Method for the detection of conflicting trajectories of aircraft

Abstract

Method for the detection of conflicting trajectories (t1, t2,...) of aircraft (A1, A2,...), comprising the following steps: a) for at least two aircraft respectively defining a trajectory indicative of the spatial position of the aircraft for a plurality of time steps, wherein - at least one portion of the trajectory characterizing an estimation of the future trajectory of the aircraft, in particular according to a flight plan or defined by a predetermined destination, and in particular - at least one point on the trajectory being indicative of the actual and / or past and / or future position of an aircraft, b) for each of the trajectories assigned to the aircraft defining an emitter function that is indicative of the positional probability distribution of the aircraft or an emission caused by the aircraft at a given spatial and temporal point of interest.

Description

[0001] Method for the detection of conflicting trajectories of aircraft

[0002] The invention relates to a method for the detection of conflicting trajectories of aircrafts according to claim 1 . The invention also relates to a data carrier on which a program for carrying out a method according to the invention is stored.

[0003] Trajectories are used for the description of the actual and / or past and / or future positions of aircraft over time. Within the scope of this invention, aircraft are considered to be any flying objects, such as manned airplanes, helicopters or unmanned aerial vehicles (UAVs). Actual positions of trajectories of aircraft are typically determined by different means of localization, such as radar or satellite based geo-localization. Future positions of aircraft are typically determined by route optimization methods.

[0004] In the context of the invention trajectories are considered to be conflicting, when they interfere with one another in a manner that a future incident is likely. It is the objective of the invention to detect future object and / or aircraft collisions. A further objective is also to detect the violation of other restrictions, such as capacity restrictions, wind conflicts, noise conflicts (etc.). Another objective of the invention is to resolve such conflicts, once a conflict is detected.

[0005] The invention solves these problems with a method according to claim 1 .

[0006] One preferable advantageous method of the aspect of the invention that allows to calculate the emitter functions efficiently, comprises the following substeps:

[0007] - using and / or aggregating a plurality of emitter functions, each emitter function being assigned an aircraft trajectory and determine a total emitter function, said total emitter function yielding an emitter value for a given spatial and temporal point of interest, and

[0008] - applying the constraint mapping to the total emitter function and obtain a conflict structure.

[0009] One alternative advantageous method of the aspect of the invention that allows to calculate the emitter functions efficiently, comprises the following substeps:

[0010] - individually applying the constraint mapping to a plurality of the emitter functions and obtain one or more emitter-based conflict structures, each emitter-based conflict structure being associated to one of the emitter functions, and

[0011] - using and / or aggregating emitter-based conflict structures assigned to the emitter functions and thereby determine an overall conflict structure. In order to simplify the calculation of the emitter functions and / or constraint functions in regions without increased significance for obstructions, a preferred aspect of the invention comprises the following substeps:

[0012] - wherein an emitter function and / or constraint function assigned to a trajectory returns a default value indicating no obstruction, in particular zero and / or without a contribution to the aggregation used, if the spatial and / or temporal distance, according to a predefined metric, between the point of interest and the trajectory exceeds a predefined threshold,

[0013] - wherein in particular said default value is returned if the point of interest (p) is outside a predefined bounding box or bounding volume that surrounds said trajectory, and / or

[0014] - wherein the constraint function having a default value indicating no obstruction outside a volume of interest.

[0015] In order to manage a plurality of different quantities affecting the same constraint, it is possible that the aggregation of emitter functions consists in point-wise combination, in particular addition, of co-located and contemporary values of the emitter functions, thereby obtaining a four-dimensional total emitter function.

[0016] In order to obtain a conflict structure that indicates the value of a potential obstruction for each four-dimensional point within a plurality of four-dimensional points, each of which is associated a time value and a position vector value,

[0017] - the constraint mapping method consists in point-wise combination, in particular multiplication, of co-located and contemporary values of the emitter function or at least one emitter function and or total emitter function and constraint function, thereby obtaining a four-dimensional conflict structure,

[0018] - wherein conflicting trajectories are detected, if the value or aggregated value of the conflict structure exceeds the threshold value in at least one temporal and spatial point, said temporal and spatial point being indicative of the time and location at which the trajectories are conflicting.

[0019] In order to obtain a conflict structure that indicates the value of a potential obstruction for each time step within a plurality of time steps,

[0020] - the constraint mapping method consists in temporal and spatial point-wise combination, in particular multiplication, of co-located and contemporary values of the emitter function or at least one emitter function and / or total emitter function and constraint function, followed by a spatial integration or summation over the constraint’s volume of interest at a plurality of time steps, and thereby obtaining a one-dimensional conflict structure,

[0021] - wherein conflicting trajectories are detected, if the value or aggregated value of the conflict structure exceeds the threshold value in at least one point in time, said point in time being indicative of the time at which the trajectories are conflicting.

[0022] In order to obtain a conflict structure that indicates an overall value of a potential obstruction,

[0023] - the constraint mapping method consists in temporal and spatial point-wise combination, in particular multiplication, of co-located and contemporary values of the emitter function or at least one emitter function and / or total emitter function and constraint function, followed by a spatial and temporal integration over the constraint’s volume of interest, thereby obtaining an overall conflict structure independent of time and location,

[0024] - wherein conflicting trajectories are detected, if the value or aggregated value of the conflict structure exceeds the threshold value.

[0025] In order to obtain a conflict structure that is in addition indicative of sources of obstruction, that are not directly related to aircraft routes, such as weather conditions or regulatory measures, a further preferred aspect of the invention comprises the following steps:

[0026] - defining one or more additional emitter functions, in particular not associated to any of the trajectories, based on the measurement and / or the forecast of temporally and spatially localized physical quantities, in particular weather conditions, such as wind speed or temperature, and

[0027] - in particular said additional emitter functions being aggregated with the emitter functions in step d) of the inventive method in order to obtain the total emitter function.

[0028] To achieve this objective, it is also possible to further comprising defining one or more additional constraints, said additional constraints not being associated to aircraft and being indicative of additional incidents, and

[0029] - in particular said additional constraints are used for aggregation in step d) in order to obtain additional conflict structures.

[0030] In order to deal with the consequences of no-fly zones or capacity limits within a predefined zone it is advantageous that

[0031] - the additional constraint has a constraint-function indicating obstruction and / or conflict only within the spatial region and, in particular time span, as defined by said capacity restriction,

[0032] - wherein the constraint-mapping is defined, - wherein the constraint is defined to be violated, if the probability that a certain number of aircraft is present within the constraint volume exceeds a certain threshold.

[0033] A preferred aspect of the invention also allows to use the invention for the iterative optimization or adaption of planned trajectories. In this regard, it is also possible if a conflict of trajectories is detected, to perform the following steps iteratively until the conflict is resolved:

[0034] - altering at least one of the conflicting trajectories by shifting in time, in particular delaying, all future waypoints of the trajectory by a predetermined amount of time, and

[0035] - determine according to the first embodiment of the method.

[0036] One preferred method to optimize and adapt trajectories in order to avoid conflicts and obstructions is characterized in that

[0037] - the trajectory of an aircraft is defined by a plurality of waypoints, each having temporal and spatial coordinates indicative of the position of the aircraft at a given time, and

[0038] - wherein if a conflict of trajectories is detected, performing the following steps iteratively until the conflict is resolved:

[0039] - altering at least one of the conflicting the trajectories of aircraft by moving at least one future waypoint in space and / or time, and

[0040] - determine according to claim 1 if the conflict still exists.

[0041] In order to speed up calculations, emitter functions and / or total emitter functions constraint functions are defined with respect to the same four-dimensional, in particular orthogonal grid, wherein in particular for each of, in particular perpendicular, spatial axes a plurality of, in particular equidistant, coordinate positions are defined, wherein for the temporal axis a plurality of, in particular equidistant, temporal coordinate positions are predefined and wherein function values of emitter functions and constraint functions are defined at coordinate positions being defined by three spatial and one temporal coordinate position of the grid.

[0042] To additionally reduce the memory consumption for the storage of function values emitter functions and / or total emitter functions constraint functions are defined having non-default or non-zero values only within a predetermined volume defined by a set of spatial and temporal coordinate positions.

[0043] To further speed up calculations within one or more bounding boxes comprising points whose spatial and / or temporal position is located between respective maximum and minimum values for each of the coordinate axes. Numerical efficiency can be increased when for spatial and / or temporal aggregation of values of emitter functions and / or total emitter functions constraint functions only values defined within the bounding boxes of the respective emitter functions and / or total emitter functions constraint functions are used.

[0044] Some exemplary embodiments of the invention and several modifications of said embodiments are described below in greater detail with respect to the following figures. Figure 1 shows schematically a plurality of two trajectories. Figure 2 shows the use of volumes to define emitter functions in a resource-efficient manner. Figure 3 schematically shows a local emitter function. Figure 4 schematically shows the mapping of trajectories to a grid structure. Figure 5 schematically shows the construction of an emitter function based on a local emitter function. Figures 6a and 6b schematically show volumes for the construction of local constraint functions. Figure 7 schematically shows conflicting trajectories.

[0045] In an exemplary embodiment of the invention (Figure 1 ) the user specifies a plurality of trajectories ti, t2, each trajectory ti, t2 being indicative of the spatial position of the aircraft Ai, A2for a plurality of time steps T0, ..., Tn. In this very example the trajectories ti, t2 comprise the actual position of the respective aircraft Ai, A2as well as planned positions of the aircraft Ai, A2according to a flight plan. For the sake of depicting this inherently four-dimensional structure, the lateral axes x, y are depicted as one axis only, while the vertical axis z and time axis T are shown directly. The present time is referred to as T0. If available, it is also possible that the trajectories also comprise past position data of an aircraft Ai, A2. The actual path of the aircraft based on the trajectory ti, t2 can be defined in various manners, for instance by interpolation using spline functions.

[0046] DEFINITION OF TRAJECTORIES

[0047] It is e.g. possible to define a trajectory ti, t2 by a plurality of waypoints (Fig. 1 ), each waypoint wi,o, Wu, Wi,2, ... and w2,o, w2,i, w2,2, ... being associated with four values, namely a three- dimensional spatial vector comprising four spatial coordinates relative to the depicted coordinate directions x, y, z and a time value T. Each waypoint Wi,0, Wu , Wi,2, ... and w2,o, w2,i , w2,2, ... therefore represents a three-dimensional spatial position, represented by the coordinate values x, y, z that is used to represent the trajectory that defines the position of the aircraft Ai, A2at a specific point in time T. In particular it is also possible that the aircraft actually occupies the point defined by the coordinate values of the waypoint at the time defined by the waypoint. However, different interpolation methods can be used to determine the position of the trajectory based on the waypoints in a manner that the waypoints do not necessarily lie on the trajectory. In order to determine the position of the aircraft Ai, A2at a point in time between time values associated to waypoints w, it is possible to define an interpolation curve for said trajectory ti, t2connecting said waypoints Wi,0, Wu, Wi,2; w2,0, w2,i, w2,2, ... via a predefined interpolation method. It is, e.g., possible to use a connected path of straight lines between the single waypoints or waypoints Wi,0, Wu, Wi,2; w2,0, w2,i, w2,2, ... to represent the trajectory ti, t2of the aircraft Ai, A2. Alternatively, it is also possible to use other interpolation curve, such as splineinterpolations achieve smooth trajectories. In all cases, waypoints can be used define the trajectory, however, it is not necessary that waypoints necessarily coincide with the aircraft position.

[0048] Likewise, the lowest spatial resolution of a trajectory ti, t2can be the length of the shortest spatial section between two waypoints Wi,0, Wu, Wi,2; w2,0, w2,i, w2,2.... The lowest temporal resolution may be the shortest time difference between two trajectory waypoints Wi,0, Wu, Wi,2; w2,0, w2,i, w2,2, .... The maximum velocity that can be adequately represented by a trajectory ti, t2, ... tnmay be calculated Additionally, these calculations may also take into account the maximum velocity optimization settings for the sections between waypoints Wi,0, Wu, Wi,2; w2,0, w2,i, w2,2....

[0049] EMITTER FUNCTIONS

[0050] In order to determine the obstruction of the future air space caused by the future part of the aircraft trajectories ti, t2, each of the aircraft or aircraft trajectory ti, t2is assigned an emitter function ai, a2. An emitter function ai, a2is, in this very example, indicative of the positional probability distribution of the aircraft A at a given spatial and temporal point of interest p. Typically, an emitter function ai, a2can be defined as a function having four parameters x, y, z, T, three of which represent spatial coordinates x, y, z of the spatial point of interest and the fourth parameter T being indicative of the time of the point of interest p. For the definition of such an emitter function ai, a2different numerical methods can be used.

[0051] USING VOLUMES TO REDUCE NUMERICAL COMPUTATION EFFORT

[0052] One preferred example to define an emitter function ai, a2for a trajectory ti, t2is to determine a four-dimensional volume VaiVa2defining a predetermined temporal and spatial vicinity around the trajectory (Figure 2). Outside said four-dimensional volume VaiVa2the emitter function ai, a2 returns a default value, in particular zero. As the results of the evaluations of the emitter function ai, a2 are typically accumulated, it is preferred to use the neutral value of said accumulation operation, so that the values of the emitter function ai, a2 outside said volume VaiVa2 do not affect the overall accumulation value. If addition is used as accumulation, the neutral value is zero.

[0053] The volume VaiVa2 can be defined by a predetermined metric that assigns a distance value between arbitrary points in the four-dimensional temporal / spatial space of the trajectories ti, t2. As an example, the volume associated with an emitter function a may be defined as the set of four-dimensional points, whose spatial distance from the contemporary point of the trajectory does not exceed a predefined threshold distance dr. This threshold distance drcan be defined by the parameters of the aircraft, such as length, wing span etc in order to make sure that the size of the volume is large enough to cover all four-dimensional spatial / temporal points that are affected by the aircraft. The size of the volume and the distance defining said volume can be further enlarged if sufficient inherent positional uncertainties are present.

[0054] By using the above definition of the emitter function ai, a2 using the volume VaiVa2, it is clear, that the emitter function yields ai, a2 zero or default values, if the spatial and / or temporal distance, according to a predefined metric, between the point of interest and the trajectory exceeds a said predefined threshold dr. This implies that there is no indication of obstruction by an aircraft Ai, A2, if the point of interest is sufficiently distant from said aircraft.

[0055] The actual function values of the emitter functions ai, a2can be defined, for example, by means of a Gauss distribution function. In this case the value of the Gauss Function is applied to the spatial distance from the point of interest p to the contemporary point at the trajectory ti, t2.

[0056] If the emitter function ai, a2 yields default values outside the defined four-dimensional volume VaiVa2, it is numerically favourable to determine in a first step, whether the point defined by the four parameters x, y, z, T provided to the emitter function a lies within the four-dimensional volume VaiVa2. If this is not the case the default value is returned. If, however, the fourdimensional point defined by the four parameters x, y, z, T lies within the four-dimensional volume VaiVa2the emitter function ai, a2 is evaluated numerically.

[0057] USING A GRID TO DEFINE AND / OR STORE EMITTER FUNCTIONS

[0058] One preferred option of the invention to store and / or define functions of arbitrary kind, also including emitter functions a and, as will be shown later, constraint functions c, is to define a four-dimensional grid G having a plurality of grid points p. Some of these points p are located within the four-dimensional volume Vai. In a very simple case, such a grid G can be defined by providing a spatial coordinate system with three axes x, y, z and a spatial origin O and a time origin T0and a time interval dT.

[0059] As an example, said origin O of the spatial coordinate system, may be set to a specific location, the coordinate axes x, y, z being the horizontal north-south-direction x, the horizontal east- west-direction y and a vertical direction z. All spatial coordinate axes x, y, z are perpendicular to one another, at least locally within the region of interest. In order to store function values with respect to this coordinate system, one can use a grid having spatial intervals dx, dy, dz of e.g. 10 meters.

[0060] In this very example one can use midnight of a specific date as temporal origin TOand temporal intervals dT of e.g. 5 seconds. In order to define an emitter function ai, a2 it is possible to define function values with respect to this grid G, i.e. with respect to one of the grid points p, and store and / or define said function values in a four-dimensional array using the array indices that indicate the spatial and temporal position T. An emitter function ai, a2 value for the position 150 meters north, 400 meters west and 1000 meters above the origin and at 00:00:25 am can be stored in the array at the index position [15, -40, 100, 5].

[0061] The grid size, i.e. the number of grid points per coordinate direction, and the temporal interval dT and spatial steps dx, dy, dz can be adapted to the needs of the actual definition of the trajectories t1 , t2. In particular it is desirable to define the grid G in a manner that the shape of the trajectory t1 , t2 can be adequately, i.e. with an error lower than a predefined threshold, represented by a series of grid points p.

[0062] The grid G is preferably orthogonal, i.e. all coordinate points are arranged on the intersections of lines arranged parallel to the coordinate axes. For the purposes of the invention, such a restriction is however not required. It is also possible to use grids, wherein all or most of the interior points or vertices of the grid have two neighbouring vertices for each spatial and temporal direction, i.e. eight neighbours for a four-dimensional grid.

[0063] EVALUATION OF FUNCTIONS ON A GRID

[0064] In order to represent the values of the single emitter function a, it is possible to use said fourdimensional grid G. In order to store and / or define a function value of the emitter function a at a specific four-dimensional grid point p with a specific spatial position x, y, z and time-value T said function value can be stored in an associative data structure by storing the function value with respect to the indices associated with said grid point p.

[0065] If a function is defined with respect to said grid G, it is clear, that data structures such as multidimensional arrays, maps or hash-maps, can be used to store and / or define function values in association with a grid point p that is defined by a spatial and temporal location within the grid G.

[0066] By defining the grid G, an emitter function ai, a2, in the following also referred to as a, has a configurable or computable minimum spatial resolution ,anc| temporal resolution ^5niinj(a) t J?The same app|jes to a trajectory tnwith additionally a maximum velocity .

[0067] One preferred way of numerically defining a four-dimensional volume V is by defining a fourdimensional cuboid bounding box V being aligned parallel to the coordinate axes x, y, z, T of the four-dimensional grid G. Such a bounding box Va’ can be defined by minimum and maximum coordinate values for each of the coordinate axes. When using arrays to store and / or define the respective function values, the required memory can be reduced.

[0068] If a four-dimensional point p is passed as a parameter to the function a, one checks, whether said point p is within the respective minimum and maximum values, i.e. it is inside the bounding box V; if this is the case, the emitter function a yields the value that is stored and / or defined with respect to the grid G. If the four-dimensional point of interest does not lie directly at the grid point p but lies between grid points within the bounding box V the function value can be obtained by interpolation methods as known from the state of the art.

[0069] One way of defining said emitter function value comprises setting the function for the overall grid G is to assign to the function a predetermined default value for all four-dimensional spatial / temporal points p of the grid G outside the volume V. Such a definition leads to faster calculations, because no further calculation is required to obtain the function value.

[0070] In order to avoid interpolation, it is preferred to use the same grid structure G for the definition of all function evaluations. If said four-dimensional point p lies outside the bounding box V, the default value, e.g. zero, is returned.

[0071] In one preferred implementation, emitter functions ai, a2 can be defined globally with a predetermined start time and end time. Between the start time and the end time the spatial part of the bounding box V for the emitter function does not vary over time, i.e. the bounding box V is time-independent and covers a predefined three-dimensional region. For the points p inside the bounding box V a function value of the emitter function is given explicitly.

[0072] DEFINING EMITTER FUNCTIONS WITH LOCAL EMITTER FUNCTIONS

[0073] It is also possible to define emitter functions a based on local emitter functions aiocthat are folded or convoluted along a predetermined trajectory t of an aircraft A. Such a local emitter function aiocdefines the emissions or effects of an aircraft A relative to a position p in the fourdimensional grid G.

[0074] In this regard the local emitter function aioc(Figure 3) is representative for the likelihood of the aircraft A being at a specific point p in space relative to the location of the position of the trajectory t at this very point in time, the origin O of the local emitter function aiocrepresenting said location of the position of the trajectory t.

[0075] In this very example, the local emitter function aiochas only non-zero or non-default values at the time T0of the temporal origin. The spatial distribution of the local emitter function aiocat the temporal origin T0can be defined, for instance, via a function having its maximum at the spatial origin O and whose value decreases with the spatial distance drfrom the origin O. One example of such spatial distribution is defined by the Gauss Function applied to the spatial distance drfrom the point of interest p to the origin O.

[0076] In order to speed up calculations later on it is also possible to define a bounding box V for the local emitter function aioc, so that values that are negligibly small can be considered to have the default or zero for the further calculations and are therefore considered to have zero or default value. In this case the bounding box V can be defined having a cuboid shape centred at the origin with respect to the spatial coordinates. In temporal direction said bounding box is flat, i.e. the local emitter function aiochas non-zero or non-default values only at the temporal origin.

[0077] An emitter function a can be derived from the local emitter function aiocby convolution or folding the local emitter function along the trajectory (Figure 5).

[0078] Such derivation can be done numerically efficiently by using the same kind of regular fourdimensional grid structure G for both the emitter function a and the local emitter function aioc. It is in particular preferrable that at least spatial steps dx, dy, dz of the grid structures G used for the representation of the emitter function a and the local emitter function aiocare identical. If, in particular, different spatial steps dx, dy, dz are used to represent said functions, it will be necessary to interpolate functions in order to carry out the following steps.

[0079] Initially one starts with an emitter function a that is assigned default or zero values for all its points. The following three steps are repeated for all time steps or temporal positions T of the grid structure G.

[0080] Figure 4 depicts a part of the grid G representative of one time step or temporal position T. In a first step the trajectory t is evaluated at said time step or temporal position T defined by the grid G. If necessary the trajectory t is interpolated on the basis of the waypoints Wi, w2so that one obtains the most accurate spatial location XTof the trajectory for the given temporal position T.

[0081] In a second step said spatial location XTis approximated by the closest spatial grid point pxT, i.e. the grid point within the four-dimensional grid G that has the least distance to the spatial location XT.

[0082] In a third step the local emitter function aiocis temporally and spatially shifted and moved in space and time so that its origin O is shifted and moved to the spatial location Xor pXTof the trajectory t at the respective time steps Ti, T2, T3. After shifting in time and moving in space the local emitter function aiocis accumulated to the emitter function a.

[0083] As, in this special case, the single volumes VTi, VT2, VT3, are disjoint and do not coincide the function values of within those volumes are solely defined by the respective local emitter function aiocthat was moved and shifted to the respective location of the trajectory t for the respective time step Ti, T2, T3. When an emitter function is defined with respect to a grid, it is advantageous to move origin of the grid defining the emitter function to a grid point of the overall four-dimensional grid G.

[0084] By repeating the above three steps (Figure 5) for all time steps Ti, T2, T3, ... in the temporal region of interest one obtains an emitter function that is indicative of the probability that the aircraft is at a specific position in space and time. Due to the use of folding or convolution of the local emitter function aiocalong the trajectory t the resulting emitter function a has a pipelike shape. In this case the bounding volume V for the emitter function a can be defined in a time dependent manner by union of the single bounding boxes VTi, VT2, VT30f the respective shifted and moved local emitter functions aioc,i aioc,2 aioc,3 moved and shifted in space and time. Such a structure is much smaller compared to a time-invariant definition of the bounding box as stated above.

[0085] It is also possible to determine other kinds of emitter functions a, such as an emitter function being indicative of the noise emitted by an aircraft having a predetermined trajectory t.

[0086] Such an emitter function a can be determined using the above method based on convolution or folding a local emitter function aiocalong the trajectory t of the aircraft A. In this case, however, one uses a different local emitter function aiocthat is indicative of the noise emission caused by an aircraft A being located at spatial origin at the time of the temporal origin. In this case the local emitter function aiochas a conic four-dimensional shape. The values of the local emitter function aiocare non-zero at the boundaries of a spherical volume. The radius of said spherical volume grows over time with the speed of sound, while the maximum values of the emitter function a decrease over time, in particular proportionally with the reciprocal of the square of time.

[0087] In order to keep calculations numerically efficient, it is preferable to use a bounding box volume V and limit the maximum time of bounding box V to specific point in time Tmax, at which the local emitter function aiochas negligible values. As the spatial propagation of sound is predetermined by the speed of sound, one can also calculate the maximum spatial dimensions of the bounding box V.

[0088] It is clear, that the actual shape and intensity of the local emitter function aiocmay vary based on specific parameters such as speed, heading and altitude of the aircraft and other factors, e.g. temperature and wind speed.

[0089] Within the scope of the invention, it is also possible to determine other emissions of aircraft, such as light, pollution by exhaust gasses etc in the same manner as described above.

[0090] DEFINING CONSTRAINTS

[0091] In order to check, whether there are conflicting trajectories ti, ... or if a trajectory ti is obstructed by another trajectory t4, a constraint is introduced for at least one trajectory (Figure 7). Each constraint is assigned a constraint function c that - based on the aircraft’s A trajectory t - indicates whether, and in particular to which extent, events at a given spatial and temporal point of interest p obstruct the flight of the aircraft A.

[0092] Constraint functions c can be defined with respect to the same four-dimensional grid structure G that was also used to define the emitter functions a. It is also preferable to define constraint functions by convolution or folding along the trajectory t associated to the respective aircraft A, just as described above with reference to emitter functions a.

[0093] In this regard, one defines a local constraint function Ciocthat has a constant non-zero value within a cylinder or sphere of a predetermined size, wherein said size can be defined by the size of the aircraft associated to the trajectory. The local constraint function Ciochas only nonzero or non-default values at the temporal origin.

[0094] The local constraint function Ciocat the temporal origin can be defined, for instance, by assigning a predetermined non-zero or non-default value to all points in space whose horizontal spatial distance from the origin is below a predetermined threshold radius and whose vertical spatial distance is below a predetermined altitude. The set of all non-zero points of the local constraint function has the shape of a cylinder with a vertical rotational symmetry. Figure 6a shows the cylindrical structure Sc containing all grid points of the local constraint function Ciocthat are assigned a constant non-default or non-zero value.

[0095] Alternatively, the local emitter function Ciocat the can be defined, for instance, by assigning a predetermined non-zero or non-default value to all points in space whose spatial distance from the origin O is below a predetermined threshold radius. The set of all non-zero points of the local constraint function Ciochas the shape of a ball or sphere. Figure 6b shows the spherical structure SB containing all grid points p of the local constraint function Ciocthat are assigned a constant non-default or non-zero value.

[0096] In order to speed up calculations later on it is also possible to define a bounding box V for the local constraint function Cioc, so that zero or default values may be omitted for the further calculations. In this case the bounding box V can be defined having a cuboid shape centred at the origin with respect to the spatial coordinates and circumscribing the above cylinder Sc or sphere SB.

[0097] Typically, the bounding boxes as well as the spheres SB and cylinders Sc are flat with respect to the time dimension, i.e. the constraint function at a specific point in time is only defined by the values of one single local constraint function Cioc. A constraint function c assigned to a trajectory t can also be defined to return a default value indicating no obstruction, in particular being zero and / or having no contribution to the aggregation used, if the spatial and / or temporal distance, according to a predefined metric, between the point of interest and the trajectory exceeds a predefined threshold.

[0098] For example (but not limited to this example), a constraint function with a 3D polygon shape may have a minimum spatial resolution that equals to the edge-length of the shortest edge or might be set to an arbitrary number. The minimum temporal resolution might be the duration of how long this constraint is active. The grid resolution should be the highest resolution of all highest emitter / constraint / trajectory resolutions.

[0099] CALCULATING THE CONFLICT STRUCTURE

[0100] Each constraint is further assigned a constraint mapping that uses at least one emitter function a and one constraint function c in order to define a conflict structure indicative of the degree of obstruction and / or conflict of the flight of the aircraft based on the events represented by the emitter function(s). The constraint mapping is therefore used to check, whether the emitter function a of one aircraft trajectory ti overlaps or coincides with the constraint function c of another aircraft trajectory ts. Such overlap or coincidence can be measured by different means and is represented by a conflict structure (Figure 7).

[0101] One way to calculate a conflict structure is to generate a total emitter function atot as an aggregation of a plurality, in particular all or all but one of the emitter functions ai, a2, a3, a4. If all emitter functions ai, a2, a3, a4are defined with respect to one grid G it is possible to obtain the total emitter function atot as an aggregation in the form of point-wise sum of the single emitter function values. In this case the volume V in which the total emitter function has nonzero or non-default values corresponds to the union of the volumes Vi, V2, V3, V4of the single emitter functions ai, a2, as, a4.

[0102] As the aircraft A4cannot collide with itself, the effects of the presence of an aircraft A4for its own safety are not relevant. It is therefore possible to determine an overall emitter function atot for testing the constraint c4of a predefined trajectory t4by adding all emitter functions ai, a2, as except the emitter function a4that is assigned to said trajectory t4. In this case effects caused by the emitter function a4of the same trajectory t4are not considered. As in this special case of the invention, the emitter-function is determined by a point-wise aggregation, namely the summation, of the single emitter values, the total emitter function is also a four-dimensional function having three spatial coordinates and one temporal coordinate. It is therefore also possible to use the data structure as described above for emitter functions and constraint functions to also represent the total emitter function.

[0103] In the next step the conflict structure is determined. As an example, the conflict structure C can be represented by a four-dimensional function and four-dimensional data structure, comparable to the emitter functions a and the constraint function c and the total emitter atot function, having three spatial and one temporal coordinate.

[0104] In this special case, the constraint mapping method consists in point-wise combination, in particular multiplication, of co-located and contemporary values of the total emitter function atot, that is obtained by summing up or aggregating the single emitter functions at, a2, a3, and constraint function c, thereby obtaining a four-dimensional conflict structure C.

[0105] In order to have a simple calculation without the necessity to interpolate function values the total emitter function etot, the constraint function c and the conflict structure are defined with respect to the same grid G (Figure 7).

[0106] In this case conflicting trajectories ti, t4are detected, if the value or aggregated value of the conflict structure exceeds the threshold value in at least one temporal and spatial point pCOnt, said temporal and spatial point pCOnt being indicative of the time and location at which the trajectories are conflicting. It is therefore possible to localize the conflict in space and time.

[0107] In an alternative embodiment of the invention, the conflict structure C can be determined as one-dimensional function only dependent on one temporal variable T. In this case, the constraint mapping method consists in temporal and spatial point-wise combination of the total emitter function atot and constraint function c, in particular multiplication, of co-located and contemporary values of the emitter function atot and constraint function c. This point-wise multiplication is followed by a spatial integration or summation over the constraint’s volume of interest at a plurality of time steps T, and thereby obtaining a one-dimensional conflict structure C. In this case, conflicting trajectories ti, t4are detected, if the value or aggregated value of the conflict structure exceeds the threshold value in at least one point in time TCOnt, said point in time TCOnt being indicative of the time at which the trajectories ti, t4are conflicting. While with such a mapping it is not possible to detect the location of the conflict, it is possible to become aware not only of potential collisions, but also of problems such as overcrowding that cannot be localized in one specific location but occur as an overall problem at the specific time. Again, it is desirable to use the same four-dimensional grid G for the total emitter function atot and the constraint function c to be able to multiply function values easily. The conflict structure C is preferably defined with regard to the temporal part of the grid G that were used by the total emitter function atot and the constraint function c.

[0108] Yet another alternative method of calculating a conflict structure C consists in calculating only one single number being representative for the degree of obstruction for a predetermined region in space and time. Still, it is desirable to use the same four-dimensional grid G for the total emitter function atot and the constraint function c to be able to multiply function values easily.

[0109] In this case, the constraint mapping method consists in temporal and spatial point-wise combination of emitter function a total emitter function atot and a constraint function c, in particular multiplication, of co-located and contemporary values of emitter function a or total emitter function atot and constraint function c. This is followed by a spatial and temporal integration or summation over the constraint’s volume of interest, thereby obtaining an overall conflict structure C independent of time and location. If the value or aggregated value of the conflict structure exceeds the threshold value, conflicting trajectories t are detected.

[0110] While with such a mapping and such a zero-dimensional conflict structure C it is not possible to detect the location and / or of the conflict, it is possible to become aware of time-independent and location-independent problems such as overcrowding that cannot be assigned in one specific location or time but occur as an overall problem within a predetermined time window and region.

[0111] For all methods described above it is possible to use only parts of the three-dimensional airspace or only a time window of interest in order to aggregate the point-wise products of the conflict function c and the total emitter function atot.

[0112] For all the above mapping methods it is also possible to firstly apply the constraint function c to each individual emitter function ai, 82, 83 via the constraint mapping to obtain an emitterbased conflict structure Ci, C2, C3 and then aggregate the single emitter-based conflict structures Ci, C2, C3 to an overall conflict structure C. If linear operations are used the resulting conflict structures are even numerically identical. In this regard it is possible to obtain a plurality of four-dimensional emitter-based conflict structures Ci, C2, C3 by individual point-wise multiplication of co-located and contemporary values of the single emitter functions ai, 82, 83 and the constraint function c. In a second step all four-dimensional emitter-based conflict structures Ci, C2, Cs are summed up in order to obtain a four-dimensional conflict structure C. This four-dimensional conflict structure C can be subject to point-wise comparison to a predetermined threshold in order to localize possible obstructions in time and space.

[0113] It is also possible to obtain a one-dimensional conflict structure representing a time-dependent function. In this case, the constraint mapping method consists of individual temporal and spatial point-wise combination of the single emitter functions ai, 82, 83 and the one constraint function c, in particular multiplication, of co-located and contemporary values of the emitter function ai, 82, 83 and constraint function c, followed by a spatial integration or summation over the constraint’s volume of interest at a plurality of time steps, and thereby obtaining a onedimensional individual emitter-based conflict structure Ci, C2, C3 for each of the single emitter functions ai, 82, as . These individual emitter-based conflict structures Ci, C2, C3 are timedependent functions being indicative for the obstruction that is caused by the trajectory associated to the single emitter function ai, 82, as to the aircraft of the trajectory ti, t2, ts associated with the constraint function c. Subsequently the individual emitter-based conflict structures Ci, C2, C3, in particular the respective values of the contemporary points of said conflict structures Ci, C2, C3, are aggregated or summed up in order to determine an overall one-dimensional conflict C structure indicating the degree of overall obstruction over time.

[0114] Finally, it is also possible to determine emitter-based conflict structures consisting of single values. In this case, the constraint mapping method consists in single temporal and spatial point-wise multiplication of the single emitter functions ai, 82, 83 and the constraint function c of co-located and contemporary values of the emitter function ai, 82, 83 and constraint function c, followed by a spatial and temporal integration or summation over the constraint’s volume of interest, thereby obtaining an emitter-based conflict structure Ci, C2, C3 independent of time and location for each of the single emitter functions ai, 82, as. These emitter-based conflict structures Ci, C2, C3 are independent from space and time and typically consist of one numerical value only. These individual emitter-based conflict structures are indicative for the obstruction that is caused by the trajectory associated to the single emitter function C to the aircraft of the trajectory associated with the constraint function ai, 82, 83. The single emitterbased Ci, C2, C3 conflict structures are summed up in order to obtain an overall conflict structure. NON-TRAJECTORY ASSOCIATED CONSTRAINTS AND EMITTERS

[0115] In some applications it is desirable to add other external constraints to the conflict check of trajectories. Such external constraints can, for instance, be defined by no-fly zones or weather conditions such as wind, fog, thunderstorms, noise etc. external weather constraints can be measured, wherein measurement variables are fed into the calculation, while other regulatory constraints may be directly defined by the user. For future events forecast data, such as weather forecast data, may be used instead of measurement data.

[0116] In order to introduce the consequences of external conditions in the calculation of a constraint, it is possible to define an additional emitter function that is not associated with an aircraft trajectory t and that is defined based on the measurement and / or the forecast of temporally and spatially localized physical quantities, in particular weather conditions, such as wind speed or temperature.

[0117] Such an additional emitter function aext has the same structure as an emitter function and is defined as a four-dimensional function, whose argument is defined by three spatial and one temporal variable. For the purposes of the invention, the additional emitter function aext is treated as any other emitter function a in order to determine the constraints. In one embodiment of the invention, these additional emitter functions aext are aggregated with the other emitter functions a in order to determine the total emitter function atot.

[0118] In another embodiment of the invention, the additional emitter functions aext are used like the other emitter functions a in order to obtain an emitter-based conflict structure, wherein also the conflict structures based on the additional emitter functions aext are used in order to determine the overall conflict structure.

[0119] To also take into account potential conflicts caused by external events and factors such as weather and / or no-fly zones it is also possible to define additional constraints and additional constraint functions cext for each of those external events or factors. The constraint functions used for the definition of such a constraint can be defined in analogy or equal to the additional emitter functions aext as described above. The constraint mapping and the threshold functions can be defined in analogy or equal to the constraint mapping and the threshold functions of the trajectory-related constraints.

[0120] NOISE EMISSIONS AND CONSTRAINT It is also possible to take into account potential the maximum noise emissions that are applied to a specific region, such as a city. In this regard one can use an emitter function a that is indicative of the noise emitted by the aircraft, as described above. Depending on the speed of the aircraft and the potential noise emissions of the aircraft one can calculate a fourdimensional emitter function a that defines the noise emissions at a specific point at a specific time caused by the airplane associated with this trajectory t.

[0121] For the purposes of the evaluation of the noise effects of the aircraft a noise-related conflict function c is defined. The noise-related constraint function c can be assigned a non-default or non-zero value for locations that shall be protected from excessive noise, such as inhabited regions. Such regions can be restricted in height, so that noise emissions are only taken into account at locations of low height above ground. Moreover, it is possible to increase the effects of noise emissions at specific times, for instance during the night time, by using higher values of the constraint function or lower thresholds. Such thresholds are typically scalar values which are time independent. A time-dependence may, however, be defined in accordance with time dependent noise emission regulations.

[0122] A noise constraint can be calculated in addition to the other constraints, wherein emitter functions, referred to as noise emitter functions as described above, are used instead of the probability based emitter functions that were used for collision detection of trajectories.

[0123] This noise emitter function is point-wise multiplied with the noise-related constraint function, as described in the corresponding constraint mapping. According to the first of the above described methods, the conflict structure is directly defined by this point-wise product. By comparing this conflict structure with a predefined threshold one can evaluate at which location and at which time the noise threshold is exceeded.

[0124] In order to evaluate the noise constraints one can aggregate, in particular sum up, all noise emitter functions of all aircraft and determine a total noise emitter function. Within the context of the invention, it is possible to accumulate or sum up the emission values over long periods of time, e.g. 24 hours. Such a restriction can be modelled as a spatial and temporal sum constraint. In order to avoid local maxima of noise, it is also possible to determine the maximum of noise emissions as an aggregate value.

[0125] NO-FLY-ZONES AND CAPACITY RESTRICTIONS A further preferred example of the invention that does not only allow to determine constraints defined by potential aircraft collision, but also other constraints caused by other reasons, such as a no-fly zone, is described in greater detail. A no-fly zone conflict is present when an aircraft would fly through an area, which it is not allowed to fly through.

[0126] Within this preferred example of the inventive method, such situation would be represented by a trajectory, i.e., defined by a multitude of waypoints in space which are interlinked with each other by straight lines or curves describing the future path of the aircraft. An aircraft position emitter following the aircraft trajectory, which could be non-zero within a spherical geometric volume, such as a cylinder surrounding the trajectory, where the values inside the volume represent the aircraft presence probability. A constraint with a geometric volume that models the no-fly zone, for instance defined by a three-dimensional polygon and - if available - a temporal restriction of said no-fly zone. The constraint function is a four-dimensional function, which yields a default or zero value indicating no obstruction, if the spatial position of said argument passed to the function is either outside the three-dimensional polygon representative for the geometry of the no-fly zone or if the time value of said argument is outside the temporal scope of the no-fly zone.

[0127] In order to evaluate the compliance with the no-fly-zone, a spatial sum constraint can be used. The constraint has a sum-limit-threshold value of zero, meaning, a conflict is given when the total aircraft presence probability within the constraint volume is larger than zero. In this very example one uses an external constraint function that is representative of the temporal and spatial localization of the no-fly zone.

[0128] A no-fly zone can be considered as a special case of a capacity restriction, i.e. the number of aircraft within a predefined area or volume is restricted to a predefined maximum number of aircraft. A no-fly-zone restricts said predefined maximum number of aircraft to zero, i.e. each aircraft entering the volume or area causes a violation of the no-fly-zone.

[0129] A maximum capacity restriction can be used in order to restrict the maximum number of aircraft within the volume to a predefined maximum. Said maximum can be defined in accordance with the restriction, i.e. if only one aircraft shall be within the volume or area at the same time the constraint threshold value is set to one. As in the above example of the no-fly-zone a spatial sum constraint is used. The threshold value of said spatial sum constraint is related or compared to the probability of finding aircraft an aircraft within the constraint area or volume.

[0130] WIND-SPEED-CONSTRAINTS Another example of an additional constraint that can be added to the inventive method is a wind-speed conflict, which can be seen as an area in space within which winds blow at speeds that are dangerous for a flying object that would fly through this area. As per the inventive method, such situation would be represented by (1 ) a trajectory describing the path of the aircraft, and (2) a (external) wind-speed (emitter) field representing the wind speeds for any point in space or time, as well as (3) a wind constraint having the form of a geometric volume in space (e.g. a sphere), and which follows the trajectory of the aircraft. Furthermore, the constraint has a point-limit threshold value that corresponds to the maximum allowed wind speed for this aircraft.

[0131] THRESHOLD COMPARISON

[0132] As already mentioned, the calculation routine of the invention sums up all emitter values, i.e. probability to find an aircraft as in the no-fly-zone example above, for all spatial points within the constraint volume. If the total probability to find an aircraft is larger than zero at any time, the constraint is violated, and a conflict is detected.

[0133] The user may define different types of thresholds relating to the conflict structures used: pointlimit, spatial-sum-limit, and total-sum-limit. By using generic constraint mappings, allowing using a set of emitters and constraint functions as well as different mathematical operations for aggregation a large variety of threshold structures can be implemented. A spatial-sum-limit (as in the latter example) constraint is violated when the sum of all emitter values inside the constraint volume is exceeding the constraint threshold for any point in time.

[0134] A constraint with a point-limit threshold is violated if the conflict structure C at any spatial point inside the constraint volume is exceeding the constraint threshold for any point in time. An example for a point-limit would be an emitter field where the emitter values represent the wind speeds. A constraint with a point limit threshold of 30 would be violated if any wind speed emitter value within the sphere exceeds 30.

[0135] A total-sum-limit constraint is violated when the spatial and temporal sum of all values of the conflict structure C inside the constraint is exceeding the constraint threshold.

[0136] PREFERRED EMBODIMENT FOR OPTIMIZATION Even though the primary objective of the invention is to identify conflicts of aircraft trajectories that, in particular, indicate potentially dangerous situations, a preferred embodiment of the invention is also capable of resolving the above mentioned conflicts.

[0137] In this preferred embodiment the data structure used for the representation of the trajectories moreover supports time-shifting of the trajectory. It is also possible to use waypoint optimization, i.e. altering waypoints of the aircraft-trajectories.

[0138] The optimization method is prioritizable by the user, i.e. the user can define which of time-shift optimization or waypoint optimization is to be applied first. Examples of further optimization parameters are the minimum / maximum velocity for the sections of the trajectory between two waypoints, the maximum distance a waypoint may be moved via optimization, the maximum time-shift a trajectory may be shifted, etc.

[0139] In order to allow trajectory optimization and trajectory adaption in preferred embodiments of the invention, single parameters of the trajectory can be adapted.

[0140] Conflict detection as provided by the invention can be employed in iterative optimization algorithms. In this regard, an original set of trajectories that was found to be conflicting or obstructed may be improved e.g., by the following methods to resolve existing conflicts.

[0141] In one embodiment of the invention, it is possible to alter at least one least one of the conflicting trajectories by shifting in time, in particular delaying, all future waypoints of the trajectory by a predetermined amount of time. In particular, one may select a trajectory for optimization or conflict resolution, if the constraint associated with this very trajectory was violated. The optimization algorithm can iteratively adapt and re-evaluate the conflict structure and check, whether the detected conflict could be resolved or at least reduced in its intensity.

[0142] Alternatively, it is also possible to resolve a conflict of trajectories by altering the shape or waypoints that define said trajectory. As mentioned above the trajectory of an aircraft can be defined by a plurality of waypoints or waypoints, each of those having temporal and spatial coordinates indicative of the position of the aircraft at a given time. If a conflict of trajectories is detected, the shape of the trajectory or the position of its waypoints or waypoints is modified in order to avoid the conflict. If the conflict structure exceeds the predefined threshold in a particular location and / or at a particular time it is also possible to modify the trajectory, whose associated conflict structure yields the conflict, at locations in the vicinity of said location and / or time. OPTIMIZATION FUNCTIONS

[0143] The inventive method also lets its user define one optimization function for each constraint. Optimization functions can be local, and are evaluated in the same way that emitter or constraint functions are calculated. Optimization functions are internally used for guiding waypoints to positions where a conflict resolution can be expected. Typically, optimization functions can be represented by scalar fields, where its gradient result in vector fields, whose vectors point to a direction of a lower likelihood of a conflict.

Claims

Claims1 . Method for the detection of conflicting trajectories (ti, t2, ...) of aircraft (Ai, A2, ...), comprising the following steps: a) for at least two aircraft (Ai, A2, ...) respectively defining a trajectory (ti, t2, ...) indicative of the spatial position of the aircraft (Ai, A2, ...) for a plurality of time steps, wherein- at least one portion of the trajectory (ti, t2, ...) characterizing an estimation of the future trajectory (ti, t2, ...) of the aircraft, in particular according to a flight plan or defined by a predetermined destination, and in particular- at least one point on the trajectory (ti, t2, ...) being indicative of the actual and / or past and / or future position of an aircraft (Ai, A2, ...), b) for each of the trajectories (ti, t2, ...) assigned to the aircraft (Ai, A2, ...) defining an emitter function (ai, a2, ...) that is indicative of the positional probability distribution of the aircraft (Ai, A2, ...) or an emission caused by the aircraft (Ai, A2, ...) at a given spatial and temporal point of interest, c) for at least one aircraft (Ai, A2, ...) defining a constraint, each constraint separately defining:- a constraint function (c) that - based on the trajectory (ti, t2, ...) - indicating whether, and in particular to which extent, events at a given spatial and temporal point of interest obstruct the flight of the aircraft (Ai, A2, ...),- a constraint mapping referring to at least one emitter function (ai, a2, ...) and a corresponding constraint function (c) in order to define a conflict structure (C) indicative of the degree of obstruction and / or conflict of the flight of the aircraft (Ai, A2, ...) based on the events represented by the emitter function (ai, a2, ...),- a threshold value or threshold structure indicative of the maximum allowable obstruction and / or conflict within the conflict structure (C), d) for at least one of the constraints assigned to an aircraft (Ai, A2, ...)- applying the constraint mapping to the plurality of emitter functions (ai, a2, ...) and obtaining a conflict structure, and34- detecting conflicting trajectories (ti, ts, ...), ifatleast one threshold as defined by the threshold structure is exceeded by a value or an aggregated value of the conflict structure (C).

2. Method according to claim 1 , wherein applying the constraint mapping comprises the substeps:- using and / or aggregating a plurality of emitter functions (ai, a2, ...), each emitter function (ai, a2, ...) being assigned an aircraft trajectory (ti, t2, ...) and determine a total emitter function (atot), said total emitter function (atot) yielding an emitter value for a given spatial and temporal point of interest (p), and- applying the constraint mapping to the total emitter function (atot) and obtain a conflict structure (C).

3. Method according to claim 1 , wherein applying the constraint mapping comprises the substeps:- individually applying the constraint mapping to a plurality of the emitter functions (ai, a2, ...) and obtain one or more emitter-based conflict structures (Ci, C2, ...), each emitter-based conflict structure (Ci, C2, ...) being associated to one of the emitter functions, and- using and / or aggregating emitter-based conflict structures assigned to the emitter functions (ai, a2, ...) and thereby determine an overall conflict structure (C).

4. Method according to any of the preceding claims,- wherein an emitter function (ai, a2, ...) and / or constraint function (c) assigned to a trajectory (ti, t2, ...) returns a default value indicating no obstruction, in particular zero and / or without a contribution to the aggregation used, if the spatial and / or temporal distance, according to a predefined metric, between the point of interest (p) and the trajectory (ti, t2, ...) exceeds a predefined threshold,- wherein in particular said default value is returned if the point of interest (p) is outside a predefined bounding box or bounding volume that surrounds said trajectory, and / or- wherein the constraint function (c) having a default value indicating no obstruction outside a volume of interest.

5. Method according to any of the preceding claims, wherein the aggregation of emitter functions (ai, a2, ...) consists in point-wise combination, in particular addition, of co-located and contemporary values of the emitter functions (ai, a2, ...), thereby obtaining a four-dimensional total emitter function (atot).

6. Method according to any of the preceding claims, wherein- the constraint mapping method consists in point-wise combination, in particular multiplication, of co-located and contemporary values of the emitter function (ai, a2, ...) or at least one emitter function (ai, a2, ...) and / or total emitter function (atot) and constraint (c) function, thereby obtaining a four-dimensional conflict structure (C),- wherein conflicting trajectories (ti, t2, ...) are detected, if the value or aggregated value of the conflict structure (C) exceeds the threshold value in at least one temporal and spatial point, said temporal and spatial point being indicative of the time and location at which the trajectories (ti , t2, ...) are conflicting.

7. Method according to any of claims 1 to 5, wherein- the constraint mapping method consists in temporal and spatial point-wise combination, in particular multiplication, of co-located and contemporary values of the emitter function (ai, a2, ...) or at least one emitter function (ai, a2, ...) and / or total emitter function (atot) and constraint (c) function, followed by a spatial integration or summation over the constraint’s volume of interest at a plurality of time steps, and thereby obtaining a one-dimensional conflict structure (C),- wherein conflicting trajectories (ti, t2, ...) are detected, if the value or aggregated value of the conflict structure exceeds (C) the threshold value in at least one point in time, said point in time being indicative of the time at which the trajectories are conflicting.

8. Method according to any of claims 1 to 5, wherein- the constraint mapping method consists in temporal and spatial point-wise combination, in particular multiplication, of co-located and contemporary values of the emitter function (ai, a2, ...) orat least one emitter function (ai, a2, ...) and / or total emitter function (atot) and constraint (c) function, followed by a spatial and temporal integration over the constraint’s volume of interest, thereby obtaining an overall conflict structure (C) independent of time and location,- wherein conflicting trajectories (ti, ts, ...) are detected, if the value or aggregated value of the conflict structure (C) exceeds the threshold value.

9. Method according to any of the preceding claims, further comprising:- defining one or more additional emitter functions (aexti), in particular not associated to any of the trajectories (ti, ts, ...), based on the measurement and / or the forecast of temporally and spatially localized physical quantities, in particular weather conditions, such as wind speed or temperature, and- in particular said additional emitter functions (aexti) being aggregated with the emitter functions (ai, a2, ...) in step d) of claim 1 in order to obtain the total emitter function.

10. Method according to any of the preceding claims, further comprising defining one or more additional constraints, said additional constraints not being associated to aircraft and being indicative of additional incidents, and- in particular said additional constraints are used for aggregation in step d) in order to obtain additional conflict structures (C).

11. Method according to claim 10, the incident being caused by the violation of a no-fly zone or capacity restriction, wherein- the additional constraint having a constraint-function indicating obstruction and / or conflict only within the spatial region and, in particular time span, as defined by said capacity restriction,- wherein the constraint-mapping is defined according to claim 6 or 7,- wherein the constraint is defined to be violated, if the probability that a certain number of aircraft is present within the constraint volume exceeds a certain threshold.

12. Method according to any of the preceding claims, wherein if a conflict of trajectories (ti, t2, ...) is detected, performing the following steps iteratively until the conflict is resolved:- altering at least one of the conflicting trajectories by shifting in time, in particular delaying, all future waypoints of the trajectory by a predetermined amount of time, and- determine according to claim 1 if the conflict still exists.

13. Method according to any of the preceding claims,- wherein the trajectory (ti, t2, ...) of an aircraft (At, A2, ...) is defined by a plurality of waypoints, each having temporal and spatial coordinates indicative of the position of the aircraft at a given time, and - wherein if a conflict of trajectories (ti, t2, ...) is detected, performing the following steps iteratively until the conflict is resolved:- altering at least one of the conflicting the trajectories (ti, t2, ...) of aircraft by moving at least one future waypoint in space and / or time, and- determine according to claim 1 if the conflict still exists.

14. Method according to any of the preceding claims, wherein emitter functions (a) and / or total emitter functions (atot) constraint functions (c) are defined with respect to the same four-dimensional, in particular orthogonal, grid (G), wherein in particular for each of, in particular perpendicular, spatial axes a plurality of, in particular equidistant, coordinate positions are defined, wherein for the temporal axis a plurality of, in particular equidistant, temporal coordinate positions are predefined and wherein function values of emitter functions and constraint functions are defined at coordinate positions being defined by three spatial and one temporal coordinate position of the grid.

15. Method according to claim 14, wherein emitter functions (a) and / or total emitter functions (atot) constraint functions (c) are defined having non-default or non-zero values only within a predetermined volume (V) defined by a set of spatial and temporal coordinate positions, in particular within one or more bounding boxes (V) comprising points whose spatial and / or temporal position is located between respective maximum and minimum values for each of the coordinate axes.

16. Method according to claim 15, wherein for spatial and / or temporal aggregation of values of emitter functions (a) and / or total emitter functions (atot) constraint functions (c) only values defined within the bounding boxes (V) of the respective emitter functions (a) and / or total emitter functions (atot) constraint functions (c) are used.

17. Data carrier on which a program for carrying out a method according to any of the preceding claims is stored.40

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