Patent Publication Number: US-8983689-B2

Title: Navigation assistance method based on anticipation of linear or angular deviations

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims priority to foreign French patent application No. FR 1200754, filed on Mar. 13, 2012, the disclosure of which is incorporated by reference in its entirety. 
     FIELD OF THE INVENTION 
     The invention relates to a method for assisting in the navigation of an aircraft  9 , making it possible to optimize the following of a target trajectory, and more particularly a method intended to optimize the manoeuvres of the aeroplane in an approach phase to the runway of the arrival airport. 
     An ongoing increase in air traffic and in the resulting workload for the pilot has been observed for some years. The number of tasks to be carried out on board is increasing. The decision time is becoming shorter and shorter whereas meanwhile there is a general trend towards reducing the number of crew members. Automated procedures, making it possible to a certain extent to release the crew from routine tasks, are becoming increasingly widely used. 
     The tracking of the approach procedures of an aircraft towards the runway of the arrival airport represents a particular issue in the aeronautic field. This flight phase is critical: although very short, it represents a predominant proportion of the accidents with loss of the craft. Having to take into account increasingly stringent environmental constraints, seeking for example to reduce pollution or sound nuisance, is making the approach procedure increasingly complex and difficult. Efforts are being made for example to minimize the distances reserved for take-off and landing, or efforts are being made to pass over determined areas with high accuracy, minimizing the nuisances and their dispersions. Another object of the new approach procedures is to increase the rate of take-offs and landings to make it possible to improve the capacity of the runways or navigate with very strict positioning constraints in the case of relief close to the runways. 
     BACKGROUND 
     Various systems exist for assisting a crew in the piloting of an aircraft, notably during an approach phase. Particularly well known among these systems are the flight management systems, called FMS, schematically represented in  FIG. 1  and comprising the following functions:
         location LOCNAV, identified  1 : making it possible to locate the aircraft by means of various geolocation tools or instruments (GPS, GALILEO, VHF radio beacons, inertial units),   flight plan FPLN, identified  2 : making it possible to input the geographic elements forming the skeleton of the route to be followed (departure and arrival procedures, way points, etc.),   navigation database NAVDB  3 : making it possible to construct geographic routes and procedures from data included in the bases (points, beacons, interception or altitude legs, etc.),   performance database PRF DB  4 : containing the aerodynamic and engine parameters of the craft,   lateral trajectory TRAJ  5 : making it possible to construct a continuous trajectory from points in the flight plan, observing the aeroplane performance levels and the containment constraints,   predictions PRED  6 : making it possible to construct an optimized vertical profile compatible with the lateral trajectory,   guidance GUIDANCE  7 : making it possible to guide, in the lateral and vertical planes, the aircraft on its 3D trajectory, while optimizing the speed,   digital data link DATALINK  8 : making it possible to communicate with the control centres, the airlines and the other aircraft.       

     In a typical approach phase as represented in FIGS.  2 . a ,  2 . b  and  2 . c , an aircraft  9  seeks to follow a target trajectory  10  to reach a landing runway  11 . Generally, an approach phase comprises a first part consisting of one or more “linear” sections  12  followed by a final “angular” section  13  converging towards a touchdown point  14 , generally situated close to the runway threshold  11 . The final angular section  13  is possibly followed by one or more linear sections  12  in the case of a go-around phase for an interrupted approach, also referred to as “Missed Approach”. On a linear section  12  as represented in FIG.  2 . b , a linear deviation  15  represents the distance separating an estimated position  16  of the aircraft  9  and a desired position  17  on the target trajectory  10 . The linear deviation  15  can be expressed by a lateral component and a vertical component. 
     On an angular section  13  as represented in FIG.  2 . c , an angular deviation  18  represents the angle formed at the touchdown point  14 , between the target trajectory  10  and a straight line D 1  joining the touchdown point  14  to the estimated position  16  of the aircraft  9 . The angular deviation  18  can be expressed by a lateral component and a vertical component. 
     In the known systems, the aim is to minimize the linear deviation on a linear section. Along a linear section produced with a navigation performance requirement, or RNP, standing for “Required Navigation Performance”, the requirement is to keep the linear deviation  15  below a limit value. When the difference exceeds the limit value, the system provides for alerting the crew to enable it to decide on the corrective measures to be performed. 
     Along a linear section, the known systems propose to the crew, by means of a human-machine interface, or HMI, graphic representation means, commonly called “monitoring” means, that make it possible to track the navigation performance. In particular, the known systems propose a tracking of the navigation performance on a linear section conforming to a current standardization, in particular the standard ICAO PBN Manual, doc 9613. 
     According to this standardization, a linear deviation  15  is graphically represented, as schematically represented in  FIG. 3 , on a first lateral deviation axis  21  and a second vertical deviation axis  22 . This is called linear monitoring  20 , the representation of a linear deviation  15 , expressed laterally  23  and vertically  24 , on the two deviation axes  21  and  22 . The linear deviation  15  is represented on the lateral deviation axis  21  according to a lateral scale  25 , called RNP, and on the vertical deviation axis  22  according to a vertical scale  26 , called V-RNP, by means of a cross  27  symbolically representing the aircraft  9 . 
     According to this standardization, when the aircraft  9  is positioned on the target trajectory  10 , it appears centred on each of the scales, lateral  25  and vertical  26 ; a deviation thus being able to be positive or negative for each of the deviation axes  21  and  22 . The equivalent distance between two RNP or V-RNP graduations is variable, for example according to the approach phases, the linear sections, the flight conditions or the aircraft type. Typically, in a navigation performed with a required navigation performance RNP, an alert will be transmitted to the crew when a linear deviation greater than 2 RNP graduations occurs. 
     As an example, in an approach phase, a tracking of the navigation performance of “RNP 0.3” type may be required. The distance between two RNP graduations is then equal to 0.3 nautical miles, and the lateral linear deviation should be centred on the trajectory with a maximum tolerance of plus or minus 1 nautical mile, corresponding to plus or minus 2 RNP, a threshold from which an alert is transmitted to the crew. It will be recalled that a nautical mile, also called NM, is a unit commonly used by the person skilled in the art in the aeronautical field, 1 nautical mile corresponding to 1852 metres. The International Civil Aviation Organization (ICAO) defines standards at international level; in particular, the RNP values of 4 NM, 1 NM, 0.3 NM or 0.1 NM are the reference values used worldwide. The principle of the navigation assistance method according to the invention applies however to any RNP value. 
     On the final “angular” section, the aim is to minimize the angular deviation  18 . In the known systems, a transmitting beacon arranged in proximity to the threshold of the landing runway  11  embodies the touchdown point  14 . The reception by the aircraft  9  of the signal transmitted by the beacon then makes it possible to determine the angular deviation  18  of the aircraft  9  relative to its target trajectory  10 . Thus, the expression ILS (Instrument Landing System) navigation applies, for an approach performed on an angular section in which the aim is to minimize the angular deviation  18 . The navigation assistance method applies also to other types of angular approaches, such as, for example, the MLS (Microwave Landing System) approaches which rely on a wireless transmitting beacon, or, for example, the FLS (FMS Landing System) approaches which rely on a virtual beacon. 
     In the systems currently implemented, nothing is defined to guarantee the maintenance of navigation performance on an angular section. The systems do not propose any sophisticated monitoring tool to enable the crew to control the descent along an angular section, and have sufficient reaction time to manoeuvre the aircraft, in particular as the approach continues and the cone of the deviations shrinks. 
     Moreover, the switchover between the two types of navigation, from linear to angular (and from angular to linear in the case of an interrupted approach), is performed with no particular management of the transition. It is possible to ensure the monitoring of the navigation performance on the linear section, then when the aircraft  9  enters into the angular section, the linear monitoring is interrupted, the crew observes the angular deviation and decides on the corrective measures to be applied, without the possibility of anticipation at the time of the transition. 
     SUMMARY OF THE INVENTION 
     The invention aims to propose a navigation assistance method for an aircraft  9  in the approach phase that mitigates the implementation difficulties cited above. The method seeks in particular to improve the capacity to manoeuvre by the crew by anticipating the deviations of the craft, in particular during an approach phase of the aircraft  9 . 
     To this end, the subject of the invention is a method for assisting in the navigation of an aircraft comprising steps for calculating and displaying:
         a linear deviation, for the aircraft in approach phase towards an arrival airport on a first section, called linear section; the linear deviation representing a distance separating an estimated position of the aircraft and a desired position on a target trajectory; the linear deviation being able to be expressed by a lateral component and a vertical component,   an angular deviation, for the aircraft in approach phase towards an arrival airport on a second section, called angular section; the angular deviation representing an angle formed at a touchdown point situated in proximity to the landing runway threshold, between the target trajectory and a straight line joining the touchdown point to the estimated position of the aircraft; the angular deviation being able to be expressed by a lateral component and a vertical component.       

     The method also comprises the following steps:
         a calculation of an anticipated deviation of the aircraft, linearly or angularly, projected to a time DT, characteristic of a reaction time of the aircraft, and of a statistical error distribution associated with this anticipated deviation,   a calculation of a probability of exceeding a predetermined target deviation, by means of the anticipated deviation and the statistical error distribution.       

     The method according to the invention makes it possible to facilitate the piloting of the aircraft by the crew. In order to improve the responsiveness of the crew, the method makes it possible, from anticipated deviations, to transmit various alerts to the crew, or else select various manoeuvres or reconfigurations making it possible to optimize the trajectory of the craft in its approach phase. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be better understood, and other advantages will become apparent, on reading the detailed description of the embodiments given as examples in the following figures. 
         FIG. 1 , already presented, represents a known navigation assistance system, commonly called FMS, 
       FIGS.  2 . a ,  2 . b  and  2 . c , already presented, represent an approach phase made up of a number of linear sections and one angular section, 
         FIG. 3 , already presented, represents means for graphically representing, or monitoring, a linear deviation, laterally and vertically, 
         FIG. 4  illustrates means for graphically representing, or monitoring, an angular deviation, laterally and vertically, 
         FIG. 5  schematically represents the navigation of an aircraft during an approach phase on an angular section, and the characteristics useful to the calculation for converting an angular deviation to an equivalent linear deviation, 
         FIG. 6  illustrates means for graphically representing the linear or angular deviations, called unified monitoring, 
         FIG. 7  schematically represents the navigation of an aircraft during an approach phase containing curvilinear portions, 
         FIG. 8  schematically represents the principle of calculation of an anticipated deviation and of an associated error, represented for an aircraft in the approach phase on an angular section, 
         FIG. 9  illustrates means for graphically representing current and anticipated deviations and statistical error distributions which are associated therewith, 
         FIG. 10  represents a schematic diagram of the navigation assistance method according to a first embodiment of the invention, 
         FIG. 11  represents a schematic representation of the navigation assistance method according to a second embodiment of the invention. 
     
    
    
     In the interests of clarity, the same elements will be given the same references in the different figures. 
     DETAILED DESCRIPTION 
       FIG. 4  illustrates means for graphically representing, or monitoring, an angular deviation, laterally and vertically. On the same principle as for a linear deviation, described in  FIG. 3 , representing an angular deviation  18  of the aircraft  9  on a lateral deviation axis  31  and a vertical deviation axis  32  is envisaged. 
     There are a number of methods for establishing an angular deviation, notably according to the transmitting beacon type which embodies the touchdown point. Whatever the method considered, it is possible to determine an angular difference between the estimated position  16  of the aircraft  9  and its desired position  17  on the target trajectory  10 . 
     The angular deviation  18  is represented by a lateral component  33  and a vertical component  34  on two angular scales, lateral  35  and vertical  36 . When the aircraft  9  is positioned on the target trajectory  10 , it appears centred on each of the scales, lateral  35  and vertical  36 ; an angular deviation  18  can thus be positive or negative on each of the deviation axes  21  and  22 . The angular scales  35  and  36  comprise graduations, commonly referred to as “dots”, corresponding to a predetermined angle value; this predetermined value generally being dependent on the distance separating the aircraft  9  from the landing runway  11 .  FIG. 4  represents means for graphically representing an angular deviation  18 , or angular monitoring  30 , making it possible to represent, on the lateral  31  and vertical  32  deviation axes, the lateral angular deviation  33  and the vertical angular deviation  34  of the aircraft  9  by means of a rhomboid  37  symbolizing the aircraft  9 , positioned on the angular scales, lateral  35  and vertical  36 . 
     Thus, the navigation assistance method comprises steps for calculating and graphically representing:
         a linear deviation  15 , for the aircraft  9  in approach phase towards an arrival airport on a linear section  12 ; the linear deviation representing the distance separating the estimated position  16  of the aircraft  9  and the desired position  17  on the target trajectory  10 ; the linear deviation  15  being able to be expressed by a lateral component  23  and a vertical component  24 ,   an angular deviation  18 , for the aircraft  9  in approach phase towards an arrival airport on an angular section  13 ; the angular deviation  18  representing the angle formed at the touchdown point  14  situated in proximity to the landing runway threshold  11 , between the target trajectory  10  and the straight line D 1  joining the touchdown point  14  to the estimated position  16  of the aircraft  9 ; the angular deviation  18  being able to be expressed by a lateral component  33  and a vertical component  34 .       

       FIG. 5  schematically represents the navigation of an aircraft  9  during an approach phase on an angular section, and the characteristics useful to the calculation for converting an angular deviation into an equivalent linear deviation. 
     Along the angular section, an angular deviation  41  is defined as the angle formed at the touchdown point  14 , between a target trajectory  44  and a straight line D 2  joining the touchdown point  14  to an estimated position  42  of the aircraft  9 . The orthogonal projection of the estimated position  46  of the aircraft  9  on the target trajectory  44  corresponds to a desired position  43  of the aircraft  9 . The distance separating the touchdown point  14  and the desired position is referenced  45 . A linear deviation  46  of the aircraft  9  corresponds to the distance separating the estimated position  42  and the desired position  43 . 
     In these conditions, the knowledge of an angular deviation  41 , for example established by means of a wireless receiver picking up the signal transmitted by a transmitting beacon, and of the distance  45 , for example established by means of the functions of location  1 , of construction of the target trajectory  5  and  6 , and of guidance  7  of the aircraft, makes it possible to calculate an equivalent linear deviation  46 . 
     According to the invention, the navigation assistance method comprises a step of conversion of the angular deviation  41  into an equivalent linear deviation  46 , observing the following mathematical relationship:
 
Dev= D *tan(Alpha)
 
in which Dev represents the linear deviation  46 , D represents the distance  45  and Alpha represents the angular deviation  41 .
 
     According to the same principle, it is possible to determine a linear deviation equivalent to the “dot” angle corresponding to a graduation on the angular scale represented on  FIG. 4 . In other words, it becomes possible to represent, on a linear scale, a projection of an angular deviation. On a linear section, a “dot” graduation corresponds to an “RNP” deviation and the scale remains identical as long as the RNP requirement does not change. On an angular section, the scale changes as a function of the distance  45 . The more the aircraft  9  approaches the touchdown point  14 , the tighter the scale becomes. 
     According to the invention, the navigation assistance method comprises a step of conversion of an angular deviation into an equivalent linear deviation, according to a similar principle. Knowing the linear deviation and the distance  45 , for example by means of the functions of location  1 , of construction of the target trajectory  5  and  6 , and of guidance  7  of the aircraft  9 , the method determines an equivalent angular deviation by means of the mathematical relationship (i) which has already been described. This conversion makes it possible, for example, to project a linear deviation onto a linear go-around section equivalent to a determined angular deviation on the final angular section. It also becomes possible to force an angular guidance before the capture of the signal transmitted by the transmitting beacon. 
     Thus, the method comprises a step of conversion of an angular deviation  41  into an equivalent linear deviation  46 , and, conversely, the conversion of a linear deviation  46  into an equivalent angular deviation  41 , observing the following mathematical relationship:
 
Dev= D *tan(Alpha)
 
in which Dev represents the equivalent linear deviation  46 , D represents a distance  45  between the touchdown point  14  and the desired position  43  on the target trajectory  10 , and Alpha represents the angular deviation  41 .
 
     Advantageously, the navigation assistance method makes it possible to track, all along the approach phase, a navigation performance, by means of a deviation that can be represented independently on a linear or angular scale. As an example, it is possible to ensure the tracking of performance linearly, during the last linear section and during the transition to the final angular section, by means of an equivalent linear deviation determined by calculation on the basis of an angular deviation. In a second stage, the crew can decide to switch over to a display of the deviations angularly, after the necessary manoeuvres on entering the angular section have been carried out. According to the same principle, it is possible, in the case of an interrupted approach, to project a navigation performance onto the linear go-around section, by calculation on the basis of the measured angular deviation. 
       FIG. 6  illustrates graphic representation means according to the invention, called unified monitoring  50 , making it possible to display a deviation of the aircraft  9  all along an approach phase. The unified monitoring  50  comprises a lateral deviation axis  51  and a vertical deviation axis  52 . A deviation of the aircraft  9  is represented by means of a lateral deviation  53  positioned on the lateral deviation axis  51  provided with a graduation scale  55 , and of a vertical deviation  54  positioned on the vertical deviation axis  52  provided with a graduation scale  56 . 
     Advantageously, it is possible to choose, for each of the deviation axes  51  and  52 , between a linear graduation scale (as represented in  FIG. 6 ) and an angular graduation scale (according to a graphic representation similar to that of  FIG. 4  which has already been described). It will also be possible to consider representing a combined scale, including, for each deviation axis, a linear scale and an angular scale. When a linear scale is selected, for example for the lateral deviation axis  51 , it is possible to represent on this axis an angular deviation of the aircraft  9  (represented by the rhomboid in  FIG. 6 ), previously converted into an equivalent linear deviation by the calculation means described previously. It is also possible to select a different scale for each of the two deviation axes  51  and  52 ; for example, the scale  55  of the lateral deviation axis  51  being linear and the scale  56  of the deviation axis  52  angular. 
     Advantageously, the unified monitoring  50  comprises, for each of the deviation axes, lateral  51  and vertical  52 , means for selecting the scales  55  and  56 , linear, angular or combined. The selection can be made manually for each of the deviation axes  51  and  52  by the crew, or can be performed automatically by means of a number of criteria dependent on the flight conditions. 
     In a preferred implementation of the invention, a first criterion provides for switching over from a linear display to an angular display on the two axes, as soon as one of the two axes switches over to angular mode. A second criterion provides for switching over from a linear display to an angular display when the distance separating the aircraft  9  from the landing runway  11  is below a predetermined threshold. A third criterion provides for switching over from a linear display to an angular display as soon as the aircraft  9  receives a signal from the transmitting beacon. 
     Advantageously, the graduations of the linear and angular scales of the lateral  51  and vertical  52  deviation axes correspond to a required navigation performance level. The graduations can be adapted to variable requirement levels during the flight of the aircraft  9 , according to the same principle as described in  FIG. 3  for the tracking of navigation performance linearly. Thus, it is possible to select, for example for the linear scales, graduations conforming to the current standardization, in particular the RNP and V-RNP scales. It becomes possible to ensure a tracking of the navigation performance, for example of “RNP 0.3” type, all along an approach phase, on a linear section and on the final angular section. 
     The navigation assistance method according to the invention is particularly advantageous because it makes it possible to track the navigation performance all along an approach phase, with no discontinuity between the different sections covered, both linear and angular. 
       FIG. 7  schematically represents the navigation of an aircraft  9  during an approach phase containing a curvilinear trajectory. 
     A target trajectory  61  comprises a curvilinear portion  62  between the touchdown point  14  and the desired position  63  of the aircraft  9  on the target trajectory  61 . The desired position  63  corresponds to the orthogonal projection of the aircraft  9  on the target trajectory  61 . The length of the curvilinear segment between the touchdown point  14  and the desired position  63  is referenced  64 . The linear deviation is referenced  65 . 
     It is possible to calculate, at each instant along this curvilinear trajectory, the distance  64  as well as the linear deviation  65 , for example by means of the functions of location  1 , of construction of the target trajectory  5  and  6 , and of guidance  7  of the aircraft  9 . From this calculation of the distance  64  and of the linear deviation  65 , it is possible to determine and display an equivalent angular deviation  66 , based on the distance  64  and the linear deviation  65 . Thus, the unified monitoring  50  can be applied in the case of an approach containing a curvilinear portion, and it becomes possible to carry out an angular approach and a tracking of the navigation performance all along the approach phase, on longilinear portions and on curvilinear portions. 
     Finally, it will also be possible to envisage integrating conditions for abandoning the unified monitoring  50  in the case where the trajectory has curvilinear portions with a radius of curvature below a predetermined threshold value; the accuracy of the linear projection becoming, in these conditions, too low. 
       FIG. 8  schematically represents the principle of calculation of an anticipated deviation DEV_ANT and of an associated statistical error distribution ERR_ANT, represented for an aircraft  9  in approach phase on an angular section  13  converging towards a touchdown point  14 . 
     In the figure, the aircraft  9  exhibits a deviation DEV_ACT relative to a target trajectory  10 . The deviation DEV_ACT can be expressed and represented independently angularly or linearly, by means of the functions described previously. 
     According to the invention, the navigation assistance method comprises steps of calculating a statistical error distribution ERR_ACT associated with the deviation DEV_ACT. In a preferred implementation of the invention, the statistical error distribution ERR_ACT is the sum of a plurality of error sources, each being taken into account in the calculation by a statistical distribution. The statistical error distribution ERR_ACT for example takes into account the errors linked to the functions of location  1 , of construction of the target trajectory  5  and  6 , or of guidance  7  of the aircraft  9 . Thus, the method determines, at each instant, the deviation DEV_ACT and a statistical error distribution ERR_ACT. 
     Thus, it is possible to determine, for a predetermined accuracy requirement EXI_PREC, a range of the deviations  70  that observes this accuracy requirement. According to the same principle, it is possible to determine, for a predetermined deviation range EXI_DEV, for example corresponding to a given required navigation performance, the probability of presence of the aircraft  9  in the deviation range EXI_DEV. 
     According to the invention, the navigation assistance method comprises a step of calculating an anticipated deviation DEV_ANT, expressed linearly or angularly, projected to a time DT, characteristic of a reaction time of the aircraft  9 , and a statistical error distribution ERR_ANT associated with this anticipated deviation DEV_ANT. 
     Advantageously, the navigation assistance method comprises a step of calculating the time DT, based on:
         a time DTH, representative of the human reaction time, calculated by means of a plurality of parameters that can vary during the flight, comprising at least a decision-taking time, a time of engagement and of verification of a guidance mode, a time of modification of the choices of the location means or a time making it possible to place the aeroplane in a more stable aerodynamic configuration,   a time DTA, representative of the manoeuvrability of the craft, calculated by means of a plurality of parameters that can vary during the flight, comprising at least one parameter representative of the speed of the aircraft, one parameter representative of the current manoeuvre for rejoining the target trajectory or one parameter representative of the other current navigation assistance methods.       

     In a preferred implementation of the invention, the time DT is equal to the longest time between the human reaction time DTH and the time representative of the manoeuvrability of the craft DTA. In an alternative implementation, the time DT will be determined by means of a sum of the times DTH and DTA, or even by means of a quadratic sum of the times DTH and DTA. 
     According to the invention, the navigation assistance method determines, for this time DT and by means of the known trajectory calculation functions, in particular the functions  6  and  7 , an anticipated deviation DEV_ANT. A number of calculation means can be implemented to determine the statistical error distribution ERR_ANT associated with the anticipated deviation DEV_ANT. 
     In a preferred implementation of the invention, the statistical error distribution ERR_ANT is the sum of a plurality of error sources, each being taken into account in the calculation by a statistical distribution. Advantageously, the error sources taken into account comprise at least the errors linked to the functions of location  1 , of construction of the target trajectory  5  and  6  or of guidance  7  of the aircraft  9 . 
     An example of calculation of the statistical error distribution ERR_ANT, based on the expected performance of the functions of location  1 , of construction of the target trajectory  5  and  6 , and of guidance  7  of the aircraft  9 , is described below. In this preferred implementation, for each of the axes (longitudinal, lateral and vertical) the error is determined in the form of a distribution Gaussian. The three error sources are then modelled in the form of:
         three vectors of the errors on the estimation of the bias:
           EB_loc: 3D vector of the bias of the location functions  1  (longitudinal, lateral and vertical)   EB_traj: 3D vector of the bias of the target trajectory construction functions  5  and  6     EB_guid: 3D vector of the bias of the functions of guidance  7  of the aircraft  9     
           a matrix of the errors on the estimation of the drifts ED, including crossed terms between axes (three-dimension square matrix)   three standard deviation vectors of the errors:
           S_loc: 3D vector of the standard deviation of the errors on the location functions  1     S_traj: 3D vector of the standard deviation of the errors on the target trajectory construction functions  5  and  6     S_guid: 3D vector of the standard deviation of the errors on the guidance functions  7  of the aircraft  9 .   
               

     The statistical error distribution ERR_ANT expressed as an overall 3D error vector is then determined by a function of the individual errors ERR_ACT, EB_LOC, EB_traj, EB_guid, ED, S_loc, S_traj, S_Guid. It is possible, for example, to use the following relationship:
 
ERR_ANT=ERR_ACT+EB_loc+EB_traj+EB_guid+ED*(DT DT DT) T   +N *( S _loc+ S _traj+ S _Guid)
 
in which DT is the characteristic time defined previously, the vector (DT DT DT) T  making it possible to obtain, by multiplication with the ED matrix, the 3D vector representing the errors on the drifts projected at the time DT. N, generally expressed as sigma, represents the expected accuracy on the calculated error.
 
     It is also possible to use a relationship of the type:
 
ERR_ANT=ERR_ACT+SQRT(EB_loc 2 +EB_traj 2 +EB_guid 2 )+ED*(DT DT DT) T   +N *( S _loc+ S _traj+ S _Guid)
 
in which SQRT corresponds to the square root function of the terms between brackets; this last relationship being particularly suited to independent errors. Other mathematical relationships on these variables are also possible according to the invention.
 
     Thus, the method determines, at each instant, the anticipated deviation DEV_ANT and a statistical error distribution ERR_ANT. It is then possible to determine, for a predetermined accuracy requirement EXI_PREC, a range of the deviations  71  that observes this accuracy requirement. According to the same principle, it is possible to determine, for a predetermined deviation range EXI_DEV, for example corresponding to a given required navigation performance, the probability of keeping, with the current trajectory, the aircraft  9  within the deviation range EXI_DEV at the time DT. 
       FIG. 9  illustrates means for graphically representing the current deviation DEV_ACT and anticipated deviation DEV_ANT, and the statistical error distributions which are associated therewith, respectively ERR_ACT and ERR_ANT. 
     The deviation DEV_ACT of the aircraft  9  is expressed linearly by a lateral component  81 , represented graphically on a lateral deviation axis  51  graduated by means of a linear scale  55 , and by a vertical component (not represented). As described previously, the deviation DEV_ACT could also be expressed and represented angularly, by means of the conversion functions described previously. 
     The anticipated deviation DEV_ANT, projected to the time DT, is expressed by a lateral component  82  represented on the same scale as the current lateral deviation  81 . 
     According to the invention, the navigation assistance method comprises a step of graphic representation of the statistical error distributions, current ERR_ACT and anticipated ERR_ANT. Thus, for each of the deviations  81  and  82 , an error interval is determined, respectively  83  and  84 , by means of the statistical error distributions ERR_ACT and ERR_ANT and for a predetermined accuracy requirement EXI_PREC. 
     The calculation and the graphic representation of an anticipated deviation DEV_ANT and of an associated statistical error distribution ERR_ANT are particularly advantageous in as much as this makes it possible to give the crew a capacity to anticipate the trajectories of the aircraft  9 . The crew has more time to react and decide on the corrective measures to be applied. 
     These tools are also particularly suited to the unified monitoring  50  described previously. In practice, it becomes possible, during a transition from a linear section to a final angular section, to maintain navigation performance tracking all along the transition. It enables the crew to anticipate the trajectory of the aircraft  9 , and to evaluate, without discontinuity, the probability of maintaining, during the transition and on the angular section, a navigation performance that conforms to a given requirement, and, if appropriate, to anticipate the necessary manoeuvres of the craft. 
       FIG. 10  represents a schematic diagram of the navigation assistance method according to a first embodiment of the invention. 
     According to this first embodiment, the navigation assistance method comprises the following three calculation steps carried out in succession:
         calculation  101  of the time DT, characteristic of a reaction time of the aircraft  9 ,   calculation  102  of an anticipated deviation DEV_ANT for this time DT and of an associated statistical error distribution ERR_ANT,   calculation  103  of a probability PROB of exceeding a predetermined target deviation EXI_DEV, for example corresponding to a required navigation performance, by means of DEV_ANT and ERR_ANT.       

     Advantageously, an alert  201  is transmitted to the crew when the probability is above a predetermined ALERT threshold, for example 95%, 99% or 99.99%. 
     Advantageously, the navigation assistance method as described in  FIG. 10  comprises one or more activation conditions, comprising at least one of the following conditions: the remaining distance to be covered to the touchdown point  14  is less than a predetermined threshold distance, the touchdown point  14  is transmitting a signal received by the aircraft  9 . Similarly, the method comprises one or more deactivation conditions, so as to interrupt the calculation, for example when the aircraft  9  reaches the landing runway  11 . 
     Thus, the navigation assistance method is activated and deactivated automatically, and a confirmation of its activation and deactivation by the crew can usefully be added. 
       FIG. 11  represents a schematic diagram of the navigation assistance method according to a second embodiment of the invention. 
     According to this second embodiment, the navigation assistance method comprises a list  100  of possible manoeuvres of the aircraft  9 , and means making it possible to evaluate the benefit of switching over to a manoeuvre in the list to improve the tracking of the navigation performance. 
     The principle of the navigation assistance method can be described as follows:
         in a first phase, the calculations  101 ,  102  and  103  are carried out in succession to determine a probability PROB of exceeding, at the time DT, a predetermined target deviation EXI_DEV, by means of the anticipated deviation DEV_ANT and of the associated statistical error distribution ERR_ANT, that is to say with the current trajectory of the aircraft  9 ,   in a second phase, the calculations  101 ,  102  and  103  are carried out in succession, iteratively for each of the possible manoeuvres in the list  100 , so as to determine, in succession:
           a time DTi, characteristic of the reaction time of the aircraft  9 , assuming that the crew switches over to the manoeuvre concerned,   an anticipated deviation DEV_ANTi and a statistical error distribution ERR_ANTI, determined for the time DTi and assuming that the crew switches over to the manoeuvre concerned,   a probability PROBi of exceeding, at a time DTi, the predetermined target deviation EXI_DEV, assuming that the crew switches over to the manoeuvre concerned.   
               

     From this calculation, different interactions with the crew can be put in place, to enable it to optimize the tracking of the navigation performance, for example by deciding to switch over to one of the manoeuvres in the list  100 . 
     Thus, a first alert  201  can be transmitted to the crew when the probability PROB determined for the current trajectory is above the predetermined ALERT threshold, for example 95%, 99% or 99.99%. A second alert  202  can be transmitted to the crew when, at the end of the calculation, all the manoeuvres exhibit a probability PROBi above the predetermined ALERT threshold. 
     Advantageously, the navigation assistance method comprises means  203  for suggesting to the crew to switch over to an alternative manoeuvre of the aircraft  9 , which exhibits a probability PROBi less than the probability PROB calculated with the current trajectory. 
     Advantageously, the means  203  make it possible to suggest to the crew to switch over to an alternative manoeuvre of the aircraft  9  that exhibits a probability PROBi below a predetermined ALERT threshold. 
     Advantageously, the means  203  comprise means for selecting the manoeuvre proposed to the crew, comprising at least one of the following selection criteria: the first manoeuvre having been the subject of the calculation of probability PROBi below the predetermined ALERT threshold is proposed, the manoeuvre which exhibits the probability PROBi closest to the predetermined ALERT threshold is proposed, the manoeuvre which exhibits the lowest probability PROBi is proposed. 
     Advantageously, the list of manoeuvres  100  comprises at least the switchover to alternative location functions  1 , the switchover to alternative target trajectory construction functions  5  and  6 , or the switchover to alternative guidance functions  7 , including, for example, the switchover to an automatic piloting mode. The list of manoeuvres  100  can also include the transmission, automatic or on demand from the crew, of specific alert code or of standardized digital messages to other aircraft or to air traffic control at the arrival airport; this transmission being carried out by means of various devices such as, for example, a transponder. 
     Advantageously, the navigation assistance method as described in  FIG. 10  comprises one or more activation conditions, comprising at least one of the following conditions: the remaining distance to be covered to the touchdown point  14  is less than a predetermined threshold distance, the touchdown point  14  is transmitting a signal received by the aircraft  9 . Similarly, the method comprises one or more deactivation conditions, so as to interrupt the calculation, for example when the aircraft  9  reaches the landing runway  11 . 
     Thus, the navigation assistance method is activated and deactivated automatically, and a confirmation of its activation and deactivation by the crew can usefully be added.