Literature Review Aircraft Trajectory Prediction By Cameron Sheridan I. Abstract The purpose of this review is to identify and analyse work that is currently being done on aircraft trajectory prediction (ATP); particularly the approach of modern day researchers to the problematic issue of the growingly clustered airspace. The benefits of this review include the exploration of several sub-topics of the literature.
Through examining the current methods towards trajectory modelling validation and the techniques that are now employed to neutralise error sources, it was found that with the modern-day approaches an algorithm and its trajectory prediction (TP) can be assessed and consequently improved upon. A number of systems pertinent to conflict are discussed and results are presented which illustrate and compare the effectiveness of heading and altitudinal resolution manoeuvres.
Additionally, a number of recent developments and innovations in the field pertinent to the technologies and techniques used are discussed, thus illustrating a clear indication of research still moving forward in this field. II. Introduction An ATP is a ‘mapping of points over a time interval [a,b] to the space R? ’ (Tastambekova et al. 2010, p. 2). Although this is correct in many senses, this explanation fails to acknowledge the intricacy and designed purpose. More accurately, a TP module has the capacity to calculate the future flight path of an aircraft given that it has been supplied with the required data, i. . the flight intent, an aircraft performance model, and finally, an estimation of the future atmospheric/environmental conditions (Swierstra and Green 2004). An aircraft trajectory is a future path of an aircraft that can be represented visually in three forms: 2D, 3D and 4D (x, y, altitude and time) with 4D the more frequently used nowadays by air traffic control (ATC) and air traffic management (ATM) due to its far more realistic representation and ease of interpretation (Vivona et al. 2010; Poretta et al. 010; Paglione and Oaks 2009). The significance of ATP is certainly appreciated. There is support for the importance of TP and the role it plays in advanced ATM operations, especially with a growingly clustered airspace in the next decade (Lee et al. 2010; Porretta et al. 2010 and Denery et al. 2011). The most crucial function of a TP however, as viewed by Lymperopoulos and Lygeros (2010), is to supply advice to ATC. Consequently, they can then make well-informed executive judgments to ensure the safety and effectiveness of our airspace.
The purpose of this study is to inform what is happening in this field through examination of both the developments within ATP and the current problems facing researchers: namely, the significant increase in air-traffic by 2025. This will be done through exploring recent literature in this field that pertains to: conflict detection and resolution; the technologies and techniques involved; and, the error sources that are involved with a prediction and their subsequent effect on the uncertainty of a prediction. III. Modelling Validation and Uncertainties
Efficiency and accuracy are two central points of this literature, which alone could be considered as the determining factors of a respectable TP model; thus, sufficient research is required to improve both, without the sacrifice of one. How does one validate the performance of an algorithm and whether its TP is ‘accurate’? The common answer it seems (Anonymous 2010 and Paglione and Oaks 2007, pp. 2) is through the degree of conformity between the measured or predicted data and the true data of an aircraft at a given time. A. Uncertainties Figure 1: Paglione and Oaks (2009) Figure 1: Paglione and Oaks (2009)
Uncertainties are perhaps the biggest hurdle in further advancements in this field. Obviously, as the prediction increases in time, the uncertainties of the flight begin to take effect – up to a point where the trajectory becomes almost impossible to predict accurately with any degree of assurance. The consequential effect of uncertainties in a prediction may result in: two or more aircrafts losing separation; an aircraft not arriving to schedule; or even, the inability to detect flaws in either the ATP algorithm or the aircraft itself, to name a few. Therefore, there is a need to lessen the ffect of these lingering burdens. In reality this is quite difficult, and as such, requires particular attention of the algorithms used by an aircraft to validate its performance. B. Modelling Validation Performance validation verifies that a TP model performs correctly, and determines the degree of accuracy of a model’s representation compared to the real system (Vivona et al. 2010 and Garcia et al. 2009). There are further ways to validate predicted data; such methods include those shown by Paglione and Oaks (2007) who looked at the associated accuracy metrics; Poretta et al. 2008) who evaluated a 4D TP model for civil aircraft; and finally, the Plan, Do, Study, Act (PDSA) evaluation process of a TP (see figure 1). This practice and its application have been shown by Paglione and Oaks (2009). Inspired by the relationship of trajectory predictors to higher level applications, the authors stressed the need for improving modelling procedures through an iterative process consisting of four stages. Fredrick et al. (2009) were able to analyse ways to validate a program with their test and evaluation process.
Particular focus was on a metrics approach which offers measures on the performance of an aircraft. This method may provide greater effectiveness in programs and is proclaimed to play a “critical role as a continuum of supporting activities for the TP programs” [Fredrick et al. (2009), pp. 9]. Vivona et al. (2010) also proposed a new methodology in her work which is designed for a similar purpose. The techniques used are titled ‘white box testing’ and ‘test bench testing’.
The former involves knowledge of the internal processes that occur within a TP model, and through this information there will be a sequence of tests which accumulate together to validate the entire TP. The latter test is slightly different in that, as opposed to analysing current state data, it requires entering input data into an algorithm’s interface and then assessing the data that was produced as a result. Both are expected to become more commonly used in the approaching years. C. Error Sources and Corrective Measures
Jackson (2010) reiterated the ineffectiveness and poor performance of automation systems in the company of errors and uncertainty sources. This suggests, and was considered equally by Paglione and Oaks (2009) and Vivona et al. (2010) that the performance of these systems is dependent on the accuracy of the TP. Consequently, the requirement to minimise all potential error sources has particular precedence in current research. Environmental factors (wind, temperature, air pressure, etc. ), along with human errors and algorithmic/system imperfections are the typical causes for the uncertainty in a prediction.
Further error sources such as: the measurement of aircraft state; aircraft performance models; knowledge of aircraft guidance modes and control targets; atmospheric model; and, clearance issues are all predicted to be integral to the improvement of TP modelling accuracy in the near future (Jackson 2010). Alternatively, rather than striving for a flawless system, processes such as the offline smoothing algorithm (Paielli 2011); application of the rapid update cycle (RUC) of the weather (Lee et al. 010); and techniques that take the perspective of the DST user [Interval based sampling technique (IBST)] (Paglione and Oaks 2007) have been established to improve aspects of a prediction model. The first of these has the capacity to improve the accuracy of DR predictions through the smoothing of the radar tracks (shown below). Blue dots Way-points Black full-line Actual path of aircraft Red curve Smoothing of track Blue dots Way-points Black full-line Actual path of aircraft Red curve Smoothing of track
This was demonstrated through application of the technique on past recorded operational error cases. The usage of RUC provides ATC with the benefit of detecting ‘regional variations of uncertainty that are related to actual weather phenomena’ (Lee et al. 2010, pp. 14). The concept behind IBST is that a trajectory provided to a controller may be old and thus filled with errors and uncertainties; so, this two-step process operates by determining the accuracy of the aircraft – through computing spatial errors - after passing through pre-determined waypoints (Paglione and Oaks 2007).
Additionally, given the effect of environmental factors on a prediction, there are procedures present to counter the influence of the sources. Russell (2010) presented the ‘consolidated storm prediction for aviation’, which is a prediction on the water content of clouds done through a grid-based prediction which may forecast predictions anywhere up to 8 hours. Results showed that this system was effective up to 2 hours as the predicted data correlated well with the observed weather within a given sector; however, as expected, when the look-ahead time increased the accuracy and reliability steadily decreased.
IV. Conflict Detection and Resolution A. Conflict Detection There has been a quantity of research on CDR within this literature, particularly over the last few years (Denery et al. 2011 Erzberger et al. 2009; Tang et al. 2008 and Paielli 2008). In order to overcome the problem of ensuring air safety, technology must exist which prevents a conflict from occurring. A conflict, in an aeronautic context, as described by Paglione and Oaks (2009) is a situation where two or more aircraft exceed the minimum separation distance standards, which can be deduced through a visual TP.
The purpose of CDR systems is to alarm ATC well in advance of a predicted collision occurring to allow preventative measures (Erzberger et al. 2009). Paielli (2008) believes that the key challenge in the next decade will be to establish an automated system that is capable of ensuring that the collision probability remains low, even in the face of a number of possible hindrances: i. e. the predicted increase in air traffic in future decades; the (at times) complexity of the system; frequent false alarms; and, the capability of CDR tools to advise the most appropriate manoeuvre.
Three of the most highly regarded and reviewed conflict systems amongst ATC (Tang et al. 2008; Paielli 2008; Paglione and Oaks 2009; and Erzberger et al. 2009) are Tactical Separation-Assisted Flight Environment (TSAFE), Conflict Probe (CP), Conflict Alert (CA), and User Request Evaluation Tool (URET). TSAFE has two primary functions 1) conformance monitoring - a process that determines the degree to which an aircraft is meeting its earlier prediction; and 2) trajectory synthesis - the construction of the 4D path.
URET was developed to help air traffic controllers by supporting a greater number of user-preferred flight profiles, and increasing both user flexibility and system capacity. ERAM is a Federal Aviation Administration system that has been designed primarily to deal with both route requests and in flight alterations swiftly. Figure 1: Poretta et al. (2010) Figure 1: Poretta et al. (2010) Paglione and Oaks (2009) highlighted the correlation between a TP’s accuracy and a decision supports tool’s (DST) performance. They assessed a number of statistical analysis models including TP metrics (i. . horizontal and vertical) and conflict probe metrics (Along-track; Cross-track; horizontal error; and, altitude). They focus on and use these accuracy metrics to establish a ratio value. Ratio= Horizontal or vertical separationMinimum allowed separation distance (i. e. parameter cut off value) As this ratio increases, the likelihood of producing false and missed conflict alerts increases– while the probability of producing valid alerts decreases. In Paglione and Oaks (2009) they identified the requirement for a ‘process improvement model’ - i. . Plan-Do-Study-Act (PDSA) - to evaluate and find possible enhancements on a studied TP system to reduce the ratio value. Investigations into false alerts and missed conflict detects have also been conducted recently by Denery et al. (2011) and Poretta et al. (2010). Processes Decisions Data that may be modified Data that may not be modified Algorithm execution flow ------- Data flow Processes Decisions Data that may be modified Data that may not be modified Algorithm execution flow ------- Data flow
The latter presented a CDR algorithm (figure 2) which shown by numerical results, is able to produce a conflict-free trajectory whilst also noting the aircrafts capabilities to perform all recommended resolution manoeuvres. Figure 2: Poretta et al. (2010) Figure 2: Poretta et al. (2010) Figure 3: Denery et al. (2011) Figure 3: Denery et al. (2011) Denery et al. (2011) highlighted consequent issues to the above problems - principally, the distraction of controllers and the need to constantly verify whether a concern exists or not.
In reply, they proposed a new algorithm, flight-intent (FI) that takes into consideration the present status of the aircraft and all available intent data. Tests were performed with this system in comparison to two other conflict detection algorithms: dual trajectory algorithm (Dual) and dead reckoning (DR). Results (figure 3) illustrate that the FI algorithm yields considerably less false alert rates, especially when the algorithm – already incorporated with area navigation (RNAV) and a noise integrated routing system (NIR) – was paired with the integrated administration and control system (IAC).
B. Conflict Resolution Additionally, Anonymous (2010) also noted that two of another CDR systems (conflict probe) faults - including conflict alerts - are that the technology is at times inefficient and will occasionally produce false alerts (or conversely, the lack thereof alerts). The CP’s performance is also compared to URET in tests performed by Santiago et al. (2010). Deductions that were made from this report included the possible benefits of increasing both the look-ahead time of a prediction to 25min, and the minimum horizontal parameters. Further investigation (Paielli 2008; Paielli et al. 009; and Denery et al. 2011) with TSAFE has been ongoing with the aim to develop an algorithm to perform at least as effectively as URET. Ryan et al. (2008) also looked at achieving this goal. They analysed and compared an emerging conflict resolution algorithm, ERAM, against URET in a quantity of tests and comparisons that were designed to evaluate the precision of the technology. ERAM’s accuracy and strategic conflict notification capabilities were belittled in comparison to the URET system, where ERAM only managed to obtain the minimum standard in two of the seven test categories.
TSAFE is often used as a back-up strategic system that computes simple resolution manoeuvres to resolve potential conflicts that are expected to occur within two minutes (Denery et al. , 2011; Paielli et al. 2009; Alonso-Ayuso et al. 2011). TSAFE and its application during en route is the primary focus of Paielli (2011). Examined in his work was the heading-trials algorithm that he developed. This system produces a number of possible manoeuvre resolutions that change the heading of the involved aircraft in ±10? increments up to ±90? f the original direction of travel. The best of these manoeuvres – in terms of cost and applicability – is then measured against the best altitude manoeuvre by means of a separation ratio (see pp. 4). His experimentation was on 100 past operational error cases where a conflict had occurred. His results (shown on table 1) illustrate the effectiveness of each manoeuvre in each particular situation. Consequently, he was able to deduce that altitudinal amendments were far more advantageous than his proposed heading algorithm. For e. g. the right most column indicates that when the separation ratio was ? 1. 2, 95% of the altitudinal amendments resulted in a successful avoidance of conflict, whilst the heading algorithm only resolved a comparably low 62% For e. g. the right most column indicates that when the separation ratio was ? 1. 2, 95% of the altitudinal amendments resulted in a successful avoidance of conflict, whilst the heading algorithm only resolved a comparably low 62% Separation ratio (? ) %| | 0. 2| 0. 4| 0. 6| 0. | 1. 0| 1. 2| No resolution| 98| 92| 74| 25| 0| 0| Heading only| 99| 95| 91| 77| 71| 62| Altitude only| 100| 100| 100| 100| 99| 95| Heading + altitude| 100| 100| 100| 100| 100| 98| Table 1: Paielli (2011) Table 1: Paielli (2011) Similarly, Paielli (2008) performed a comparable experiment with a restricted focus on altitude manoeuvres. His results further validated the success of such resolution procedures, particularly when augmented altitude amendments were supplemented to the input data (see table 2).
The purpose of adding these amendments in his experiment was to compensate for the controllers negligence or inability to do so at the time of the conflict occurring. Note: Other tests and procedures that were tested in (Paeilli 2008) are not shown, i. e. altitude rejections; temporary altitudes; step altitudes; and, critical level-offs. Note: Other tests and procedures that were tested in (Paeilli 2008) are not shown, i. e. altitude rejections; temporary altitudes; step altitudes; and, critical level-offs. | Separation ratio (? ) %| | 0. | 0. 4| 0. 6| 0. 8| 1. 0| 1. 2| No resolution| 99| 94| 75| 29| 0| 0| Augmented altitude amendments| 100| 99| 99| 97| 94| 90| Table 2: Paeilli (2008) Table 2: Paeilli (2008) Note was made in both reports that operational error cases are by no means a precise representation of the computer-generated routine operation that occurred. Given the importance of conflict detection and resolution it is important that ample research continues in this field to ensure the safety and welfare of all air traffic. V. Techniques and Technologies A. Technologies
CDR could not be possible if there wasn’t the appropriate equipment present today to compute the complex algorithms that are used. A 4D TP is established upon no easy means. Cate et al. (2008) articulate that it not only requires (at times) convoluted formulas, but also the technology and methodologies to then dissect and string together the state and intent data of the aircraft. The techniques and technologies currently utilised are crucial in this field. Already discussed above are a number of systems which are integral to the concept of trajectory prediction as they all serve a specific purpose.
This is exemplified when looking at the conflict detection and resolution component of this literature, where there are often four stages to the process: 1) Traffic collision avoidance system (TCAS) which focuses on the immediate future (<1-2min) (Paielli 2011); 2) Short term conflict alert (STCA) which operates anywhere between 2-5min (Shakarian and Haraldsdottir 2001); 3) Tactical controller tools (TCT) which concentrates on up to 8-10min (Leone 2009 and Graffica 2009); and finally, 4) Mid-term conflict detection (MTCD) which will look ahead anywhere up to 20-30min (Graffica 2009 and Lymperopoulos et al. 010). Systems that look any further in advance typically become ineffective due to the dependence of their predictions accuracy on look-ahead time (Russell 2010). Prediction accuracy ? 1Look ahead time Huang and Chung (2011) presented a TP model through their Heirachical timed coloured Petri net (HTCPN) models that is composed of seven different stages during the aircrafts trajectory. This model differs from those that have been presented by (Cate et al. 2008 and Paglione and Oaks 2009) in that 1) their models consist of a three-stage process; and 2) far more input information is required to produce a trajectory.
Different still, a TP model has been shown to be represented by an algorithm with many procedures covering difficult mathematical equations of motion (Lymperopolous and Lygeros 2010). As would be expected, with such an intricate form of technology comes a quantity of DSTs, modelling techniques and algorithms to go with it. We require a large range of prediction technologies to both further aid the pilot and ATCs and to meet the particular needs of the interested automation concept (Cate et al. 2008). Tests and comparisons on differing DSTs are continuing (Denery et al. 2011; Vivona et al. 010; and Pagilone and Oaks 2007) and they have confirmed that with the inclusion of particular technologies, a TP system can have an improvement in accuracy without sacrificing either functionality or efficiency. The use of mathematics and observations are verified for two important TP filtering methods: Kalman Filtering (KF), and Particle Filtering (PF) [Lymperopolous and Lygeros (2010); Lymperopolous et al. (2010) and Delahaye and Puechmorel (2009)]. There are two differing key issues between the two filters - i. e. the inability to handle either high dimensional states or non-linear dynamics.
Consequently, a new filtering algorithm, sequential conditional particle filter, was proposed to resolve this problem. Pan and Schonfeld (2009) also explored this technology, demonstrating through ‘splitting a graph with cycles into several directed cycle-free subgraphs’ its enhanced performance compared to other current methods of particle filtering. B. Techniques Data shown by Denery et al. (2011) illustrate the considerable improvements of accuracy and efficiency between their tested algorithms (Dual, DR and FI) with the inclusion of systems such as IAC, NIR, and RNAV (see pp. ). The concept of TP interoperability between systems has also been considered as a potential point of source for advancement in this field (McNally et al. 2010 and Cate et al. 2008). In short, this concept consists of two (or more) unlike automation systems which may compare their disagreeing trajectories and data to result in a similar prediction. This would prove particularly beneficial for air-to-ground base control and traffic flight management due to correlation between the two systems.
Mujumdar and Padhi (2011) provided an overview of seven encouraging online path-planning methods tested by unmanned aerial vehicles: graph search, potential field method, vision-based neutral networks and minimum effort guidance to list a few. Two common advantages amongst these methods were the ability to compute promptly without the expense of accuracy and the capability to account for environmental information through regular trajectory updates. These benefits correlate well with the necessities of a sought-after algorithm. Modern research is making serious headway towards establishing sound modelling procedures.
This is critical as without the appropriate technologies and methods to compute the mathematical representations and data, innovations in this field would not be conceivable. VI. Critical Assessment It rapidly became apparent the quantity of research that has already been done (especially in the past 2-3 years) and that research is still ongoing. The universal desire to constantly improve on each individual part of a TP modelling process is confirmation of its vital importance in not only contemporary society, but our future airspace.
The range of exploration and advancements in this literature is both comprehensive and widespread. Every few years, it seems each component of a TP model is enhanced to accommodate for the rapid innovations in modern technology; consequently, this then allows for additional research and analysis in search of further improvements. There were often limitations in the tests that were performed, as often only one (sometimes two) type of aircraft were used during experimentation. The data also, is often decorated by removing plenty of outliers from the tight parameters set.
If current research is to progress any further, we must divert away from the existing trend of producing monotonous findings with similar solutions in reports and journals, i. e. modifications to current methodologies; more convoluted analysis; or simply, the suggestion that ‘further work needs to be completed in this area of study’. VII. Conclusion and Open Questions Current research into the TP algorithms that are used specifically for CDR are continuing due to its significance in this field; though, there is a lot of further study required to effectively manage the increasing number of challenges facing ATM in the foreseeable future.
For this to occur, the modern techniques and prediction models that are employed must be innovated and evolved even further. The present technologies utilised in constructing a trajectory prediction appear to be effective. Similarly, the techniques which are employed to improve any imperfections or inaccuracies during the modelling process are very specifically designed to serve their own designed purposes. Even still however, the greatest obstacle that needs to be overcome – and surely, where further research must be applied - is reducing the overall effect of error sources and subsequently reducing the uncertainties in the predictions.
Given the recent growth of advancements in this field, one may expect that both researchers and developers will be able to competently confront any arising issues in this field of aeronautic technology. In conclusion, a few unanswered questions are immediately brought to mind: * To what extent will the role humans play as decision support systems in response to any complications following any possible system malfunctions or incompetencies. * Does there exist a minimum set of constraints for a given prediction, such that an algorithm is simply unable to compute with any assuring accuracy?
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