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NASA NTRS2008

Using LDPC Code Constraints to Aid Recovery of Symbol Timing

A method of utilizing information available in the constraints imposed by a low-density parity-check (LDPC) code has been proposed as a means of aiding the recovery of symbol timing in the reception of a binary-phase-shift-keying (BPSK) signal representing such a code in the presence of noise, timing error, and/or Doppler shift between the transmitter and the receiver. This method and the receiver architecture in which it would be implemented belong to a class of timing-recovery methods and corresponding receiver architectures characterized as pilotless in that they do not require transmission and reception of pilot signals. Acquisition and tracking of a signal of the type described above have traditionally been performed upstream of, and independently of, decoding and have typically involved utilization of a phase-locked loop (PLL). However, the LDPC decoding process, which is iterative, provides information that can be fed back to the timing-recovery receiver circuits to improve performance significantly over that attainable in the absence of such feedback. Prior methods of coupling LDPC decoding with timing recovery had focused on the use of output code words produced as the iterations progress. In contrast, in the present method, one exploits the information available from the metrics computed for the constraint nodes of an LDPC code during the decoding process. In addition, the method involves the use of a waveform model that captures, better than do the waveform models of the prior methods, distortions introduced by receiver timing errors and transmitter/ receiver motions. An LDPC code is commonly represented by use of a bipartite graph containing two sets of nodes. In the graph corresponding to an (n,k) code, the n variable nodes correspond to the code word symbols and the n-k constraint nodes represent the constraints that the code places on the variable nodes in order for them to form a valid code word. The decoding procedure involves iterative computation of values associated with these nodes. A constraint node represents a parity-check equation using a set of variable nodes as inputs. A valid decoded code word is obtained if all parity-check equations are satisfied. After each iteration, the metrics associated with each constraint node can be evaluated to determine the status of the associated parity check. Heretofore, normally, these metrics would be utilized only within the LDPC decoding process to assess whether or not variable nodes had converged to a codeword. In the present method, it is recognized that these metrics can be used to determine accuracy of the timing estimates used in acquiring the sampled data that constitute the input to the LDPC decoder. In fact, the number of constraints that are satisfied exhibits a peak near the optimal timing estimate. Coarse timing estimation (or first-stage estimation as described below) is found via a parametric search for this peak. The present method calls for a two-stage receiver architecture illustrated in the figure. The first stage would correct large time delays and frequency offsets; the second stage would track random walks and correct residual time and frequency offsets. In the first stage, constraint-node feedback from the LDPC decoder would be employed in a search algorithm in which the searches would be performed in successively narrower windows to find the correct time delay and/or frequency offset. The second stage would include a conventional first-order PLL with a decision-aided timing-error detector that would utilize, as its decision aid, decoded symbols from the LDPC decoder. The method has been tested by means of computational simulations in cases involving various timing and frequency errors. The results of the simulations ined in the ideal case of perfect timing in the receiver.

Jones, Christopher↗
NASA NTRS2014

NASA's Asteroid Redirect Mission: A Robotic Boulder Capture Option for Science, Human Exploration, Resource Utilization, and Planetary Defense

NASA is examining two options for the Asteroid Redirect Mission (ARM), which will return asteroid material to a Lunar Distant Retrograde Orbit (LDRO) using a robotic solar electric propulsion spacecraft, called the Asteroid Redirect Vehicle (ARV). Once the ARV places the asteroid material into the LDRO, a piloted mission will rendezvous and dock with the ARV. After docking, astronauts will conduct two extravehicular activities (EVAs) to inspect and sample the asteroid material before returning to Earth. One option involves capturing an entire small (~4 - 10 m diameter) near-Earth asteroid (NEA) inside a large inflatable bag. However, NASA is also examining another option that entails retrieving a boulder (~1 - 5 m) via robotic manipulators from the surface of a larger (~100+ m) pre-characterized NEA. The Robotic Boulder Capture (RBC) option can leverage robotic mission data to help ensure success by targeting previously (or soon to be) well- characterized NEAs. For example, the data from the Japan Aerospace Exploration Agency's (JAXA) Hayabusa mission has been utilized to develop detailed mission designs that assess options and risks associated with proximity and surface operations. Hayabusa's target NEA, Itokawa, has been identified as a valid target and is known to possess hundreds of appropriately sized boulders on its surface. Further robotic characterization of additional NEAs (e.g., Bennu and 1999 JU3) by NASA's OSIRIS REx and JAXA's Hayabusa 2 missions is planned to begin in 2018. This ARM option reduces mission risk and provides increased benefits for science, human exploration, resource utilization, and planetary defense. Science: The RBC option is an extremely large sample-return mission with the prospect of bringing back many tons of well-characterized asteroid material to the Earth-Moon system. The candidate boulder from the target NEA can be selected based on inputs from the world-wide science community, ensuring that the most scientifically interesting boulder be returned for subsequent sampling. In addition, the material surrounding the boulder can be collected from the surface, thus providing geological contextual information and additional samples of NEA regolith. The robotic manipulators used for capturing the boulder will ensure some of the surface remains undisturbed and that the boulder will retain its structural integrity, which will preserve the context of any samples collected by the astronauts and ensure a high level of science return. Human Exploration: Due to the coherent nature of the boulder that will be collected, entire encapsulation of the asteroid material is not required. This facilitates exploration and sample collection of the boulder by astronauts in a variety of ways. The total time for EVA during the crew portion of the mission is very limited. Current estimates are that each of the two EVAs will only last four hours. The RBC option will allow crew members to have good situational awareness of the work site and quickly identify sample sites of interest. In addition, the samples to be collected can be readily accessed without having to deal with removal of an encapsulation system, which adds extra complexity and risk for the astronauts during EVA. Resource Utilization: One of the most crucial aspects for resource utilization is the identification and collection of appropriate materials (e.g., volatiles, organics, metals, etc.) that contain components of interest. Prior characterization of NEAs is required in order to increase the likelihood that appropriate materials will be returned. Ground-based observations of small (<10 m) NEAs are challenging, but characterization efforts of larger targets have demonstrated that NEAs with volatiles and organics have been identified. Two potential targets for the RBC option (Bennu and 1999 JU3) have been previously identified as potentially rich in resources, and both are already targets of currently planned robotic missions that will characterize their physical properties in great detail. Planetary Defense: The RBC option involves interaction with a well- characterized potentially hazardoussized NEA that would enable NASA to conduct one or more planetary defense demonstrations. The primary method would use the collected boulder to augment the mass of the ARV and perform an Enhanced Gravity Tractor (EGT) demonstration on the NEA. Additionally, other approaches could be demonstrated during the mission, such as Ion Beam Deflection (IBD) and/or observation of a Kinetic Impactor (KI). The relative effectiveness of a slow push-pull method such as the EGT or IBD could be directly compared and contrasted with the results of the more energetic KI method on the target NEA. Conclusions: This boulder option for NASA's ARM can leverage knowledge of previously characterized NEAs from prior robotic missions, which provides more certainty of the target NEA's physical characteristics and reduces mission risk. This increases the return on investment for NASA's future activities with respect to human exploration, resource utilization, and planetary defense.

Abell, P.↗
NASA NTRS2009

Motion Cueing Algorithm Modification for Improved Turbulence Simulation

Atmospheric turbulence cueing produced by flight simulator motion systems has been less than satisfactory because the turbulence profiles have been attenuated by the motion cueing algorithms. Cardullo and Ellor initially addressed this problem by directly porting the turbulence model output to the motion system. Reid and Robinson addressed the problem by employing a parallel aircraft model, which is only stimulated by the turbulence inputs and adding a filter specially designed to pass the higher turbulence frequencies. There have been advances in motion cueing algorithm development at the Man-Machine Systems Laboratory, at SUNY Binghamton. In particular, the system used to generate turbulence cues has been studied. The Reid approach, implemented by Telban and Cardullo, was employed to augment the optimal motion cueing algorithm installed at the NASA LaRC Simulation Laboratory, driving the Visual Motion Simulator. In this implementation, the output of the primary flight channel was added to the output of the turbulence channel and then sent through a non-linear cueing filter. The cueing filter is an adaptive filter; therefore, it is not desirable for the output of the turbulence channel to be augmented by this type of filter. The likelihood of the signal becoming divergent was also an issue in this design. After testing on-site it became apparent that the architecture of the turbulence algorithm was generating unacceptable cues. As mentioned above, this cueing algorithm comprised a filter that was designed to operate at low bandwidth. Therefore, the turbulence was also filtered, augmenting the cues generated by the model. If any filtering is to be done to the turbulence, it will utilize a filter with a much higher bandwidth, above the frequencies produced by the aircraft response to turbulence. The authors have developed an implementation wherein only the signal from the primary flight channel passes through the nonlinear cueing filter. This paper discusses three new algorithms. Testing shows that the new methods provide the pilot with a more realistic sensation of turbulence; the cues are not attenuated by algorithm. Results of offline testing show the credibility of the models. Offline test verification was based primarily on the evaluation of the power spectral density of the outputs and the time response.

Ercole, Anthony V.↗
NASA NTRS2021

NASA Electric Vertical Takeoff and Landing (eVTOL) Aircraft Technology for Public Services – A White Paper

History has shown that our personal life is highly dependent on the technology that people have developed. A strategic scan of the aerospace environment at the beginning of the 21st century strongly suggests that the world might be approaching a new age of airpower—the era of electrified/hybrid aircraft propulsion. Undeniably, starting from the Montgolfier Brothers balloon flight in 1783, to the Wright Brothers piston engine flight in 1903, and the jet engine of the 1960s, or the space age of today, one can say that leaps in propulsion technology have marked the different ages of human flight. The technological advancements, brought at the beginning of 21st century by the revolution in data exchange, computational power, sensors, wireless communication, internet, and autonomy, contributed to the vision of this new age of propulsion we are approaching. Historically, conventional vertical takeoff and landing (VTOL) aircraft have been equipped with propulsion units relying on complex internal combustion machines (turbines, piston engines, for example), and complex mechanical arrangements (gearboxes, shafts, variable pitch propeller). By contrast, electric VTOL aircraft (eVTOL)1 rely on simpler propulsion units (electric motors and in some cases fixed-pitch propellers). This promotes redundancy and improves tolerance to failures, in turn improving safety. The use of simpler electric propulsion units should also allow significant acquisition and operating cost reductions. Whether full-electric (relying solely on batteries) or hybrid-electric (relying on a combination of batteries, fuel-powered engines, and generators.), eVTOLs are also expected to generate less noise and air pollution than conventional aircraft with similar payloads. According to the 2019 Annual Review of IATA (International Air Transport Association) [ref.1], due to an expected increase in air transport traffic by 5% every year and a doubling of air transport passenger numbers to 8.2 billion by 2037 significant challenges are posed to the aviation industry. Furthermore, this report does not factor in the expected demand for short-range (intra-city) air transportation, which is in development and yet to be operational. The increased demand to fly creates a responsibility to expand in a sustainable manner and an endeavor to develop more environmentally-friendly aircraft. eVTOL aircraft, either piloted or autonomous, is gathering considerable interest worldwide. Modern and novel full-electric or hybrid-electric eVTOL configurations enable a new paradigm shift in air transportation as the aviation industry remains committed to its goals of carbon-neutral growth from 2020 onwards and cutting CO2 emissions to half 2005 levels by 2050. While electric power has been used for decades, recent developments in mobile electric/hybrid propulsion coupled with advanced materials and autonomous systems may create the possibility to transition into the next age of air mobility propelled by electric/hybrid VTOL aircraft technology. Although eVTOL aircraft might seem like an incremental improvement or even a counterintuitive regression with regard to past VTOL development, it has in fact the potential to transform air mobility across a wide range of government applications. Previous transformations in aviation generated dramatic leaps in performance, but the cost was commensurate with performance, limiting quantity produced. This next age appears to take a different approach. Performance may not increase, but at this moment technology is poised for future urban mobility that will spawn commercial passenger drone services, that is, autonomous (pilotless) air taxis and thereby add a new dimension to the urban transportation mix of the future [ref. 2]. Advances in electric propulsion, autonomous flight technology, and 5G communication networks will enable this fast new-growing market to become a reality. It is now time to envision the introduction of electric/hybrid eVTOL aircraft for Public Services2. We believe that in the next decades eVTOL aircraft will have the potential to become an essential tool to Public Service agencies around the world in applications such as firefighting, public safety, search and rescue, disaster relief and law enforcement. This is due to several major factors. • First, with the increasing popularity of small, unmanned aircraft vehicles (UAVs) or drones, many companies today are focusing on the development of passenger UAVs designed to accommodate up to five passengers or equivalent cargo payload. Many such configurations are electric or hybrid-electric designs with VTOL capabilities. Several of these projects have started a flight test program and many more are expected to be in the experimental and development phase in 2020. Such revolutionary vehicles could be in commercial operations by 2030. These eVTOL systems could be ready for selected Public Services missions even sooner. • Second, although these advanced eVTOL vehicles under development still need access to fuel (hybrid) and/or electric charging capability, they can take off and land from almost anywhere. Therefore, such vehicles, both manned and unmanned can be successfully integrated for the critical missions of the Public Services with extra deployment flexibilities. • Third, advancement in electric propulsion systems in the automotive industry together with NASA’s leading efforts in electrification of aircraft propulsion systems, FAA’s ongoing active eVTOL certification programs, and EASA’s proposed framework for the certification of electric/hybrid small category VTOL aircraft in Europe [ref. 3] will help accelerate industry electric propulsion system development and integration. • Finally, eVTOL vehicles could be deployed for Public Services sooner than air taxi or other commercial applications, since Public Services missions may be more easily approved based on specific mission criteria, localized airworthiness authority for public-use aircraft3, and are normally operating under centralized airspace management and control by the theater command. Moreover, public perception and acceptance are generally less of a concern when operations save lives and benefit the wider community. The prioritized introduction of eVTOL aircraft in Public Services is ambitious, but we believe it is achievable in the coming decades if fundamental enablers (people and technologies) are engaged in defining the objectives and needs of these missions. The revolution that is currently taking place in eVTOL aircraft represents an unprecedented opportunity to develop a safer, more affordable, more available and more environmentally friendly future of vertical flight. To ensure that these novel aircraft meet the future expectations of Public Services, it is essential to take a collaborative and multi-disciplinary approach to their development, across engineering disciplines, policy-making, program management, business case development, manufacturing, and flight demonstrations. It should be noted that the term eVTOL (in the near term) used throughout this publication implies aircraft capable of transporting up to 5 persons which may or may not include a pilot if operated fully autonomously, assuming an average of 200 pounds (91 kg) per person or equivalent payload and a range up to 60 miles plus a suitable reserve. Hybrid or hydrogen powered eVTOLs would have greater range. For example, a “3-seat” eVTOL aircraft may only be able to carry two fully equipped firemen, and payload capacity is more relevant when used for the supply mission. Moreover, this paper concentrates on the “last-mile” solutions with a deployment time of no more than 6 hours. Although not specifically discussed in this document, it is understood that the future of Transformative Vertical Flight in general and Public Services, in particular, will also involve smaller UAVs that will undoubtedly play a crucial role in future aerial operations. For example, smaller unmanned aircraft may be used to dispatch medical supplies, portable filtration systems or perform the Search task of future Search and Rescue (SAR) operations. Close collaboration between the aircraft industry, the Civil Aviation Authorities (CAA), e.g., Federal Aviation Administration (FAA), European Aviation Safety Agency (EASA), Transport Canada Civil Aviation (TCCA) and the Department of Defense (DoD) certifiers, will help identify Public Services requirements, define expectations and limit development cost and timescales. Take the US Air Force Agility Prime as an example, the majority of the eVTOL application opportunities and mission elements identified are in line with the NASA TVF WG-4 objectives and use cases. Together, it forms a strong partnership to accelerate the development, certification, and practical deployment for public service missions. The US Air Force Agility Prime has been a collaboration partner on this white paper, and provided valuable input and recommendations. Most of the eVTOL public service mission elements discussed in this paper and additional use cases envisioned by the NASA TVF WG-4 team are shared by the Agility Prime program. The focus and efforts of the Agility Prime in product and system development, industry and government partnership, accelerated certifications as well as early test and deployment are totally in sync with the path forward recommended by this white paper. This kind of collaboration and partnership will help enable the practical use of the eVTOL for public service missions, benefit the eVTOL public acceptance, and accelerate the eVTOL industry revolution.

Johnny T. Doo↗
NASA NTRS2006

NASA Taxonomies for Searching Problem Reports and FMEAs

Many types of hazard and risk analyses are used during the life cycle of complex systems, including Failure Modes and Effects Analysis (FMEA), Hazard Analysis, Fault Tree and Event Tree Analysis, Probabilistic Risk Assessment, Reliability Analysis and analysis of Problem Reporting and Corrective Action (PRACA) databases. The success of these methods depends on the availability of input data and the analysts knowledge. Standard nomenclature can increase the reusability of hazard, risk and problem data. When nomenclature in the source texts is not standard, taxonomies with mapping words (sets of rough synonyms) can be combined with semantic search to identify items and tag them with metadata based on a rich standard nomenclature. Semantic search uses word meanings in the context of parsed phrases to find matches. The NASA taxonomies provide the word meanings. Spacecraft taxonomies and ontologies (generalization hierarchies with attributes and relationships, based on terms meanings) are being developed for types of subsystems, functions, entities, hazards and failures. The ontologies are broad and general, covering hardware, software and human systems. Semantic search of Space Station texts was used to validate and extend the taxonomies. The taxonomies have also been used to extract system connectivity (interaction) models and functions from requirements text. Now the Reconciler semantic search tool and the taxonomies are being applied to improve search in the Space Shuttle PRACA database, to discover recurring patterns of failure. Usual methods of string search and keyword search fall short because the entries are terse and have numerous shortcuts (irregular abbreviations, nonstandard acronyms, cryptic codes) and modifier words cannot be used in sentence context to refine the search. The limited and fixed FMEA categories associated with the entries do not make the fine distinctions needed in the search. The approach assigns PRACA report titles to problem classes in the taxonomy. Each ontology class includes mapping words - near-synonyms naming different manifestations of that problem class. The mapping words for Problems, Entities and Functions are converted to a canonical form plus any of a small set of modifier words (e.g. non-uniformity NOT + UNIFORM.) The report titles are parsed as sentences if possible, or treated as a flat sequence of word tokens if parsing fails. When canonical forms in the title match mapping words, the PRACA entry is associated with the corresponding Problem, Entity or Function in the ontology. The user can search for types of failures associated with types of equipment, clustering by type of problem (e.g., all bearings found with problems of being uneven: rough, irregular, gritty ). The results could also be used for tagging PRACA report entries with rich metadata. This approach could also be applied to searching and tagging failure modes, failure effects and mitigations in FMEAs. In the pilot work, parsing 52K+ truncated titles (the test cases that were available), has resulted in identification of both a type of equipment and type of problem in about 75% of the cases. The results are displayed in a manner analogous to Google search results. The effort has also led to the enrichment of the taxonomy, adding some new categories and many new mapping words. Further work would make enhancements that have been identified for improving the clustering and further reducing the false alarm rate. (In searching for recurring problems, good clustering is more important than reducing false alarms). Searching complete PRACA reports should lead to immediate improvement.

Malin, Jane T.↗
NASA NTRS1995

Mode Transitions in Glass Cockpit Aircraft: Results of a Field Study

One consequence of increased levels of automation in complex control systems is the presence of modes. A mode is a particular configuration of a control system that defines how human command inputs are interpreted. In complex systems, modes also often determine a specific allocation of control authority between the human and automated systems. Even in simple static devices (e.g., electronic watches, word processors), the presence of modes has been found to cause problems in either-the acquisition or production of skilled performance. Many of these problems arise due to the fact that the selection of a mode causes device behavior to be mediated by hidden internal state information. For these simple systems, many of these interaction problems can be solved by the design of appropriate feedback to communicate internal state information to the human operator. In complex dynamic systems, however, the design issues associated with modes seem to trancend the problem of merely communicating internal state information via displayed feedback. In complex supervisory control systems (e.g., aircraft, spacecraft, military command and control), a key function of modes is the selection of a particular configuration of control authority between the human operator and automated control systems. One mode may result in full manual control, another may result in a mix of manual and automatic control, while a third may result in full automatic control over the entire system. The human operator selects an appropriate mode as a function of current goals, operating conditions, and operating procedures. Thus, the operator is put in a position of essentially trying to control two coupled dynamic systems: the target system itself, and also a highly complex suite of automation controlling the target system. From a historical perspective, it should probably not come as a surprise that very little information is available to guide the design of mode-oriented control systems. The topic of function allocation (i.e., the proper division of control authority among human and computer) has a long history in human-machine systems research. Although this research has produced some relevant guidelines, a design approach capable of defining appropriate allocations of control function between the human and automation is not yet available. As a result, the function allocation decision itself has been allocated to the operator, to be performed in real-time, in the operation of mode-oriented control systems. A variety of documented aircraft accidents and incidents suggest that the real-time selection and monitoring of control modes is a weak link in the effective operation of complex supervisory control systems. Research in human-machine systems and human-computer interaction has barely scraped the surface of the problem of understanding how operators manage this task.The purpose of this paper is to present the results of a field study which examined how operators manage mode selection in a complex supervisory control system. Data on mode engagements using the Boeing B757/767 auto-flight system were collected during approach and descent into four major airports in the East Coast of the United States. Protocols documenting mode selection, automatic mode changes, pilot actions, quantitative records of flight-path variables, and verbal reports during and after mode engagements were collected by an observer from the jumpseat. Observations were conducted on two typical trips between three airports. Each trip was be replicated 11 times, which yielded a total of 22 trips and 66 legs on which data were collected. All data collected concerned the same flight numbers, and therefore, the same time of day, same type of aircraft, and identical operational environments (e.g., ATC facilities, weather patterns, traffic flow etc.)

Degani, Asaf↗
NASA NTRSDate not supplied

Monitoring Airspace Complexity and Determining Contributing Factors

The national airspace has evolved over many years to accommodate increased traffic demand [1] while simultaneously maintaining one of the safest forms of transportation [2], [3]. One of the reasons for this success is the ability of the system and the operators to adapt and accommodate to situations that routinely disrupt optimal operations. These situations may include: adverse weather, delays, early arrivals, equipment outages, and other factors that are outside the operators ability to control. These factors can lead to states where automation is unable to properly handle these issues and therefore air traffic controllers and pilots have to intervene, ultimately increasing communication between operators resulting in higher workload. As controller workload increases to handle sub-optimal operating conditions this can be viewed as an increase in complexity. The reasoning for this is because humans are now required to make tactical decisions in response to external factors, resulting in a departure from the strategic plan where operations would be more efficiently managed. Human operators control airspace complexity under rigid regulations that are constantly changing. The airspace is divided into sectors and the number of aircraft assigned to each controller is limited for safe handling. There has been past work that devised airspace complexity metrics in commercial aviation and related these metrics to controller workload (e.g., [4],[5]). The upper bounds on the system load are pre-determined. Such bounds on complexity make for a safe system, but the system cannot scale and adapt to autonomous, dense, and heterogeneous traffic, including the many types of Unmanned Aerial Vehicles (UAVs) envisioned to be added to the operations. We hypothesize that, as traffic density and heterogeneity grow, and other key metrics change, there will be phase transitions at which the way traffic should be managed changes significantly [6]. We offer a method for in-time detection of contributing factors that lead to phase transitions, characterized by increased complexity. To the best of our knowledge, there is no tool similar to our proposed effort that identifies such contributing factors or precursor patterns. To define the scope we are proposing to measure complexity from the viewpoint of the Terminal Radar Approach Control Facilities (TRACON) controller’s perspective. In particular we are analyzing arrivals into KSFO. With safety as the top concern for airspace operators, it is important to recognize that as density and heterogeneity grow, the focus of the system will change. Times of the day when the airspace has low density and heterogeneity, the flights will follow more efficient paths where the aircraft move on established routes that are more or less directly to the destination. However, when density and heterogeneity increases, the system will begin changing focus to avoiding conflicts and collisions and route the flights in a more flexible way. Higher flexibility requires more communication and coordination between controllers and pilots which the current automation is unable to handle. This paper proposes a novel approach that monitors airspace complexity at multiple scales, uses a Machine Learning-based tool that predicts when operations will transition to a regime of greater complexity, and identifies actions that can reduce the complexity while still maintaining efficient and safe operations. We demonstrate our proposed approach using data from multiple complementary sources. This includes, but is not limited to: historical aircraft surveillance data from NASA’s Sherlock Data Warehouse [7], METAR weather data, and airport configuration data from Aviation System Performance Metrics (ASPM). The surveillance data flight paths are sampled at a variable sample rate — increasing as the aircraft approaches the airport. This is due to how Sherlock manages flight track stitching between different radar facilities which have different sampling rates. The weather and performance data are logged at defined intervals throughout the day at a courser refresh rate. In addition to the logged data and metrics, we leverage pre-defined Standard Terminal Arrival Routes (STARs) procedures to characterize the path of each flight. Each flight files for one of these routes in the flight plan well before entering the terminal airspace, and approximately follows the route until it leaves the STAR, typically on the final fix of a runway transition. However, most flights do not always fly the full STAR procedure to completion [8], but the majority do adhere to the fixes within the common route of the procedure. Our approach leverages fixes in the common route of each of the STARs to build a reference path to the airport. This allows us to characterize the flight paths in what we are defining as the “maneuvering area” (the airspace between the STAR and before the flight is lined up on the runway’s final approach) to determine how off nominal the flights are to calculate its complexity score. Determining airspace complexity is a concept that does not have a concrete answer. In designing this metric, we consider what increases the workload for the air traffic controllers. Consequently more specialized vectoring maneuvers results in higher workload. Accordingly, we start with a theory: each flight has a direct path it takes from the STAR’s common route to the final approach’s outer marker fix for the flight’s landing runway. It is important to note that the direct path is only used as a reference. If the majority of the flights have a large consistent offset as compared to other routes it does not necessarily mean that those flights have higher complexity. We are merely building a distribution based on this direct path for that particular STAR and runway pair to determine the normal mode of operations for that route. Flights that are in the upper tail of these distributions will result in higher complexity scores and flights that fly in the median will represent the normal mode of operations and therefore will have lower complexity scores. Since flights following each STAR route take different paths to the airport, we have a different distribution for each STAR route and therefore can model these distributions to compute a complexity score from their respective normalized distributions. To evaluate the effectiveness of our proposed airspace complexity metric we will compare against an established approach based on trajectory clustering [9]. This unsupervised learning technique consists of the following steps: (1) identify the general maneuvering areas (waypoints) by performing $\kappa$-means or DBSCAN clustering on locations where aircraft frequently turn based on the surveillance radar track data, (2) map flight trajectories onto sequences of waypoints, and (3) cluster the sequences based on their common subsequences. From a high-level perspective, this baseline model learns nominal operations in the airspace through the sequence of waypoints that are representative of where aircraft change direction and defines deviations from the nominal operations as “complex.” Therefore, more deviations from the nominal operations correspond to higher complexity values. For our validation, we re-implemented this technique and tune model hyper-parameters to correctly detect waypoints for the arrival traffic into the San Francisco bay area. We will compute the complexity measure over a one-year period using our proposed technique as well as the baseline. Our validation will be based on each technique’s ability to detect a set of undesirable outcomes (e.g., go-arounds, holding patterns, average time in the airspace, etc.). Since our current complexity metric is derived from the offset from the direct reference path, it’s important to understand what causes these offsets. In many of the flights with high offset distance, flights performing holding patterns and S turns can be observed. These maneuvering tactics are utilized to add distance between the aircraft and the destination runway to prevent multiple flights from having conflicting arrival times. In order to predict a rise in complexity (or the precursor to complexity), it’s necessary to be able to identify these potential conflicts (which in turn, result in higher offsets). To do this, we define a “representative flight” for each STAR route and runway pair. This flight is approximately the path the flight would take if there was a clear path with no other flights in the airspace — including the time remaining to the airport. We first identify the flights for a given STAR runway pair using the offset to the reference path distributions that fall between the 44-55 percentiles. This yields the flights that conform to the most normal mode of operation. Each of these flights is partitioned based on the percent complete from the entry point into the maneuvering areas from 0\% – 100\% complete. Then for each percent “bin”, we take the median value of the flight’s latitude/longitude coordinates, airspeed, and (non causal) time remaining to the airport to construct a lookup table for each percent complete bin on a given route. As a flight enters the maneuvering area, we can find the estimated arrival time of a flight to the airport by finding the closest point to the representative path’s percent complete bin (relative to the flight’s current position at any snapshot in the airspace) and therefore retrieve the corresponding remaining time left on the “representative path”. We assume that the flight will follow the representative path to completion when deriving these estimates. We can then compare these estimated arrival times against other flights for the same snapshot in time to identify potential conflicts. If more flights are estimated to arrive within a tolerance window than there are runways available, then we have a potential conflict. We can use this derived measure along with other factors expected to add disruption to the operation such as weather and runway configuration changes as an input to machine learning tools to detect precursors that increases in our complexity measure. This novel method will assist in uncovering insights into the contributing factors that lead to increased complexity that may allow for in-time responses to avoid reaching a high complexity state in the airspace.

complexity↗