare the performance of triangle center approaches, including centroid, LP, FP, and RWC, multiple Monte Carlo iterations are simulated with the following setups: (a) random

69 54 measurement noise and fixed target location, and (b) random measurement noise and random target location. Three sensors are located at ( 50 3, 50), (50 3, 50), and (0,100),which form an equilateral triangle inscribed in a circle with radius 100 m. (a) Random measurement noise and fixed target location One target is located at (30,30), and the measurements are affected by random noise. Table 4-1 shows five sets of measurement noise realizations and the subsequently calculated locations of centroid, LP, FP and RWC obtained using Eq. (4.9), Eq. (4.13), Eq. (4.14), and Eq. (4.20), respectively. Among the triangle center approaches, centroid has the worst estimation accuracy. Table 4-1: Comparison of various triangle center approaches for fixed target and standard deviation = 5 m. Test # Target (m) Measurement Noises (m) Centroid (m) LP (m) FP (m) RWC (m) 1 (30, 30) (9.9, 1.6, 1.5) (41.7, 34.9) (39.5, 33.6) (39.7, 33.7) (39.9, 33.9) 2 (1.1, 4.1, 8.3) (24.3, 24.5) (29.6, 27.6) (28.5, 27.4) (29.4, 27.3) 3 ( 6.5, 9.4, 1.6) (17.1, 27.5) (19.9, 29.3) (19.2, 29.4) (19.9, 29.0) 4 ( 2.1, 6.6, -1.3) (22.4, 30.4) (25.0, 31.9) (24.4, 31.9) (24.8, 31.7) 5 ( 2.6, 2.7, 8.1) (23.1, 23.1) (27.2, 25.5) (26.3, 25.3) (27.1, 25.3) 1000 Monte Carlo iterations are simulated under different level of noise variance. Since triangle center approaches require six intersections, cases of mode 0, mode 2, and mode 4 are excluded from the analysis, but the data will be used later in WT and RAWT to test their performance under more severe scenarios. As the noise variance increases from 0.1 m 2 to 5 m 2, about 4% -20% of the samples are discarded. The number of iterations is selected such that the number of mode 2 and mode 4 cases is sufficiently large to conduct proper analysis.

70 55 Localization performance comparison in terms of average estimation error and rootmean-squared-error (RMSE) are shown in Figure 4-11 and Figure 4-12, respectively. It is clear that traditional centroid localization renders largest estimation error, and in addition, the average error between centroid and other approaches is as significant as 25%. Moreover, FP and LP estimation errors are similar although LP has slightly better estimation accuracy. Figure 4-11: Average errors of 1000 Monte Carlo simulations with random noise variance and fixed target location.

71 56 Figure 4-12: RMSE of 1000 Monte Carlo simulations with random noise variance and fixed target location. (b) Random measurement noise and random target location In this Section, the setup is the same as previous Section, except the target is placed randomly with uniform distribution in FOV from 200 to 200 m in both x and y directions. It is important to understand the performance of each trilateration approach at various target locations. Five sets of measurement noise realizations at different target locations are provided in Table 4-2, and the calculated locations for each triangle center approach can be directly compared. The performance trends are similar to fixed target location.

72 57 Table 4-2: Comparison of various triangle center approaches for random target and standard deviation = 5 m. Test # Target (m) Measurement Noises (m) Centroid (m) LP (m) FP (m) RWC (m) 1 (195.3, 173.3) (2.2, 1.6, 10.4) (180.9, 188.7) (184.0, 182.0) (180.6, 181.6) (181.4, 187.9) 2 (18.2, 40.3) (2.0, 10.4, 7.5) (10.2, 38.2) (13.7, 41.2) (12.7, 42.0) (13.8, 40.1) 3 ( 66.5, 147.9) ( 4.7, 4.4, 8.7) ( 77.4, 136.9) ( 75.9, 141.3) ( 78.1, 142.3) ( 75.9, 139.4) 4 ( 119.9, 6.7) ( 9.6, 5.9, 3.6) ( 123.9, 19.8) ( 120.9, 14.6) ( 118.8, 16.1) ( 122.2, 15.8) 5 (174.2, 26.6) ( 6.2, 4.5, 1.0) (169.7, 17.1) (173.5, 25.3) (177.2, 23.1) (171.1, 21.5) Again, 1000 Monte Carlo iterations are simulated. Figure 4-13 and Figure 4-14 indicate among all triangle center approaches the centroid localization results in worst performance. In addition, while RWC seems to have the best performance at one fixed target location, LP in general yields the smallest estimation error at various target locations. Figure 4-13: Average errors of 1000 Monte Carlo simulations with random noise variance and random target location.

73 58 Figure 4-14: RMSE of 1000 Monte Carlo simulations with random noise variance and random target location Enhanced algorithms for severe trilateration scenario Depending on the sensor placement, target location, and corrupted range measurement, three range circles do not always create six intersections, which will make the triangle center approaches invalid. WLOG, let us assume that the range between the target and sensor S 1, is small, and there is a possibility that the range circle ( x1, y1, r1 ) lies completely within ( x2, y2, r 2), or x3 3 3 (, y, r ), or both. The number of intersections is consequently reduced. Therefore, the localization algorithm cannot solely rely on having six intersections. In addition, an additional step is required for triangle center approaches to identify PQ 1 1R1 correctly. If the chosen three intersections fail to form the desired triangle, the triangle center approaches may lead to large estimation error.

74 59 In this section, two algorithms for severe trilateration scenarios are discussed. WT can be deemed as an extension of RWC by assigning weight to each of the intersections, regardless of the number of intersections. RAWT is capable to deal with the extreme case of zero intersection by adjusting the range circles with appropriate offset and post-generating additional intersections. WT and RAWT are closely related to particle filtering (PF) with advantages and limitations. While WT and RAWT are considered coarse-grained due to the small number of intersections (particles), their computational load is significantly lower than PF Weighted trilateration RWC can be readily extended by assigning the weights to all of the intersections, not merely to the vertices of PQ 1 1R1. Each intersection is evaluated and assigned with a weight, and then final estimate location is the weighted-sum of all intersections. Identification of the trilateration mode and finding PQ 1 1R1 are no longer necessary. Nevertheless, while is dependent on the radius of the circumcircle of PQ 1 1R1 in RWC, needs to be pre-selected and is application-specific for different accuracy requirements. However, it is obvious that WT cannot work in mode 0 although it has been shown in Figure 4-4 that occurrence of mode 0 is very rare. In mode 2, large estimation error is expected because of insufficient sample diversity. In fact, most of the time, one intersection is selected as final estimate because of its dominant weight. Therefore, it is suggested to post-generate additional intersections in mode 2 and mode 0 through adjusting the range circles, as discussed in the next section.

75 Range-adjusted weighted trilateration In the extreme trilateration cases of mode 2 and mode 0, it is desired to create additional range intersections. One straightforward approach is to adjust the range circles with a sufficient offset, offset r, that is at least three times of the measurement noise standard deviation. In addition to the original three measurement range circles with radii, ri measurement, i 1,2,3, another six range circles with radii as max measurement r r r offset, i 1,2,3 and i i min measurement r r r offset, i 1,2,3 will be i i introduced. Three annuli with inner radius min r i and outer radius max r i are then formed, and these three annuli should overlap, as shown in Figure For normal distributed measurement noise, the probability of the magnitude of the measurement noise being larger than and hence the possibility of obtaining no overlapping area is insignificant. offset r is only 0.3% Out of these nine range circles, there will be at most 54 intersections. The next step is to find the extended intersections, I m, that satisfy the following condition: min max i m i i r dist( I ( x, y), S ) r, i 1,2,3, m 54 (4.21) I m defines the overlapping area that the target is likely to reside. Subsequently, each of the extended intersections will be evaluated and proper weights will be assigned according to Eq. (4.21).

76 61 Figure 4-15: The extended intersections define an overlapping area. Triangle center approaches require six intersections, but WT and RAWT are insensitive to the number of intersections. While this is an advantage of WT and RAWT over triangle center approaches, it makes it difficult to perform an absolutely fair comparison. Therefore, the simulation in this Section is intended to demonstrate how WT and RAWT handle the severe scenarios like mode 4 and mode 2, which triangle center approaches cannot deal with. The data used in this Section are those discarded in Section 4.1.2, and the estimation results are provided in Figure 4-16 and Figure It can be seen that WT and RAWT are capable to provide acceptable estimation results for severe trilateration scenarios although the estimation error is slightly larger. Furthermore, RAWT has better performance at the cost of additional computational resources.

77 62 Figure 4-16: Average errors of WT and RAWT for mode 4 and mode 2. Figure 4-17: RMSE of WT and RAWT for mode 4 and mode 2.

78 Estimation error over range It is important to know how the trilateration techniques performance deteriorates over wide FOV. Therefore, the performance results of all techniques under mode 6 are compared Monte Carlo iterations are simulated with various range from 100 m to 1000 m. The noise standard deviation is set as 5 m. It is shown in Figure 4-18 and Figure 4-19 that centroid localization degrades rapidly as distance between target and sensors increases. WT and RAWT approaches have the smallest RMSE when the map size is large. However, when the target range is not large, WT and RAWT provide marginal improvement. Although average error of RWC is the smallest, its RMSE is larger than WT and RAWT. As more intersections imply better diversity, WT and RAWT is more robust at random target location under random measurement noise.

79 64 Figure 4-18: Average errors of all trilateration techniques under different map sizes. Figure 4-19: RMSE of all trilateration techniques under different map sizes.

80 Particle filter algorithm Recursive Bayesian estimation and particle filter algorithm are briefly reviewed in this section. Furthermore, a simple multi-target estimation method based on particle filter is proposed for the application of ADS-B radar system. A discrete time estimation problem is considered here. The state vector is denoted by x t whose temporal evolution is given by the state equation: x t = f t (x t-1, v t-1) (4.22) 2 where f t is the state transition function and v t N(0, v) is the process noise with zero mean and 2 variance v. In the ADS-B radar system, the components of the state vector will be target locations. Without prior information about the target motions via estimating target velocities and 2 accelerations, the system transition function will be identity matrix with v sufficiently large in order to cover the motion uncertainty. At each discrete time point an observation y t, related to the state vector, can be represented as follows: y t = h t (x t,n t ), (4.23) where h t is a possibly nonlinear function of the state, x t, and the measurement noise, 2 n N(0, ) is the measurement noise with zero mean and variance. The measurement noise t 2 v n is uncorrelated with the process noise. In the simulation, y t will be the calculated range information, and h t is the process to obtain the target ranges through TOA technique. Let D t

81 66 denote all of the available information, y 1,...,y t, at time. The non-linear prediction density is given via the Chapman-Kolmogorov equation: p( x D ) p( x x ) p( x D ) dx t t1 t t1 t1 t1 t1. (4.24) When new measurement inputs arrive, the solution to compute the posterior distribution p( x D ) of the state vector, given past observations, is given by using Bayes theorem: t t p( y x ) p( x D ) p( x D ) p( y x ) p( x x ) p( x D ) dx t t t t1 t t t t t t1 t1 t1 t1 p( yt Dt1 ) (4.25) Where 1 p( y x ) p( x D ) dx t t t t1 t (4.26) is a normalizing constant. Particle filter [56], [57] is recursive Bayesian filter based on Monte Carlo simulations. It is also known as sequential Monte Carlo methods, bootstrap filtering [58], and the condensation algorithm in computer vision [59], and is very suitable for non-linear and non-gaussian applications as often encountered in the real world. A particle filter is essentially composed of three stages: prediction, update, and resampling. The prediction stage uses the system model to predict the state probability density function (PDF) forward from one measurement time to the next. Since the state is usually subject to unknown disturbances, prediction generally spreads the state PDF. The update operation takes the latest measurement to modify the prediction PDF using

82 67 Bayes s formula. A resampling step was introduced by Gordon et al. [60] in order to discard the particles with very low weights to improve the algorithm efficiency. When probabilities of many particles are too small, it is wise to use those particles on other potential target locations during searching. Particle filters work by providing a Monte Carlo approximation to the probability density function (PDF) which can be easily updated to incorporate new information as it arrives. All the possible locations, i.e. where particles lie, will be assigned with a weighting function corresponding to how likely a target occurs at the particle location. An approximate numerical integration method to solve Eq. (4.25) is described below. (i) Particle generation: Within the field of view (FOV), create N particles and associated weights ( n n t1, w( t1)) n1,..., N x x according to the uniform distribution. (ii) Prediction: Particles propagate according to evolution Eq. (4.22). (iii) Measurement update: Use the available measurements to compute the likelihood of each particle and update the weights of all particles with a posteriori density. This is accomplished using i i i t t1 t t w( x ) w( x ) p( y x ) (4.27) where the final weights sum to one, viz., N i w( x t ) 1. i1 (iv) Systematic resampling: After a predetermined number of iterations, take N samples with replacement from the current particle set based on w( x ). (v) Iteration: Letting t t 1, repeat the process until desired estimation error is achieved. i t

83 Simplified resampling mechanism For abruptly changing systems, Interacting Multiple Model (IMM) method [61] [63] and Generalized Pseudo-Bayesian (GPB) [64] are widely used in the target tracking literature. To reduce the computational complexity on the ADS-B radar system, these approaches are not adopted. In fact, we do not even use the motion equation since the dynamic model of the object cannot be obtained. In the prediction step, particles are simply scattered with a large variance that is able to cover abrupt motion changes. Assume there are two targets around the own aircraft equipped with ADS-B radar system. Each particle will be assigned two weights according to the state PDF. In order to eliminate the particles with weights that are both low, we first randomly pick a number r within 1 [0, N ]. Then we add 1 N to r and select the particle which corresponds to the value of r. If both of the weights of a particle are lower than 1 N, then they are very likely to be neglected when we jump to the next pick. By repeating this procedure, all the particles that have both low weights will be discarded and only those particles with at least one high weight will survive. Parts of the particles will be representing Target 1 if their first weights are clearly larger than the second ones. After resampling, the number of particles remains unchanged. Figure 4-2 depicts the idea of resampling for multiple targets. The resampling step removes particles that are improbable to be targets, but it requires additional processing latency. Hence, we would like to intelligently pick up the right time to do the resampling step. The parameter N eff, the effective sample size, can be used to measure the degeneracy of the algorithm [65], [66]. Once the particles spread out all over the place and only a certain amount of particles are meaningful, N eff will become small. This is the right time to spend extra computational expense to discard low weight particles. A good estimate

84 69 of the effective sample size can be achieved with the quantity N eff N 1 i 2 [ w( x t )]. The i1 resampling step is performed when the number of meaningful particles is less than a predetermined threshold, N threshold. This enables the particle filter algorithm to simply do resampling at appropriate times. The numerical approximation of adaptive resampling for m targets is given as follows, if m is known. Figure 4-20: Resampling mechanism for multiple targets. The procedure is described below: (i) Set up N threshold, which represents the number of the meaningful particles, to be within [0,1]. i (ii) Derive wnew {max( w k ) k1,..., m, i 1,..., N}. (iii) Calculate 1 N 1 i 2 Neff 1 N [ N w k 1], k 1,..., m. i1 (iv) If min{ Neff ( w1 ),, Neff ( wm )} Nthreshold, then take N samples with replacement from the current particle set using w new.

85 Supplementary particle filter algorithm As the ADS-B radar measurement is available once per second and the PF can be completed in the order of one-tenth of a second, most of the time the system is idling and waiting for the new measurement. To improve the estimation performance, some sort of upsampling process is desirable and can be realized through piecewise constant interpolation between successive measurements. We name the algorithm using interpolated measurement on PF as the supplementary particle filter (SPF). Before the new measurement arrives, SPF performs iteratively using the current observation as if the target were static. Standard PF is vulnerable to sample impoverishment because a finite number of particles are used to approximate a continuous distribution. The benefit of SPF over standard PF is that SPF minimizes the estimation error when the sample size is not sufficiently large. SPF provides improved estimation accuracy because particles will be redistributed to high likelihood areas over iterations although the same measurement information is reused. The sample resolution is essentially enhanced during SPF iterations, thereby improving the estimation performance. SPF not only improves the estimation accuracy between successive measurements, but also benefits further the estimation result when new measurement arrives because more particles are already allocated to local mode of the posterior density. Through extensive simulation analysis, it has been noticed that PF takes many iterations to converge. While the ADS-B message is available only once a second, a few dozen seconds may be needed to obtain accurate estimated target locations. However, for the pilots to react on imminent collisions, it is critical to improve the convergence rate and estimation accuracy in spite of the low measurement update rate. Overall, the convergence rate of SPF is about 2-3 times faster than PF and the estimation error of SPF is about one half of the estimation error using standard PF. The gain is significant especially during the very first few measurements.

86 Performance Comparisons In order to ascertain the effectiveness of the algorithm for the ADS-B radar system, the transmitted signal is simulated according to the ADS-B radar message format, which follows the requirements of the ADS-B signal specification. The ADS-B radar waveform, as shown in Figure 4-21, is generated by adding random bi-phase modulation into each bit of the ADS-B signal. The signals received by multiple sensors are essentially the attenuated and delayed replica of the transmitted signal with measurement noise, n. The sensor locations are not restricted, and in the simulation setup, the sensors are circularly positioned and 30 meters apart, using the maximum available distance on an airplane. The transmitted ADS-B radar signal and the returned signals received by the four sensors are shown in Figure The time differences between the transmitted and received signals are used to calculate the ranges from the target to each of the sensors. Since the ADS-B radar signal is broadcast every second, a new measurement will also arrive approximately once per second. Figure 4-21: Transmitted ADS-B radar signal waveform.

87 72 Figure 4-22: Transmitted ADS-B radar signal and received signals from four sensors. Without prior estimation of motion model, additional positional uncertainty is incorporated in the state transition equation to allow the particles to have the potential to move around and to compensate the unknown maneuver while searching for the best solution. As long as one or a few particles are able to follow the target, the calculated weights will be high, and subsequently, in the next resampling step a large amount of particles will be drawn to the neighboring regions of the particles that have high weights. In the simulation, the positional uncertainty is set to 300 m after considering the relative aircraft speed and the finite amount of particles. By taking into account the detection range of 10 km and the computational load for multi-target tracking, the number of particles is chosen to be 10,000 and Nthreshold 5% for the following three simulation scenarios: (1) constant velocity with random acceleration and direction noise, (2) basic flight maneuvers, and (3) multiple targets.