EP3415860A1 - Method for predicting the trajectory of a hostile aircraft, particularly in the context of anti-air defence - Google Patents

Method for predicting the trajectory of a hostile aircraft, particularly in the context of anti-air defence Download PDF

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EP3415860A1
EP3415860A1 EP18175386.4A EP18175386A EP3415860A1 EP 3415860 A1 EP3415860 A1 EP 3415860A1 EP 18175386 A EP18175386 A EP 18175386A EP 3415860 A1 EP3415860 A1 EP 3415860A1
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aircraft
point
trajectory
probability
impact
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EP3415860B1 (en
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Pierre STOLZ
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Thales SA
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Thales SA
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F41—WEAPONS
    • F41G—WEAPON SIGHTS; AIMING
    • F41G7/00—Direction control systems for self-propelled missiles
    • F41G7/20—Direction control systems for self-propelled missiles based on continuous observation of target position
    • F41G7/22—Homing guidance systems
    • F41G7/2206—Homing guidance systems using a remote control station
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F41—WEAPONS
    • F41G—WEAPON SIGHTS; AIMING
    • F41G7/00—Direction control systems for self-propelled missiles
    • F41G7/20—Direction control systems for self-propelled missiles based on continuous observation of target position
    • F41G7/22—Homing guidance systems
    • F41G7/224—Deceiving or protecting means
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F41—WEAPONS
    • F41H—ARMOUR; ARMOURED TURRETS; ARMOURED OR ARMED VEHICLES; MEANS OF ATTACK OR DEFENCE, e.g. CAMOUFLAGE, IN GENERAL
    • F41H11/00—Defence installations; Defence devices
    • F41H11/02—Anti-aircraft or anti-guided missile or anti-torpedo defence installations or systems

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  • the present invention relates to a method for predicting the trajectory of a hostile aircraft. It concerns in particular the naval air defense by the prediction of the objective of a hostile aircraft attacking a ship among several possible, the aircraft may be for example a missile. More generally, the invention applies to all anti-aircraft defenses where it is necessary to provide the attacked target among several.
  • a set of ships that may be attacked by hostile aircraft is, for example, a frigate, a major naval vessel and several important naval vessels that are not necessarily armed.
  • the frigate is for example followed at a distance of about 15 km for the naval ship, the two unarmed buildings following the frigate more closely.
  • the major armed building has powerful defenses to protect itself, such as an aircraft carrier, but it nevertheless requires to be defended by a first barrier of defense consisting of the frigate. The latter must for example remove 80% of the dangers.
  • the object of the invention is in particular to reduce this uncertainty rate.
  • the subject of the invention is a method for predicting the trajectory of a hostile aircraft, characterized in that the predicted trajectory ends on a fictitious impact point according to a predicted objective point targeted by the 'aircraft.
  • the main advantages of the invention are that it is applicable to countering many types of hostile aircraft, that it adapts to different types of trajectories of these aircraft and that it can adapt to existing systems. .
  • the figure 1 shows an example of a set of buildings represented by their location points F, C1, C2, HV.
  • a frigate F is ahead of a building of high value HV able to defend itself, an aircraft carrier for example.
  • a distance of about 15 km separates, for example, the frigate from the high-value building.
  • Two buildings C1, C2, called thereafter buildings consorts, follow the frigate.
  • the adjacent buildings C1, C2 are for example located in a circular zone of 6.5 km radius centered on the frigate F.
  • the frigate can fulfill its mission only if it knows what a hostile aircraft aims hence the need to predict the intended target.
  • the figure 1 present at a given moment, by a point H, the position of a hostile aircraft.
  • two trajectories T1, T2 are for example still possible. It is nevertheless necessary to predict as early as possible what is the right trajectory.
  • calculation means define the trajectory of a missile so that it meets the predicted trajectory of the hostile aircraft, the point of impact between the two gears taking place at the intersection of the two trajectories.
  • Hostile aircraft are for example missiles with great maneuverability, especially for short turns.
  • the figure 2 illustrates main steps for the implementation of the method according to the invention.
  • a first step 1 predicts a goal point targeted by a spotted aircraft, including hostile.
  • a second step 2 determines a fictitious point of impact according to the predicted objective goal point.
  • a third step 3 determines a trajectory of the aircraft ending at the previously determined fictitious impact point.
  • This trajectory is subsequently taken into account by anti-aircraft means, a missile for example, to define a meeting point between the latter and the hostile aircraft to which this trajectory is attributed, the destruction of the hostile aircraft being done by example at this meeting point.
  • anti-aircraft means a missile for example
  • a fictitious point of impact to define the trajectory of the identified aircraft and not using the predicted objective point, improves makes the chances of success of hitting a hostile aircraft. Indeed, once the objective point of the aircraft predicts, several trajectories are possible between this aircraft and the predicted objective point. All these trajectories can not for example be memorized by the calculation means associated with an anti-aircraft missile, these calculation means defining in particular from a predicted trajectory of the aircraft the meeting point of the latter with the missile.
  • a single trajectory can for example be memorized by the calculation means whereas by playing on one of the ends of this trajectory, the meeting point calculated on this trajectory can effectively correspond to the actual encounter of the missile or any other means of air defense and hostile aircraft.
  • An objective of the method according to the invention is therefore to provide the anti-aircraft missile, based on radar information and the position of the ships, the predicted position of the impact between a hostile aircraft and the missile so as to promote interception of the hostile aircraft.
  • the figure 3 illustrates an example of possible implementation of the method according to the invention by two substeps 11, 12, a first substep 11 of classification of potentially attackable ships followed by a second substep of determining the target objective .
  • the figure 4 present in the plane ( x, y ) the position O of a analyzed building and the position D of a hostile aircraft, all the buildings being analyzed successively.
  • the curve 41 represents a cubic trajectory, corresponding to the relation (1), for which the definition of the boundary conditions makes it possible to define the coefficients of the relation (1).
  • a principle adopted consists, for example, in associating a ship with a probability Pcap that is all the greater as the aircraft's heading of the runway. compared to the analyzed building is weak.
  • the probability Pcap is equal to 0. If ⁇ is between ⁇ min and ⁇ max, the probability decreases linearly from 1 to 0 as illustrated by figure 5 it is 1 when ⁇ is less than ⁇ min.
  • the hypothesis is for example that the closer a target is to a ship, the more likely it is to be targeted.
  • Relation (4) thus ensures a rather severe discrimination in distance between 5 km and 15 km.
  • the objective is to determine which vessels are being used to maneuver the hostile aircraft. This detection is based for example on the exploitation of the results of a linear regression on the last estimated positions.
  • the purpose of the linear regression on the last estimated positions makes it possible as far as possible to avoid an error in estimating the direction taken by the hostile aircraft. Only for example the window containing the last four positions estimated by the multifunction radar is considered.
  • the figure 6 illustrates the maneuver detection criterion.
  • a hostile aircraft H has successively three speed vectors V 1 , V 2 , V 3 .
  • the probability of maneuvering depends, for example, on the relative position of the last three speed vectors. V 1 , V 2 , V 3 relative to the aforementioned line 61, this probability increasing when these vectors are successively approaching the line, that is to say that the angle they make with the line decreases.
  • the probability Pm freezes at 1, that is to say, it no longer intervenes in the combination with the other criteria.
  • the probability Pm is fixed at 1 for example after a given number of speed vectors. V 4 successive aircraft on the same side of the line; this number may be equal for example to 3.
  • the classification of the ships is done, by combining for each of them the results of the three previously defined probabilities Pcap , Pdis and Pm.
  • the first possibility is simply to detain the vessel with the probability of being targeted at the highest Pv .
  • the second possibility is to calculate a center of gravity from the position of each weighted vessel by its probability of being targeted Pv, the calculated center of gravity then being considered as the point targeted by the aircraft. This second solution makes it possible to eliminate discontinuities.
  • the second step 2 determines a fictitious point of impact according to this predicted objective, this objective possibly being, for example, the vessel with the highest probability of be targeted or the center of gravity as previously calculated.
  • the second step 2 makes it possible to approximate the predicted cubic trajectory. of the real trajectory, in particular by reducing its curvature.
  • the second step 2 consists, in particular, of the target objective determined in step 1, to calculate a fictitious point of impact which reduces the curvature, by reducing the distance D and the heading angle ⁇ when these are too important.
  • the reduction of the curvature of the cubic trajectory thus brings the latter closer to the real trajectory.
  • the fictitious point of impact is for example located on the line segment between the predicted objective objective and the orthogonal projection of this predicted objective on the line borne by the speed vector of the hostile aircraft as illustrated by FIG. figure 8 .
  • the predicted objective is, for example, either the vessel with the highest probability of being targeted or the center of gravity of vessels weighted by their probabilities of being targeted.
  • the figure 8 represents by a point P and a vector V , the position and the speed vector of a hostile aircraft, the torque ( P, V ) still being called track as it was seen previously.
  • the second step determines for example a fictitious impact point I located on the line segment 81 between the position 0 of the predicted objective, located for example in the center of the x, y axis system , and the orthogonal projection N from this objective on the right 82 passing through the position P of the aircraft and carried by its speed vector V .
  • This fictitious point of impact is used as a new boundary condition to define the predicted cubic trajectory, starting from the fact that this trajectory ends at this point of fictitious impact.
  • the shape of the curvature is given by the relation (5) and the decrease of D and ⁇ decreases the curvature.
  • the figure 9 shows that the new distance D ' between the aircraft and the fictitious point of impact is less than the distance D between the predicted objective and the aircraft. It is the same for the course angles ⁇ ', ⁇ .
  • the coefficient ⁇ is a function of the distance D and the angle of heading ⁇ .
  • This coefficient ⁇ can for example be defined by neglecting the influence of the distance D. This can be especially enabled by the fact that the targets concerned are for example between 5 km and 15 km, in this range of distance only the influence the heading angle ⁇ being preponderant.
  • the figure 10 illustrates with a diagram an example of a possible determination of the coefficient ⁇ represented on the ordinate as a function of the heading angle ⁇ represented on the abscissa.
  • the coefficient ⁇ is limited for example to 0.5, especially not to reduce too much the length of the cubic trajectory. Indeed, the time the hostile aircraft has to travel the cubic trajectory to the point of fictitious impact must be large enough to allow an anti-aircraft missile to calculate the interception time. In this case, the fictitious impact point I is located on the first half of the segment [ ON ] starting from the position O of the predicted target objective.
  • a new cubic trajectory 101 is calculated in the third step 3 of the method according to the invention taking into account a point of fictitious impact as defined above. As the radius of curvature of the new cubic trajectory 101 has significantly decreased with respect to the first cubic trajectory 73, this new cubic trajectory is considerably closer to the real trajectory.
  • the trajectory 101 thus defined is then provided for example to an anti-aircraft missile whose calculation means will determine its point of intercept with the aircraft on the same trajectory.

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  • Engineering & Computer Science (AREA)
  • General Engineering & Computer Science (AREA)
  • Chemical & Material Sciences (AREA)
  • Combustion & Propulsion (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Radar Systems Or Details Thereof (AREA)
  • Regulating Braking Force (AREA)

Abstract

L'invention concerne un procédé de prédiction de la trajectoire d'un aéronef hostile.The invention relates to a method for predicting the trajectory of a hostile aircraft.

Le procédé comporte une première étape (1) de prédiction d'un point d'objectif visé par un aéronef, une deuxième étape (2) de détermination d'un point d'impact fictif fonction du point d'objectif prédit et une troisième étape (3) de détermination d'une trajectoire finissant sur le point d'impact fictif.The method comprises a first step (1) for predicting an objective point targeted by an aircraft, a second step (2) for determining a fictitious impact point according to the predicted objective point, and a third step (3) determining a trajectory ending at the fictitious impact point.

Application : Défense navale antiaérienne.

Figure imgaf001
Application: Naval anti-aircraft defense.
Figure imgaf001

Description

La présente invention concerne un procédé de prédiction de la trajectoire d'un aéronef hostile. Elle concerne notamment la défense antiaérienne navale par la prédiction de l'objectif visé par un aéronef hostile attaquant un navire parmi plusieurs possibles, l'aéronef pouvant être par exemple un missile. Plus généralement l'invention s'applique à toutes défenses antiaériennes où il est nécessaire de prévoir la cible attaquée parmi plusieurs.The present invention relates to a method for predicting the trajectory of a hostile aircraft. It concerns in particular the naval air defense by the prediction of the objective of a hostile aircraft attacking a ship among several possible, the aircraft may be for example a missile. More generally, the invention applies to all anti-aircraft defenses where it is necessary to provide the attacked target among several.

Un ensemble de navires susceptible d'être attaqué par des aéronefs hostiles est constitué par exemple d'une frégate, d'un bâtiment naval important armé et de plusieurs bâtiments navals importants non nécessairement armés. La frégate est par exemple suivie à une distance d'environ 15 km pour le bâtiment naval armé, les deux bâtiments non armés suivant la frégate de façon plus rapprochée. Le bâtiment important armé a de puissants moyens de défense pour se protéger, c'est par exemple un porte-avions, mais il nécessite néanmoins d'être défendu par une première barrière de défense constituée de la frégate. Cette dernière doit par exemple supprimer 80 % des dangers.A set of ships that may be attacked by hostile aircraft is, for example, a frigate, a major naval vessel and several important naval vessels that are not necessarily armed. The frigate is for example followed at a distance of about 15 km for the naval ship, the two unarmed buildings following the frigate more closely. The major armed building has powerful defenses to protect itself, such as an aircraft carrier, but it nevertheless requires to be defended by a first barrier of defense consisting of the frigate. The latter must for example remove 80% of the dangers.

En cas d'attaque aérienne, des systèmes permettent actuellement de prévoir lequel des bâtiments est visé par l'aéronef hostile, ce peut être a priori indifféremment la frégate, le bâtiment important armé ou un des bâtiments importants. Ces systèmes utilisent notamment des radars qui effectuent des mesures échantillonnées de la trajectoire d'un aéronef hostile, par exemple toutes les secondes. A chaque échantillonnage, un vecteur vitesse de l'aéronef est déduit. Une donnée constituée de la position mesurée et de la vitesse de l'aéronef est généralement appelée une piste. Le système de défense utilise la suite des pistes d'un aéronef hostile repéré pour prédire lequel des bâtiments est visé par cet aéronef. Les systèmes actuels présentent encore un taux d'incertitude qui constitue un point faible de leur action de défense antiaérienne.In the event of an air attack, systems currently make it possible to predict which of the buildings is targeted by the hostile aircraft, it can be a priori indifferently the frigate, the important armed building or one of the important buildings. These systems use in particular radars that perform sampled measurements of the trajectory of a hostile aircraft, for example every second. At each sampling, a velocity vector of the aircraft is deduced. Data consisting of the measured position and the speed of the aircraft is generally called a track. The defense system uses the suite of tracks of a hostile aircraft identified to predict which of the vessels is targeted by that aircraft. Current systems still have an uncertainty rate which is a weak point in their air defense action.

Le but de l'invention est notamment de réduire ce taux d'incertitude.The object of the invention is in particular to reduce this uncertainty rate.

A cet effet, l'invention a pour objet un procédé de prédiction de la trajectoire d'un aéronef hostile, caractérisé en ce que la trajectoire prédite finit sur un point d'impact fictif fonction d'un point d'objectif prédit visé par l'aéronef.To this end, the subject of the invention is a method for predicting the trajectory of a hostile aircraft, characterized in that the predicted trajectory ends on a fictitious impact point according to a predicted objective point targeted by the 'aircraft.

L'invention a pour principaux avantages qu'elle s'applique pour contrer de nombreux types d'aéronefs hostiles, qu'elle s'adapte à différents types de trajectoires de ces aéronefs et qu'elle peut s'adapter à des systèmes déjà existants.The main advantages of the invention are that it is applicable to countering many types of hostile aircraft, that it adapts to different types of trajectories of these aircraft and that it can adapt to existing systems. .

D'autres caractéristiques et avantages de l'invention apparaîtront à l'aide de la description qui suit faite en regard des dessins annexés qui représentent :

  • la figure 1 : un ensemble de bâtiments navals et un aéronef hostile repérés par leur position ;
  • la figure 2 : une succession d'étapes pour un exemple de mise en oeuvre possible du procédé selon l'invention ;
  • la figure 3 : une décomposition possible d'une première étape du procédé selon l'invention ;
  • la figure 4 : une trajectoire possible d'un aéronef hostile ;
  • la figure 5 : une loi de probabilité élémentaire fonction de l'angle de cap d'un aéronef hostile ;
  • la figure 6 : une évolution possible de vecteurs vitesses d'un aéronef hostile par rapport à un navire donné ;
  • la figure 7 : une trajectoire estimée d'un aéronef hostile et la trajectoire réelle de ce dernier ;
  • les figures 8 et 9 : une illustration d'une méthode possible pour obtenir un point d'impact fictif fonction d'un objectif visé par un aéronef hostile ;
  • la figure 10 : une illustration d'un exemple de loi possible donnant la position du point d'impact fictif précité en fonction de l'angle de cap de l'aéronef ;
  • la figure 11 : les trajectoires de la figure 7 ainsi qu'une trajectoire de l'aéronef tenant compte du point d'impact fictif précité.
Other characteristics and advantages of the invention will become apparent with the aid of the following description made with reference to the appended drawings which represent:
  • the figure 1 : a set of naval vessels and a hostile aircraft spotted by their position;
  • the figure 2 a succession of steps for an example of possible implementation of the method according to the invention;
  • the figure 3 a possible decomposition of a first step of the process according to the invention;
  • the figure 4 : a possible trajectory of a hostile aircraft;
  • the figure 5 : a basic probability law based on the heading angle of a hostile aircraft;
  • the figure 6 : a possible evolution of velocity vectors of a hostile aircraft with respect to a given ship;
  • the figure 7 : an estimated trajectory of a hostile aircraft and the actual trajectory of the latter;
  • the Figures 8 and 9 : an illustration of a possible method for obtaining a fictitious point of impact according to an objective targeted by a hostile aircraft;
  • the figure 10 : an illustration of an example of a possible law giving the position of the aforementioned fictitious impact point as a function of the heading angle of the aircraft;
  • the figure 11 : the trajectories of the figure 7 and a trajectory of the aircraft taking into account the aforementioned fictitious impact point.

La figure 1 présente un exemple d'ensemble de bâtiments représentés par leurs points d'emplacement F, C1, C2, HV. Une frégate F devance un bâtiment de haute valeur HV capable de se défendre, un porte-avions par exemple. Une distance d'environ 15 km sépare par exemple la frégate du bâtiment de haute valeur. Deux bâtiments C1, C2, appelés par la suite bâtiments consorts, suivent la frégate. Les bâtiments consorts C1, C2 sont par exemple situés dans une zone circulaire de 6,5 km de rayon centrée sur la frégate F. En cas d'alerte, la frégate ne peut remplir sa mission que si elle connaît ce que vise un aéronef hostile, d'où la nécessité de prédire la cible visée.The figure 1 shows an example of a set of buildings represented by their location points F, C1, C2, HV. A frigate F is ahead of a building of high value HV able to defend itself, an aircraft carrier for example. A distance of about 15 km separates, for example, the frigate from the high-value building. Two buildings C1, C2, called thereafter buildings consorts, follow the frigate. The adjacent buildings C1, C2 are for example located in a circular zone of 6.5 km radius centered on the frigate F. In case of alarm, the frigate can fulfill its mission only if it knows what a hostile aircraft aims hence the need to predict the intended target.

La figure 1 présente à un instant donné, par un point H, la position d'un aéronef hostile. A cet instant, deux trajectoires T1, T2 sont par exemple encore possibles. Il est nécessaire néanmoins de prédire le plus tôt possible quelle est la bonne trajectoire. Une fois la bonne trajectoire définie, celle-ci peut être transmise par exemple à un système de lancement de missiles antiaériens. Connaissant cette trajectoire, des moyens de calcul définissent la trajectoire d'un missile de telle sorte que celle-ci rencontre la trajectoire prédite de l'aéronef hostile, le point d'impact entre les deux engins ayant lieu à l'intersection des deux trajectoires. Les aéronefs hostiles sont par exemple des missiles présentant de grandes facilités de manoeuvres, notamment pour des virages courts.The figure 1 present at a given moment, by a point H, the position of a hostile aircraft. At this moment, two trajectories T1, T2 are for example still possible. It is nevertheless necessary to predict as early as possible what is the right trajectory. Once the proper trajectory is defined, it can be transmitted for example to an anti-aircraft missile launch system. Knowing this trajectory, calculation means define the trajectory of a missile so that it meets the predicted trajectory of the hostile aircraft, the point of impact between the two gears taking place at the intersection of the two trajectories. . Hostile aircraft are for example missiles with great maneuverability, especially for short turns.

La figure 2 illustre des étapes principales pour la mise en oeuvre du procédé selon l'invention.The figure 2 illustrates main steps for the implementation of the method according to the invention.

Une première étape 1 prédit un point d'objectif visé par un aéronef repéré, notamment hostile.A first step 1 predicts a goal point targeted by a spotted aircraft, including hostile.

Une deuxième étape 2 détermine un point d'impact fictif fonction du point prédit d'objectif visé.A second step 2 determines a fictitious point of impact according to the predicted objective goal point.

Enfin, une troisième étape 3 détermine une trajectoire de l'aéronef finissant sur le point d'impact fictif précédemment déterminé.Finally, a third step 3 determines a trajectory of the aircraft ending at the previously determined fictitious impact point.

Cette trajectoire est par la suite prise en compte par des moyens antiaériens, un missile par exemple, pour définir un point de rencontre entre ce dernier et l'aéronef hostile à qui est attribuée cette trajectoire, la destruction de l'aéronef hostile se faisant par exemple en ce point de rencontre. Faire appel à un point d'impact fictif pour définir la trajectoire de l'aéronef repéré et non pas faire appel au point d'objectif prédit, améliore en fait les chances de succès de frapper un aéronef hostile. En effet, une fois le point d'objectif de l'aéronef prédit, plusieurs trajectoires sont possibles entre cet aéronef et le point d'objectif prédit. Toutes ces trajectoires ne peuvent pas par exemple être mémorisées par les moyens de calcul associés à un missile antiaérien, ces moyens de calcul définissant notamment à partir d'une trajectoire prédite de l'aéronef le point de rencontre de celui-ci avec le missile. Selon l'invention, une seule trajectoire peut par exemple être mémorisée par les moyens de calcul tandis qu'en jouant sur une des extrémités de cette trajectoire, le point de rencontre calculé sur cette trajectoire peut effectivement correspondre à la rencontre réelle du missile ou de tout autre moyen de défense antiaérienne et de l'aéronef hostile. Un objectif du procédé selon l'invention est donc de fournir au missile antiaérien, à partir d'informations radar et de la position des navires, la position prédite de l'impact entre un aéronef hostile et le missile de façon à favoriser l'interception de l'aéronef hostile.This trajectory is subsequently taken into account by anti-aircraft means, a missile for example, to define a meeting point between the latter and the hostile aircraft to which this trajectory is attributed, the destruction of the hostile aircraft being done by example at this meeting point. Using a fictitious point of impact to define the trajectory of the identified aircraft and not using the predicted objective point, improves makes the chances of success of hitting a hostile aircraft. Indeed, once the objective point of the aircraft predicts, several trajectories are possible between this aircraft and the predicted objective point. All these trajectories can not for example be memorized by the calculation means associated with an anti-aircraft missile, these calculation means defining in particular from a predicted trajectory of the aircraft the meeting point of the latter with the missile. According to the invention, a single trajectory can for example be memorized by the calculation means whereas by playing on one of the ends of this trajectory, the meeting point calculated on this trajectory can effectively correspond to the actual encounter of the missile or any other means of air defense and hostile aircraft. An objective of the method according to the invention is therefore to provide the anti-aircraft missile, based on radar information and the position of the ships, the predicted position of the impact between a hostile aircraft and the missile so as to promote interception of the hostile aircraft.

La figure 3 illustre un exemple de mise en oeuvre possible du procédé selon l'invention par deux sous-étapes 11, 12, une première sous-étape 11 de classement des navires potentiellement attaquables suivie d'une deuxième sous-étape de détermination de l'objectif visé.The figure 3 illustrates an example of possible implementation of the method according to the invention by two substeps 11, 12, a first substep 11 of classification of potentially attackable ships followed by a second substep of determining the target objective .

Un des buts de la première sous-étape 11 est de classer les navires potentiels en fonction de leur probabilité d'être visés par l'aéronef hostile. Les critères pour définir une trajectoire de l'aéronef sont par exemple les suivants :

  • l'accélération maximale de l'aéronef hostile ;
  • l'alignement de la trajectoire ou du vecteur vitesse de l'aéronef avec la ligne de visée ;
  • la distance entre l'hostile et son but ;
  • la détection de manoeuvre.
One of the purposes of the first substep 11 is to classify potential vessels based on their likelihood of being targeted by the hostile aircraft. The criteria for defining a trajectory of the aircraft are for example the following:
  • the maximum acceleration of the hostile aircraft;
  • aligning the trajectory or velocity vector of the aircraft with the line of sight;
  • the distance between the hostile and his goal;
  • maneuver detection.

Concernant l'accélération maximale de l'aéronef hostile, celui-ci est supposé ne pas pouvoir dépasser une accélération maximale notée Γmax par exemple égale à 10 g, g étant l'accélération de la pesanteur. Cette limitation de l'accélération permet de ne pas prendre en considération les navires trop improbables dans la mesure où l'accélération maximale donne le rayon de courbure minimum de l'aéronef.Regarding the maximum acceleration of the hostile aircraft, it is assumed that it can not exceed a maximum acceleration noted Γmax for example equal to 10 g, where g is the acceleration of gravity. This limitation of the acceleration makes it possible not to take into consideration ships that are too improbable insofar as the maximum acceleration gives the minimum radius of curvature of the aircraft.

Une trajectoire cubique de l'aéronef hostile est par exemple définie dans le plan horizontal (x, y) par la relation cubique suivante : y = ax 3 + bx 3 + cx + d

Figure imgb0001
A cubic trajectory of the hostile aircraft is for example defined in the horizontal plane ( x, y ) by the following cubic relation: there = ax 3 + bx 3 + cx + d
Figure imgb0001

La figure 4 présente dans le plan (x, y) la position O d'un bâtiment analysé et la position D d'un aéronef hostile, tous les bâtiments étant analysés successivement. La courbe 41 représente une trajectoire cubique, répondant à la relation (1), pour laquelle la définition des conditions aux limites permet de définir les coefficients de la relation (1). L'aéronef présente un vecteur vitesse V faisant un angle Ψ avec la droite x passant par les points O et D précités, tel que la distance OD vaut D.
on a alors : Ψ = 0 , 5 arc sin 2 Γ 0 D 3 V 2

Figure imgb0002
The figure 4 present in the plane ( x, y ) the position O of a analyzed building and the position D of a hostile aircraft, all the buildings being analyzed successively. The curve 41 represents a cubic trajectory, corresponding to the relation (1), for which the definition of the boundary conditions makes it possible to define the coefficients of the relation (1). The aircraft presents a speed vector V making an angle Ψ with the line x passing through the points O and D above, such that the distance OD is D.
we then have: Ψ = 0 , 5 bow sin 2 Γ 0 D 3 V 2
Figure imgb0002

Par conséquent, un navire n'est plus atteignable par l'aéronef hostile si l'angle Ψ est supérieur en valeur absolue à l'angle Ψmax = 0 , 5 arc sin 2 Γmax D 3 V 2

Figure imgb0003
Γmax étant l'accélération maximale de l'aéronef.Consequently, a ship can no longer be reached by the hostile aircraft if the angle Ψ is greater in absolute value than the angle Ψmax = 0 , 5 bow sin 2 Γmax D 3 V 2
Figure imgb0003
 Where max is the maximum acceleration of the aircraft.

Les navires qui ne sont plus atteignables ne sont pas pris en compte dans le classement des navires potentiels.Ships that are no longer reachable are not considered in the ranking of potential vessels.

Concernant l'alignement de la trajectoire ou du vecteur vitesse de l'aéronef avec la ligne de visée, un principe retenu consiste par exemple à associer à un navire une probabilité Pcap d'autant plus forte que le cap de la piste de l'aéronef par rapport au bâtiment analysé est faible.Regarding the alignment of the trajectory or the speed vector of the aircraft with the line of sight, a principle adopted consists, for example, in associating a ship with a probability Pcap that is all the greater as the aircraft's heading of the runway. compared to the analyzed building is weak.

Si le cap de la piste par rapport au bâtiment analysé est noté Ψ, selon le principe retenu précédemment, si Ψ est supérieur à l'angle Ψmax défini par la relation (3) précédente, la probabilité Pcap est égale à 0. Si Ψ est compris entre Ψmin et Ψmax, la probabilité décroît linéairement de 1 à 0 comme l'illustre la figure 5, elle vaut 1 quant Ψ est inférieur à Ψ min.If the course of the track compared to the analyzed building is noted Ψ, according to the principle previously retained, if Ψ is greater than the angle Ψmax defined by the preceding relation (3), the probability Pcap is equal to 0. If Ψ is between Ψmin and Ψmax, the probability decreases linearly from 1 to 0 as illustrated by figure 5 it is 1 when Ψ is less than Ψ min.

Concernant la distance entre l'aéronef hostile et son but, l'hypothèse est par exemple faite que plus une cible est proche d'un navire, plus celui-ci est susceptible d'être visé.Regarding the distance between the hostile aircraft and its purpose, the hypothesis is for example that the closer a target is to a ship, the more likely it is to be targeted.

En notant Pdis la probabilité du navire d'être visé par l'aéronef hostile selon le critère distance, Pdis est défini par la relation suivante : Pdis = e − d 2 7

Figure imgb0004
avec d = D Df
Figure imgb0005

  • D est la distance de l'aéronef au navire
  • Df est une distance déterminée, par exemple Df =5.000m
By noting Pdis the probability of the ship being targeted by the hostile aircraft according to the distance criterion, Pdis is defined by the following relation: Pdis = e - d 2 7
Figure imgb0004
 with d = D Df
Figure imgb0005
  • D is the distance from the aircraft to the ship
  • Df is a determined distance, for example Df = 5.000m

La relation (4) assure alors ainsi une discrimination assez sévère en distance entre 5 km et 15 km.Relation (4) thus ensures a rather severe discrimination in distance between 5 km and 15 km.

Concernant la détection de manoeuvre, l'objectif est de déterminer quels sont les navires vers lesquels se déroule la manoeuvre de l'aéronef hostile. Cette détection repose par exemple sur l'exploitation des résultats d'une régression linéaire sur les dernières positions estimées. Le but de la régression linéaire sur les dernières positions estimées permet de se mettre autant que possible à l'abri d'une erreur d'estimation de la direction prise par l'aéronef hostile. Seule par exemple la fenêtre contenant les quatre dernières positions estimées par le radar multifonctions est considérée.With regard to maneuver detection, the objective is to determine which vessels are being used to maneuver the hostile aircraft. This detection is based for example on the exploitation of the results of a linear regression on the last estimated positions. The purpose of the linear regression on the last estimated positions makes it possible as far as possible to avoid an error in estimating the direction taken by the hostile aircraft. Only for example the window containing the last four positions estimated by the multifunction radar is considered.

La figure 6 illustre le critère de détection de manoeuvre. Un aéronef hostile H présente successivement trois vecteurs vitesses V 1, V 2, V 3. Plus le vecteur vitesse de l'aéronef s'approche de la droite 61, passant par le navire Ni considéré et l'aéronef, plus la probabilité Pm, appelée probabilité de manoeuvre, augmente. La probabilité de manoeuvre dépend par exemple de la position relative des trois derniers vecteurs vitesses V 1, V 2, V 3 par rapport la droite précitée 61, cette probabilité augmentant quand ces vecteurs se rapprochent successivement de la droite, c'est-à-dire que l'angle qu'ils font avec la droite diminue.The figure 6 illustrates the maneuver detection criterion. A hostile aircraft H has successively three speed vectors V 1 , V 2 , V 3 . The more the speed vector of the aircraft approaches the line 61, passing through the vessel Ni considered and the aircraft, the higher the probability Pm, called the maneuvering probability, increases. The probability of maneuvering depends, for example, on the relative position of the last three speed vectors. V 1 , V 2 , V 3 relative to the aforementioned line 61, this probability increasing when these vectors are successively approaching the line, that is to say that the angle they make with the line decreases.

Dès qu'un vecteur vitesse V 4 franchit la droite, c'est-à-dire que son angle relatif avec celle-ci change de signe, la probabilité Pm se fige à 1, c'est-à-dire qu'elle n'intervient plus dans la combinaison avec les autres critères. Pour réduire la sensibilité à des valeurs erronées, la probabilité Pm est figée à 1 par exemple après un nombre donné de vecteurs vitesse V 4 successifs de l'aéronef situé du même côté de la droite ; ce nombre peut être égal par exemple à 3.As soon as a speed vector V 4 crosses the line, that is to say that its relative angle with this one changes sign, the probability Pm freezes at 1, that is to say, it no longer intervenes in the combination with the other criteria. To reduce the sensitivity to erroneous values, the probability Pm is fixed at 1 for example after a given number of speed vectors. V 4 successive aircraft on the same side of the line; this number may be equal for example to 3.

Le classement des navires se fait, en combinant pour chacun d'eux les résultats des trois probabilités précédemment définies Pcap , Pdis et Pm. The classification of the ships is done, by combining for each of them the results of the three previously defined probabilities Pcap , Pdis and Pm.

Ainsi pour le navire n°i, sa probabilité Pv(i) d'être visé est égale au produit Pcap(i), Pdis(i), Pm(i). Thus, for ship No. i, its probability Pv (i) of being targeted is equal to the product Pcap (i), Pdis (i), Pm ( i ) .

Les navires sont par exemple classés selon la probabilité Pv= Pcapx Pdisx Pm. The ships are for example classified according to the probability Pv = Pcapx Pdisx Pm.

Pour la deuxième sous-étape 12 de détermination de l'objectif visé, deux possibilités sont par exemple possibles.For the second sub-step 12 of determining the objective, two possibilities are possible for example.

La première possibilité consiste simplement à retenir le navire ayant la probabilité d'être visé Pv la plus élevée.The first possibility is simply to detain the vessel with the probability of being targeted at the highest Pv .

La seconde possibilité consiste à réaliser le calcul d'un barycentre à partir de la position de chaque navire pondérée par sa probabilité d'être visé Pv, le barycentre calculé étant alors considéré comme le point visé par l'aéronef. Cette seconde solution permet notamment d'éliminer des discontinuités.The second possibility is to calculate a center of gravity from the position of each weighted vessel by its probability of being targeted Pv, the calculated center of gravity then being considered as the point targeted by the aircraft. This second solution makes it possible to eliminate discontinuities.

Dans le cas de quatre navires potentiels, la position O de l'objectif visé est alors par exemple donné par la relation suivante : O → = ∑ i = 1 4 Pv i . X → i ∑ i = 1 4 Pv i

Figure imgb0006
x (i) indiquant la position du ième navire.In the case of four potential vessels, the position O of the objective is then given for example by the following relation: O → = Σ i = 1 4 pv i . X → i Σ i = 1 4 pv i
Figure imgb0006
 x ( i ) indicating the position of the i th vessel.

Une fois réalisée la première étape 1 de prédiction d'un objectif visé par l'aéronef, la deuxième étape 2 détermine un point d'impact fictif fonction de cet objectif prédit, cet objectif pouvant être par exemple le navire de plus forte probabilité d'être visé ou le barycentre tel que calculé précédemment.Once the first step 1 of prediction of an objective targeted by the aircraft has been completed, the second step 2 determines a fictitious point of impact according to this predicted objective, this objective possibly being, for example, the vessel with the highest probability of be targeted or the center of gravity as previously calculated.

Il a été vu précédemment que la trajectoire d'un hostile a été approximée à bord d'un missile de défense, par exemple, par une trajectoire cubique 41.It has been previously seen that the trajectory of a hostile has been approximated aboard a defense missile, for example, by a cubic trajectory 41.

Pour D et Ψ grands, la courbure de la trajectoire cubique est donc importante. Ainsi, comme l'illustre la figure 7, si l'on se place au début de la manoeuvre 72 sur la trajectoire 71 d'un aéronef hostile à une distance d'environ 20 km avec un angle de cap Ψ environ égal à 60°, la trajectoire cubique calculée 73 s'éloigne de façon importante de la trajectoire vraie de l'aéronef.For D and Ψ large, the curvature of the cubic trajectory is important. Thus, as illustrated by figure 7 if it is placed at the beginning of the maneuver 72 on the trajectory 71 of a hostile aircraft at a distance of about 20 km with a heading angle Ψ approximately equal to 60 °, the calculated cubic trajectory 73 moves away important way of the true trajectory of the aircraft.

Néanmoins, si les moyens de calcul du missile de défense antiaérienne ne peuvent extrapoler qu'un seul type de trajectoire, en l'occurrence par exemple une trajectoire cubique, la deuxième étape 2 selon l'invention, permet de rapprocher la trajectoire cubique prédite 73 de la trajectoire réelle, notamment en réduisant sa courbure.Nevertheless, if the means for calculating the anti-aircraft defense missile can extrapolate only one type of trajectory, in this case for example a cubic trajectory, the second step 2 according to the invention makes it possible to approximate the predicted cubic trajectory. of the real trajectory, in particular by reducing its curvature.

La deuxième étape 2 consiste notamment, à partir de l'objectif visé déterminé lors de l'étape 1, à calculer un point d'impact fictif qui réduit la courbure, en réduisant la distance D et l'angle de cap Ψ lorsque ces derniers sont trop importants. La réduction de la courbure de la trajectoire cubique rapproche ainsi cette dernière de la trajectoire réelle.The second step 2 consists, in particular, of the target objective determined in step 1, to calculate a fictitious point of impact which reduces the curvature, by reducing the distance D and the heading angle Ψ when these are too important. The reduction of the curvature of the cubic trajectory thus brings the latter closer to the real trajectory.

Le point d'impact fictif est par exemple situé sur le segment de droite compris entre l'objectif visé prédit et la projection orthogonale de cet objectif prédit sur la droite portée par le vecteur vitesse de l'aéronef hostile comme l'illustre la figure 8. L'objectif visé prédit est par exemple soit le navire ayant la plus forte probabilité d'être visé, soit le barycentre des navires pondérés de leurs probabilités d'être visés.The fictitious point of impact is for example located on the line segment between the predicted objective objective and the orthogonal projection of this predicted objective on the line borne by the speed vector of the hostile aircraft as illustrated by FIG. figure 8 . The predicted objective is, for example, either the vessel with the highest probability of being targeted or the center of gravity of vessels weighted by their probabilities of being targeted.

Dans un système d'axes horizontaux perpendiculaires qui ne sont plus orientés comme ceux de la figure 4, la figure 8 représente par un point P et un vecteur V , la position et le vecteur vitesse d'un aéronef hostile, le couple (P,V ) étant encore appelé piste comme il a été vu précédemment.In a system of perpendicular horizontal axes which are no longer oriented like those of the figure 4 , the figure 8 represents by a point P and a vector V , the position and the speed vector of a hostile aircraft, the torque ( P, V ) still being called track as it was seen previously.

La deuxième étape détermine par exemple un point d'impact fictif I situé sur le segment de droite 81 compris entre la position 0 de l'objectif prédit, situé par exemple au centre du système d'axes x, y, et la projection orthogonale N de cet objectif sur la droite 82 passant par la position P de l'aéronef et portée par son vecteur vitesse V . Ce point d'impact fictif est utilisé comme nouvelle condition aux limites pour définir la trajectoire cubique prédite, partant du fait que cette trajectoire finit en ce point d'impact fictif. L'allure de la courbure est donnée par la relation (5) et la diminution de D et Ψ en diminue la courbure. La figure 9 montre que la nouvelle distance D' entre l'aéronef et le point d'impact fictif est inférieure à la distance D entre l'objectif prédit et l'aéronef. Il en est de même pour les angles de cap Ψ',Ψ.The second step determines for example a fictitious impact point I located on the line segment 81 between the position 0 of the predicted objective, located for example in the center of the x, y axis system , and the orthogonal projection N from this objective on the right 82 passing through the position P of the aircraft and carried by its speed vector V . This fictitious point of impact is used as a new boundary condition to define the predicted cubic trajectory, starting from the fact that this trajectory ends at this point of fictitious impact. The shape of the curvature is given by the relation (5) and the decrease of D and Ψ decreases the curvature. The figure 9 shows that the new distance D ' between the aircraft and the fictitious point of impact is less than the distance D between the predicted objective and the aircraft. It is the same for the course angles Ψ ', Ψ.

La position du point d'impact fictif I sur le segment [ON] 81, est donné par la relation suivante : OI = αON

Figure imgb0007
The position of the fictitious impact point I on the segment [ ON ] 81, is given by the following relation: OI = αON
Figure imgb0007

D'après les caractéristiques de la trajectoire cubique, le coefficient α est fonction de la distance D et de l'angle de cap Ψ. Ce coefficient α peut par exemple être défini en négligeant l'influence de la distance D. Cela peut être notamment permis par le fait que les cibles concernées sont par exemple situées entre 5 km et 15 km, dans cette plage de distance seule l'influence de l'angle de cap Ψ étant prépondérante.According to the characteristics of the cubic trajectory, the coefficient α is a function of the distance D and the angle of heading Ψ. This coefficient α can for example be defined by neglecting the influence of the distance D. This can be especially enabled by the fact that the targets concerned are for example between 5 km and 15 km, in this range of distance only the influence the heading angle Ψ being preponderant.

La figure 10 illustre par un diagramme un exemple de détermination possible du coefficient α représenté en ordonnée en fonction de l'angle de cap Ψ représenté en abscisse.The figure 10 illustrates with a diagram an example of a possible determination of the coefficient α represented on the ordinate as a function of the heading angle Ψ represented on the abscissa.

Aux petits angles Ψ, par exemple pour Ψ<20°, l'utilisation d'un point d'impact I ne se justifie par exemple pas. Dans ce cas α= 0, I = 0. Il n'y a pas de point d'impact fictif. Le point d'impact pris en compte est l'objectif visé prédit.At small angles Ψ, for example for Ψ <20 °, the use of a point of impact I is not justified for example. In this case α = 0 , I = 0. There is no point of fictitious impact. The point of impact taken into account is the predicted objective.

Quand l'angle Ψ est supérieur à 70° par exemple, le coefficient α est limité par exemple à 0,5, notamment pour ne pas trop réduire la longueur de la trajectoire cubique. En effet, le temps que met l'aéronef hostile pour parcourir la trajectoire cubique jusqu'au point d'impact fictif doit être suffisamment grand pour permettre à un missile antiaérien de calculer le temps d'interception. Dans ce cas, le point d'impact fictif I est situé sur la première moitié du segment [ON] en partant de la position O de l'objectif visé prédit.When the angle Ψ is greater than 70 ° for example, the coefficient α is limited for example to 0.5, especially not to reduce too much the length of the cubic trajectory. Indeed, the time the hostile aircraft has to travel the cubic trajectory to the point of fictitious impact must be large enough to allow an anti-aircraft missile to calculate the interception time. In this case, the fictitious impact point I is located on the first half of the segment [ ON ] starting from the position O of the predicted target objective.

La figure 11 reprend les trajectoires 71, 73 de la figure 7. Une nouvelle trajectoire cubique 101 est calculée dans la troisième étape 3 du procédé selon l'invention en tenant compte d'un point d'impact fictif tel que défini précédemment. Le rayon de courbure de la nouvelle trajectoire cubique 101 ayant nettement diminué par rapport à la première trajectoire cubique 73, cette nouvelle trajectoire cubique s'est considérablement rapprochée de la trajectoire réelle.The figure 11 resumes the trajectories 71, 73 of the figure 7 . A new cubic trajectory 101 is calculated in the third step 3 of the method according to the invention taking into account a point of fictitious impact as defined above. As the radius of curvature of the new cubic trajectory 101 has significantly decreased with respect to the first cubic trajectory 73, this new cubic trajectory is considerably closer to the real trajectory.

La trajectoire 101 ainsi définie est ensuite fournie par exemple à un missile antiaérien dont les moyens de calcul vont déterminer son point d'interception avec l'aéronef sur cette même trajectoire.The trajectory 101 thus defined is then provided for example to an anti-aircraft missile whose calculation means will determine its point of intercept with the aircraft on the same trajectory.

La mise en oeuvre du procédé selon l'invention a été illustrée pour la défense antiaérienne de navires. Néanmoins, le procédé selon l'invention peut s'appliquer à la défense antiaérienne d'un ensemble de bâtiments terrestres, mobiles ou non.The implementation of the method according to the invention has been illustrated for the anti-aircraft defense of ships. Nevertheless, the method according to the invention can be applied to the anti-aircraft defense of a set of land buildings, mobile or not.

Claims (18)

Procédé de prédiction de la trajectoire d'un aéronef hostile (HV, C1, CL, F) vis-à-vis de bâtiments, caractérisé en ce que la trajectoire prédite (101) finit sur un point d'impact fictif (I) fonction d'un point d'objectif prédit (O) visé par l'aéronef (H).Method for predicting the trajectory of a hostile aircraft (HV, C1, CL, F) vis-à-vis buildings, characterized in that the predicted trajectory (101) ends on a point of fictitious impact ( I ) function a predicted objective point ( O ) targeted by the aircraft (H). Procédé selon la revendication 1, caractérisé en ce que l'objectif prédit à un instant donné est le bâtiment (HV, C1, C2, F) ayant la plus forte probabilité d'être visé par l'aéronef (H) en fonction des paramètres de vol de ce dernier.Method according to Claim 1, characterized in that the objective predicted at a given instant is the building (HV, C1, C2, F) with the highest probability of being targeted by the aircraft (H) according to the parameters flight of the latter. Procédé selon la revendication 1, caractérisé en ce que l'objectif prédit est le barycentre des bâtiments (HV, C1, C2, F) susceptibles d'être visés par l'aéronef (H) pondérés par leur probabilité d'être visés par ce dernier.Method according to claim 1, characterized in that the predicted objective is the centroid of the buildings (HV, C1, C2, F) likely to be targeted by the aircraft (H) weighted by their probability of being targeted by this latest. Procédé selon l'une quelconque des revendications précédentes, caractérisé en ce qu'il comprend une première étape (1) de prédiction d'un point (O) d'objectif visé par un aéronef, une deuxième étape (2) de détermination d'un point d'impact fictif (I) fonction du point d'objectif prédit et une troisième étape (3) de détermination d'une trajectoire (101) finissant sur le point d'impact fictif.Method according to any one of the preceding claims, characterized in that it comprises a first step (1) for predicting an objective point ( O ) targeted by an aircraft, a second step (2) for determining an a fictitious impact point ( I ) according to the predicted objective point and a third step (3) for determining a trajectory (101) ending at the fictitious impact point. Procédé selon la revendication 4, caractérisé en ce que la première étape (1) comporte une première sous-étape (11) de classement des bâtiments (HV, C1, C2, F) en fonction de leur probabilité d'être visés par l'aéronef hostile.Method according to claim 4, characterized in that the first step (1) comprises a first sub-step (11) of classification of the buildings (HV, C1, C2, F) according to their probability of being covered by the hostile aircraft. Procédé selon la revendication 5, caractérisé en ce que la probabilité est fonction de l'accélération maximale de l'aéronef hostile.Method according to claim 5, characterized in that the probability is a function of the maximum acceleration of the hostile aircraft. Procédé selon l'une quelconque des revendications 5 ou 6, caractérisé en ce que la probabilité est fonction de l'angle de cap (Ψ) de l'aéronef défini par l'angle que fait le vecteur vitesse de l'aéronef avec sa ligne de visée.Method according to one of Claims 5 or 6, characterized in that the probability is a function of the heading angle (Ψ) of the aircraft defined by the angle made by the speed vector of the aircraft with its line of sight. Procédé selon l'une quelconque des revendications 5 à 7, caractérisé en ce que la probabilité est fonction de la distance de l'hostile au bâtiment.Method according to any one of claims 5 to 7, characterized in that the probability is a function of the distance of the hostile to the building. Procédé selon l'une quelconque des revendications 5 à 8, caractérisé en ce que la probabilité est fonction d'une probabilité de manoeuvre (Pm) elle-même fonction de l'évolution du vecteur vitesse par rapport à la droite reliant l'aéronef au bâtiment, la probabilité augmentant quand le vecteur s'approche de cette droite, et restant figée à 1 lorsqu'il franchit la droiteMethod according to any one of claims 5 to 8, characterized in that the probability is a function of a maneuvering probability ( Pm ) which is itself a function of the evolution of the velocity vector with respect to the straight line connecting the aircraft to the building, the probability increasing when the vector approaches this line, and remaining fixed at 1 when it crosses the right Procédé selon la revendication 9, caractérisé en ce que la probabilité de manoeuvre (Pm) se fige à 1 après qu'un nombre donné de vecteurs vitesse successifs ( V 4) soit resté du même côté de la droite.Method according to claim 9, characterized in that the maneuvering probability (Pm) freezes at 1 after a given number of successive velocity vectors ( V 4 ) stayed on the same side of the line. Procédé selon l'une quelconque des revendications précédentes, caractérisé en ce que le point d'impact fictif (I) est situé sur le segment de droite (81) compris entre le point d'objectif prédit (O) et la projection (N) de ce point sur la droite (82) portée par le vecteur vitesse ( V ) de l'aéronef.Method according to one of the preceding claims, characterized in that the imaginary point of impact ( I ) lies on the line segment (81) between the predicted objective point ( O ) and the projection (N). from this point on the right (82) carried by the speed vector ( V ) of the aircraft. Procédé selon la revendication 11, caractérisé en ce que lorsque l'angle de cap (Ψ) de l'aéronef est grand, le point d'impact fictif (I) constitue le milieu du segment (81).A method according to claim 11, characterized in that when the heading angle (Ψ) of the aircraft is large, the fictitious point of impact ( I ) constitutes the middle of the segment (81). Procédé selon l'une quelconque des revendications 11 ou 12 caractérisé en ce que l'angle de cap (Ψ) de l'aéronef est faible, le point d'impact fictif est égal au point d'objectif prédit (O).Method according to any one of claims 11 or 12 characterized in that the angle of heading (Ψ) of the aircraft is low, the fictitious point of impact is equal to the predicted objective point ( O ). Procédé selon l'une quelconque des revendications 11 à 13, caractérisé en ce que lorsque l'angle de cap (Ψ) est compris entre deux angles donnés, la position du point d'impact fictif (I) varie du point d'objectif prédit (O) pour l'angle (Ψ) le plus faible, au milieu du segment (61) pour l'angle (Ψ) le plus élevé.Method according to any one of claims 11 to 13, characterized in that when the heading angle (Ψ) is between two given angles, the position of the imaginary point of impact ( I ) varies from the objective point predicts ( O ) for the lowest angle (Ψ), in the middle of the segment (61) for the highest angle (Ψ). Procédé selon la revendication 14, caractérisé en ce que la position du point d'impact fictif (I) varie linéairement en fonction de l'angle de cap Ψ.Method according to Claim 14, characterized in that the position of the imaginary point of impact ( I ) varies linearly as a function of the heading angle Ψ. Procédé selon l'une quelconque des revendications 14 à 15, caractérisé en ce que la position du point d'impact fictif (I) varie pour les angles de cap (Ψ) variant sensiblement entre 20° et 70°.Method according to one of Claims 14 to 15, characterized in that the position of the fictitious impact point ( I ) varies for the course angles (Ψ) varying substantially between 20 ° and 70 °. Procédé selon l'une quelconque des revendications précédentes, caractérisé en ce que la trajectoire prédite (101) de l'aéronef est définie par une équation cubique.Method according to any one of the preceding claims, characterized in that the predicted trajectory (101) of the aircraft is defined by a cubic equation. Procédé selon l'une quelconque des revendications précédentes, caractérisé en ce que les bâtiments (HV, C1, C2, F) sont des navires.Method according to one of the preceding claims, characterized in that the buildings (HV, C1, C2, F) are ships.
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CN111783358A (en) * 2020-07-02 2020-10-16 哈尔滨工业大学 Bayesian estimation-based long-term trajectory prediction method for hypersonic aircraft
CN111783358B (en) * 2020-07-02 2022-10-04 哈尔滨工业大学 Bayesian estimation-based long-term trajectory prediction method for hypersonic aircraft

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