SCHUSTER, Wolfgang Horst-Werner Alexander (110 More Close, London W14 3BW, GB)
| Claims A method of providing a vehicle trajectory prediction comprising: receiving, at a processor, a script defining an intended trajectory D(t) for the vehicle, wherein said intended trajectory D(t) comprises at least a vehicle start position and a subsequent vehicle position along the intended trajectory D(t), and wherein the script sets a required vehicle speed at each of the vehicle start position and the subsequent vehicle position; the method further comprising: receiving, at the processor, information regarding the instantaneous state X(t) of the vehicle at least at said vehicle start position, receiving, at the processor, information regarding vehicle operational performance; simulating control of the vehicle using the received intended trajectory D(t) and vehicle instantaneous state X(t) information; and outputting the predicted vehicle trajectory which results from said simulation. A method as claimed in claim 1 wherein the vehicle is any of: an aircraft, a train, a terrestrial vehicle and a water-based vehicle. A method as claimed in claim 1 or claim 2 further comprising receiving, at the processor, information regarding the environment surrounding the vehicle at a vehicle position along the intended trajectory D(t), for use in simulating control of the vehicle. A method as claimed in claim 3 wherein the information regarding the environment surrounding the vehicle includes information on any of the surrounding: temperature, T(t) pressure, wind field W(t), or any other environmental variable. A method as claimed in any of claims 1 to 4 further comprising simulating operation of the vehicle to follow the intended trajectory and receiving, at the processor, updated information regarding the instantaneous state X(t) of the vehicle as a result of said simulated operation. 6. A method as claimed in claim 5 further comprising providing a feedback loop between the vehicle operation simulation and the vehicle control simulation. 7. A method of defining an intended trajectory D(t) for a vehicle, comprising defining at least a vehicle start position and a subsequent vehicle position along the intended trajectory, and further setting a required vehicle speed at each of the vehicle start position and the subsequent vehicle position. 8. A method as claimed in any of claims 1 to 7 wherein defining an intended trajectory D(t) for the vehicle further comprises setting at least one of: a required vehicle start time at the vehicle start position and a required vehicle arrival time at said subsequent vehicle position. 9. A method as claimed in any of claims 1 to 8 wherein the intended trajectory D(t) is defined by at least one configuration change for the vehicle. 10. A method as claimed in claim 9 wherein the vehicle is an aircraft and wherein the configuration changes used for defining the intended trajectory D(t) include any of: intended aircraft aerodynamic configuration, intended landing gear configuration, intended ground track direction, intended flight path angle, intended required initial ground speed, intended holding area mode defining if the aircraft is flying within a holding area or not, intended expedited descent mode and reference frame update. 11. A method of simulating vehicle operation comprising: receiving, at a processor, information regarding the instantaneous state X(t) of the vehicle; receiving, at the processor, a measure of at least one control variable F(t) that can be controlled during operation of the vehicle; receiving, at the processor, information regarding the environment surrounding the vehicle; using the received instantaneous state X(t), control variable F(t) and environment information to determine a relationship representing the change of vehicle instantaneous state X(t) over time; and simulating operation of the vehicle based on said determined relationship. 12. A method as claimed in claim 11 wherein the vehicle is an aircraft and wherein the instantaneous state X(t) of the vehicle comprises a measure at least one of: 3-dimensional (x, y, h) aircraft position, aircraft true airspeed VTAS, aircraft heading angle Ψ(ΐ), and the aircraft mass m(t). 13. A method as claimed in claim 11 or claim 12 wherein the vehicle is an aircraft and wherein the at least one control variable F(t) comprises a measure of any of: engine thrust T, bank angle φ, flight-path angle (FPA) y and drag coefficient Co- 14. A method as claimed in any of claims 11 to 13 wherein the information received regarding the environment surrounding the vehicle comprises information regarding at least one of: a wind-field W(t) and a temperature T(t). 15. A method as claimed in claim 14 wherein the temperature T(t) comprises at least one of: a measured temperature and a predicted temperature. 16. A method as claimed in claim 15 wherein the temperature T(t) comprises an optimally averaged combination of a measured temperature and a predicted temperature. 17. A method as claimed in any of claims 14 to 16 wherein the wind- field W(t) comprises a measure of wind- field along any of 3 dimensions. 18. A method as claimed in any of claims 14 to 17 wherein the wind- field W(t) comprises at least one of: a measured wind field and a predicted wind field. 19. A method as claimed in claim 18 wherein the wind-field W(t) comprises an optimally averaged combination of a measured wind field and a predicted wind field. 20. A method as claimed in any of claims 11 to 19 wherein the determined relationship representing the change of vehicle instantaneous state X(t) over time is expressed as: i = VTAS ■ cos Ψ · cos γ + wx y = VTAS · sin Ψ · cos γ + wy h = VTAS■ sin γ + wz ■ T D I T C D - S ■ p V T VTAS = COS Ε T ~ \ h 8 ' sm 7 \ = cos Ε T ■ + g ■ sm γ m m ) m CL - S - p V∑ sm (γ + ε τ ) · sin φ Ψ ■ sin φ + τ■ T + W x sm φ + T + W, m ■ V T m■ V cos r m =—η■ T 21. A method as claimed in any of claims 11 to 20 further comprising setting aircraft operational limitations on at least one variable representing the instantaneous state X(t) of the vehicle and/or on at least one control variable F(t) that can be controlled during operation of the vehicle. 22. A method of simulating vehicle control comprising: receiving, at a processor, information regarding the instantaneous state X(t) of the vehicle; receiving, at the processor, a script defining an intended trajectory D(t) for the vehicle; receiving, at the processor, information regarding the environment surrounding the vehicle; receiving, at the processor, one or more instructions for determining a control variable F(t) that can be controlled during operation of the vehicle; using said one or more instructions and the received instantaneous state X(t), intended trajectory D(t) and environment information to determine a value of a control variable F(t) that can be controlled during operation of the vehicle; and simulating control of the vehicle using the determined control variable F(t). 23. A method as claimed in claim 22 wherein the information received regarding the environment surrounding the vehicle comprises information regarding at least one of: a wind-field W(t) and a temperature T(t). 24. A method as claimed in claim 22 or claim 23 wherein the processor receives a plurality of possible instructions for determining a control variable F(t), the method further comprising selecting an instruction from said plurality of possible instructions for use in determining the control variable F(t), according to an instantaneous operating mode of the vehicle. 25. A method as claimed in any of claims 22 to 24 wherein the intended trajectory D(t) defines one or more transition points, the method further comprising determining, at the processor, whether the vehicle has passed by or passed over one of said transition points. 26. A method as claimed in any of claims 1 to 6 or 22 to 25 wherein simulating vehicle control includes determining the instantaneous speed requirements of the vehicle. 27. A method as claimed in claim 26 wherein said instantaneous vehicle speed requirements are determined using: a required vehicle speed at a predetermined vehicle position along the intended trajectory D(t), a required time of arrival of the vehicle at a predetermined vehicle position along the intended trajectory D(t) and a measure of the wind-field W(t) surrounding the vehicle. 28. A method as claimed in claim 27 wherein determination of the instantaneous vehicle speed requirements further comprises consideration of actual distance travelled by the vehicle during a trajectory, including distance travelled during non- linear motion of the vehicle. 29. A method as claimed in any of claims 26 to 28 wherein the vehicle is an aircraft, the method further comprising using one or more values received at the processor representing state X(t) and intended trajectory D(t) of the aircraft to calculate any of: the required thrust, flight path angle, aircraft bank angle, change in aircraft heading, aircraft turn radius, and coefficient of drag for the aircraft. 30. A method as claimed in claim 29 wherein a measure of the wind-field W(t) surrounding the vehicle is also used in the calculation of any of: the required thrust, flight path angle, aircraft bank angle, change in aircraft heading, aircraft turn radius, and coefficient of drag for the aircraft. 31. A method of determining the instantaneous bank angle (φ) requirement for an aircraft during simulation of control of said aircraft, the method comprising: receiving, at a processor, information regarding the instantaneous state X(t) of the aircraft; receiving, at the processor, an intended trajectory D(t) for the aircraft; receiving, at the processor, information regarding a wind- field W(t) surrounding the aircraft; using the received instantaneous state X(t), intended trajectory D(t), and wind-field W(t) information to determine an error pHE(t) in the instantaneous heading direction of the aircraft; deriving the instantaneous bank angle(cp) requirement using said determined error pHE(t) and a gain factor (k) using the relationship: φ = k * pHE(t) 32. A method as claimed in claim 30 or 31 further comprising selecting the gain factor (k) for use in the simulation from a comparison of a resulting error when the bank angle φ is applied in the simulation at a range of values of gain factor (k), wherein the selected gain factor (k) is the lowest value of (k) at which the error is at its minimum value. 33. A method as claimed in claim 32 wherein the error used for selecting the gain factor is any of a cross-track error (CTE) and Euclidean error. 34. A method as claimed in any of claims 30 to 33 further comprising receiving, at the processor, information regarding temperature T(t) surrounding the aircraft. 35. A vehicle trajectory prediction tool arranged and operable to carry out the method according to any of claims 1 to 34. 36. A processing means programmed and operable to execute instructions for carrying out the method according to any of claims 1 to 34. 37. A record carrier having instructions stored thereon for execution by a processing means to carry out the method according to any of claims 1 to 34. 38. The record carrier of claim 37 wherein said record carrier includes an optical, magnetic or solid state storage means or a readable signal. 39. A computer program including instructions executable by a processing means for carrying out the method according to any of claims 1 to 34. 40. A method, apparatus or system as described herein or substantially as shown in the appended figures. |
Background The demand for travel and movement of goods is rapidly increasing worldwide. In particular, the use of aircraft and demand for airspace is growing. The skies in Europe and elsewhere are becoming congested and current airspace capacity is approaching its limit. As a consequence, traditional Air Traffic Management (ATM) approaches are beginning to struggle to satisfy capacity demands. This results in delays and a negative impact on the economy, as well as environmental and safety concerns. It is expected that air traffic globally will increase by a factor of between 2 and 3 in the next 15 to 20 years. Therefore there is an urgent need to develop new Air Traffic Management (ATM) methods in order to increase airspace capacity and efficiency without jeopardising safety and whilst minimising the environmental impact of air traffic. The Single-European-Sky ATM Research (SESAR, 2006 - 2008) and Next Generation Air
Transportation System (RTCA, 2009) are initiatives which recognise that at the core of a more efficient navigation is the need to guarantee common situational awareness between all traffic and Air Traffic Control (ATC), and improve the ability to visualise the evolution of air traffic as a function of time. Key to both is the ability to accurately and reliably predict 4D aircraft trajectories and distribute these between all the relevant partners, including ATC and surrounding traffic. Therefore, the performance and reliability of Trajectory Prediction (TP) will be a major factor in future ATM performance.
Trajectory Prediction (TP) is expected to be at the core of future Air Traffic Control (ATC) Decision Support Tools (DSTs) including Conflict Detection and Resolution (CDR) tools, and Airborne Self-separation Assistance Systems (ASAS). High-performance TP has the potential to reduce controller workload and increase airspace capacity, by improving the capability of ATC to perform the necessary synchronisation and separation activities in advance. This would enable the anticipation and detection of conflicts earlier, making it possible to provide an optimised strategic approach to conflict resolution instead of the current inefficient tactical processes which aim to resolve conflicts of the ATC only once they are detected which tends to be at a relatively late stage. Current ATC methods rely on, for example, the use of radar tracks. These have an associated margin of error that is becoming unacceptable with the increase of air traffic density worldwide.
There are a number of aspects that can be considered for trajectory prediction (TP) including characterisation of the aircraft intent in order to define an intended or target flight path for an aircraft, characterisation of environmental conditions, experienced by the aircraft during flight, modelling of the aircraft dynamics and modelling of the flight-management system (FMS) that controls operation of the aircraft to meet its intent as closely as possible. A predicted trajectory output by a TP model essentially is the path which the modelled FMS would control the aircraft to take, in order to stick as closely as possible to the intended flight path, bearing in mind environmental conditions and operational limitations of the modelled aircraft dynamics.
Many state-of-the-art TP methods are based upon a three-dimensional point-mass model and make a number of simplifying assumptions about the mathematical models underlying aircraft dynamics. In particular, the actual and anticipated states of the aircraft are not realistically emulated. Such states are typically modelled based on predefined settings obtained from a database such as the Eurocontrol BADA data set (Eurocontrol, 2009b). However, such oversimplification and reliance on assumption can lead to inaccuracies in trajectory prediction.
"Performance evaluation of a novel 4D trajectory prediction model for civil aircraft ", Poretta et al, The Journal of Navigation (2008), 61, 393 to 420 proposes one possible trajectory prediction model for civil aircraft. It addresses some of the limitations of prior art models and proposes an enhanced TP model. That document focuses on two main aspects of trajectory prediction:
1. Consideration of the Estimated Time of Arrival (ETA) in the evaluation of the True Air Speed (TAS) to be tracked by an aircraft during the flight. Whilst previous models used the thrust settings for a given phase of operation and accepted the resulting "nominal" speed, using the
ETA allows a more accurate estimation of the speed requirements for a specified flight leg and thus enhances the accuracy of the resulting trajectory prediction. 2. Consideration of aircraft dynamics and operational limitations for lateral guidance and subsequent bank-angle requirements determination.
However, a number of limitations still remain that require resolution in order to further improve the performance of trajectory predictions.
The model described in Poretta et al (referenced above) still relies on Eurocontrol BADA Data Set inputs for many important measures such as thrust settings. However these predetermined settings are not always representative of actual thrust settings used by an aircraft, particularly during the climb and the descent phases of flight. This can result in significant trajectory prediction errors. Poretta et al also relies on the BADA Data Set for computing flight path angles using an assumed energy share factor (ESF). This ESF specifies how much of the available aircraft power will be allocated to the change in height and to the change in speed of the aircraft. However the predefined values in the BADA Data Set cannot consider the actual state of the aircraft during flight or the required allocation of thrust to the rate of change of height and to the change in speed of the aircraft in order to follow its intended or target flight path in practice.
Further limitations of prior art models include the assumption of an average aircraft speed to be achieved for a given flight segment between two predefined points in the aircraft's intended flight path in order to compute the instantaneous speed requirements of the aircraft for that flight segment. Such an assumption typically results in an instantaneous and stepwise speed change requirement at the beginning of each flight segment in a predicted trajectory, which is unrealistic and unobtainable in practice for an aircraft in flight. Thus, the predicted speed profile in prior art trajectory prediction models can differ significantly from the actual speed profile of a real aircraft over the course of a flight, with the consequence of potentially significant along-track errors for the predicted aircraft trajectory.
Prior art approaches also do not fully account for the effect of wind on aircraft trajectory. In particular, they do not consider the effects of the lateral biased component of the wind. This again can result in an offset between a predicted trajectory and an actual trajectory of a real aircraft.
There are legal requirements across the world regarding the allowable lateral separation between aircraft in airspace and the allowable time interval between consecutive aircraft passing a point in airspace. In order to be realisable and safe for use in practice for conflict resolution, air traffic control (ATC) and so on, an aircraft trajectory prediction tool must accurately reflect the actual path taken by the aircraft being modelled to within a safety margin. Such a safety margin can be, at very most, half of the required lateral separation for any given area through which an aircraft is to travel. In practice, if a trajectory prediction tool is to be used for ATC, it would have to be much more accurate than that, and would have some in-built resilience to input data errors and to changing inter-aircraft spacing requirements, both over time and between different regions of airspace.
Although aircraft is mainly discussed herein, similar requirements and considerations apply for other vehicles, including trains, terrestrial vehicles such as cars, and water-based vehicles such as ships. No prior art trajectory prediction tool or model offers a suitable solution to match the trajectory prediction requirements for any of these vehicle types.
The invention is set out in the claims.
By providing a vehicle trajectory prediction, forecasts can be made regarding traffic and its control, for example in resolving potential conflict and thus avoiding collisions. Because a script defines an intended trajectory for the vehicle, wherein that trajectory comprises at least a vehicle start position and a subsequent vehicle position along the intended trajectory as well as a required vehicle speed at each of said positions, a unique and unambiguous intended track or path for the vehicle is set out. By using the intended trajectory in combination with vehicle instantaneous state information, taking into account vehicle operational performance, simulation of vehicle control can be carried out accurately, simulating realistic control of the vehicle, and thus the resulting vehicle trajectory prediction is reliable and highly useful for real world application.
By also receiving information regarding the environment surrounding the vehicle at a vehicle position along the intended trajectory, and using that information in simulating control of the vehicle, the simulation becomes even more realistic and thus the resulting predicted vehicle trajectory will more closely reflect the actual vehicle trajectory that will be taken in practice. Because the method can comprise simulating operation of the vehicle to follow the intended trajectory, as well as control of the vehicle during that process, the resulting predicted vehicle trajectory is further enhanced. Furthermore, by setting a required vehicle start time at the vehicle start position and a required vehicle arrival time at a subsequent vehicle position along the intended trajectory, the intent of the vehicle is better defined and thus the resulting simulation of operation and control of the vehicle can lead to an enhanced, more realistic vehicle trajectory prediction.
By simulating vehicle operation using instantaneous state information regarding the vehicle, a measure of at least one control variable that can be controlled during operation of the vehicle, and information regarding a wind-field surrounding the vehicle, a realistic simulation, which takes into account the major factors which affect vehicle operation in the real world, is provided.
By simulating vehicle control using information regarding the instantaneous state of the vehicle, its intended trajectory, and information regarding wind- field surrounding the vehicle, simulation of vehicle control can also be reliably and realistically achieved, taking into account the major factors that affect vehicle control in the real world.
Figures
Embodiments will now be described, by way of example, with reference to the figures of which:
Figure 1 shows an exemplary Trajectory prediction (TP) model, according to the embodiments described;
Figure 2 is a simplified illustration of the main forces acting on an aircraft during flight;
Figure 3 shows a trajectory Change Point (TCP) during "Fly Over" mode according to the TP model;
Figure 4 shows a trajectory Change Point (TCP) during "Fly By" mode according to the TP model;
Figure 5 shows lateral guidance provided by the TP model;
Figure 6 shows heading correction for lateral bias component of the wind, provided by the TP model;
Figure 7 shows an estimation of distances flown in Fly By mode;
Figure 8 shows an estimation of distances flown in Fly Over mode;
Figure 9 shows speed profiles as a function of initial speed, that satisfy the same average speed requirements according to prior art TP models;
Figure 10 shows maximum Cross Track Error (CTE) as a function of gain factor k used in computation of bank angle according to the present TP model; and Figure 11 is a table comparing navigation system performance requirements and performance of the present TP model.
Overview
A high performance, robust trajectory prediction (TP) model is provided that makes maximum, optimal use of information of both aircraft state during operation, including operational environment factors, and its intent. The embodiments described enable the TP model to be both aerodynamically realistic and operationally realistic. It makes intelligent use of the knowledge of which operational parameters are available from aircraft on-board sensors and whether and how such parameters would realistically be used by an aircraft (auto) pilot in determining an aircraft's flight path in practice. Therefore the trajectory prediction achieved by the model is scientifically accurate, minimising the use of assumptions and predefined database values, and is also realistic and closely representative of an actual trajectory that would be followed by an aircraft in flight.
The intent of the aircraft is accurately defined in the present model. In particular, speed requirements and requirements for time of arrival of the aircraft at various points along the intended trajectory are specified. This provides constraints on the aircraft for simulation of its operation and control, and thus provides certainty with respect thereto. It also enables more realistic operation and control to be simulated by, for example, removing step-wise discontinuities in speed over the course of the predicted trajectory.
As mentioned above, many prior art trajectory prediction models rely on predefined values and settings from databases such as the Eurocontrol BADA Data Set. It has been found that there are some errors in existing Data Set values, which will have a knock on effect on the accuracy of any resulting trajectory prediction model. Naturally, some errors will have a more serious effect on the resulting model than others, depending for example on how and where in the model they are used. Furthermore, the use of predefined settings and values does not always accurately reflect a real operational environment. It will be appreciated that, in practice, an aircraft will adapt its flight path in order to meet its intent and also in response to the surrounding operational environment at any given time during flight. The present embodiments therefore maximise the use of operational, environment and intent information in order to provide improved trajectory predictions. In particular, they take account of the effects of wind on real aircraft operation and include wind factors both when determining actual operation of an aircraft for which a trajectory prediction is being made, and when
determining errors that would be corrected by an aircraft during that period of operation.
Detailed Description
Aircraft Intent "Aircraft intent" as discussed herein is a structured set of instructions describing unambiguously the intended operational state of an aircraft over a given time-horizon. Before a given flight begins, aircraft intent can be defined using information such as the scheduled take off point and landing point of the aircraft, shortest distance therebetween, possible aircraft (x, y, h) locations along the flight path, estimated or required arrival times of the aircraft at such locations, aircraft speed requirements and the scheduled take off and arrival times. Furthermore, predetermined information such as allowed or non-allowed regions of airspace for travel therethrough by aircraft may be used. In addition, a possible input for aircraft intent is the gain factor "k", obtained the performance characterisation from previous flights. This is discussed further below. Because it defines intent of the aircraft, the flight script according to the present model does not need to be updated or to take instantaneous conditions into account over the course of a flight. However, it is possible to update a flight script during the course of a flight for the purpose of, for example, conflict resolution. This can be done, for example, using information received from an air traffic controller (ATC) if such information might affect the ability or likelihood of the aircraft to follow the initially set intended flight path.
The set of instructions which define aircraft intent for a given flight determines the evolution of the dynamic state of the aircraft, as computed by a "Trajectory Prediction" (TP) model or tool. This is because the model makes a basic assumption that an aircraft would follow each instruction to within the limits of its operational capability, taking into consideration surrounding environmental factors such as wind in order to match its intended flight path as closely as possible. Each instruction for aircraft intent is defined by a start-time and an end-time, thereby specifying the length of time during which a given instruction is to be executed. A set of instructions forms an operation, which unambiguously determines the intended aircraft motion during the given time interval or flight segment. The point in space and time at which a change in such a set of instructions occurs, and hence a change occurs in the intended aircraft motion, is referred to as a Trajectory Change Point (TCP). The time-ordered sequence of such TCPs defines the intended aircraft trajectory for a flight, i.e. the flight-script (FS). According to the embodiments described herein, each Trajectory Change Point (TCP) in the flight script (FS) may be defined by the following variables:
• A Way Point (WP), defined by instantaneous the horizontal and vertical position of an aircraft in terms of latitude (x), longitude (y) and height (h).
• A Required Time of Arrival (RTA), describing the exact time at which the aircraft is required to fly-over or fly-by the TCP. This is distinct from the Expected Time of Arrival (ETA). ETA corresponds to the time at which the aircraft is expected at the next TCP without any special attempt to reach it at a given time. Conversely, if an RTA is set, the aircraft adapts its configuration in order to reach the TCP at the specific time provided in the Flight Script (FS).
• A Required Initial Ground Speed (RIGS), describing the speed at which the aircraft is required to fly at the TCP. This is to ensure reliability and robustness of the TP model as described further below.
• Turn-Modes (TM), describing whether the aircraft is expected to "fly-over" or "fly-by" the TCP, also described further below.
• Holding Modes (HM), describing whether the TCP belongs to a "holding area" in the vicinity of a target landing point.
• Expedited Descent Modes (EDM), describing the spoiler configuration from the current TCP until the next TCP, which can have an effect on drag and speed of aircraft descent.
Of particular note is the inclusion of the "Required Initial Ground Speed" (RIGS) for each TCP in the flight-plan. The flight script (FS) according to the present TP model embodiments is defined such that, for each flight segment, the aircraft intent is unambiguous. This means, inter alia, that there is a unique target or intended speed profile for an aircraft between TCP's. This is not seen in prior art models and, as discussed in detail below, provides significant advantages thereover.
In order to optimise the performance of trajectory prediction (TP) in the present model, a TCP is allocated for each point in space at which a change would occur in any of the following operational, aerodynamic or geometric configurations for an aircraft which is following its intended trajectory or flight script: aircraft aerodynamic configuration such as change in spoilers, flaps or landing gear, non-linear variation in intended ground-speed (or preferably true airspeed), instantaneous track or heading, instantaneous flight-path-angle, thrust settings, intended holding area-mode, intended expedited descent mode, environmental factors and reference frame. The more of these criteria that are taken into consideration, the more accurate the target FS representation of the true trajectory is, and hence the more accurate the performance of the trajectory prediction (TP) process will be.
Trajectory Prediction Model
Figure 1 depicts the basic framework of a trajectory prediction (TP) model proposed according to the embodiments described herein. The model can be physically implemented in any suitable hardware or software means to provide a trajectory prediction module. As can be seen from Figure 1, there are three basic logical units within the present TP model: Input Data (ID), Aircraft Dynamic Systems (ADS) and Flight Management Systems (FMS). Each of these is discussed in turn below. Input Data (ID
The choice and treatment of input data is critical to the reliability of any trajectory prediction model. As can be seen from Figure 1, the present trajectory prediction (TP) model uses as an input the flight script (FS), which includes navigation and operational data setting out a intended flight path for the aircraft for a given flight. Thus, through use of the flight script, aircraft intent is considered. Additional navigation and operational data is provided from the aircraft initial state at the beginning of the flight. In addition, the environmental factors are used as input data for the model, including information obtained from an atmospheric model (ISA) regarding the surrounding environment of an aircraft during flight and, notably, measured and/or forecast wind- field components to represent the effect of wind on the path of an aircraft during flight, as well as measured and/or forecast temperature. Furthermore, predetermined aircraft performance data is used as input data in the present trajectory prediction (TP) model.
In order to provide improved trajectory prediction, the trajectory prediction model described herein embodies intelligent choices with respect to input data for the model which enable it to more realistically predict aircraft trajectory. The model makes use of some predefined parameters from available data sets but aims to limit the use of such predefined information to the more accurate, reliable parameters such as aircraft dimensions. Where existing data sets have been shown to be inaccurate or unrealistic, and especially when such inaccuracies or offsets from reality result in degradation of the resulting trajectory prediction, the model aims to instead use actual aircraft state and intent data, available from onboard diagnostics, as inputs for the present trajectory prediction TP model. Because such information is available from onboard diagnostics, it is realistic to assume, according to the TP model, that a real aircraft could and would use that data, rather than relying on predefined settings.
The aircraft dynamic system (ADS) discussed further below models the aircraft dynamic system of an aircraft for which trajectory prediction is being provided. As can be seen in Figure 1 , the ADS uses inputs regarding aircraft initial state, aircraft performance data and environmental factors. The trajectory prediction model according to Figure 1 also operates a feedback loop between the aircraft dynamics system (ADS) and the flight management system (FMS) (discussed further below) which emulates control of the aircraft in order to follow the flight script (FS), as set out in more detail below. According to the model shown in figure 1 , the Aircraft Dynamics System (ADS) requires an initial input vector of data X(to) that defines the initial state of the aircraft at the time at which TP commences. The data consists of the initial time t 0 , aircraft position x(t 0 ), true-airspeed (TAS) VrAs(to), magnetic heading ΨΜ(ΪΟ), bank-angle <p(to) and flight-path-angle y(to). Magnetic heading is the direction pointed to by the aircraft's nose with respect to the magnetic pole. Bank angle is the angle between a line drawn through the aircraft wingtip and the local horizon and flight path angle is the angle between the aircraft longitudinal axis and the local horizon.
Each of the data values for X(t 0 ) can be obtained from aircraft onboard sensors. Furthermore, the initial mass m(to) of the aircraft is required and can be obtained from the take-off mass (mro) and the fuel-consumption rate dm(t)/dt associated with aircraft thrust settings. The fuel-flow rate is obtained from aircraft performance data available in BADA (Eurocontrol, 2009b). Additionally, the specification of the spoiler, flap and landing gear configurations, available from the Flight Management System (FMS), is required. A key input to the ADS and the FMS is the wind field, which can be divided into linear and stochastic components. The linear wind-field is obtained using either information available from the nearest (in both position and time) wind- field measurements and/or forecasts, such as the meteorological data available to and provided by ATC. Alternatively or additionally, the last wind- field measurement made onboard the aircraft can be used. Wind field measurements can be carried out on board the aircraft using any suitable known method. Wind speed can be measured, for example, using the ground speed and air speed measurements of the aircraft as well as measurements of ground track and heading, which are readily obtainable. In practice, any suitable combination of measures and predicted windfields may be used. For example, if trajectory prediction is to be provided in the short term, for example of the order of five to ten minutes in advance, it may be more accurate to use measured wind-field rather than relying on predictions. Conversely, if a trajectory prediction is to be made over a longer period of time, for example an hour or more, it may be more useful to use predicted wind-fields than to rely on a wind- field measurement that will be one hour out of date at the end of the predicted trajectory. According to an embodiment, it is possible to provide optimal averaging between measured and forecast wind- fields, thereby harnessing the advantageous aspects of both predicted and measured wind- field values. This allows for a more robust set of inputs to the trajectory prediction model and hence a more reliable resulting trajectory prediction.
In contrast to the present TP model, prior art models do not fully account for the fact that, in practice, an aircraft's control system or pilot may make use of real onboard measurements in order to account for operational environment of an aircraft. Instead prior art models tend to rely solely on predicted measures. Because the present TP model can use the last wind-field measurements made on board the aircraft in addition or as an alternative to predictions, it makes uses of actual conditions experienced by aircraft. It also reflects realistic operation of aircraft control since no additional sensors are required to make use of the actual wind- field and so an aircraft may use it in practice. The stochastic wind-component accounts for deviations from the linear or nominal wind- field. Various known models have been proposed that assume a random wind- field with a Gaussian distribution. However, no conclusive experimental evidence has been provided to support this assumption. Further work is thus required to demonstrate the validity of such models. As a result, the stochastic component set to zero in the model of Figure 1 and instead a linear wind model is accounted for during the trajectory prediction process. In practice it has been found that setting this stochastic component to zero does not introduce significant errors into the trajectory prediction model. Therefore, the present (TP) model according to Figure 1 embodies an intelligent, efficient choice in setting the stochastic wind component to zero, rather than using a potentially incorrect non-zero model or dedicating computational power on running such a model, whilst not compromising on the accuracy of the resulting trajectory prediction.
Further inputs used by the ADS are Aircraft Performance Data (APD), specifying aircraft operational characteristics. Typical parameters include aircraft type, mass information, parameters related to the aircraft flight envelope and aerodynamics, as well as fuel consumption as a function of thrust settings. These parameters are independent of dynamically varying conditions for any given flight or aircraft so can be reliably obtained from suitable APD sets, such as Eurocontrol's BADA. Additionally, since aircraft instantaneous performance varies with the surrounding state of the atmosphere e.g. temperature and pressure, an atmospheric model is required. The model according to Figure 1 can adopt the International Standard Atmosphere (ISA) model (ICAO, 1964) developed by the International Civil Aviation Organisation (ICAO).
Alternatively or additionally, actual temperature and pressure measurements may be used as inputs for the trajectory position (TP) model as described herein. As with consideration of wind- field as discussed above, optimal averaging may be employed with respect to temperature and/or pressure values used in the model so that the state of the atmosphere as input into the model is derived from both actual instantaneous measurements and reliable predictions of future measurements. In a further development over prior art models, a more accurate measure of aircraft mass can be used as an input to the TP model, rather than relying on predefined mass measurements and fuel consumption rates. Independent mass estimations are available from onboard sensors on an aircraft and thus can be included in the present TP model. It is possible to take or estimate an initial mass of an aircarft before flight and to use fuel flow thereafter, which can be very accurately measured on an aircraft, to dynamically update the aircraft mass value used in the TP model. By way of an example, the initial mass of the aircraft can be gauged by weighing passengers, luggage and other payloads as well as fuel individually and adding those measures to the empty aircraft weight which can be obtained from reliable data sets. Alternatively or additionally, the overall weight of an aircraft including its fuel, luggage, other payload and passengers could be measured before take off using a suitable measuring scale or other device at the airport for example at the aircraft stand, on the apron, the taxiway or the runway. It will be appreciated that obtaining and updating an accurate estimate for aircraft mass in such a manner is highly valuable in ensuring the accuracy of the resulting trajectory prediction.
Aircraft Dynamics System (ADS)
In the ADS unit of the model according to Figure 1 , aircraft motion can be modelled using a 6 Degree-Of-Freedom (DOF) Point-Mass-Model (PMM), derived from basic aerodynamics and Newtonian laws. In an advantage over prior art approaches, the model as illustrated in Figure 1 embodies intelligent choices with respect to input data to the FMS, including what information is used, which parameters are predefined and which are computed, and as to how such data is treated within the model, to make the six degrees of motions equations more realistic. Therefore the ADS enables the provision of more accurate trajectory predictions than prior art models can provide.
Civil aircraft operate near trimmed flight conditions at all times, allowing instantaneous aircraft motion to be described by a non-linear control system with six state -variables X(t). These are the 3-dimensional (3D) position (x,y,h), as well as the aircraft true airspeed V T AS, the aircraft heading angle Ψ(ΐ), defined with respect to the east-direction positive counter-clockwise, and the aircraft mass m(t). Mathematically the state-vector is represented as:
X( = [x(t\ y(t), h(t), V TAS (0, Ψ( , m(t)]
[1]
According to the present TP model, aircraft dynamics are controlled by the following input variables: engine thrust T, bank angle φ, flight-path angle (FPA) γ and drag coefficient Co- These emulate practical dynamic measures which are available for control to pilots who, for example, control the drag coefficient o by changing aircraft configuration parameters, including flaps, slats, spoilers and landing gear. Therefore, the ADS input variables according to an embodiment of the present TP model are expressed by a function Fig. 1 , wherein:
¥(t) = [T, φ, r , C D ]
[2] As shown in Figure 1 and as will be understood further from the description below, the input variables defined by F(t) are used by the model as inputs to the non-linear flight control system (FCS), which emulates aircraft control during operation. The output of the FCS can then be fed back to the ADS in order to update the simulated aircraft dynamics and hence to improve the accuracy of the overall TP model.
In practice during flight, aircraft dynamics are disturbed by the surrounding wind- field. To improve trajectory prediction, the present model takes such disturbance into account when simulating aircraft dynamics in the ADS. Wind- field may be represented according to the model by a 3D input vector W(t), describing the wind- field components along the x, y and height directions as:
W(t) = [w x (t), w y (t) , w z (t)] . [3]
Using X(t), F(t) and W(t), representing the instantaneous state, chosen input variables and wind- field respectively, the model can use information derivable from onboard sensors and, to a limited extent, some chosen predefined parameters, to emulate the dynamics of an aircraft over the course of a flight.
Using vectors X(t), F(t) and W(t), the aircraft motion according to the ADS unit of the present TP model can unambiguously be described by the following non-linear control system, derived using known Newtonian dynamics: i = V TAS ■ cos Ψ · cos γ + w x
y = V TAS · sin Ψ · cos γ + w y
h = V TAS - sin γ + w z
D C D - S - p V T
V JAS =— - cos ε Ί ■ + g ■ sm γ ■ cos ε , ■ + g ■ sm γ
C L - S - p V, sin (y + ε T ) · sin φ __
Ψ sin φ + τ■ T + W x TAS sm φ + —_ T — —■ T + W
m■ V T ■ V TAS - cos
-η■ T These equations can be used extensively in emulating aircraft motion and control and in outputting a resulting trajectory prediction according to the present model, as described in detail below. Forces Acting on an Aircraft
Figure 2 is a simplified illustration of the main forces acting as an aircraft during flight, which are taken into account by the ADS in the present trajectory prediction (TP) model embodiments. The forces are accounted for in equation [4] above. In equation [4], D is the total drag, S is the total wing surface area obtained from BADA, p the air density computed using the ISA model and g the gravitational constant set to 9.80665 m/s 2 . Furthermore, L is the lift, Ci the aerodynamic lift coefficient, τ a parameter taking into consideration a small vertical component of the thrust that exists even under level-flight conditions, ε Τ the thrust-offset angle with respect to the wing-chord as shown in Figure 2.
W xy is the wind- force acting perpendicular to the flight-direction, and η a factor describing the fuel consumption rate as a function of thrust, obtained from BADA.
According to an embodiment, is computed as
[5]
where, Sbody/iat is the lateral surface area of the aircraft body, and
- 1
a■ ,
l+ i
depending on whether the aircraft turns into the wind or away from it respectively. It will be appreciated that equation [5] is one example of how W xy may be computed in order to take wind- field into account when modelling aircraft dynamics according to the present TP model. However any suitable derivation of the wind force acting perpendicular to the flight direction may be used according to the present model.
In practical terms for trajectory prediction, W xy is the impact that the wind- force acting perpendicular to the flight direction has on aircraft heading change, i.e. the side wind. It can be obtained using either a predicted wind- field and/or using information available from aircraft onboard sensors. By taking side wind into consideration in this manner, the model is better able to model aircraft dynamics realistically and thus to provide a realistic projection of what an aircraft would do in practice. By considering W xy , the present TP model can distinguish, for example, between a situation where there is an error in the predicted heading, which the FMS must correct using lateral guidance, and when the predicted heading is deliberately offset from the intended aircraft track direction obtained from the flight script, in order to accommodate a side-wind in the manner that a real aircraft would do in practice. If during flight, an aircraft encounters a side wind it will ride the side wind, travelling sideways with its heading turned into the wind, rather than resisting it and thus being pushed off-track by the wind. Prior art models that do not take side wind into account when modelling aircraft dynamics erroneously assume that an aircraft will entirely resist the force of the side wind during flight, and thus provide an inferior trajectory prediction to that which is achievable according to the present TP model.
The lateral aircraft body surface-area, used in side wind calculation according to the present model, is not included in BADA, and is therefore estimated according to an embodiment of the model using a simple formulation:
^body Hat ~ Δ · Λ
where Δ is the aircraft diameter and Λ is the aircraft length. However, any suitable method for estimating lateral aircraft body surface area may be used.
The thrust-offset angle may be set to zero in the present TP model. Since this angle is typically very small, neglecting it does not have any significant impact upon TP performance. Therefore, again the present TP model makes an intelligent, efficient choice with respect to its aircraft dynamics emulation.
Vertical lift is also used in the aircraft dynamics system (ADS) emulation. Under trimmed flight conditions, the vertical lift balances the aircraft weight, including a correction term for the thrust- angle offset, and is derived as:
[6]
Note that if e r is set to zero and an aircraft is level-flight, the classical equation is regenerated as:
[7]
In order to maximise efficiency and eliminate redundant calculations, the present TP model sets aircraft operational limitations that reflect real behaviour and experience of an aircraft in flight. Aircraft operational limitations are emulated by applying a constraint to both the state and the input variables of the model as follows:
^ ^ {.^airport ' ^max J
V e [^min ' ^max ]
™ e [ΒΙ Λ , /Β-„]
£ [ Lr reverse ? Γ max 1 J
n [8]
The minimum and maximum values are specific to each aircraft type and can be derived from model specific parameters within the BADA database. Note that height at airport h airport , may be negative for some airports. Furthermore, it should be noted that in equation [4] above the effects of the vertical wind-gradient are not taken into consideration. It is contemplated to include these effects in embodiments of the present TP model. However the associated performance benefits are expected to be small. Flight Management System (FMS)
The third unit of the trajectory prediction (TP) model as exemplified in Figure 1 is the Flight Management System (FMS). The FMS is a control system which emulates typical (auto-) pilot procedures. It uses a set of instructions to compute the required flight control parameters F(t) for the predicted trajectory, based on the aircraft current state X(t) as obtained from the ADS, the intent information obtained from the Flight Script (FS), and environmental parameters and emulates resulting flight control.
As will be understood from Figure 1 , the flight management system (FMS) can receive aircraft performance data for simulating aircraft control. For example, aircraft control could be simulated based on the assumption that the aircraft follows its intended trajectory as closely as possible within the limits of operational capability of the aircraft. Alternatively or additionally, other constraints or conditions may be set for simulation of aircraft control. For example, the simulation may work on the basis that an aircraft will follow its intended trajectory to within a specific margin of error with respect to one or more variables defined in the intended trajectory. The control simulation may assume that certain aspects of the intended trajectory must be met exactly or to within a relatively small margin of error, and/or may assume that other aspects may allowably not be met or may be missed by a relatively larger margin of error. It will be appreciated that the exact simulation scheme employed in the model will depend on the aircraft or other vehicle being considered as well as the details of the intended trajectory.
The instructions to be followed by the FMS are formulated by a Flight Operation Mode System (FOMS), discussed in detail below, based on a set of discrete variables describing the
instantaneous operating mode of the aircraft. In the current TP model, each operating mode, e.g. accelerating, decelerating or constant speed, can be described by a combination of eight discreet variables as set out below. Depending on the variable or variables which best defines the instantaneous operating mode of an aircraft for which a trajectory is being predicted, the FMS will use a corresponding instruction or set of instructions in order to emulate aircraft control within the model. The discrete variables are as follows:
1. "Acceleration Mode" (AM)
2. "Climb Mode" (CM)
3. "Climbing Flight Phase" (CL FP)
4. "Descending Flight Phase" (DES FP)
5. "Reduced Power Mode" (RPM)
6. "Speed Hold Mode" (SHM)
7. "Troposphere Mode" (TrM) and
8. "TCP index" (TCP).
The instantaneously-applicable instructions based on the above variables are used by the FMS to emulate operation of the aircraft, attempting to minimise any deviations from the intended trajectory. When the FMS uses the instruction from the FOMS to compute the required flight control parameters for a given moment in time during the flight, the result is a vector of four dimensional position of the aircraft with respect to ground at that moment in time. The combination of the computed 4D positions for a sequence of points in time provide the predicted trajectory for the flight. The prediction can be made quite short-term, of the order of a few minutes, or may be extended to the longer term, for example a few hours ahead. The prediction may also be updated over the course of a flight so as to accurately reflect all the information available to the model. Flight Operation Mode System (FOMS)
As described above, the flight operation mode system (FOMS) provides instruction for the flight management system (FMS) to calculate the instantaneous flight control parameters for the predicted trajectory, based on aircraft state information received from the aircraft dynamic system (ADS) and the flight script (FS) that specifies the aircraft's intent.
The flight operation mode system (FOMS) according to the presently-described model embodies two key developments as compared to prior art models: enhanced consideration of the turn- modes of the aircraft in the formulation of instructions for the FMS and elimination of aircraft height information in the TCP update condition, as it is not in line with operational procedures experienced in practice. Turn Modes
A distinction is made by the present FOMS between flyby and fly over modes in the
determination of whether an aircraft has passed a transition point between trajectory change points (TCP's) as defined in the flight script (FS).
According to the present TP model, relative angles are used by the FOMS to confirm whether an aircraft has passed a transition point, rather than relying on the distance between the aircraft and such a transition point, as done in prior art models. According to such prior art models, if an aircraft is to fly by a transition point rather than directly fly over it, the flight operation management system might instruct for the aircraft to retrace its path in order to hit, or at least pass more closely by, the transition point and thus stick within the intended path set by the FS. Of course, this is counter to what an aircraft would do in practice and to what is most efficient for the progress of an aircraft, therefore such a prior art model would produce unrealistic predictions at some transition points. To avoid this, the present model has provided an improved functionality wherein the distinction between fly by and fly over is made.
For the fly-over scenario, a new update condition that is representative of operational procedures has been implemented in the present TP model. As shown in Figure 3, a given TCP is deemed to have been reached if the aircraft, indicated by the "star", has crossed the perpendicular to the median of the angle (ΔΨ) subtending the current and next flight segments in the FS.
This condition is satisfied if
. (ΔΨ - π
sin I ■ ω \≥0
2
[9]
In the case of "fly-by" turn modes, the aircraft follows the arc at TCPj+i as shown in Figure 4. As can be seen therein, when an aircraft flies by a trajectory change point (TCP), it begins the turn before that TCP is reached. Therefore the distance travelled by the aircraft from one TCP to the next will not simply be the linear distance therebetween, but will include the distance covered in the anticipatory turn of the aircraft. This is not something that prior art models take into account. It is highly advantageous to take the turning distance into account for fly by turns, as done according to the present TP model.
In order to provide for turn-anticipation, as required by fly-by turns, a threshold is computed to determine the "anticipation-distance". This distance is a function of the turn-radius under nominal bank-an le conditions at TCP + i and is computed using Newtonian equations of motion as:
[10] where nom is the target angle of bank. Therefore, the aircraft should initiate a turn at a distance d from the previous TCP (TCP,) such that the following condition is satisfied as shown in Figure 4: d > d i - 5 [11]
As soon as this condition is satisfied in the present TP model, the TCP is updated and the aircraft is deemed to be on course to TCPi+2. The aircraft does not have to directly fly over a TCP in order to progress to the next one, according to the present TP model. Therefore the TP model implements efficient yet intelligent computation to better reflect real operation of an aircraft, and thus to increase the accuracy of the resulting trajectory prediction. Flight Control System
The other key aspect of the Flight Management System (FMS) according to embodiments of the present TP model is a Flight Control System (FCS). The FCS can use the control variables described by F(t) see Eq. [2], i.e. thrust, bank-angle, flight-path-angle and drag coefficient. Each of those variables is adjusted by the FCS, taking into account the aircraft instantaneous state X(t), FOMS instructions for how to calculate required control parameters, and FS information about the intended flight path, in order to emulate aircraft control with the goal to minimise deviations from the intended 4D trajectory described in the FS.
Previous models have adopted various strategies in relation to controlling the above-mentioned four variables. A key limitation of prior art approaches is that they often use predefined recommended settings provided by BADA, without fully accounting for instantaneous aircraft state or intent. Hence a new Flight Control System (FCS) is set out herein which includes new thrust and flight-path-angle controllers, and an enhanced lateral controller. In comparison to previous models, these controllers more accurately emulate actual aircraft control and operational procedures. This is in line with the overall approach of the present TP model embodiments to minimise reliance on pre-defined parameter settings and instead to make maximum use of aircraft intent information. The FCS makes use of the required rates of vertical changes and speed changes from the flight script (FS) to determine thrust and flight-path angle settings for the trajectory prediction, as described below.
FCS Speed Control As will be appreciated from the detailed descriptions that follow below of thrust control, flight path angle control and lateral guidance, robust and accurate speed control is key to high- performance trajectory prediction in the present TP model. It will be appreciated that even relatively small speed inaccuracies can result in significant along-track errors over prolonged time horizons. Prior art trajectory prediction models largely ignore along track errors since, essentially, these are difficult to control. Furthermore, currently there is little by way of official guidance or specification as to along track performance requirements for trajectory prediction models to be realisable in practice. However this may change over time and, furthermore, if a trajectory prediction model is to be used for practical applications such as estimating collision risks and supporting decision making at air traffic control (ATC) level, along track errors cannot be ignored.
Since the along track error is cumulative, resulting from errors arising in all of the flight segments of a flight path added together, the inputs in any along track error correction model or tool must be highly accurate. It has been found that, according to the presently described TP model embodiments, the along track position of an aircraft can be predicted within a very small error margin over the course of a flight. Much of this accuracy may be contributed to the thorough speed requirements of the TP model described herein.
As the skilled person will appreciate, speed profiles, in order to be realistic, must not show any discontinuities. In other words, an aircraft cannot adjust its speed in a step-wise manner and a trajectory prediction should reflect this limitation. Prior art approaches compute the average speed requirement for each segment of a flight path in a point-to-point manner, not considering acceleration between trajectory change points (TCP's). A key limitation of such an approach is that it effectively creates a step-function in the intended true air speed (TAS) profile, with discontinuities between adjacent flight segments and speed oscillations. To address this problem with prior art models, the present TP model employs a new strategy for the determination of aircraft instantaneous TAS, as computed by the FCS, taking into account aircraft operational procedures and limitations. The strategy considers instantaneous acceleration requirements to meet the Required Time of Arrival (RTA) as well as the Required Instantaneous Ground Speed (RIGS) at the next TCP as set out in the above-described flight script (FS), taking into
consideration environmental factors such as wind. Therefore instantaneous speed requirements computed by the FCS take into account both intent and instantaneous state information for the aircraft.
The first step in the determination by the FCS of the required TAS for a predicted aircraft trajectory is the computation of the distance from the instantaneous aircraft position to the next target TCP, as defined in the flight script (FS). As discussed above, this distance computation is complicated by turn-anticipation, as the actual distance to any given TCP depends on the turn- mode and the change in heading between consecutive segments. Hence, several steps are required, starting with an initial estimate of the distance to the target TCP. This is computed as the sum of straight-line distances: tgt-l
d A ltgt = d A/M (t) + ∑d,
[12] where dM+i is the straight-line distance from the instantaneous aircraft position to the next TCP and d m are the straight-line distances between TCP m and TCP m +i. An estimate of the average speed required to reach the target TCP at RTA(TCP tge t) is then computed based on the time available to reach this target TCP: RTA(TCP lgl ) - t
[13]
This estimate of the average speed required to reach the TCP at the relevant required time of arrival (RTA) is used by the FCS of the present model to compute the turn-radii required to achieve the appropriate change in heading between two subsequent trajectory segments as defined in the flight script (FS) using Eq. [30] - derived in the Lateral Guidance and Bank Angle Control section below - and replacing the V T AS with <V ESTIMATE >. This turn-radius is then used in the computation of an improved estimate of the actual distance to be flown by the aircraft to reach its next target.
With regards to the specific turn-modes when computing the distance to the next TCP, the fly-by mode should account for the fact that the aircraft anticipates the turn at TCP i+ i, and follows the arc-of-circle shown in Figure 7 to join the next segment. Accordingly, the distance to TCPj+i for the fly-by mode is computed as follows:
[14] where d^gis shown as a bold line in Figure 7 and d, is the total straight-line distance between
In the case of the fly-over mode, it is assumed that the aircraft uses common operational procedures and flies along the arc-of-circle shown in Figure 8, using a nominal bank-angle. The distance flown between TCP i+ i and TCP i+ 2 is then computed as:
M , = d M - 2 ■ R M ■ sin (ΔΨ Ι+1 ) + 2 · R M ■ ΔΨ
[15]
An improved estimate of the actual distance flown by the aircraft is then given by:
tgt-l
d A / tgt m,eff
m=next
[16]
The computed distance to the next TCP is then used together with the RTAs set by the flight script (FS) to compute the aircraft's instantaneous speed requirements, as shown below.
Computation of Instantaneous Speed and Acceleration Requirements
The TP model described herein computes the required instantaneous True Air Speed (TAS) to be achieved by an aircraft in flight by using the acceleration requirement aft) to compute the ground speed requirements as follows: v GS (t + At) = v GS (t) + a(t) - At
[17]
The computation of the acceleration aft), based on the current speed, the distance d A/tgt between the current position and the target TCP, and the time available to reach the target TCP at RTA tgt , is very sensitive to the initial speed:
[18]
A variation in the initial speed at any instant in time can result in significant variations in the estimates of the required accelerations, with the consequence of significantly different speed profiles. The resulting oscillatory behaviour of the ground speed requirement is illustrated in Figure 9. It can be seen that all three speed profiles shown in this figure satisfy the average speed requirements for each of the segments, yet the overall 4D trajectory flown by each is significantly respectively different. Since aircraft make smooth adjustments in their speed, it is essential that the speed at the end of a given segment corresponds to the speed requirement at the beginning of the following segment. However, prior art models cannot achieve such continuity, as Figure 9 demonstrates.
The present TP model addresses the oscillatory behaviour as shown in Figure 9, which prior art models allow. It does so by setting a requirement on the initial ground speed at the beginning of each segment. As a result, the Required Initial Ground Speed (RIGS) is introduced into the FS, as described above.
By requiring a given initial ground speed for each TCP in the flight script, the characterisation of aircraft intent according to the present model is significantly enhanced because the flight script (FS) speed profile is significantly constrained. In essence, by having a target speed at each trajectory change point (TCP), a unique speed profile is defined in the flight script. That is, the speed profile achieved within the flight script according to the present TP model can only take one form when viewed on the scale of speed and rate of change of speed. Therefore, for practical purposes and real implementation of trajectory prediction, the speed profile in the flight script (FS) is unambiguous. This provides significant advantages over the prior art by realistically emulating actual aircraft behaviour, yet in an efficient way.
According to the present TP model, the required aircraft acceleration can be expressed either as a function of the speed requirements or as a function of the distance and time requirements as shown by the following two equations respectively:
Λ RIGS(t M ) - v GS (t) A
a(t) = ; 1+1 ' , GS w and
(t M - t)
[19]
[20]
With a simple transformation, these two equations can be combined into one, to uniquely define the required acceleration in terms of distance, speed and target speed at each TCP:
RIGS 2 (t M ) - v G 2 S (t)
a{t)
2 - d A / tgt
[21] Note that the time-factor in the denominator has been eliminated in the computation of the acceleration. The ground speed requirements can be computed using Eq. [17]. This method according to the present TP model is robust against variations in the initial speed VGS as may occur, for example, as a result of operational environmental factors such as varying wind- fields. The true airspeed vector (TAS) can be computed as the sum of the required ground-speed vector and the instantaneous wind- field vector:
V nom ~ V GS ~ ^ xy
[22]
This speed and acceleration are used as an input to the FCS which determines the appropriate thrust and flight-path-angle settings. Therefore the benefits of the unique, accurate speed profile determination in the present TP model are extended to other computational process performed by the model.
Rate of Climb Descent (ROCD
In known TP models, BADA recommendations for both thrust and energy store factor (ESF) settings are used to determine the flight-path angle. The model as described herein improves performance accuracy by using aircraft intent information from the flight script (FS) to determine an instantaneous target ROCD which, in combination with nominal speed v nom , determines the appropriate thrust and flight-path-angle settings to be used throughout the flight as discussed further below. Here, the instantaneous target ROCD is computed from the difference between the current height and the height of the next TCP. The time available to execute this change in height is given by the ratio of the instantaneous distance to the target TCP and the required ground- speed. Mathematically this is expressed as:
ROCD = (h M - h(t))x
[23]
FCS Thrust Controller
Once instantaneous speed requirements have been established, the present TP model can reliably emulate many aspects of the flight control. One such aspect of control emulated by the FCS is thrust control. In prior art models for thrust, instantaneous values are set to balance the drag acting on the aircraft during level-flight while, for climb and descent, predefined fixed values are set based on BADA recommendations, accepting the Rate of Climb Descent (ROCD) that is obtained as a result of these settings. The drawback of this approach is that neither the instantaneous ROCD nor the acceleration required to follow the intended aircraft trajectory are considered. That is, both state and intent of the aircraft are ignored. In the present model, the thrust of the aircraft is modelled according to the climb-mode and the acceleration-mode variables describing the instantaneous operating mode of the aircraft and the corresponding flight control emulation instructions from the FOMS. According to those instructions, during climb and descent, the thrust is determined based on both flight-path-angle and acceleration requirements. Newtonian laws of motion enable the derivation of the required thrust as follows:
T = T cmise + m - g - sm r + m - a . [24] where γ is the required flight-path-angle, "a " the rate-of-change of speed and T crujse the thrust under level-flight and constant speed conditions, essentially determined by the drag acting on the aircraft:
_ C D ■ P - S
1 cruise TAS 1 J
In Eq. [24], both γ and "a " can be positive or negative and are computed from aircraft instantaneous True Air Speed (TAS) and Rates of Climb and Descent (ROCD) requirements. Both the rate of change of speed and the true airspeed for use in thrust calculation according to the present model can be computed by the FMS from the instantaneous state information from the ADS and from the aircraft intent found in the flight script (FS) for the trajectory prediction (TP) model as described above. By using the computed speed and acceleration requirements, computable by the FMS, and feeding them into the thrust controller unit of the TP model, enhanced accuracy is achieved efficiently since inputs that are readily available in the model are used by the Flight Management System (FMS) in order to control the aircraft to keep its intended flight path as closely as possible.
It will be appreciated that, in practice, a real aircraft would calculate actual thrust in order to control the path of the aircraft over time to stick as closely as possible to a flight script setting out an intended flight path. Therefore, by actually computing thrust rather than relying on predefined fixed values, the present TP model better emulates real world flight management and control. The thrust computation can be carried out taking into account the variation between different aircrafts and variations in operational environment and conditions experienced during different respective flights. The thrust calculation as described herein makes use of the recognition that there is sufficient information available from onboard aircraft sensors to compute actual thrust requirements, such that doing so does not require additional sensors or place a particular computational burden on an aircraft control system. Therefore it is an efficient and intelligent choice to calculate thrust as part of the emulation of control procedures by the Flight Management System of the present TP model.
Flight Path Angle Controller
In a further development as compared to prior art TP models, the present TP model can consider flight path angle control. Prior art models compute the flight-path angle using an assumed Energy Share Factor (ESF) recommended by BADA. The ESF is introduced in BADA to specify how much of the available power is allocated to the change in height and to the change in speed (Eurocontrol, 2009b) of an aircraft. However, the values provided by BADA do not consider the actual instantaneous state of the aircraft during any given flight or the required allocation of thrust to the rate-of-change of height and to the change in speed in order to actually adhere to the intended flight-path as defined by the flight script. A more realistic flight path angle (FPA) is determined herein based on both the ROCD and the speed requirements. These requirements are determined from the aircraft instantaneous state obtained from the Aircraft Dynamic System (ADS) and the next target TCP state-requirements obtained from the FS. Therefore, again the model increases accuracy by making a calculation rather than relying on predefined values, but does so using instantaneous speed requirements and the required rate of climb or descent, that are derivable by the FMS using aircraft intent and instantaneous state information. Hence this increased accuracy with respect to flight path angle (FPA) is achieved efficiently, and introduces little or no computational burden into the TP model, whilst making the TP model more realistic.
The FPA γ can be determined as:
[26] where V GS is the ground speed. However, it will be appreciated that another suitable reference frame, including air mass, may be used.
Although not considered in equation [26] above, it is possible to also take the vertical wind-field into account in order to compute flight path angle according to the present TP model. The vertical wind field is derivable from onboard measurements and could be integrated into the calculation as shown in equation [26] in any suitable manner.
During the climb and descent phases, the FPA controls the aircraft TAS. During level-flight, the FPA controls the ROCD required to correct any small deviations from the nominal altitude as a result of, for example, a variation in the vertical wind-gradients. Therefore it is an important parameter for which improved accuracy has a positive effect on the overall trajectory prediction (TP) process. It is also possible to take the angle of attack into account when calculating flight path angles for control emulation by the Flight Management System (FMS). Angle of attack is the angle between the chord line of an aircraft wing and a flight path angle. Put another way, it is the angle between where the aircraft nose is pointing and the direction which it is flying with respect to the horizon. However, angle of attack is already implicitly taken into account in the Aircraft Dynamic System (ADS) of the TP model as illustrated in figure 1. Since the TP model operates a feedback loop between the Aircraft Dynamic System (ADS) and Flight Management System (FMS), it has been recognised that there is no particular benefit with respect to accuracy of the resulting predicted trajectory if the angle of attack is also taken into account for flight path angle control in the Flight Management System. If it is desired to incorporate the angle of attack into equation 14, the values for angle of attack may be taken from predetermined data or may be derived using information from onboard aircraft sensors for example during level flight.
It should be noted that thrust settings during climb and descent determine the ROCD, whilst thrust controls the TAS in level-flight conditions when γ is approximately zero in the TP model. This is operationally significant since the model therefore mirrors the way in which aircraft are actually operated in practice. Furthermore, because of the interrelationship between the instantaneous speed, ROCD, and other control parameters in the model, by improving accuracy as discussed above with respect to calculation of instantaneous speed requirements, many aspects of the model are improved. Lateral Guidance and Bank Angle Control
In a further enhancement of aircraft control emulation by the flight management system (FMS) of the present model, lateral guidance is provided. Lateral guidance is needed to correct lateral offsets from the required trajectory as defined in the FS, referred to as Cross-Track Errors (CTE) and Heading Errors (HE). The present TP model also considers environmental factors for lateral guidance.
The heading angle Ψ between two TCP's is shown in figure 5. Neglecting the thrust-offset angle stantaneous change in heading is computed by the present TCP model as:
[27]
In turn, the heading angle controls the horizontal position of the aircraft through the following change in lateral position: x = V TAS ■ cos( Ψ ) · cos( γ ) + w x
y = · sin( Ψ ) · cos( χ ) + w [28] As can be seen from Figure 5, cross track error (CTE) is a measure of the lateral offset between the intended trajectory of an aircraft between first and second trajectory change points and the model-predicted trajectory that will be taken by an aircraft at any given point in time when it is travelling between those two points. The CTE is the error perpendicular to the intended trajectory, i.e. the shortest horizontal distance between the predicted point and the intended trajectory at a given instant in time. It may be defined using a distance or as a function of the angle β as seen in Figure 5 and as discussed further below. Heading error (HE) is defined as the offset between the intended heading of an aircraft at any given point in time as obtained from the flight script, taking into account environmental parameters, and the predicted heading direction of the aircraft at that point in time.
In a development as compared to prior art TP models, the present TP model takes both environmental parameters and the intended trajectory from the flight script into account when determining whether there is a heading error in the predicted trajectory that should be offset using lateral guidance from the FMS. Because environmental parameters are considered in addition to the intended trajectory set out in the flight script, the present TP model can account for a situation in which an aircraft would deliberately fly at a heading that is different from the ground track direction of its intended trajectory in order to accommodate a side wind or other surrounding wind condition, rather than flying a heading corresponding to the ground-track direction and being pushed away from its intended track, in order to stick more closely to the intended trajectory set out in the flight script.
Lateral guidance is assumed to be provided in the present TP model by adjusting exclusively the bank-angle, which controls the heading of the aircraft. Bank angle determines the tilt of the aircraft with respect to the horizon and thus controls the horizontal direction in which the aircraft is pointed and travelling in.
According to the presently-described TP model, the bank-angle is determined by the flight control system (FCS) using a linear controller, based on a strategy similar to Porretta et al (2008), but with two innovations: inclusion of the wind- factor in the computation of the turn-radius and in the heading error. In order to minimise potential deviations from the intended trajectory, the controller (FCS) initiates suitable corrections for both the CTE and the HE as soon as they are observed in the present TP. The bank angle controller aspect of the FCS computes the bank-angle required to get the aircraft back on track at the appropriate heading. The required bank angle is a function of both the CTE δ as shown in Figure 5, and the HE ΔΘ.
The cross track error (CTE) may be expressed as a distance δ as mentioned above and as shown in Figure 5. Alternatively or additionally, CTE may be expressed as a function of the angle β(ΐ). This angle, shown in Figure 5, is defined as the difference between the nominal or required heading of the current flight segment obtained from the flight script (FS) and the vector pointing from the current aircraft location to point on the flight path for that segment. Point "I" is defined as the intersection of the current segment with the arc of circle of a nominal turn initiated by the aircraft from its current location A at its maximum angle of bank. The angle β(ί) effectively interpreted as an additional heading error, simplified here as:
[29] Assuming that aircraft height and True Air Speed (TAS) are constant during the turn, the turn radius for the nominal turn initiated by the aircraft and maximum bank angle may be computed as:
m - g - tar{(p nom ) + W R
According to a unique, advantageous feature of the present TP model, the term W R is introduced in equation [30] above to account for the impact of the horizontal wind- force upon the turn-radius. Therefore, the model not only accounts for wind effects during "steady state" conditions such as linear flight, when wind can push an aircraft away from its intended trajectory, but can also account for the effects of wind during changes in the track of the aircraft during its predicted trajectory. For a constant aircraft height, W R is related to W XY discussed above as follows:
W R « m - V TAS - W v
[31] where all parameters have the same meaning as above.
A further enhancement to the bank-angle controller according to the present TP model embodiments is the consideration of the wind-factor in the computation of the heading error ΑΘ which contributes to the overall heading error pHE as set out below. In prior art approaches, this heading error is computed as the difference between the current heading O JAS of an aircraft at a given point in time as determined by the FCS and the intended heading associated with the current flight-segment θ, / , + ι ^ computed from the FS:
A0(t) = 0 TAS - 9 ili+l
[32] However, in the presence of a bias in the lateral component of the wind which would occur in practice during aircraft flight, the prior art equation [32] above will result in constant heading error and a cross-track error because the aircraft is constantly pushed off its intended track by the wind. In an advantageous development over the prior art, the present TP model recognises that, in real-life, in the presence of lateral winds, an aircraft is required to compensate for the effect of the wind by turning its heading into the wind. This is illustrated in Figure 6. Expressing this mathematically; given a wind- field vector to xy , the TAS vector V JAS must be such that the vector resulting from the sum of the True Air Speed TAS and the wind- field is parallel to the direction vector de fined by the current segment according to the flight script (FS). Mathematically the target heading 6 tg t in the presence of a lateral wind-field can be expressed as:
[33]
Where A9 w is the angular offset causes by the bias in the lateral component of the wind. Taking the above into account in the present model, the effective heading error Αθ(ΐ) of the aircraft is then given by:
Αθ(ή = 6 TAS -0 tgt = θ ΤΑ8 - {θ ίη+ι + A6 W )
[34]
This heading error results in a trajectory prediction that the aircraft will be effectively flying sideways, referred to as "crabbing", wherein the aircraft is subject to a side wind. Bank-angle settings provided by the controller are saturated between minimum and maximum permissible values of effective heading error (HE) and sideways movement associated with the operating limits of the given aircraft type. Such saturation assures that the TP model reflects the aircraft is operating within its capabilities at all times.
Once (t) and Δθ(ΐ) have been computed, an overall heading error can be determined by the present TP model. Because the present TP model recognises that the offset due to wind is not an error per se, but reflects real aircraft operation, it defines the overall heading error as a pseudo- heading error combining the angular representations of CTE and HE, given by:
pHE(t) = Αθ(ή+ β(ή
[35]
In order to predict how an aircraft would be controlled in flight to account for lateral offsets from its intended flight path, the linear controller is used in the present TP model to minimise the overall pHE, and to determine the corresponding bank angle to be implemented, based on the determined pHE. This is expressed mathematically as:
f[S{t),A0{t)] = kx pHE{t) As can be seen from equation [36], the bank angle determined according to the present TP model includes a constant gain factor k. As discussed in detail below, this constant gain factor has been calculated for the present model. It is also possible to include a wind factor in equation [36], to further account for wind effects on the required bank angle.
Therefore, the present TP model determines a real life bank angle, which is well defined for an aircraft in practice, rather than relying on predetermined settings or assumptions that lead to inaccuracies, as done by prior art models. Tuning Controller Gain for Lateral Guidance
In order to yet further enhance the aircraft lateral guidance control according to the present TP model, a new method to evaluate the controller gain is provided that consists of comparing the statistics of the resulting CTE when the bank angle is calculated and applied within the TP model for different values of the gain factor k as shown in Figure 10. This gain factor k is used in equation [22] and is a scaling factor between the instantaneous pseudo-heading error of the aircraft as calculated by the FMS from errors, and the bank angle that is required to get the aircraft back on to its intended trajectory. As shown in figure 10, in the range of k = [1.0 to 2.4] , large variations in the maximum CTE are observed. This is the result of the inability of the aircraft to follow its intended trajectory since it is not "allowed" to bank sufficiently using the applied bank angle. Upon reaching a value of k = 2.4, the curve becomes approximately flat. The reason for this behaviour is that any further increase in the allowable maximum bank-angle does not improve the ability of the aircraft to follow its turn and as a result no increase in performance is expected. From an operational perspective, the aircraft would use the minimum bank-angle that is required to maintain a given turn-radius in order not to "overshoot" its trajectory and cause it to zigzag around its centreline. Therefore, a value of k = 2.4 is adopted in this TP model. Such value has been found to be realistic from an operational perspective, especially when turning into the wind. By compensating for lateral wind using a wind- field factor in turn radius computation, the accuracy of the turn radius that the present trajectory model uses to emulate control is improved. This is done in an efficient, computationally intelligent manner, using readily available operational parameters. It thus mirrors realistic aircraft control and provides a more accurate trajectory prediction. Whilst some existing TP models do account to an extent for CTE, HE and limitations due to aircraft performance, none account for the impacts of wind. The result is a systematic and deterministic bias in the cross-track and heading errors associated with the predicted trajectory from prior art models. Moreover, the gain-factor is taken for granted, resulting in an incorrect estimation of the actual bank angle used during turns in prior art models. Hence the present TP model has several unique advantages over the prior art.
Coefficient of Drag Cn One aspect of onboard control not developed according to the embodiments described herein is coefficient of drag. The coefficient of drag C D is specified in existing models as a function of the coefficient of lift C L . Furthermore, the expressions recommended for the calculation of Co depend on the discrete variables which specify the phase of flight. For example, changes in the aircraft configuration during the descent alter the aerodynamic drag force, and are modelled using appropriate correction factors or incremental terms in the proposed expressions for C D - In the approach phase, additional terms account for approach-specific flap and landing-gear settings, both of which increase the drag. Similarly, when the use of spoilers is required by an expedited descent, an appropriate multiplication factor is used to boost the coefficient of drag. According to the present TP model, the coexistence of drag is treated similarly to the treatment of Poretta et al (2008). It has been found that coefficient as drag is only potentially important, as far as accurate trajectory prediction is concerned, during the descent or approach phase of a flight. Whilst the present trajectory model does not look at coefficient of drag in detail during that phase, it can adapt the thrust configuration of the aircraft during descent as part of the feedback control between the flight management system (FMS) and aircraft dynamic system (ADS). Hence again the model treats a parameter, in this case coefficient of drag, in an intelligent and efficient way, without compromising accuracy of the resultant trajectory predictions.
Use of the present TP Model in Practice
The performance of the presently described TP model has been validated using real flight trials in European Airspace. Detailed Flight Data Records (FDR) as a function of time were provided by EUROCONTROL (Eurocontrol, 2009c). The FDR include aircraft 4D position, attitude, thrust settings, speed (True and Calibrated Air Speeds, Ground Speeds and ROCD) and environmental conditions (wind- field, temperature and pressure). The FDR used to characterise the performance of the TP model are for a 3-hour Boeing 737-500 aircraft flight on 16 November 2005 from Sofia International Airport in Bulgaria (ICAO Code: LBSF) to Sheremetyevo International Airport in Moscow (ICAO Code: UUEE).
All the necessary aircraft performance parameters were taken from the BADA set (Eurocontrol, 2009b). Additionally, the aircraft diameter, length and total lateral aircraft-body surface area were taken from available data sources.
The present TP model requires as input the aircraft intent in the form of TCPs, with the associated RTAs and RIGSs. These are not directly available from the FDR, and were allocated through a backward analysis in order to provide a set of instructions unambiguously describing the intended operational state of the aircraft over the flight, so as to eliminate uncertainty and thus enable the present TP model to be tested thoroughly. The resulting FS is a time-ordered sequence of TCPs that accounts for the most significant changes in the aircraft configuration, such as heading, TAS, ROCD and in the environmental conditions, such as wind. The present TP model was run using a flight script defined using FDR as described above, along with wind- field predictions and performance factors as inputs, as illustrated in Figure 1. The reliability of the model was then tested by comparison of the resultant trajectory prediction to the actual trajectory followed by an aircraft in practice. By way of example, trajectory prediction (TP) performance can be evaluated in terms of Euclidean Errors (EE), defined as the 3D distance between the actual aircraft position and the nominal position calculated by the model for each point in time along the predicted trajectory. The EE may be projected along-track and
perpendicular to the nominal track in the horizontal and the vertical, to evaluate respectively the Along Track Errors (ATE), Cross-Track-Errors (CTE) and Radial Errors (RE), as well as the Altitude-Errors (AE). Furthermore, the performance of the aircraft in meeting the RTAs is evaluated as Time-of- Arrival Errors (TAE). These are computed as the difference between the nominal time and the actual time of the aircraft for each point along the trajectory.
It was shown that, overall, there is very good agreement of the predicted trajectory output by the present TP model with the true trajectory of the aircraft. An interesting parameter is the TAE, which is effectively a measure of the level of capability of the present TP model to accurately predict the arrival time at a given TCP, and is an important consideration in the assessment of 4D conflict detection and resolution strategies where timing is a key factor. Comparison with Prior Art Models
The performance of the current model has also been compared to the model in Porretta et al (2008) based on the same portion of a flight and a sampling interval of approximately 60 seconds for the wind- field. The performance differences are highly significant, with improvements in the overall maximum prediction errors by over 95% with other prediction errors also significantly improved. Overall, the performance improvements can be attributed to a significant enhancement in the level of realism applied in the presently described TP model, with focus on emulating, as much as possible, practical aircraft operational procedures. Amongst others, the significant improvement in the maximum errors should be noted. This reduction in maximum errors is especially relevant, as it defines the overall reliability of the TP model in being able to
"guarantee" a certain worst-case performance. This is essential for real world implementations of the model.
Wind Data and Look Ahead Times (LAT)
As discussed above, the wind-data for the present model can be obtained either from wind- prediction models and/or from onboard aircraft measurements. Similarly, the temperature data can be obtained either from temperature prediction models and/or onboard aircraft measurement. In order to emulate larger Look-Ahead Times (LAT), the wind and temperature samples used in the present TP model can be down-sampled by varying factors. It has been found that wind-field uncertainties have the largest impact on the ATE and TAE, with relatively minor impacts upon CTE and AE. Any significant difference between the actual and estimated along-track wind- components leads to a significant difference in the estimation of the required TAS. Since ATE is integrated over time, even relatively small offsets in TAS can result in significant ATE over time. For CTE and AE, the impact is less significant, since the required true heading and the required altitude are well-known from the flight-script, and are both independent of the wind- field. Any impact of the lateral or vertical components of the wind- field is thus easily corrected by the flight control system (FCS) of the present model. Irrespective of the LAT, all parameters in the present TP model are at a level that is significantly better than the currently allocated globally lateral navigation system performance requirements for the en-route, the terminal area (TMA), the Initial Approach (IA), Intermediate Approach (IMA) and Non-Precision Approach (NPA), as well as departure even for relatively large time-horizons (e.g. 60 minutes). The CTE is smaller than the lateral accuracy requirements and the maximum CTE is smaller than the Alert Limit requirements. A comparison is shown in Fig 11. The results for the IA, IMA, NPA and departure have been extrapolated, based upon the assumption that the wind- field sampling is finer during those phases of operation, hence the reduced time-horizon. Benefits and Implementations of the TP Model
It will be understood from the detailed description above that two key factors are at the core of four dimensional (4D) Trajectory Prediction (TP): representation of aircraft intent and the actual TP model used to simulate aircraft behaviour. TP is limited by the capability of the Flight Script (FS) to accurately represent actual flight trajectories. Therefore, a realistic and unambiguous representation of aircraft intent is critical. In turn, the TP model must emulate as far as possible practical operational procedures in following the trajectory defined by the FS. In the context of these two factors, the presently described TP model embodies a number of innovations.
Specifically, the model includes an advanced Flight Control System for trajectory prediction, benefiting from novel controls of speed, thrust and flight-path-angle, as well as an enhanced lateral controller. These developments lead to the definition of a new FS, able to more realistically define the aircraft intent with respect, in particular, to speed at TCP's.
The new developments described herein have been shown to result in significantly better TP compared to state-of-the-art models. Previous trajectory prediction models have been limited in their applicability in real time operational context due to their relatively poor performance. The TP model described herein has a level of performance that is around 20 times better than previous models, bringing its performance to a level where, for example, the navigation performance requirements of Civil Commercial Aviation for most flight phases can be met. In fact, the performance of the model is significantly better than the instantaneous positioning requirements of aircraft for the en-route sector, as well as for flight-phases up to and including NPA and departure. The ability to predict aircraft trajectories to this high level of performance is expected to have significant benefits. Advanced decision support tools (DSTs) based upon TP will reduce controller workload, one of the key factors limiting airspace capacity. Moreover improved TP will allow more advanced conflict detection and improved conflict resolution for onboard
aircraft safety systems, thereby contributing towards enhancing the safety, efficiency and capacity of air travel.
The trajectory prediction tool described herein may be implemented for various purposes. For example, to estimate collision risks between two vehicles, for example two aircraft, by air navigation service providers (ANSP) and others, for example unmanned aerial systems (UAS) operators. The TP tool may also be used to support decision making, for example for conflict detection and resolution, by ANSP's, UAS operators and others. This will serve to enhance the safety, efficiency and capacity of air travel by enabling more anticipatory decision making, rather than the current reactive or tactical processes used.
As mentioned in the background section above, SESAR and NextGen are initiatives that seek to provide more efficient navigation by guaranteeing common situational awareness between all traffic and air traffic control and by improving the ability to visualise the evolution of air traffic as a function of time. By using the TP model described herein, for example by using the proposed flight plan or flight script information, the aim for such initiative can be achieved. Furthermore, possible implementation of the TP model described herein are not limited to air traffic. An analogous model may be used for rail, road and maritime sectors and again may be used in such sectors for collision risk estimation and collision avoidance systems for terrestrial and sea vehicles.
The computational and processing steps of the model during operation to produce a predicted trajectory can happen at an aircraft itself, such that a resulting trajectory would be transmitted to the ATC. Alternatively, raw data could be streamed from the aircraft to the ATC and the computations of the predicted trajectory could take place at the ATC itself. Furthermore, trajectory predictions and/or raw data can be streamed between aircraft for enhanced air traffic control and for real world implementation such as conflict resolution.
The present TP model provides reliable trajectory predictions since it takes into account, at various stages of the modelling process, both the intent and state of the aircraft. Furthermore, the actual physics of the equations of motion used by the model are more accurately taken into account than has been the case for TP prior art models.
Unlike prior art models, the present TP model provides speed control and thrust control that is reliable, accurate and operationally realistic. The model recognises that an aircraft would make use of information available from onboard sensors and therefore uses such information in the emulation of aircraft operation and control, rather than relying on predetermined data. There is a feedback loop provided between the aircraft dynamics system (ADS) and the flight management system (FMS) of the TP model. As a result of this feedback loop, the model can compensate for some errors in the parameters used, for example if there is an error in a predefined setting used by the model. Therefore the model is resilient and the trajectory prediction output therefrom will not be degraded significantly by initial input errors.
The TP model provided herein not only provides advantages over prior art models but takes a very different approach to modelling. Rather than relying existing approaches and assumptions, the model addresses trajectory predictions from a realistic perspective, both scientifically and operationally, and makes intelligent, accurate choices on that basis. These choices include input to use, which parameters should be derived or computed and which can be reliably taken from predetermined settings, and the choice of which values in the mathematical calculations should be improved and which can be assume or ignored without affecting the accuracy of the resulting trajectory predictions.
The present TP model is highly useful in practice, since the trajectory prediction provided can be scaled from very short term, for example two minutes, to much longer term, for example of the order of thirty minutes, without significant degradation of the resulting trajectory prediction. If the model uses purely forecast (e.g. environmental) parameters, it can extend its future prediction time. Conversely actual past measurements are also used this may restrict how far in advance trajectory predictions can be made but may improve the accuracy of the resulting trajectory predictions.
The trajectory prediction model may be implemented using any suitable hardware or software means. Instructions for running the model may be recorded on a computer readable medium or other suitable record carrier, including optical magnetic and solid state storage. The instructions for running the model and/or any data used within the model may also be recorded, stored and/or transmitted using any appropriate signal.
A computer or other suitable processing means may be programmed to execute instructions for running the described model. The processing means may also be used for compilation of the flight script (FS). Furthermore, a computer program may be provided for use in a computer or other suitable processing means in order to implement the described model.
Although references are given above to the model configuration shown in Figure 1 , it will be appreciated that variations thereon are also contemplated. For example, other operational or environmental factors may be input to the ADS and/or the FMS for running of the model.
Furthermore, the FMS may control any or all of the thrust, lateral offset, bank angle, flight path angle and coefficient of drag, or any other suitable variable according to the present TP model. The TP model according to the presently described embodiment provides enhancement with respect to the choice of input data, the simulation of aircraft dynamics and the simulation of flight management. Many of these advantages are interlinked, for example the setting of required initial ground speed (RIGS) for each TCP in the flight script can then be used by the flight controller system (FCS) to better emulate control of operational parameters such as thrust and flight-path angle. As well as providing an improved flight script setting out the intent of an aircraft, the present TP model thoroughly considers aircraft state, in particular with respect to its
environmental surroundings. This is done both in computing errors that the FCS can correct and predicting actual movement of the aircraft, for example during turns. No prior art approaches provide such a sophisticated representation of aircraft intent or state, nor do they emulate aircraft operation and control in as accurate and reliable a manner as the present TP model does.
Therefore a significantly enhanced TP modelling tool and approach is provided.
References:
.html (2009a).
Eurocontrol Experimental Centre, User Manual for the Base of Aircraft Data (BADA), Revision 3.7, EEC Note 10/04, (2009b).
Eurocontrol, Reference Validation Data Base, Eurocontrol TP team website (2009c).
Glover W. and Lygeros J., A Multi-Aircraft Model for Conflict Detection and Resolution
Algorithm Validation, Technical Report WP1, Deliverable D1.3, HYB RIDGE (July 2003).
Glover W. and Lygeros J., A Stochastic Hybrid model for Air Traffic Control Simulation, Hybrid Systems: Computation and Control, ser. LNCS, R. Alur and G. Pappas, Springer Verlag, no. 2993, pp. 372-386, 2004.
ICAO, Manual of the ICAO Standard Atmosphere, ICAO Doc 7488 (1964).
Porretta M., Dupuy M-D, Schuster W., Majumdar A., Ochieng W., Performance Evaluation of a Novel 4D Trajectory Prediction Model for Civil Aircraft, Journal of Navigation, Volume 61 , Issue 03, July 2008, pp 393-420.
RTCA, NextGen Mid-Term Implementation Task Force, RTCA Task Force 5 (2009).
Schuster W. et al., High Accuracy Navigation Report, ANASTASIA D3.2.3.2 (April 2008).
SESAR Consortium, http://www. eurocontrol. int/sesar • /public/ tandard page/documentation, html. Deliverables Dl - D6 (2006 - 2008).
Vilaplana Ruiz M.A., COURAGE Domain Analysis Deliverables D2.1 and D3.1, The Boeing Research & Technology Europe, Madrid, Spain, 2005.