In Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 239–248, Seattle, WA, November 2018. Prescriptive Analytics System for Long-Range Aircraf Conflict Detection and Resolution Samet Ayhan∗ Pablo Costas Hanan Samet University of Maryland Boeing Research & Technology University of Maryland College Park, Maryland Europe College Park, Maryland [email protected] , [email protected] [email protected] ABSTRACT 1 INTRODUCTION At the present time, there is no mechanism for Air Navigation In the present Air Trafc Management (ATM) system, Airline Op- Service Providers (ANSPs) to probe new fight plans fled by the erations Center (AOC) personnel fle a fight plan for a particular Airlines Operation Centers (AOCs) against the existing approved fight. The fled fight plan usually contains 2D coordinates of the fight plans to see if they are likely to cause conficts or bring sector fxed way points and the planned initial cruise speed and cruise trafc densities beyond control. In the current Air Trafc Control altitude in addition to their speed and changes along the route. (ATC) operations, aircraft conficts and sector trafc densities are It does not include the time information for the way points and the resolved tactically, increasing workload and leading to potential existing information is not routinely updated by the ATM systems. safety risks and loss of capacity and efciency. Moreover, the fled fight plan is not checked against other fight We propose a novel Prescriptive Analytics System to address a plans to probe potential interference with other aircraft or iden- long-range aircraft confict detection and resolution (CDR) problem. tify sector trafc complexity before the aircraft departs. Airspace Given a set of predicted trajectories, the system declares a confict sector complexity and aircraft separation assurance are dealt with when a protected zone of an aircraft on its trajectory is infringed tactically just a few minutes before the aircraft enters the sector or upon by another aircraft. The system resolves the confict by pre- is likely to have a confict with other aircraft. scribing an alternative solution that is optimized by perturbing at It is estimated that by 2040 the USA alone can expect an in- least one of the trajectories involved in the confict. To achieve crease of more than 68% in the commercial air trafc [10]. Hence, a this, the system learns from descriptive patterns of historical tra- new concept of operations is needed to accommodate this increase jectories and pertinent weather observations and builds a Hidden in volume. To meet this challenge ahead of us, new technologies Markov Model (HMM). Using a variant of the Viterbi algorithm, and procedures for next generation ATM are being developed in the system avoids the airspace volume in which the confict is de- the context of the Next Generation Air Transportation System tected and generates a new optimal trajectory that is confict-free. (NextGen) [8] in the USA and the Single European Sky ATM Re- The key concept upon which the system is built is the assumption search (SESAR) [32] in Europe. The SESAR and NextGen concept that airspace is nothing more than horizontally and vertically con- of operations require a paradigm shift from a highly structured catenated set of spatio-temporal data cubes where each cube is and fragmented system that is heavily reliant on tactical decision considered as an atomic unit. We evaluate our system using real making and with few strategic planning functions based on un- trajectory datasets with pertinent weather observations from two certain information, to an integrated one based on collaborative continents and demonstrate its efectiveness for strategic CDR. strategic management of trajectories and information sharing [35]. In the future ATM systems to be built under NextGen and SESAR, CCS CONCEPTS the trajectory becomes the fundamental element of new sets of • Information systems → Data analytics; • Computing method- operating procedures collectively referred to as Trajectory-Based ologies → Dynamic programming for Markov decision pro- Operations (TBO). The underlying idea behind TBO is the concept cesses; • Applied computing → Aerospace; of business trajectory which is the trajectory that will best meet airline business interests. The TBO concept of operations and the KEYWORDS notion of business trajectory will result in more efcient 4D tra- jectories. Thus, the future ATM system should ofer fexibility to Prescriptive Analytics; Hidden Markov Model; Time Series accommodate business trajectories, while bearing the primary goal ∗Senior Engineer at Boeing Research & Technology. of safety in mind. Overall, the next generation ATM paradigm shift requires more safe and efcient CDR due to fact that maintaining Permission to make digital or hard copies of all or part of this work for personal or the separation minima among the vast volume of aircraft that fy classroom use is granted without fee provided that copies are not made or distributed their versions of most optimal business 4D trajectories becomes for proft or commercial advantage and that copies bear this notice and the full citation on the frst page. Copyrights for components of this work owned by others than ACM more challenging. must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, Hence, we introduce a Prescriptive Analytics System to address to post on servers or to redistribute to lists, requires prior specifc permission and/or a the long-range aircraft CDR problem. The system performs CDR in fee. Request permissions from [email protected]. SIGSPATIAL ’18, November 6–9, 2018, Seattle, WA, USA two steps: In the frst step, given a set of predicted trajectories in © 2018 Association for Computing Machinery. the form of a 4D joint spatio-temporal data cubes on a 3D grid net- ACM ISBN 978-1-4503-5889-7/18/11...$15.00 work, the system declares a confict if one of the aircraft’s predicted https://doi.org/10.1145/3274895.3274947 In Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 239–248, Seattle, WA, November 2018. trajectory segment overlaps with the other’s protected zone at the domain and on confict (i.e., collision) detection and resolution. An same time interval in the future. Obviously, the more accurate the excellent survey of various CDR methods is presented in [13]. In predicted trajectories, the more accurate the detection of the con- this survey, Kuchar et al. propose a taxonomy to categorize the fict as the separation minima will be on the containment volume basic functions of CDR modeling methods. The proposed taxonomy of each predicted trajectory. In the second step, the system builds a includes: dimensions of state information (lateral, vertical, or three- stochastic model, HMM that learns from the historical trajectories dimensional); method of state propagation (nominal, worst-case, and their correlation with the pertinent weather parameters. Using or probabilistic); confict detection threshold; confict resolution a variant of the Viterbi algorithm, the CDR System prescribes an method (prescribed, optimized, force feld, or manual); maneuvering optimal solution by perturbing at least one of the 4D trajectories options (speed change, lateral, vertical, or combined maneuvers); involved in the confict. and management of multiple aircraft conficts (pairwise or global). In summary, the contributions of this paper are as follows: Confict detection methods can be classifed as nominal, worst- • We propose a cube-shaped protected zone surrounding each case, and probabilistic techniques. The nominal technique projects aircraft that can be expanded by joining the neighboring the current states into the future along a single trajectory without cubes horizontally and vertically, yielding a protected zone taking uncertainties into account [9, 37]. The worst-case technique with a desired size. This idea resonates with the assumption assumes that an aircraft will perform any of a set of maneuvers that an airspace is nothing more than a set of concatenated and a confict is predicted if any of the maneuvers could cause a spatio-temporal data cubes around a 3D grid network, where confict [34, 38]. The disadvantage of the worst-case technique is each cube is considered as an atomic unit. that it can declare a confict as soon as there is a minimum likelihood of a confict within the defnition of the worst-case trajectory model • We propose a scalable Prescriptive Analytics System to strate- thereby leading to false positives. The probabilistic approach ofers gically address the aircraft CDR problem. Given a set of pre- a balance between relying on either a single trajectory model as in dicted trajectories, the system declares a confict when a the nominal technique or a set of worst-case maneuvers. Instead protected zone of an aircraft on its trajectory is infringed it models uncertainties to describe potential changes in the future upon by another aircraft at the same time interval in the trajectory [14, 21, 40]. future. Upon a confict, the system executes our confict res- Once a confict has been detected, the next step in the CDR pro- olution algorithm and prescribes a solution that resolves cess is to initiate the confict resolution phase by determining the the confict by perturbing at least one of the 4D trajectories course of action. The confict resolution method and the maneuver- involved in the confict. ing options are two major factors in defning the course of action. • We conduct extensive experiments based on real trajectory Confict resolution methods can be categorized as a) prescribed, b) and weather data from two continents and demonstrate that optimized, c) force-feld, and d) manual. The prescribed resolution our CDR System can detect and resolve conficts with lateral method provides a fxed maneuver based on a set of predefned and vertical accuracies that are within the boundaries of procedures [5]. Hence, depending on the nature of the confict, the conventionally accepted minimum separation values, set predefned resolution maneuver is automatically performed, mini- by the ANSPs. This translates to the fact that, ANSPs can mizing the response time. However, it does not compute the optimal now detect and resolve potential conficts before the aircraft resolution path for the aircraft, resulting in a less efcient trajectory. depart, resulting in safer and greener airspace with more The optimized method provides a confict resolution strategy with efciency and capacity, and thereby reducing the air trafc the lowest cost based on a certain cost function (separation, fuel, controller workload. time, workload, etc.) [9]. In the force-feld resolution method, each Our Prescriptive Analytics System can be used as a ground-based aircraft is treated as a charged particle and the resolution maneu- strategic CDR system by air trafc fow managers to resolve poten- vers are defned using repulsive forces between the aircraft [41]. tial interference among large volume of aircraft and identify high Although it is practical when properly applied, it may require a high density and complex sector trafc before the aircraft depart. The level of guidance on the fight deck especially when the aircraft set of optimized resolutions should improve ATM automation and vary their speed over a wide range. The manual resolution method reduce the workload of air trafc controllers. The rest of the paper allows users to generate potential resolution options and provide is organized as follows. Section 2 reviews related work. Section 3 feedback if the option is viable [40]. During the resolution phase, introduces preliminary concepts followed by Section 4 where our some CDR approaches only ofer a single maneuver [9], while oth- Prescriptive Analytics System is described. Section 5 presents the ers ofer a combination of maneuvers [15]. Obviously, the more results of our experiments, while Section 6 discusses the results. maneuvering options the CDR approach ofers, the more likely an Concluding remarks are drawn in Section 7. efcient solution can be provided to a confict. Our CDR approach has some similarities with [6] due to fact that both approaches 2 RELATED WORK consider the airspace as a set of cubic cells, called the grid model, Trajectory data plays a large role in the problem of aircraft CDR. declare a confict if one of the aircraft’s predicted trajectory seg- Trajectories have been the subject of much work in the spatial ments overlaps with the other’s protected zone, and propose an domain with a focus on cars along roads [30]. The focus has been optimized 4D trajectory for the confict resolution. However, unlike on their generation (e.g., [31]), queries (e.g., [18, 20, 26, 28, 29]), our study, they attempt to address tactical CDR (short-term and and matching (e.g., [12, 17, 27]). This data is collected continuously medium-term) by using Particle Swarm Optimization [6]. and is quite voluminous. Instead, we address the aircraft fight In Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 239–248, Seattle, WA, November 2018.

Figure 1: A sample crossing confict and a PZ. (left) regular Figure 2: Simplifed depiction of a pairwise CDR. representation, (right) our unique representation. Summarizing the above literature and comparing to the proposed minima criteria. Formally, given a pair of predicted aircraft trajec- prescriptive analytics approach, we make the following remarks. tories formed by a set of aircraft positions T = [p ,p ,...,p ], First, our method considers dimensions of state information as 4D. i i1 i2 im T = [p ,p ,...,p ], upon confict resolution, all the distance val- Second, our system is scalable, i.e. it can address CDR problem j j1 j2 jn ues d between the pairs of aircraft positions are greater than the among multiple aircraft. Given a set of aircraft trajectories in 4D, i,j separation minima d > d . our CDR System declares a confict if any of the aircraft’s predicted i,j s trajectory segment overlaps with the other’s protected zone at the Defnition 3.5. Long-range CDR is a process in which confict same time interval in the future. In our approach, one or more cubic detection and resolution is carried out several hours before the cells forming the airspace is considered to be a confict detection potential confict occurs. Hence, long-range CDR is strategically threshold. Next, we compute and prescribe an optimized solution performed before the departure for better planning, whereas mid- which is a confict-free 4D trajectory. Our approach addresses the range and short-range CDR are tactically performed while the CDR problem strategically over a time horizon of several hours to aircraft is airborne. compute confict-free 4D trajectories for optimal fight plans and less complex sector trafc densities. Unlike online CDR approaches in which distance between pre- dicted future aircraft positions are constantly computed and com- 3 PRELIMINARIES pared with separation minima upon receipt of each new aircraft The primary concern of the ANSPs, for example; the FAA in the position, our approach is ofine and uses a 3D grid network as a USA and EUROCONTROL in Europe is to assure safety, which is reference system. In our approach, raw trajectories are transformed quantifed by the number of resolved conficts. into aligned trajectories causing aircraft to move along grid points. This results in confict queries being computed at grid points only. Defnition 3.1. A confict is an event in which two or more In addition, unlike most other CDR approaches, our system consid- aircraft come closer than a certain distance to one another. ers a cube shaped PZ surrounding each aircraft. This idea resonates Defnition 3.2. Separation minima are encoded by lateral and with the fact that our approach creates virtual data cubes around vertical separation, forming a bounding volume around each air- grid points, forming an overall airspace. Each cube is defned by its craft, a protected zone(PZ). Currently, the minimum lateral separa- centroid, the original grid point, and associated weather parameters tion for en-route airspace is 5nmi. It is 3nmi inside the terminal that remain homogeneous within the cube during a period of time. radar approach control (TRACON) area. The minimum vertical With this vision, we defne trajectories as a set of 4D joint cubes. separation is 2000 ft above the altitude of 29000 ft (FL290) and 1000 This uncommon representation of 4D trajectories enables us to ft below FL290. Due to fact that lateral and vertical separation are view conficts and PZ from a unique perspective. Hence, in our view, specifed by single distance values, the resulting PZ becomes a PZ is a cube that can be expanded by joining the neighboring cubes cylinder. Each aircraft is assumed to be surrounded by a PZ that horizontally and vertically. The process yields a PZ with a desired moves along the aircraft. size. In our study, we use a PZ of variable size. It can be made up of a single cube or expanded by a number of cubes in each direction Defnition 3.3. Confict detection is a process that evaluates on each axis reaching a larger volume. Figure 1 illustrates a PZ the separation between any pair of aircraft, by comparing the dis- in two diferent forms. The PZ on the left is formed by a cylinder. tance between them with the separation minima. Formally, given The PZ on the right is formed by 27 cubes. Figure 2 illustrates a a pair of predicted aircraft trajectories formed by a set of aircraft sample pairwise CDR. Aircraft #1 departs before aircraft #2. Both = = positions Ti [pi1,pi2,...,pim], Tj [pj1,pj2,...,pjn] where each aircraft move one cube at a time. In Figure 2a. aircraft #1 and #2 point p is defned by its 4D spatio-temporal parameters (latitude, are located at cube J7 and K6, respectively. This causes a confict longitude, altitude, and timestamp), distance values between them as aircraft #2 intrudes aircraft #1’s PZ outlined in red. In Figure 2b. di,j are computed and compared with the separation minima ds the confict is resolved by a lateral shift to cube L6 by aircraft #2. and a confict is declared if any of distance values is less than the No confict occurs from here on as aircraft #1 follows cubes in gray separation minima di,j < ds . (K7, L7, M7, N 7,O7, P7, R7, S7) and aircraft #2 follows cubes in blue Defnition 3.4. Confict resolution is a process that generates (M7, N 8, N 9, N 10,O11, P11, R11, S11,T 11) until they land at their a feasible safe alternative trajectory by fulflling the separation pertinent . In Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 239–248, Seattle, WA, November 2018.

Algorithm 1: Pairwise Confict Detection Result: Detected confict or no confict Input :Trajectory pairs Ti , Tj , Protected Zone PZi Output:Conficting trajectory segment pjs or null

1 Ti ← [pi1,pi2,...,pim] 2 Tj ← [pj1,pj2,...,pjn]

3 foreach ts ∈ (pis ∩ pjs ) do 4 if pjs ⊂ PZis then 5 return p Figure 3: Overview of the CDR System. js 6 end 4 PRESCRIPTIVE ANALYTICS SYSTEM FOR 7 end CDR 8 return null Figure 3 shows overview of the proposed Prescriptive Analytics System for a simplifed pairwise CDR. Predicted trajectory #1 and #2 are generated by our Aircraft Trajectory Prediction System [2]. weather observations are realizations of hidden aircraft positions Our confict detection algorithm takes predicted trajectories along i.e. trajectory segments and the transitions between the underlying with separation minima as input. The output of the process is a hidden segments following a Hidden Markov model [22]. This as- data cube defned by its 4D position, where confict, if any, occurs. sumption considers a fnite set of states, each of which is associated The next process in the pipeline is the confict resolution, where with a probability distribution over all possible trajectory segments. a variant of the Viterbi algorithm is performed to avoid the con- Transitions among the states are managed by a set of probabilities. ficting trajectory segment. The process perturbs at least one of the The states are not visible, but the pertinent observations are. Given trajectories involved in the confict, generating a new optimized a sequence of observations, the system trains an HMM, and derives path and thereby resulting in confict-free trajectories. hidden states, aircraft positions that correspond to the weather 4.1 Pairwise Confict Detection observations. The system computes the most likely sequence of aircraft positions in three steps: The predicted trajectories along with the size of the PZ are fed into • our pairwise confict detection algorithm, presented in Algorithm 1. In the training data processing step, the system transforms The algorithm declares a confict if a PZ of an aircraft is infringed raw trajectories into aligned trajectories and fuses weather upon by another aircraft at the same time interval in the future. parameters for each grid point along aligned trajectories. To achieve this, the system uses a 3D grid network with a Formally, given a pair of predicted trajectoriesTi = [pi1,pi2,...,pim] spatial resolution of 6km x 6km as a reference system. and Tj = [pj1,pj2,...,pjn] where each trajectory is formed by a set of segments defned by their 4D spatio-temporal centroid parame- • In the test data processing step, the system resamples the ters latitude, longitude, altitude, and timestamp, along with PZ for weather parameters to generate buckets with distinct ranges and feeds them into the time series clustering algorithm [3] trajectory Ti in data cubes, we want to return the very frst tra- to produce input observations. jectory segment pjs , if a confict occurs, null otherwise. Note that each aircraft position along predicted trajectories are recorded once • In the fnal step, the HMM parameters generated in the frst every minute. To compute this, we start with the departure point of two steps and the fight time computed by our Estimated the aircraft that departs beforehand, and keep moving forward, one Time of Arrival (ETA) Prediction System [1] are used as grid point at a time. With the departure of the second aircraft, we input to the Viterbi algorithm. The output is the optimal compare the trajectory segment pjs with PZis at each time instance state sequence, joint 4D cubes defning aircraft trajectories. ts to see if pjs overlaps with PZis . Note that Algorithm 1 assumes During the confict resolution stage, our current CDR System that all the PZs have the same defnition. makes use of the frst two steps, outlined above. However, unlike the 3rd step of the process, our current CDR System avoids the cubes 4.2 Pairwise Confict Resolution where the confict is detected. Hence, the CDR System prescribes an Our confict resolution approach shares a common ground with our optimized solution by perturbing at least one of the 4D trajectories, previous Trajectory Prediction System [2] as they both attempt to involved in the confict. The process executes as follows: In addition address an optimization problem; given a set of weather observations, to the regular HMM parameters of transition, emission, and initial what is the most likely sequence of aircraft positions? However, unlike probabilities, the system uses confict-free probabilities where each the previous system [2], the current confict resolution algorithm state is assigned a probability value indicating how confict-free it avoids the spatio-temporal data cubes where the confict is detected. is. The parameters are fed into a variant of the Viterbi Algorithm, To recapitulate our approach to the optimization problem, we briefy in which the system computes the optimal state sequence by con- review our previous Trajectory Prediction System [2] here. sidering the maximum HMM probabilities. Due to fact that the Given a set of historical trajectories along with pertinent weather trajectory segments that are part of the frst aircraft’s trajectory are observations, the system works based upon an assumption that the assigned low confict-free probabilities, the system avoids selecting In Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 239–248, Seattle, WA, November 2018. them during the Viterbi process, yielding a confict-free trajectory Algorithm 2: Confict Detection for Multiple Aircraft for the second aircraft. Result: Detected confict or approved optimal trajectory Now, we present a variant of the Viterbi algorithm. Note that our Input :A new predicted trajectory Ti , constraints list previous Trajectory Prediction System [2] characterized an HMM CLPZ by the following elements: Output:Conficting trajectory segment pi or updated • N , the number of states in the model. States S = {S1, S2,..., SN } constraints list CLPZ are represented by reference points’ coordinates (latitude, 1 Ti ← [pi1,pi2,...,pin] longitude, altitude) that form aligned trajectories. We denote 2 CLPZ ← [PZ1, PZ2,..., PZm] state at time t as qt . • M, the number of distinct observation symbols per state. Ob- 3 foreach ts ∈ (pi &CLPZ ) do 4 PruneAndSearch servations V = {v1,v2,...,vM } are represented by weather parameters (temperature, wind speed, wind direction, humid- 5 if pi ⊂ CLPZ then ity) recorded at grid points. 6 return pi 7 • The state transition probability distribution A = {aij } is the end probability of an aircraft discretely transitioning from one 8 else state i to another j along its aligned trajectory, where 9 Insert pi into CLPZ 10 end = [ + = | = ] ≤ ≤ aij P qt 1 Sj qt Si , 1 i, j N 11 end • The observation symbol probability distribution in state j, B = bj (k) is the probability of discrete weather parameters having been observed at that specifc state, where 4.3 CDR for Multiple Aircraft Our pairwise CDR solution can be scaled to address CDR for multi- 1 ≤ j ≤ N ple aircraft which can be used towards better planning of airspace b (k) = P[v at t |q = S ], j k t j 1 ≤ k ≤ M sector densities. Similar to the current fight planning procedures, we propose predicted trajectories to be processed on a frst come = • The initial state distribution π {πi } is the probability of frst served basis. For the sake of simplicity, consider an empty an aligned trajectory beginning at a state i, where airspace. The airspace will be fully available to the frst predicted trajectory. Hence, the frst trajectory’s optimal set of data cubes will π = P[q = S ], 1 ≤ i ≤ N i 1 i be reserved in the airspace. This process will introduce a set of con- These parameters form an HMM, compactly denoted by λ = straints in the form of PZs by the frst trajectory to the second and {A, B, and π }. Now, we propose an additional parameter; following trajectories during its fight time. Any confict between the frst and second trajectory will be detected and resolved using • = ( ) The confict-free probability distribution in state j, C cj k our pairwise CDR solution. Once resolved, a new set of constraints is the probability of a confict not occurring at that specifc will be introduced by the second trajectory. The next trajectory in state, where the queue will need to satisfy the constraints introduced by the pre- 1 ≤ j ≤ N vious trajectories and so on. This also means that the next trajectory c (k) = P[v at t |q = S ], j k t j 1 ≤ k ≤ M will need to avoid the PZs in the constraints list while generating its optimal set of data cubes during the confict resolution phase. Hence, the lower the confict-free probability for a particular state, This process will be repeated until one or more fights land, which the lower likelihood of that state to be included in the most probable will result in the removal of all pertinent constraints from the list path. With this new parameter, an HMM can be expanded and which will free up the particular sections of airspace. = denoted by λ = {A, B, π and C} Formally, given a new predicted trajectory Tj [pj1,pj2,...,pjl ] The next step in the process is to choose a corresponding state and a time series of existing constraints listCLPZ = [PZ1, PZ2,..., PZi , = sequence Q = q1,q2,...,qT that best explains the observation se- ..., PZm], where PZi [pzi1,pzi2,...,pzik ] along their existing tra- = = quence O = O1,O2,...,OT given the model λ. A variant of the jectories T [T1,T2,...,Ti ,...,Tn], where Ti [pi1,pi2,...,pik ], we Viterbi algorithm [39] that is based on dynamic programming ad- want to detect and resolve conficts among these trajectories Tj and dresses this problem. The key component in the algorithm is the T (i.e. one vs. all). Note that PZi is formed by a set of data cubes, optimal probability, δt (j) is computed as follows: each defned by 4D spatio-temporal parameters around its centroid pij . With this approach, the implementation and management of constraints list is of central importance. In our implementation, we t = Ö map time instances to data cubes forming PZs, which are stored in δt (j) max πq1bq1 (o1)cq1 (o1) (aqj−1,qj bqj (oj )cqj (oj )) q , ...,q − 1 t 1 j=2 an Octree data structure, where there is one Octree for each time instance. Hence, when a new trajectory comes in, the pertinent Oc- Due to their low confict-free probabilities, a variant of the Viterbi tree is located based on the trajectory’s time instance. We declare a algorithm avoids trajectory segments where the confict is detected, confict if the trajectory segment is found in the Octree. We process and generates a new optimized path. all pairs of possibly conficting data cubes using spatial indexing In Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 239–248, Seattle, WA, November 2018. techniques to prune the search (e.g., [23, 25]). Our scalable confict Table 1: A set of European and U.S.A. airports. detection algorithm for multiple aircraft is presented in Algorithm 2. To keep the constraints list up-to-date, we periodically check AirportCode AirportName and delete the pertinent Octree if any of the time instances has LEAL Alicante–Elche expired. Once a confict has been detected, a variant of the Viterbi LEBL –El Prat Airport algorithm is performed where all the data cubes included in the LECO A Coruña Airport constraints list for the pertinent time instance are avoided to fnd a LEIB confict-free, optimized path for the new trajectory. To achieve this, LEMD Adolfo Suárez Madrid-Barajas Airport we assign a minimum number to the confict-free probabilities of LEMG Málaga Airport those data cubes included in the constraints list. LEMH LEPA Palma de Mallorca Airport Algorithm 3: Confict Resolution for Multiple Aircraft LEVC Result: A confict-free optimized trajectory LEVX Vigo–Peinador Airport Input :# of states N , # of distinct observations M, LEZL Airport transition probabilities A, emission probabilities B, KATL Hartsfeld-Jackson Atlanta initial probabilities π, constraints list CLPZ KBOS Boston Logan International Airport Output:A confict-free optimized trajectory To and KDFW Dallas/Fort Worth International Airport updated constraints list CLPZ KJAX Jacksonville International Airport 1 S ← [p1,p2,...,pi ,...,pn] KLGA NewYork LaGuardia Airport 2 CLPZ ← [PZ1, PZ2,..., PZm] KMIA Miami International Airport KORD Chicago O’Hare International Airport 3 foreach t ∈ ((p ∈ S)& CL ) do s i PZ KPIT Pittsburgh International Airport 4 PruneAndSearch ⊂ 5 if pi CLPZ then so there would be no conficts to fnd. Hence, we used a total of 16 ← × −100 6 cpi 1 10 European and USA pairs of fights that were in close proximity to 7 end cause potential conficts when a minimal perturbation was applied. 8 else ← 9 cpi 1 5.1 Setup 10 end The raw trajectory data from Europe was provided by Spanish 11 end ANSP, ENAIRE using a radar surveillance feed with a 5 seconds 12 VariantOfViterbi update rate. The raw data was wrangled as part of the Data-driven ← ( ) ( ) Ît ( ( ) ( )) AiRcraft Trajectory prediction research (DART) project under the 13 To max πs1bs1 o1 cs1 o1 j=2 asj−1,sj bsj oj csj oj s1, ...,st −1 SESAR Joint Undertaking Work Programme [33]. The European trajectory data contains all commercial domestic fights for Spain, 14 foreach ts ∈ ((po ∈ To)& CLPZ ) do a total of 119,563 raw trajectories and 80,784,192 raw trajectory 15 Insert po into CLPZ points for the period of January through November 2016. The felds 16 end of the raw trajectory data are as follows: fight no, departure airport, arrival airport, date, time, aircraft speed in X, Y, Z directions, and position information (latitude, longitude, altitude). Note that, as a Formally, given the number of states N , number of distinct ob- preprocessing step, we downsampled raw trajectory data from the servations per state M, state transition probability distribution A, original resolution of 5 seconds to 60 seconds and aligned them to observation probability distribution B, and initial state probability our 3D reference grid [2]. The raw trajectory data from the USA was distribution π, along with a confict-free probability distribution extracted from an Aircraft Situation Display to Industry (ASDI) data for all data cubes included in the constraints list at time instances feed [11] which is recorded once in every 60 seconds and provided t = [t1, t2,..., tn], we want to form an HMM λ, and train it to fnd in near real-time by the FAA. The USA trajectory data contains the optimized path that is confict-free. Our confict resolution al- fights between 8 major airports, a total of 4,628 raw trajectories and gorithm for multiple aircraft is presented in Algorithm 3. 450,919 raw trajectory points for the period of May 2010 through December 2015. The felds of the raw trajectory data are as follows: 5 EVALUATION source center, date, time, aircraft Id, speed, latitude, longitude and To evaluate our system, we generated a number of test cases using altitude. Both European and USA weather data were extracted from real trajectory and weather data from Europe and USA. Table 1 the Global Forecast System (GFS), provided by the NOAA [16]. The shows the European and USA airports forming the routes we used original data has 28-km spatial and 6-hour temporal resolution and in our evaluation. Although the ideal evaluation would use real it contains over 40 weather parameters including atmospheric, cloud trajectories in actual conficts, this is infeasible due to the nature of and ground attributes for each grid point as part of its 3D weather ATC operations, where the controller would interfere and separate model. Hence, for this study’s geographic volume and time period the aircraft as soon as they are likely to infringe upon one another, of interest, over 160TB of weather data was collected. In Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 239–248, Seattle, WA, November 2018.

Table 2: Sizes of training and test datasets.

TraininдSetSize TestSetSize TraininдSetSize TestSetSize TestCase# Route#1 Route#2 #trjs #pts #trjs #pts #trjs #pts #trjs #pts 1 LEAL-LEBL 1118 55116 200 9860 LEMD-LEIB 2572 125623 200 9769 2 LEAL-LEBL 1118 55116 19 937 LEMD-LEMH 1056 68141 19 1226 3 LEAL-LEBL 1118 55116 152 7493 LEPA-LEMD 5116 306128 152 9095 4 LEBL-LEMG 1704 127451 43 3216 LEMD-LEMH 1056 68141 43 2775 5 LEBL-LEMG 1704 127451 180 13463 LEPA-LEMD 5116 306128 180 10771 6 LEBL-LEZL 2404 183343 41 3127 LEMD-LEAM 1434 70128 41 2005 7 LEBL-LEZL 2404 183343 46 3508 LEMD-LEMH 1056 68141 46 2968 8 LEBL-LEZL 2404 183343 164 12508 LEMG-LEMD 1403 75408 164 8815 9 LEBL-LEZL 2404 183343 210 16016 LEPA-LEMD 5116 306128 210 12566 10 LEIB-LEBL 1360 53443 259 10178 LEPA-LEMD 5116 306128 259 15498 11 LEIB-LEBL 1360 53443 158 6209 LEPA-LEVC 1426 50467 158 5592 12 LEMG-LEBL 1563 114767 38 2790 LEMD-LEAM 1434 70128 38 1858 13 LEMG-LEBL 1563 114767 46 3378 LEMD-LEIB 2572 125623 46 2247 14 LEZL-LEBL 2380 186299 40 3131 LEMD-LEIB 2572 125623 40 1954 15 KDFW-KJAX 1355 153970 19 2159 KATL-KMIA 1296 108005 19 1583 16 KLGA-KORD 1155 131454 62 7056 KPIT-KBOS 822 57490 62 4339 Due to fact that our current system aims at addressing the CDR number of conficts in each case and found which bin they belong problem before departure, at least a pair of predicted trajectories are to. The outcome is presented as a set of histograms in Figure 5. Our needed as input. Hence, we used our previous system [2] to generate algorithm detected 87.2% of the conficts within the frst bin size a pair set of predicted trajectories. Next, we searched and found a and 99% of the conficts within the frst two bin sizes on all 16 test number of trajectory points between the two fights’ trajectories cases. Note that the confict detection can only be as accurate as in the frst and second pair, where the date, latitude, longitude, and the predicted trajectories. Hence, these errors can be attributed to altitude values matched, and time mismatched. By perturbing one the accuracy of our Trajectory Prediction System [2], defned by of the fights’ departure time we virtually created conficts, where the horizontal, and vertical error of 14.981nmi and 1589.452ft both aircraft traversed the same trajectory point at the same time. respectively along the entire test trajectories. Table 2 shows the fnal size of training and test data in number To resolve the conficts, we ran our confict resolution algorithm of trajectories (#trj) and points (#pts). Note that trajectory data as highlighted in Section 4.2. Figure 6 is a closer look at one of alone contains over 4 million trajectory points. In Table 2, the test the detected and resolved conficts by our system. In all fgures, data represents the conficting trajectories. Aside from these 1,677 the yellow cubes and white cubes represent the frst and second trajectory pairs, we also bootstrapped by drawing 100 additional fight’s, respectively, predicted trajectories. The red line parallel to trajectory pairs with replacement from the trajectory set to test the white cubes represents the frst fght’s actual trajectory and the for the false positive cases. Hence, we evaluated our CDR System’s red line parallel to the yellow cubes represents the second fight’s efectiveness with a total of 3,554 (3,354 + 200) test trajectories on actual trajectory. As both aircrafts move one cube at a time in the all 16 test cases. fight direction, the PZ illustrated in the cyan cube around the current position of the frst fight also moves forward in the form 5.2 Results of a sliding window. The frst fgure on the far left shows where each aircraft is at time t − , represented respectively by the solid We evaluated our CDR System by comparing the output of confict s 1 white cubes for the frst and yellow cubes for the second fight. detection and confict resolution with the ground truth on 16 test The second fgure from the left captures the confict detected at cases. Figure 4 illustrates the pairs with pertinent training and test time interval t by our system illustrated with a solid red cube. data in white and yellow lines for these test cases. To evaluate our s The actual confict occurs at where the red lines intersect. Note confict detection capability we used trajectory prediction accuracy that both the predicted confict position and the actual confict metrics as outlined in [19] and computed horizontal and vertical position are within the frst fight’s PZ. The third fgure from the errors e , e . To compute the errors, we fed a pair set of horiz vert left is the 3D view of the second fgure from the left. The actual and predicted trajectories generated by our previous system [2] into predicted confict positions are only 2 cube sizes away from each our confict detection algorithm and compared the locations of other, considering the center of the cube as the predicted position virtual conficts versus locations of conficts detected by our CDR of the aircraft. The fgure in the far right illustrates the optimized system. Next, we created 4 bin sizes, where each bin size is an solution to the confict by our system. The frst fight’s trajectory integer multiple of 5nmi of lateral and 2000ft of vertical distances, has been perturbed vertically and the confict has been resolved conventionally accepted as minimum separation values for enroute by our system. The altitude of the second fight has been elevated airspace by ANSPs. Table 3 presents the pertinent condition for resulting in confict being resolved. Note that due to assignment each bin. Using horizontal and vertical error values, we counted the In Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 239–248, Seattle, WA, November 2018.

Figure 4: Visual representation of training and test data for conficting pairs of fights. of low confict-free probabilities to the 3D grid points inside of the Table 3: Horizontal and vertical error ranges for the bins. PZ, the system avoids selecting them during the confict resolution stage, generating confict free trajectories. Condition Bin As the fnal evaluation step, we executed our confict resolu- 0nmi ≤ ehoriz ≤ 5nmi ∧ 0ft ≤ evert ≤ 2000ft 5nmi,2000ft tion algorithm on all conficts formed by 1677 trajectory pairs and 5nmi < ehoriz ≤ 10nmi ∨ 2000ft < evert ≤ 4000ft 10nmi,4000ft computed accuracy values based on the number of successful resolu- 10nmi < ehoriz ≤ 15nmi ∨ 4000ft < evert ≤ 6000ft 15nmi,6000ft tions. Due to the fact that our confict resolution algorithm resolved 15nmi < ehoriz ≤ 20nmi ∨ 6000ft < evert ≤ 8000ft 20nmi,8000ft the vast majority of conficts on all test cases, we provide aggre- gated results overall, rather than provide results for each test case. prediction accuracy during the cruise phase is often considerably Table 4 presents accuracy values for each bin. Note that, to resolve higher than the climb and descent phases of the fight. 2) All con- the conficts, we treated each bin diferently based on their varying ficts we used in our experiments took place during the cruise sizes so that only relevant 3D grid points were avoided. The process phase of the fights. With 6.012nmi of mean horizontal error on perturbed the trajectory for the second fight, generated an optimal the confict positions, our confict detection algorithm found 99% alternative and yielded confict-free trajectories. of conficts within the frst two bins of separation minima (10nmi, 4000ft). We also verifed that between none of the additional 100 6 DISCUSSION trajectory pairs where the virtual confict has never occurred was Our confict detection algorithm reached 6.012nmi of mean hori- falsely detected as a confict by our system. Our confict resolution zontal error. Note that this value is considerably less than 14.981nmi, algorithm’s mean accuracy was over 97% on all test cases. Though, the mean horizontal error by our Trajectory Prediction System [2] it is interesting to see that it was unable to reach 100% accuracy, along the entire trajectory points including climb, cruise and de- given the fact that all it had to do was avoid the selected 3D grid scent phases of a fight. This is due to two major facts: 1) Trajectory points when generating the new confict-free optimal trajectory. In Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 239–248, Seattle, WA, November 2018.

Figure 5: Confict detection histograms showing how many conficts were captured by our CDR System in each bin. The reason for that was the sparse distribution of data cubes, i.e. These goals can be achieved in the planning phase before aircraft lack of data over the 3D grid network. The algorithm was unable depart, improving ATM automation and reducing the air trafc to connect the new trajectory segments from start to end due to controller workload. disconnection. Hence, our CDR System craves for more data to Table 4: Accuracy of our confict resolution algorithm. reach higher accuracy values. These results validate the efectiveness of our system on the long- range CDR problem. However, this is not to say that strategic CDR Accuracy will detect and resolve conficts once for all and no more conficts Bin1 (5nmi, 2000ft) 98.4% will occur during the fight. There will likely be some convective Bin2 (10nmi, 4000ft) 97.4% weather patterns shaping after departure. These sudden changes Bin3 (15nmi, 6000ft) 93.7% causing potential conficts should be addressed tactically by short Bin4 (20nmi, 8000ft) 100.0% and or medium-range CDR systems while the aircraft is airborne. 7 CONCLUSION Although we were not able to fnd, there may also likely be some We have presented a novel Prescriptive Analytics System address- exceptional cases where false positive conficts may be found. These ing a long-range CDR problem. Our experiments on real trajectory cases should also be addressed tactically by short and or medium- and weather datasets from two continents verify that our system range CDR systems. Note that the larger the selected PZ value, the achieves lateral and vertical accuracies that are within the bound- higher probability of fnding and resolving the conficts between aries of conventionally accepted minimum separation values, set trajectories. However, that also means less denser sectors resulting by the ANSPs. With our system, ANSPs can detect and resolve in inefcient use of airspace. Hence, the tradeof should be handled potential conficts long before the aircraft depart, resulting in safer carefully by the ANSPs. and greener skies with higher efciency and capacity, and thereby Overall, we propose our system to be used by AOCs to fle more reducing the air trafc controller workload. realistic fight plans. Our system can also be used by ANSPs to vali- Some future work could involve adding a spatial browsing ca- date that the fled fight plans do not cause conficts with previously pability [4, 7, 24] for the trajectories as well as incorporating our approved fight plans or increase any sector trafc complexities. methods in a distributed spatial environment [36]. In Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pages 239–248, Seattle, WA, November 2018.

Figure 6: Illustration of a detected and resolved pairwise confict by our system.

8 ACKNOWLEDGEMENTS Head, SC, 1–18. [20] S. Peng, J. Sankaranarayanan, and H. Samet. 2016. SPDO: High-Throughput Road This work was supported in part by the NSF under Grants IIS-13- Distance Computations on Spark Using Distance Oracles. In Proceedings of the 20791 and IIS-18-16889. We are grateful to the Boeing Research 32nd IEEE Int’l Conference on Data Engineering. Helsinki, Finland, 1239–1250. & Technology Europe, a member of the project DART [33] team [21] M. Prandini, J. Hu, J. Lygeros, and S. Sastry. 2000. A Probabilistic Approach to Aircraft Confict Detection. IEEE Transactions on Intelligent Transportation for providing the European trajectory data used in this study. The Systems 1, 4 (December 2000), 199–220. project DART has received funding from the SESAR Joint Under- [22] L. Rabiner. 1990. Readings in Speech Recognition. Morgan Kaufmann, San Francisco, CA, Chapter A Tutorial on Hidden Markov Models and Selected taking under Grant Agreement No. 699299 under the European Applications in Speech Recognition, 267–296. Union’s Horizon 2020 Research and Innovation Programme. [23] H. Samet. 2006. Foundations of Multidimensional and Metric Data Structures. Morgan-Kaufmann, San Francisco, CA. [24] H. Samet, H. Alborzi, F. Brabec, C. Esperança, G. R. Hjaltason, F. Morgan, and E. REFERENCES Tanin. 2003. Use of the SAND spatial browser for digital government applications. Commun. ACM 46, 1 (January 2003), 63–66. [1] S. Ayhan, P. Costas, and H. Samet. 2018. Predicting Estimated Time of Arrival [25] H. Samet and M. Tamminen. 1986. An improved approach to connected compo- for Commercial Flights. In Proceedings of the 24nd ACM SIGKDD Int’l Conference nent labeling of images. In Proceedings of Computer Vision and Pattern Recogni- on Knowledge Discovery and Data Mining. , UK, 33–42. tion’86. Miami Beach, FL, 312–318. [2] S. Ayhan and H. Samet. 2016. Aircraft Trajectory Prediction Made Easy with [26] J. Sankaranarayanan, H. Alborzi, and H. Samet. 2005. Efcient query processing Predictive Analytics. In Proceedings of the 22nd ACM SIGKDD Int’l Conference on on spatial networks. In Proceedings of the 13th ACM Int’l Symposium on Advances Knowledge Discovery and Data Mining. San Francisco, CA, 21–30. in Geographic Information Systems. Bremen, Germany, 200–209. [3] S. Ayhan and H. Samet. 2016. Time Series Clustering of Weather Observations in [27] J. Sankaranarayanan, H. Alborzi, and H. Samet. 2006. Distance Join Queries on Predicting Climb Phase of Aircraft Trajectories. In Proceedings of the 9th ACM Spatial Networks. In Proceedings of the 14th ACM Int’l Symposium on Advances in SIGSPATIAL IWCTS. San Francisco, CA, 25–30. Geographic Information Systems. Arlington, VA, 211–218. [4] F. Brabec and H. Samet. 2007. Client-based spatial browsing on the world wide [28] J. Sankaranarayanan and H. Samet. 2009. Distance oracles for spatial networks. web. IEEE Internet Computing 11, 1 (January/February 2007), 52–59. In Proceedings of the 25th IEEE Int’l Conference on Data Engineering. Shanghai, [5] B. Carpenter and J. Kuchar. 1997. Probability-based Collision Alerting Logic for China, 652–663. Closely-spaced Parallel Approach. In Proceedings of the 35th Aerospace Sciences [29] J. Sankaranarayanan and H. Samet. 2010. Query processing using distance oracles Meeting and Exhibit. Reno, NV, 1–8. for spatial networks. IEEE Transactions on Knowledge and Data Engineering 22, 8 [6] J. Cobano, D. Alejo, G. Heredia, and A. Ollero. 2013. 4D Trajectory Planning (August 2010), 1158–1175. in ATM with an Anytime Stochastic Approach. In Proceedings of the 3rd Int’l [30] J. Sankaranarayanan and H. Samet. 2010. Roads belong in databases. IEEE Data Conference on ATACCS. Naples, Italy, 1–8. Engineering Bulletin 33, 2 (June 2010), 4–11. [7] C. Esperança and H. Samet. 2002. Experience with SAND/Tcl: a scripting tool for [31] J. Sankaranarayanan, H. Samet, and H. Alborzi. 2009. Path oracles for spatial spatial databases. Journal of Visual Languages and Computing 13, 2 (April 2002), networks. PVLDB 2, 1 (August 2009), 1210–1221. 229–255. [32] SESAR. 1999. Single European Sky ATM Research. http://www.eurocontrol.int/ [8] FAA. 2009. The NextGen. https://www.faa.gov/nextgen/ dossiers/single-european-sky [9] FAA. 2012. Trafc Alert and Collision Avoidance System (TCAS II). [33] SESAR. 2017. DART. http://dart-research.eu/the-project/ https://www.faa.gov/other_visit/aviation_industry/airline_operators/airline_ [34] M. Shewchun, J. Oh, and E. Feron. 1997. Linear Matrix Inequalities for Free Flight safety/info/all_infos/media/2012/InFO12010.pdf Confict Problems. In Proceedings of the 36th IEEE Conference on Decision and [10] FAA. 2015. TAF. http://taf.faa.gov/Downloads/TAFSummaryFY2015-2040.pdf Control. San Diego, CA, 2417–2422. [11] FAA. 2016. Aircraft Situation Display to Industry. http://www.fy.faa.gov/ASDI/ [35] M. Soler, A. Olivares, E. Stafetti, and J. Cegarra. 2011. Multi-phase Optimal [12] E. Jacox and H. Samet. 2008. Metric space similarity joins. ACM Transactions on Control Applied to 4D Business Trajectory Strategic Planning in Air Trafc Database Systems 33, 2 (June 2008), 7. Management. In Proceedings of the 1st Int’l Conference on ATACCS. Barcelona, [13] J. Kuchar and L. Yang. 2000. A Review of Confict Detection and Resolution Spain, 68–78. Modeling Methods. IEEE Transactions on Intelligent Transportation Systems 1, 4 [36] E. Tanin, A. Harwood, and H. Samet. 2005. A distributed quadtree index for (December 2000), 179–189. peer-to-peer settings. In Proc. of the 21st IEEE Int’l Conf. on Data Engineering. [14] W. Liu and I. Hwang. 2011. Probabilistic Trajectory Prediction and Confict Tokyo, Japan, 254–255. Detection for Air Trafc Control. Journal of Guidance, Control, and Dynamics 34 [37] A. Valenzuela and D. Rivas. 2009. Confict Detection and Resolution in Converging (November 2011), 1779–1789. Air Trafc. In 9th AIAA ATIO Conference. Hilton Head, SC, 1–13. [15] P. Menon, G. Sweriduk, and B. Sridhar. 1999. Optimal Strategies for Free-Flight [38] A. Vink, S. Kauppinen, J. Beers, and K. Jong. 1997. Medium-term Confict Detec- Air Trafc Confict Resolution. Journal of Guidance, Control, and Dynamics 22 tion in EATCHIP Phase III. In Proceedings of the 16th DASC. AIAA/IEEE Digital (March 1999), 202–211. Avionics Systems Conference. 45–52. [16] NOAA. 2016. NCEP Global Forecast System. https://www.ncdc.noaa.gov/ [39] A. Viterbi. 1967. Error Bounds for Convolutional Codes and an Asymptotically data-access/model-data/model-datasets/global-forcast-system-gfs Optimum Decoding Algorithm. IEEE Transactions on Information Theory 13, 2 [17] S. Nutanong, E. H. Jacox, and H. Samet. 2011. An incremental Hausdorf distance (April 1967), 260–269. calculation algorithm. PVLDB 4, 8 (August 2011), 506–517. [40] L. Yang and J. Kuchar. 1998. Using Intent Information in Probabilistic Confict [18] S. Nutanong and H. Samet. 2013. Memory-efcient algorithms for spatial network Analysis. In AIAA GNC Conference and Exhibit. Boston, MA, 797–806. queries. In Proceedings of the 29th IEEE Int’l Conference on Data Engineering. [41] K. Zeghal and E. Hofman. 1999. Design of Cockpit Displays for Limited Delega- Brisbane, Australia, 649–660. tion of Separation Assurance. In Proceedings of the 18th Digital Avionics Systems [19] M. Paglione and R. Oaks. 2007. Implementation and Metrics for a Trajectory Conference. St. Louis, MO, 1–8. Prediction Validation Methodology. In AIAA GNC Conference and Exhibit. Hilton