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

Abstract

The invention relates to a method for predicting the trajectory of a hostile aircraft.

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: Naval anti-aircraft defense.

Description

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.

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.

The object of the invention is in particular to reduce this uncertainty rate.

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.

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. .

• 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.

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.

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.

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.

Finally, 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. 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.

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 .

• 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.

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.

A cubic trajectory of the hostile aircraft is for example defined in the horizontal plane ( x, y ) by the following cubic relation: $$\mathrm{there}={\mathit{<figure-callout\; id="3"\; label="ax"\; filenames="imgf0002.png"\; state="\{\{state\}\}">ax</figure-callout>}}^3+{\mathit{<figure-callout\; id="3"\; label="bx"\; filenames="imgf0002.png"\; state="\{\{state\}\}">bx</figure-callout>}}^3+\mathit{cx}+d$$

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: $$\mathrm{\Psi }=0,5\mathit{<figure-callout\; id="2"\; label="bow\; sin"\; filenames="imgf0002.png"\; state="\{\{state\}\}">bow\; </figure-callout>}\sin \left(\frac{2\mathrm{\Gamma }\left(0\right)\mathrm{D}}{3{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0002.png"\; state="\{\{state\}\}">V</figure-callout>}}^2}\right)$$

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 $$\mathrm{\Psi max}=0,5\mathit{<figure-callout\; id="2"\; label="bow\; sin"\; filenames="imgf0002.png"\; state="\{\{state\}\}">bow\; </figure-callout>}\sin \left(\frac{2\mathrm{\Gamma max}\mathit{D}}{3{\mathrm{<figure-callout\; id="2"\; label="V"\; filenames="imgf0002.png"\; state="\{\{state\}\}">V</figure-callout>}}^2}\right)$$

Where max is the maximum acceleration of the aircraft.

Ships that are no longer reachable are not considered in the ranking of potential vessels.

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.

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.

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.

avec $d=\frac{D}{\mathit{Df}}$

• 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: $$\mathit{Pdis}=e-\frac{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="imgf0002.png"\; state="\{\{state\}\}">d</figure-callout>}}^2}{7}$$

with $d=\frac{D}{\mathit{Df}}$

• D is the distance from the aircraft to the ship
• Df is a determined distance, for example Df = 5.000m

Relation (4) thus ensures a rather severe discrimination in distance between 5 km and 15 km.

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.

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.

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.

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.

Thus, for ship No. i, its probability Pv (i) of being targeted is equal to the product Pcap (i), Pdis (i), Pm ( i ) .

The ships are for example classified according to the probability Pv = Pcapx Pdisx Pm.

For the second sub-step 12 of determining the objective, two possibilities are possible for example.

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.

x (i) indiquant la position du i^ème navire.In the case of four potential vessels, the position O of the objective is then given for example by the following relation: $$\overrightarrow{O}=\frac{{\displaystyle \underset{i=1}{\overset{4}{\Sigma }}}\mathit{pv}\left(i\right)\mathrm{.}\overrightarrow{X}\left(i\right)}{{\displaystyle \underset{i=1}{\overset{4}{\Sigma }}}\mathit{pv}\left(i\right)}$$

x ( i ) indicating the position of the i ^th vessel.

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.

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.

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.

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.

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.

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.

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.

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.

The position of the fictitious impact point I on the segment [ ON ] 81, is given by the following relation: $$\mathit{OI}=\mathit{\alpha ON}$$

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.

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.

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.

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.

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.

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.

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)

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). 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. 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. 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. 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. Method according to claim 5, characterized in that the probability is a function of the maximum acceleration of the hostile aircraft. 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. 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. Method 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 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. 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. 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). 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 ). 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). 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. 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 °. 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. Method according to one of the preceding claims, characterized in that the buildings (HV, C1, C2, F) are ships.

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