# Patent

## Title
Method for aiding navigation making it possible to manage a vertical constraint in an anticipated manner

## Abstract

A method for aiding navigation is provided, implemented in a flight management system, for the construction of a vertical trajectory of an aircraft following a predetermined lateral trajectory between a departure point and an arrival point; the departure point and arrival point furthermore being characterized by predefined altitudes, respectively Hd and Ha, and predefined speeds, respectively Vd and Va. The method comprises the steps of: selection of a transition manoeuvre in terms of altitude and speed from a predetermined list of manoeuvres; determination of a manoeuvre point PM on the lateral trajectory, of altitude Hd and of speed Vd, from which the transition manoeuvre must be initiated so as to allow the aircraft to reach at the arrival point the predefined speed Va and the predefined altitude Ha.

## Background
CROSS-REFERENCE TO RELATED APPLICATION
This application claims priority to foreign French patent application No. FR 1201898, filed on Jul. 5, 2012, the disclosure of which is incorporated by reference in its entirety.
FIELD OF THE INVENTION
The invention relates to a method for aiding navigation for the construction of a vertical trajectory of an aircraft following a predetermined lateral trajectory between a departure point and an arrival point. More particularly it pertains to a method for determining a point of the lateral trajectory from which a change of altitude and of speed of the aircraft is initiated, making it possible to reach the arrival point at a predetermined altitude and a predetermined speed.
BACKGROUND
Systems for aiding navigation have experienced a significant upsurge in order to cope with the constant increase in air traffic and with the resulting growing work load for the pilot. To reconcile an ever shorter decision time and a general trend to reduce the number of crew members, numerous automated procedures have been developed, with the aim of freeing the crew from routine tasks, and in a general manner, of improving the in-flight performance of an aircraft.
Thus, the known systems for aiding navigation have means for computing trajectories between waypoints defined in a flight plan advised by the pilot. The trajectories, computed at the start of the flight and updated regularly in the course of the flight, are a support for the manoeuvres of the aircraft, which are decided by the pilot or by an automatic piloting system. In the known prior art, the computed trajectory is split between a lateral trajectory, typically a latitude and a longitude, and a vertical profile applied to this lateral trajectory to take into account constraints, for example regarding the relief or the management of fuel consumption.
These existing trajectory computation means turn out nevertheless to be insufficient for certain particular flight phases. Procedures for which a requirement in terms of both altitude and speed of the aircraft is associated with a waypoint have notably made their appearance. The known systems have no navigation aid for this type of procedure, the crew decides only the moment and the manoeuvres to be engaged to allow the aircraft to reach target altitude and speed at the requested waypoint. It is therefore desirable to have means for aiding navigation for these particular flight phases, notably to warn the crew and accompany them in their manoeuvres.
Known among systems for aiding navigation are flight management systems, termed FMS, a functional architecture of which is shown diagrammatically in FIG. 1. In accordance with the ARINC standard 702, they ensure notably the functions of:

    
    
        Navigation LOCNAV, 170, for performing optimal location of the aircraft as a function of the geo-location means (GPS, GALILEO, VHF radio beacons, inertial platforms, etc.),
        Flight plan FPLN, 110, for inputting the geographical elements constituting the skeleton of the route to be followed (departure and arrival procedures, waypoints, etc.),
        Navigation database NAVDB 130, for constructing geographical routes and procedures with the help of data included in the bases (points, beacons, interception or altitude legs, etc.),
        Performance database, PRF DB 150, containing the craft's aerodynamic and engine parameters,
        Lateral trajectory TRAJ, 120, for constructing a continuous trajectory on the basis of the points of the flight plan, complying with the performance of the aircraft and the confinement constraints,
        Predictions PRED, 140, for constructing an optimized vertical profile on the lateral trajectory,
        Guidance, GUID 200, for guiding in the lateral and vertical planes the aircraft on its 3D trajectory, while optimizing the speed,
        Digital data link DATALINK, 180, for communicating with the control centres and other aircraft.
    
    


On the basis of the flight plan FPLN defined by the pilot, consisting of a list of so-called waypoints, a lateral trajectory is determined as a function of the geometry between the waypoints and/or the altitude and speed conditions. On the basis of this lateral trajectory, a prediction function PRED defines an optimized vertical profile taking account of possible altitude, speed and time constraints, if any. Accordingly, the FMS system has performance tables PERFDB 150, which define the modeling of the aerodynamics and engines. The prediction function PRED 140 implements the equations of aircraft dynamics. These equations are based numerically on values contained in the performance tables for computing drag, lift, and thrust. By double integration, the speed vector and the position vector of the aeroplane are deduced therefrom. This predictive computation function is well known to the person skilled in the art and is not repeated in detail here, the method according to the invention uses this function for the construction of a vertical trajectory.
FIG. 2 illustrates the principle of a transition manoeuvre in terms of altitude and speed of an aircraft. Starting from a flight phase carried out at an initial altitude and an initial speed, it is sought to reach a predetermined altitude Ha and a predetermined speed Vd through a transition manoeuvre. FIG. 2 illustrates the case of a manoeuvre making it possible to increase the altitude of the aircraft and to reduce its speed; the principle of the transition also applies to the other possible combinations, ascending or descent, to a higher or lower speed.
The upper graphic presents the evolution of the altitude profile and the lower graphic the evolution of the speed profile between a manoeuvre start point PM and an end point 10 of a transition manoeuvre. For reasons of simplicity, a rectilinear lateral trajectory is represented by the abscissa axis; the transition manoeuvre applies to a non-rectilinear trajectory according to the same principle.
The transition manoeuvre comprises three successive segments:

    
    
        A first segment 11, commonly called OPEN1, in the course of which the altitude and the speed evolve according to two constant gradients; a substantially constant thrust being delivered by the aircraft's propulsion system. This segment is continued until a predetermined intermediate speed SPD_INT is reached.
        A second segment 12, commonly called OPEN2, in the course of which the thrust and the orientation of the aircraft are adapted to ensure a constant speed and an evolution of the altitude according to a constant gradient. This segment is continued until the target altitude 14 of the transition end point 10 is reached.
        A third segment 13, commonly called LVL, in the course of which the altitude is maintained constant, and the speed evolves according to a constant gradient until the target speed 15 of the transition end point 10 is reached.
    
    


This type of transition manoeuvre in terms of altitude and speed in three successive segments is a manoeuvre commonly implemented in the course of a flight. Other manoeuvres exist to allow a transition between an altitude and a speed of departure and arrival. For example, by defining an intermediate speed SPD_INT equal to the arrival speed, a two-segment transition manoeuvre is carried out. The method described by the present invention applies according to the same principle to these other transition manoeuvres.
Let us also note that the type of manoeuvre and its constraint parameters, such as for example the intermediate speed value SPD_INT, are input parameters of the previously described prediction function PRED. Typically, the function makes it possible to determine a vertical trajectory by defining a certain number of parameters such as a target altitude and speed, a type of manoeuvre and its constraint parameters.
Nevertheless, there does not exist any automated procedure making it possible to integrate altitude and speed requirements at a waypoint with the vertical trajectory computation. Stated otherwise, the crew alone must determine when to initiate the transition manoeuvre to allow the aircraft to reach target altitude and speed at the desired waypoint.
Such is the case notably when the crew receives instructions from the air traffic control containing a requirement in terms of altitude and/or speed. The following instructions notably, not implemented in a deployment norm but standardized forthwith, are considered to be among these air traffic control instructions:

    
    
        CLIMB TO REACH [A] BY [B], (i.e. climb to an altitude [A] for a position [B]),
        DESCEND TO REACH [A] BY [B], (i.e. descend to an altitude [A] for a position [B]),
        REACH [A] BY [B], (i.e. reach an altitude [A] for a position [B]),
        CROSS [A] AT [B], (i.e. cross the position [A] at the altitude [B]),
        CROSS [A] AT OR ABOVE [B], (i.e. cross the position [A] at an altitude at least equal to [B]),
        CROSS [A] AT OR BELOW [B], (i.e. cross the position [A] at an altitude at most equal to [B]),
        CROSS [A] AT AND MAINTAIN [B], (i.e. cross the position [A] at the altitude [B] and maintain your altitude),
        CROSS [A] BETWEEN [B1] AND [B2], (i.e. cross the position [A] between the altitude [B1] and the altitude [B2]).
    
    


SUMMARY OF THE INVENTION
The general idea of the present invention consists of a method for computing the start point of a manoeuvre of the aircraft making it possible to reach the target altitude and speed at a specified arrival point. This manoeuvre start point makes it possible to construct a possible vertical trajectory between a departure point and an arrival point. The method according to the invention is an iterative process, the convergence of which is ensured in a deterministic number of passes, so as to guarantee the response time of the function.
For this purpose, the subject of the invention is a method for aiding navigation, implemented in a flight management system, for the construction of a vertical trajectory of an aircraft following a predetermined lateral trajectory between a departure point and an arrival point; the said departure point and arrival point furthermore being characterized by predefined altitudes, respectively Hd and Ha, and predefined speeds, respectively Vd and Va. The method comprises the steps of:

    
    
        selection of a transition manoeuvre in terms of altitude and speed from a predetermined list of manoeuvres,
        determination of a manoeuvre point PM on the lateral trajectory, of altitude Hd and of speed Vd, from which the transition manoeuvre must be initiated so as to allow the aircraft to reach at the arrival point the predefined speed Va and the predefined altitude Ha.
    
    


Advantageously, the manoeuvre point PM is determined by an iterative process comprising an initialization step, consisting in positioning an initial manoeuvre point PM0, on the lateral trajectory, between the departure point and the arrival point, and an iterative step consisting of:

    
    
        a predictive computation of a vertical trajectory between the departure and arrival point, comprising a transition segment, between an intermediate manoeuvre point PMi on the lateral trajectory and a point of attainment on the lateral trajectory, allowing the aircraft to attain the altitude Ha and the speed Va through the transition manoeuvre; the intermediate manoeuvre point PMi being defined in a first iterative loop as the initial manoeuvre point PM0; the intermediate manoeuvre point PMi being defined in a first iterative loop as the initial manoeuvre point PM0,
        a computation of a new intermediate manoeuvre point PMi+1, y shifting the manoeuvre point PMi on the lateral trajectory by a distance Di separating the point of attainment from the arrival point along the lateral trajectory;
        the said iterative process being interrupted when the distance Di is less than a predetermined threshold; the manoeuvre point PM being defined as the intermediate manoeuvre point PMi at the moment of interruption of the iterative process.
    
    


Advantageously, the initial manoeuvre point PM0 is determined on the basis of the arrival point by means of a segment of constant slope of predetermined angle.
Advantageously, a transition manoeuvre comprises three successive segments:

    
    
        a first segment, in the course of which the altitude and the speed of the aircraft evolve according to two constant gradients, until a target intermediate speed is reached,
        a second segment, in the course of which the speed of the aircraft is maintained constant and the altitude evolves according to a constant gradient, until a target altitude,
        a third segment, in the course of which the altitude of the aircraft is maintained constant, and the speed evolves according to a constant gradient, until a target speed.
    
    


Advantageously, the initial manoeuvre point PM0 is determined on the basis of the arrival point by means of an estimation of lateral length of each of the segments of the transition manoeuvre, by assigning predetermined values to the gradients of speed and of altitude of each of the segments.
Advantageously, the initial manoeuvre point PM0 is determined for a mass of the aircraft computed by a Breguet formula, at a dummy point defined by an altitude identical to the departure point and lateral coordinates identical to the arrival point.
Advantageously, the initial manoeuvre point PM0 is determined for a mass of the aircraft computed by a Breguet formula, at a dummy point defined by an altitude identical to the departure point and lateral coordinates computed by means of a segment of constant slope of predetermined angle joining the dummy point to the arrival point along the lateral trajectory.
Advantageously, the initial manoeuvre point PM0 is determined on the basis of the arrival point by a predictive trajectory computation, carried out backwards and allowing the aircraft to attain the altitude Hd and the speed Vd through the transition manoeuvre.
Advantageously, the initialization step furthermore comprises a computation of an anticipated initial point PA0 on the lateral trajectory, positioned between the departure point and the initial manoeuvre point PM0, and a predictive computation of trajectory between the departure point and the anticipated initial point PA0, making it possible to limit the predictive trajectory computation of the iterative step to the segment joining the anticipated initial point PA0 and the arrival point.
Advantageously, the anticipated initial point PA0 is determined by means of the following formula:

DA0=K×DM0,

in which DA0 is a distance separating the anticipated initial point PA0 from the initial manoeuvre point PM0, DM0 is a distance separating the initial manoeuvre point PM0 from the arrival point, and K is a predetermined coefficient.

Advantageously, the coefficient K is determined by means of the following formula:

K=WINDMAX/TASMIN,

in which WINDMAX is an estimation of maximum wind speed between the initial manoeuvre point PM0 and the arrival point, and TASMIN is an estimation of minimum speed of the aircraft between the initial manoeuvre point PM0 and the arrival point.

Advantageously, the method comprises a step of computing a position correction of the manoeuvre point PM, at least as a function of the altitude of the departure and arrival point, of a distance separating the manoeuvre point PM and the arrival point along the vertical trajectory, and of a speed of the aircraft at the manoeuvre point PM; the said correction being determined so as to make it possible to take into account a constraint regarding time of transit at the arrival point.
The invention also pertains to a flight management system comprising code instructions making it possible to perform the computation steps of the method for aiding navigation having the characteristics described above.



BRIEF DESCRIPTION OF THE DRAWINGS
The invention will be better understood and other advantages will become apparent on reading the detailed description of the modes of implementation given by way of example in the following figures:
FIG. 1, already presented, represents a known system for aiding navigation, commonly called FMS;
FIG. 2, already presented, illustrates the principle of a phase of transition, in terms of altitude and speed, of an aircraft;
FIGS. 3a, 3b, 3c, 3d, 3e, 3f, 3g, 3h, 3i and 3j describe the principle of the method for constructing a vertical trajectory according to a first variant of the invention;
FIGS. 4a and 4b describe the principle of the method for constructing a vertical trajectory according to a second variant of the invention;
FIGS. 5a and 5b describe the principle of the method for constructing a vertical trajectory according to a third variant of the invention;
FIGS. 6a, 6b, 6c, 6d, 6e, 6f and 6g describe the principle of the method for constructing a vertical trajectory according to a fourth variant of the invention.



For the sake of clarity, the same elements will bear the same reference tags in the various figures. As mentioned in the case of FIG. 2, the trajectory of the aircraft is represented in the figures in a more easily representable simplified case where the lateral trajectory is rectilinear. Thus the rectilinear lateral trajectory is represented on the abscissa axis, the vertical profile is represented on the ordinate axis. Of course, the method according to the invention applies in an identical manner to a non-rectilinear lateral trajectory. A point of the lateral trajectory is therefore characterized by two coordinates, generally a latitude and a longitude. Likewise, one speaks of distance separating two points along the lateral trajectory in order to recall that this distance is not the length of a rectilinear segment joining the two points but the distance traversed by an aircraft following the lateral trajectory between the two points.
DETAILED DESCRIPTION
FIGS. 3a, 3b, 3c, 3d, 3e, 3f, 3g, 3h, 3i and 3j describe the principle of the method for constructing a vertical trajectory according to a first variant of the invention.
An aircraft following a predetermined lateral trajectory between two waypoints, a departure point 20 and an arrival point 21, is considered. The departure point 20 is characterized by coordinates Xd on the lateral trajectory, typically a latitude and a longitude, by a predetermined altitude Hd, and by a predetermined speed Vd. Likewise, the arrival point 21 is characterized by coordinates Xa on the lateral trajectory, by a predetermined altitude Ha and by a predetermined speed Va.
It is sought to construct a vertical trajectory between the departure point and the arrival point comprising a first segment carried out at constant altitude and speed, and a second transition segment making it possible to reach the arrival point at the altitude Ha and the speed Va by means of the selected transition manoeuvre.
In a first variant of the invention, the method comprises a first step of estimating the mass of the aircraft at the moment of the transition manoeuvre. As illustrated in FIG. 3b, the method firstly determines coordinates X2 of a dummy point 22 on the lateral trajectory, defined as the point of the lateral trajectory making it possible to attain the arrival altitude Ha at the arrival point 21 by means of a segment of constant slope of predetermined angle. Thus, the coordinates X2 can be computed through the following relation:

X2=Xa−(Ha−Hd)/tan α

in which Xa and X2 are the coordinates on the lateral trajectory of the points 21 and 22, Ha and Hd are the altitude of the arrival point 21 and departure point 20, and α is an angle of predetermined slope. For example, a mean slope of 3° may be chosen.

On the basis of the coordinates X2, a mass M2 of the aircraft is determined by means of a formula termed the Breguet formula. This formula is well known to the person skilled in the art and is not repeated here in detail. For the understanding of the present invention, the following simplified Breguet formula makes it possible to determine the mass M2:

M2=Md×exp(−(X2−Xd)×WFE/(Md×TASd)

in which M2 and Md are aircraft masses at the points 22 and 20, X2 and Xd are the coordinates on the lateral trajectory of the points 22 and 20, WFE (or Engine Fuel Flow in English) represents a mean fuel consumption at the point 22, and TASd (True Air Speed) represents a speed of the aircraft in the air mass at the point 20.

On the basis of the mass M2 thus computed, the method determines two points on the lateral trajectory, as illustrated by FIG. 3c: an initial manoeuvre point PM0 and an anticipated initial point PA0. The distance separating the arrival point 21 from the initial manoeuvre point PM0 along the lateral trajectory is denoted DM0; and DA0 denotes the distance separating the initial manoeuvre point PM0 from the anticipated initial point PA0 along the lateral trajectory.
The initial manoeuvre point PM0 is determined on the basis of the previously computed mass M2 and by means of simple formulae which do not take into account the conditions outside the aircraft. Thus, FIGS. 3d and 3e illustrate two possible modes of implementation for computing the coordinates of the point PM0 on the lateral trajectory.
In a first mode of implementation represented by FIG. 3d, the distance DM0 is computed as the sum of the lateral lengths of three segments 23, 24 and 25, constituting the segment of transition to the arrival point 21. The principle consists in determining the point PM0 on the basis of the arrival point, based on the segments of the chosen transition manoeuvre, for example such as is described in FIG. 2. Thus, starting from the arrival point 21, the method successively determines:

    
    
        a segment 23 of length DX3, making it possible to reduce, at constant altitude, the aircraft speed from the value Va of the arrival point 21 to a predetermined intermediate speed SPD_INT; the gradient of speed evolution being a calibratable computation parameter.
        a segment 24 of length DX2, making it possible to reduce, at constant speed, the altitude of the aircraft from the value Ha of the arrival point 21 to an intermediate altitude H2;
        a segment 25 of length DX1, making it possible to reduce the altitude from the value H2 to the value Hd of the departure point 20, and to reduce the speed from the value SPD_INT to the value Vd of the departure point; the gradient of speed evolution being an adjustable computation parameter;

the distance DM0 being determined by the sum of the lengths DX1, DX2 and DX3.

    
    


In this first mode of implementation, an iterative process makes it possible to define the intermediate altitude H2 while complying with the predetermined speed gradients of the segments 23, 24 and 25. In this process, the segment 25 is determined first, then we determine a segment 24 of set length which gives us an altitude H2ini, and then we determine the segment 23. As a function of the mismatch in position and altitude between the end of the segment 23 and the position Xd and altitude Hd, the length of the segment 24 is corrected until the segment 23 converges onto the values of position Xd and of altitude Hd.
A second mode of implementation makes it possible to dispense with this iterative step for the computation of the initial manoeuvre point PM0 on the basis of the arrival point. As represented in FIG. 3e, the method determines the distance DM0, on the basis of the arrival point 21, by means of the following three segments:

    
    
        a segment 26 of length DX3′, making it possible to reduce, at constant altitude, the aircraft speed from the value Va of the arrival point 21 to a predetermined intermediate speed SPD_INT; the gradient of speed evolution being a calibratable computation parameter;
        a segment 27 of length DX2′, making it possible to reduce, at constant speed, the aircraft altitude from the value Ha of the arrival point 21 to the altitude Hd of the departure point 20; the gradient of evolution of the altitude being a calibratable computation parameter;
        a segment 28 of length DK2′, making it possible to reduce the speed from the value SPD_INT to the value Vd of the departure point; the gradient of speed evolution being a calibratable computation parameter; the distance DM0 being determined by the sum of the lengths DX1′, DX2′ and DX3′.
    
    


This second mode of implementation makes it possible advantageously to do without an iterative loop, required for the computation of the intermediate altitude H2 in the first mode of implementation.
The two previous modes of implementation have in common the computation of the initial manoeuvre point PM0 on the basis of the arrival point by means of an estimation of lateral length of each of the segments of the transition manoeuvre, by assigning predetermined values to the gradients of speed and of altitude of each of the segments.
Moreover, the initial manoeuvre point PM0 is advantageously determined for a mass of the aircraft computed by a Breguet formula, at a dummy point 22 defined by an altitude identical to the departure point and lateral coordinates computed by means of a segment of constant slope of predetermined angle joining the dummy point to the arrival point along the lateral trajectory.
For these two modes of implementation, the distance DA0 separating the anticipated initial point PA0 from the initial manoeuvre point PM0 along the lateral trajectory is thereafter determined through the following formula:

DA0=K×DM0 

in which DA0 is the distance separating the anticipated initial point PA0 from the initial manoeuvre point PM0, DM0 is the distance separating the initial manoeuvre point PM0 from the arrival point, and K is a predetermined coefficient.

Advantageously, the coefficient K takes account of the exterior conditions and in particular of the maximum wind speed. It is for example determined by means of the following formula:

K=WINDMAX/TASMIN 

in which WINDMAX is an estimation of the maximum speed of the wind between the initial manoeuvre point PM0 and the arrival point 21, and TASMIN is an estimation of the minimum speed of the aircraft between the initial manoeuvre point PM0 and the arrival point 21.

On the basis of this computation of the initial manoeuvre point PM0 and of the anticipated initial point PA0, the method determines, as represented in FIG. 3f, a vertical trajectory joining the departure point 20 to the anticipated initial point PA0 by means of a predictive computation with a constant altitude equal to Hd as constraint. Stated otherwise, the method advantageously comprises a step of computing an anticipated initial point PA0 and a predictive computation of trajectory between the departure point 20 and the anticipated initial point PA0, making it possible to limit the predictive trajectory computation of the iterative step to the segment joining the anticipated initial point PA0 and the arrival point 21.
FIGS. 3g, 3h and 3i describe the iterative process making it possible to determine the manoeuvre point PM on the basis of the initial manoeuvre point PM0. By convention, the manoeuvre point PM computed in the course of an iteration is denoted PMi, the manoeuvre point computed in the following iteration is denoted PMi+1.
In a first step of the iterative process described by FIG. 3g, a vertical trajectory is determined by means of a predictive computation, with as constraint a constant altitude equal to Hd between the anticipated initial point PA0 and the manoeuvre point PMi, and as constraint the requirement to attain the altitude Ha and the speed Va starting from the manoeuvre point PMi by means of the selected transition manoeuvre. In this variant, the predictive computation determines a vertical trajectory consisting of the three segments 11, 12 and 13 and which finishes at the altitude Ha at a point of attainment 30. The distance separating the point of attainment 30 from the arrival point 21 is referenced Di. This distance can be positive or negative depending on whether the computed point of attainment 30 is situated before or after the arrival point along the lateral trajectory.
In a second step, described by FIG. 3h, of the iterative process, the lateral coordinates of a manoeuvre point PMi+1 are determined on the basis of the lateral coordinates of the manoeuvre point PMi by adding the distance Di along the lateral trajectory.
The iterative process continues by repeating a predictive computation with PMi+1 as start point of the transition manoeuvre. The iterative process is interrupted when the distance Di is less than a predetermined threshold. The vertical trajectory thus obtained, represented in FIG. 3i, satisfies the double constraint of maintaining a longest possible first trajectory portion carried out at constant altitude and constant speed, and of guaranteeing that the target altitude and speed are reached at the arrival point 21 by means of a predetermined transition manoeuvre; the said manoeuvre being able to be subject to diverse calibratable constraints such as an intermediate speed. The choice of the type of transition manoeuvre and of its constraints makes it possible to adapt the trajectory computation to demands, internal to the aircraft (manoeuvrability of the craft) or from outside (requests from the air traffic control, meteorological constraints, etc.).
The main steps of the method according to the first variant of the invention are gathered together in the flowchart of FIG. 3j. In this first variant, the method comprises an acquisition step 31, making it possible to ensure that the information required for the computation is available (values characteristic of the departure and arrival points, lateral trajectory between these two points, choice of the transition manoeuvre and quantization of its constraints, etc.). A step 32 estimates the mass at a point 22 as described in FIG. 3b. A step 33 consists in computing an initial manoeuvre point PM0 and an anticipated initial point PA0 as represented in FIGS. 3c, 3d and 3e; two modes of implementation of the computation of the initial manoeuvre point PM0 being illustrated by FIGS. 3d and 3e. A step 34 determines by predictive computation a vertical trajectory from the departure point 20 to the anticipated initial point PA0, as represented in FIG. 3f. On the basis of the initial manoeuvre point PM0 and of the anticipated initial point PA0, an iterative process 38 makes it possible to determine the manoeuvre point PM. The iterative process 38 thus comprises a step 35 of predictive computation of a vertical trajectory between the anticipated initial point PA0 and a point of attainment 30. As long as the distance Di separating the point of attainment 30 from the arrival point 21 remains greater than a predetermined threshold, the iterative process continues, the distance Di is added to the lateral coordinates of the point PMi before relaunching a predictive trajectory computation. The iterative process stops when Di is below the threshold, the manoeuvre point PM and the vertical trajectory are determined.
Advantageously, the number of iterative loop is low and deterministic since the equations for the dynamics of an aircraft in the vertical plane, which are used during the integration, are locally convex and ensure convergence to the optimum in a deterministic number of steps. Numerically, for N subsonic transport aircraft, convergence is ensured in fewer than 2 iterations.
FIGS. 4a and 4b describe the principle of the method for constructing a vertical trajectory according to a second variant of the invention. This second variant simplifies the method according to the first variant through a simplified computation of the mass.
The principle of the estimation of the mass is illustrated in FIG. 4a. A mass M2′ is determined at a dummy point 41 with lateral coordinates Xa and with altitude Hd, assuming a path of the aircraft carried out at constant altitude equal to Hd between the departure point and the point 41. In contradistinction to the first variant, the estimation of mass is not carried out at an intermediate point that is computed to approximate the manoeuvre start point. This step is eliminated so as to simplify the computation, the mass M2′ is determined by means of a Breguet formula:

M2′=Md×exp(−(Xa−Xd)×WFE/(Md×TASd))

in which M2′ and Md are aircraft masses at the points 41 and 21, Xa and Xd are the coordinates on the lateral trajectory of the points 21 and 20, WFE represents a mean fuel consumption at the point 41, and TASd represents a speed of the aircraft in the air mass at the point 20.

The other steps of the computation are identical to the first variant. The main steps of the method in this second variant are represented in the flowchart of FIG. 4b. The initialization of the iterative loop 38 contains steps 31, 33, 34 already described for the first variant, and a step 42 of simplified computation of the mass M2′ such as detailed hereinabove. Steps 35, 36 and 37 of the iterative loop 38 are identical to the first variant.
In this variant, the initial manoeuvre point PM0 is thus advantageously determined for a mass of the aircraft computed by a Breguet formula, at a dummy point defined by an altitude identical to the departure point and lateral coordinates identical to the arrival point. By simplifying the mass computation, the second variant of the method makes it possible to lighten the computational load and to free up memory for the computer which hosts the method for aiding navigation.
FIGS. 5a and 5b describe the principle of the method for constructing a vertical trajectory according to a third variant of the invention. This third variant further simplifies the method through a simplified computation of the initial manoeuvre point PM0.
The principle of the computation of the initial manoeuvre point PM0 is illustrated in FIG. 5a. The initial manoeuvre point PM0 and distance DM0 are determined on the basis of the arrival point 21 by assuming a transition carried out by means of a segment of constant slope of predetermined angle. Thus the distance DM0 can be computed through the following relation:

DM0=(Ha−Hd)/tan α′

in which DM0 is the distance separating the initial manoeuvre point PM0 and the arrival point 21 along the lateral trajectory, Ha and Hd are the altitude of the arrival point 21 and departure point 20, and α′ is an angle of predetermined slope. For example, an angle α′ of 3° may be chosen.

The computation of the initial manoeuvre point PM0 is thus simplified; moreover, the estimation of mass is no longer required to determine PM0, this step is eliminated from the method.
The distance DA0 separating the anticipated initial point PA0 from the initial manoeuvre point PM0 along the lateral trajectory is determined as in the case of the first variant through the following formula:

DA0=K×DM0 

in which K is a predetermined coefficient, which can be determined as a function of the exterior conditions and in particular of the maximum speed of the wind.

The main steps of the method in this third variant are represented in the flowchart of FIG. 5b. The initialization of the iterative loop 38 contains steps 31 and 34 already described for the first variant, and a step 51, such as detailed hereinabove, of simplified computation of the initial manoeuvre point PM0 and of the anticipated manoeuvre point PA0. Steps 35, 36 and 37 of the iterative loop 38 are identical to the first variant.
Thus, the initial manoeuvre point PM0 is determined simply on the basis of the arrival point by means of a segment of constant slope of predetermined angle. By simplifying the computation of the initial manoeuvre point PM0, and by eliminating the mass computation, the third variant of the method makes it possible to further lighten the computational load and to free up more of the memory of a computer hosting the method for aiding navigation.
FIGS. 6a, 6b, 6c, 6d, 6e, 6f and 6g describe the principle of the method for constructing a vertical trajectory according to a fourth variant of the invention. The general idea of this fourth variant is to determine the initial manoeuvre point PM0 by means of the function PRED for backward predictive computation on the basis of the arrival point 21.
Accordingly, an estimation of the mass at the arrival point 21 is required. On the basis of the departure point 20, the method determines by means of a predictive computation, as represented in FIGS. 6a and 6b, a vertical trajectory joining the departure point 20 to a dummy point 101 whose lateral coordinates are identical to those of the arrival point 21 with a constant altitude equal to Hd as constraint. It would also be possible to use a Breguet formula instead of the predictive computation to obtain the mass, but it is less accurate and would lead to an additional iteration. A mass M0 implemented for the backward predictive computation illustrated in FIG. 6c is thus obtained. Through this backward predictive computation, the method then determines a vertical trajectory for the selected transition manoeuvre, for example consisting of the three segments 11, 12 and 13 of the transition described in FIG. 2. The backward vertical trajectory finishes at the altitude Hd at a point defining the initial manoeuvre point PM0. A difficulty of this fourth variant resides in the fact that the lateral coordinates of the point of intersection 61 between the segments 11 and 12, are not known a priori. To solve this difficulty, an iterative loop is set up, the backward predictive computation is repeated until a stable position of the initial manoeuvre point PM0 is obtained. Thus, in this variant the initial manoeuvre point PM0 is determined on the basis of the arrival point 21 by a predictive trajectory computation, carried out backwards and allowing the aircraft to attain the altitude Hd and the speed Vd through the transition manoeuvre.
On the basis of the initial manoeuvre point PM0 thus computed, a “forward” predictive computation makes it possible to determine a vertical trajectory between the departure point 20 and a point of attainment 62, as illustrated in FIG. 6d. The method is thereafter similar to the previous variants, as illustrated in FIGS. 6e and 6f. The distance Di separating the point of attainment 62 and the arrival point 21 along the lateral trajectory makes it possible to correct the position of the initial manoeuvre point PMi. The iterative process continues as long as Di remains greater than a predetermined threshold.
The main steps of the method in this fourth variant are represented in the flowchart of FIG. 6g. The initialization of the iterative loop 38 contains step 31 already described, a step 63 of predictive computation at constant altitude equal to Hd and a step 64 making it possible to determine PM0 by means of a backward predictive computation as described hereinabove. Steps 35, 36 and 37 of the iterative loop 38 are identical to the other variants.
Thus, this fourth variant of the method determines the initial manoeuvre point PM0 on the basis of the arrival point 21 through a predictive trajectory computation, carried out backwards and allowing the aircraft to attain the altitude Hd and the speed Vd through the transition manoeuvre. This variant of the method is more complex to implement, it requires in particular, in order to determine the initial manoeuvre point PM0, the integration of a first iterative loop. On the other hand, it makes it possible to determine PM0 with a very good accuracy. Thus, convergence in 1 iteration is ensured. Moreover, if the backward integration has converged right from the first pass (i.e. if (Hd, Xd) has been reached at the point PM0 during this backward integration), it is not necessary to launch the predictive computation starting from PM0 since the predictions at the various intermediate points are already available.
There exist flight phases for which a time constraint, associated with a waypoint, is imposed. In this case, the speed of the transition, in particular the intermediate speed SPD_INT, can be modified in the course of the transition, if it is desired to be able to comply with this time constraint at the arrival point. This speed variation can modify the rate of climb or of descent of the aircraft and therefore jeopardize the handling of the altitude at the arrival point. For example, a more sizable climb speed may entail a lower climb rate.
To address this constraint, the method envisages an additional margin so as to be able to ensure compliance with the target altitude and an optional time constraint. By way of example, the position of the manoeuvre point PM is corrected by means of the following formula:

DMcorr=VSest/(VSest−C)×DM 

in which DM is the distance separating the manoeuvre point PM from the arrival point 21 along the lateral trajectory, DMcorr is the corrected distance so as to accommodate the time constraint, C is a constant to be dimensioned as a function of the desired margin, and VSest is determined through the following formula:

VSest=(Ha−Hd)/DM×GS 

in which Ha and Hd are the altitude of the arrival point 21 and departure point 20 and GS is the speed of the aircraft at the moment of the computation. Moreover, when (VSest−C)<1, the method applies (VSest−C)=1.

Thus, in a possible mode of implementation, the method advantageously comprises a step of computing a position correction for the manoeuvre point PM, at least as a function of the altitude of the departure and arrival point, of a distance separating the manoeuvre point PM and the arrival point along the vertical trajectory, and of a speed of the aircraft at the manoeuvre point PM; the said correction being determined so as to make it possible to take into account a constraint regarding time of transit at the arrival point.
The vertical trajectory computation function according to the invention can therefore be implemented according to several possible variants. The choice between these variants arises as a compromise between the accuracy expected in the determination of the manoeuvre point PM and the time for computing the function, and the associated computational resources.
The variants presented have the following characteristics in common. They pertain to a method for aiding navigation, implemented in a flight management system of FMS type, for the construction of a vertical trajectory of an aircraft following a predetermined lateral trajectory between a departure point and an arrival point; the said departure point and arrival point furthermore being characterized by predefined altitudes, respectively Hd and Ha, and predefined speeds, respectively Vd and Va; the said method comprising the steps of:

    
    
        selection of a transition manoeuvre in terms of altitude and speed from a predetermined list of manoeuvres,
        determination of a manoeuvre point PM on the lateral trajectory, of altitude Hd and of speed Vd, from which the transition manoeuvre must be initiated so as to allow the aircraft to reach at the arrival point 21 the predefined speed Va and the predefined altitude Ha.
    
    


Advantageously, the manoeuvre point PM is determined by an iterative process comprising an initialization step, consisting in positioning an initial manoeuvre point PM0, on the lateral trajectory, between the departure point 20 and the arrival point 21, and an iterative step 38 consisting of:

    
    
        a predictive computation of a vertical trajectory between the departure and arrival point, comprising a transition segment, between an intermediate manoeuvre point PMi and a point of attainment, allowing the aircraft to attain the altitude Ha and the speed Va through the transition manoeuvre; the intermediate manoeuvre point PMi being defined in a first iterative loop as the initial manoeuvre point PM0,
        a computation of a new intermediate manoeuvre point PMi+1, by shifting the manoeuvre point PMi on the lateral trajectory by a distance Di separating the point of attainment from the arrival point along the lateral trajectory; the said iterative process being interrupted when the distance Di is less than a predetermined threshold; the manoeuvre point PM being defined as the intermediate manoeuvre point PMi at the moment of interruption of the iterative process.
    
    


The invention also pertains to a flight management system comprising code instructions making it possible to perform the steps of the method for aiding navigation having the characteristics defined above. This new function can be integrated into an FMS system, for real-time trajectory optimization.
It will be possible moreover to envisage the display destined for the crew of one or more quantities determined by means of the method. Consideration is given in particular to the display of the manoeuvre point PM, and to the setting up of a visual and/or audible device making it possible to alert the crew according to a periodicity which increases the closer one approaches the initial manoeuvre point.

## Claims

1. A method for aiding navigation, implemented in a flight management system, for construction of a vertical trajectory of an aircraft following a predetermined lateral trajectory between a departure point and an arrival point, the departure point and the arrival point being characterized by predefined altitudes, respectively Hd and Ha, and predefined speeds, respectively Vd and Va, the method comprising:
selecting, using the flight management system, a transition manoeuvre in terms of altitude and speed from a predetermined list of manoeuvres;
determining, using the flight management system and by an iterative process, a manoeuvre point PM on the predetermined lateral trajectory, between the departure point and the arrival point, of altitude Hd and of speed Vd, from which the transition manoeuvre must be initiated so that the aircraft acquires, through the transition manoeuvre, the predefined speed Va and the predefined altitude Ha only upon reaching the arrival point;
displaying the manoeuvre point PMto a crew on a man-machine interface; and
causing the aircraft to carry out the transition manoeuvre so that the aircraft acquires the predefined speed Va and the predefined altitude Ha only upon reaching the arrival point,
wherein the manoeuvre point PM is determined, using the flight management system, by the iterative process comprising an initialization step, the initialization step comprising positioning an initial manoeuvre point PM0, on the lateral trajectory, between the departure point and the arrival point, and an iterative step comprising:
predictively computing, using the flight management system, a vertical trajectory between the departure point and the arrival point, comprising a transition segment, between an intermediate manoeuvre point PMi on the lateral trajectory and a point of attainment on the lateral trajectory, allowing the aircraft to attain the predefined altitude Ha and the predefined speed Va through the transition manoeuvre, the intermediate manoeuvre point PMi being defined in a first iterative loop as the initial manoeuvre point PM0;
computing, using the flight management system, a new intermediate manoeuvre point PMi+1, by shifting the intermediate manoeuvre point PMi on the lateral trajectory by a distance Di separating the point of attainment from the arrival point along the lateral trajectory; and

interrupting, using the flight management system, the iterative process when the distance Di is less than a predetermined threshold, the manoeuvre point PM being defined as the intermediate manoeuvre point PMi at the interruption of the iterative process.

2. The method according to claim 1, wherein the initial manoeuvre point PM0 is determined based on the arrival point on a segment of constant slope of predetermined angle.

3. The method according to claim 1, wherein a transition manoeuvre comprises three successive segments:
a first segment, during which an altitude and a speed of the aircraft evolve according to two constant gradients, until a target intermediate speed is reached,
a second segment, during which the speed of the aircraft is maintained constant and the altitude evolves according to a constant gradient, until a target altitude is reached, and
a third segment, during which the altitude of the aircraft is maintained constant, and the speed evolves according to a constant gradient, until a target speed is reached.

4. The method according to claim 3, wherein the initial manoeuvre point PM0 is determined based on the arrival point by an estimation of lateral length of each of the segments of the transition manoeuvre, by assigning predetermined values to the gradients of speed and of altitude of each of the segments.

5. The method according to claim 4, wherein the initial manoeuvre point PM0 is determined for a mass of the aircraft computed by a Breguet formula, at a dummy point defined by an altitude identical to the departure point and lateral coordinates identical to the arrival point.

6. The method according to claim 4, wherein the initial manoeuvre point PM0 is determined for a mass of the aircraft computed by a Breguet formula, at a dummy point defined by an altitude identical to the departure point and lateral coordinates computed on a segment of constant slope of predetermined angle joining the dummy point to the arrival point along the lateral trajectory.

7. The method according to claim 1, wherein the initial manoeuvre point PM0 is determined based on the arrival point by a predictive trajectory computation, carried out backwards and allowing the aircraft to attain the altitude Hd and the speed Vd through the transition manoeuvre.

8. The method according to claim 1, wherein the initialization step further comprises computing an anticipated initial point PA0 on the lateral trajectory, positioned between the departure point and the initial manoeuvre point PM0, and a predictive computation of trajectory between the departure point and the anticipated initial point PA0, making it possible to limit the predictive trajectory computation of the iterative step to the segment joining the anticipated initial point PA0 and the arrival point.

9. The method according to claim 8, wherein the anticipated initial point PA0 is determined by the following formula:


DA0=K×DM0,


in which DA0 is a distance separating the anticipated initial point PA0 from the initial manoeuvre point PM0, DM0 is a distance separating the initial manoeuvre point PM0 from the arrival point, and K is a predetermined coefficient.

10. The method according to claim 9, wherein the coefficient K is determined by the following formula:


K=WIND/TASMIN,


in which WINDMAX is an estimation of maximum wind speed between the initial manoeuvre point PM0 and the arrival point, and TASMIN is an estimation of a minimum speed of the aircraft between the initial manoeuvre point PM0 and the arrival point.

11. A flight management system configured to:
select a transition manoeuvre, using the flight management system, in terms of altitude and speed from a predetermined list of manoeuvres;
determine, using the flight management system and by an iterative process, a manoeuvre point PM on a predetermined lateral trajectory, between a departure point and an arrival point, of altitude Hd and of speed Vd, from which the transition manoeuvre must be initiated so that an aircraft acquires, through the transition manoeuvre, a predefined speed Va and a predefined altitude Ha only upon reaching the arrival point;
display the manoeuvre point PM to a crew on a man-machine interface; and
cause the aircraft to carry out the transition manoeuvre so that the aircraft acquires the predefined speed Va and the predefined altitude Ha only upon reaching the arrival point,
wherein the manoeuvre point PM is determined, using the flight management system, by the iterative process comprising an initialization step, the initialization step comprising positioning an initial manoeuvre point PM0, on the lateral trajectory, between the departure point and the arrival point, and an iterative step comprising:
predictively computing, using the flight management system, a vertical trajectory between the departure point and the arrival point, comprising a transition segment, between an intermediate manoeuvre point PMi on the lateral trajectory and a point of attainment on the lateral trajectory, allowing the aircraft to attain the predefined altitude Ha and the predefined speed Va through the transition manoeuvre, the intermediate manoeuvre point PMi being defined in a first iterative loop as the initial manoeuvre point PM0; 
computing, using the flight management system, a new intermediate manoeuvre point PMi+1, by shifting the intermediate manoeuvre point PMi on the lateral trajectory by a distance Di separating the point of attainment from the arrival point along the lateral trajectory; and
interrupting, using the flight management system, the iterative process when the distance Di is less than a predetermined threshold, the manoeuvre point PM being defined as the intermediate manoeuvre point PMi at the interruption of the iterative process.