Collaborative interception area rapid calculation method for high maneuvering target

Abstract

The invention discloses a rapid calculation method for a collaborative interception area for a high maneuvering target, and belongs to the technical field of collaborative guidance control of multiple aircrafts. The method comprises the following steps: establishing an aircraft motion model and a target motion model; based on the aircraft motion model and the target motion model, respectively calculating an interceptable area of the aircraft at the predicted hit moment and a maneuvering escape area of the target at the predicted hit moment; projecting the maneuvering escape area and the aircraft interceptable area from a three-dimensional space to a two-dimensional plane, and dividing the approximated bounded area into a high probability area, a medium probability area and a low probability area according to the drop point probability; and calculating the minimum number of interceptors required for covering the high-probability area, the medium-probability area and the low-probability area and the circle center coordinate and the covering radius of each interceptor, and preferentially covering the high-probability area. According to the invention, full coverage of the target prediction maneuvering escape area is realized, the real-time requirement in an actual task can be met, and the method has a good application prospect.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-aircraft cooperative guidance and control, and in particular relates to a method for quickly calculating a cooperative interception zone for a highly maneuverable target. Background Art

[0002] Space defense technology has made significant progress in recent years, but at the same time, the intelligence and maneuverability of targets are also increasing. Hypersonic vehicles, in particular, combine high speed and high maneuverability with excellent concealment and penetration capabilities. Therefore, the interception of highly maneuverable targets is an urgent problem to be solved. Given the high speed and high maneuverability of targets, interceptors lack speed and maneuverability, making it difficult for a single interceptor to effectively intercept such targets. Therefore, coordinated interception by multiple interceptors has become a research hotspot in recent years. However, due to the inaccurate detection of highly maneuverable targets in modern complex missions, early warning systems struggle to obtain accurate target motion information and can only determine the target's likely location. Furthermore, each interceptor has a limited interceptable area. To ensure that the interception areas of multiple interceptors nearly or completely cover the target's likely location, efficient area coverage optimization methods are needed.

[0003] Area coverage optimization primarily addresses the positioning of interceptors. Specifically, each interceptor is assigned an optimal position based on a corresponding algorithm and ultimately remains there, achieving optimal perception and coverage of a given mission area. For example, combining the virtual force algorithm with the Lloyd-Voronoi algorithm reduces system redundancy and improves the overall area coverage of the system. Alternatively, intelligent algorithms are used to optimize area coverage, deriving a closed-form optimal intercept guidance law for accelerating targets. For multi-interceptor coordinated interception with uncertain mid-range target information, a stochastic optimization problem is proposed to design the optimal parameters for the relative motion between the aircraft and the target at the handover time, ensuring interception probability while using fewer interceptors. While virtual force-based coverage methods offer rapid convergence in solving coverage problems, their optimization performance needs improvement. Intelligent algorithm-based coverage methods also suffer from slow convergence and limited exploration capabilities, undermining the real-time requirements of practical missions. Therefore, a more effective area coverage optimization method is urgently needed. Summary of the Invention

[0004] Technical issues to be solved:

[0005] In order to avoid the shortcomings of the existing technology, the present invention provides a method for quickly calculating the cooperative interception area for highly maneuverable targets. It proposes a method based on the disk coverage theory to decompose the elliptical area into a combination of multiple disks, and analytically calculates the minimum number of interceptors and their positions required for coverage. It also proposes a method for quickly calculating the cooperative interception area of ​​interceptors. Combined with probability analysis (high, medium, and low probability area division), the target maneuver escape area is approximated from unbounded to bounded, and the coverage strategy is optimized through probability layering. The number of interceptors used and the center of each interceptable area are analyzed. Subsequently, the proposed method is verified through simulation, and the full coverage of the target's predicted maneuver escape area is stably achieved. The algorithm operation time is significantly shortened compared with the optimized area coverage method, which can meet the real-time requirements of actual tasks and has good application prospects.

[0006] The technical solution of the present invention is: a method for quickly calculating a coordinated interception zone for a high-maneuverability target, the specific steps of which are as follows:

[0007] The aircraft motion model is established based on the line-of-sight coordinate system at the initial moment; the target motion model is constructed in the inertial coordinate system;

[0008] Based on the aircraft motion model and the target motion model, respectively calculating the interceptable area of ​​the aircraft at the predicted impact moment and the maneuverable escape area of ​​the target at the predicted impact moment;

[0009] Projecting the maneuverable escape area and the aircraft interceptable area from three-dimensional space to a two-dimensional plane, approximating the unbounded characteristics of the maneuverable escape area through a bounded area, and dividing the approximated bounded area into a high probability area, a medium probability area, and a low probability area according to the probability of landing point;

[0010] Based on the disk covering theory, the minimum number of interceptors required to cover the high probability area, medium probability area and low probability area, as well as the center coordinates and coverage radius of each interceptor are analytically calculated, and the high probability area is covered first.

[0011] A further technical solution of the present invention is: the expression of the aircraft motion model is:

[0012]

[0013] Where A m ,B m for

[0014]

[0015] 0 3×3 ,I 3×3 are 3×3 zero matrix and identity matrix respectively; is the acceleration vector of the aircraft;

[0016] in, is the position vector of the aircraft, is the velocity vector;

[0017] The expression of the target motion model is:

[0018]

[0019] Where A T ,B T They are the system matrix and input matrix, as shown below:

[0020]

[0021] X T is the target position vector, U T is the acceleration vector of the target.

[0022] A further technical solution of the present invention is: the interceptable area is recorded as M(t0), which represents the motion state at time t0 and the control effect after time t0. e The set of positions that can be reached at any time is called the aircraft interceptable area; the expression is as follows:

[0023]

[0024] Where, t0 represents the initial time of the aircraft, t e Indicates the moment when the aircraft hits, a max Represents acceleration and vector; Indicates the coordinates of the zero control terminal position of the aircraft;

[0025] The maneuverable escape area is denoted as R and is expressed as:

[0026]

[0027] Where, X T (t e )and are the target hitting time t e The mean and covariance matrix of the motion state at each moment, N represents the normal distribution.

[0028] A further technical solution of the present invention is: the specific method of projecting the maneuverable escape area and the aircraft interceptable area from three-dimensional space to a two-dimensional plane includes: converting the mean point and covariance matrix of the target maneuverable escape area to a plane coordinate system through a conversion matrix from an inertial coordinate system to a line of sight coordinate system;

[0029] The projection of the aircraft interceptable area in the plane is expressed as:

[0030]

[0031] That is, (p y ,p z ) is the center of the circle and the radius is R(t e ,t0) disk;

[0032] The projection of the maneuverable escape area in the plane is:

[0033]

[0034] Where,

[0035]

[0036] Among them, L(q ε ,q β ) is the transformation matrix from the inertial coordinate system to the line of sight coordinate system, is the coordinate of the origin of the reference sight coordinate system in the inertial coordinate system, [x T (t e ),y T (t e ),z T (t e )] T is the coordinate of the mean point of the maneuvering escape area in the inertial coordinate system, is the covariance matrix of the maneuver escape region in the inertial coordinate system.

[0037] A further technical solution of the present invention is that the bounded area after the maneuverable escape area is approximated is an ellipse, which is expressed as follows:

[0038]

[0039] Where, σ y (t e ) and σ z (t e ) represent the major and minor axes of the ellipse respectively.

[0040] A further technical solution of the present invention is: the specific method of dividing the approximated bounded area into a high probability area, a medium probability area and a low probability area is:

[0041] The bounded area is defined as an ellipse, and based on the 3 sigma principle of Gaussian distribution, the ellipse is divided into the following principles:

[0042] High probability area: a sub-ellipse with the center of the ellipse as the circle center, the major semi-axis as the first threshold, and the minor semi-axis as the second threshold;

[0043] Medium probability area: the annular area with the center of the ellipse as the center, the major semi-axis at the third threshold and greater than the first threshold, and the minor semi-axis at the fourth threshold and greater than the second threshold, and the high probability area is deducted;

[0044] Low probability area: an annular area with the center of the ellipse as the center, the major semi-axis of the ellipse as the major semi-axis of the bounded area, and the minor semi-axis as the minor semi-axis of the ellipse as the bounded area, and the medium probability area is deducted.

[0045] A further technical solution of the present invention is that the high probability area, the medium probability area and the low probability area are divided as follows:

[0046] The semi-major axis is The minor axis is ellipse;

[0047] The semi-major axis is The minor axis is Subtract the ellipse

[0048] The semi-major axis is The minor axis is Subtract the ellipse

[0049] A further technical solution of the present invention is that the specific process of analytically calculating the minimum number of interceptors required to cover the high probability area, the medium probability area, and the low probability area, as well as the coordinates of the center of each interceptor and the coverage radius is as follows:

[0050] When the length of the major axis of the ellipse, the length of the minor axis and the radius of the disk satisfy b≤R≤a, 2(V-1)+1 disks are distributed equally along the major axis; the coordinates of the center of the 2(V-1)+1 disks are (0,0). Among them, it is necessary to meet R represents the radius of the disk, a represents the length of the major axis of the ellipse, b represents the length of the minor axis of the ellipse, and V represents the multiple of the radius of the circle to the major axis of the ellipse; the number of disks is the minimum number of interceptors;

[0051] When the length of the major axis of the ellipse, the length of the minor axis and the radius of the disk satisfy b = R; , 4 (V-1) disks are used to cover the ellipse boundary and the central area; the center coordinates of the 4 (V-1) disks are

[0052] When the length of the major axis, the minor axis and the radius of the disk satisfy R <b<MR; When , 2(M+1)(V-1)+M+1=(M+1)(2V-1) disks are used to cover the ellipse boundary and the central area;

[0053] The coordinates of the centers of 2(M+1)(V-1)+M+1=(M+1)(2V-1) disks are M represents the multiple of the circle radius to the minor axis of the ellipse;

[0054] When the ellipse center is offset, the center of the covering disk is translated to the offset ellipse center.

[0055] A further technical solution of the present invention is: the strategy of the disk covering the ellipse includes: after covering the high probability area, if it is necessary to cover the medium and low probability areas, the full area coverage is achieved by increasing the number of disks or adjusting the distribution direction of the disks.

[0056] A collaborative interception zone construction system for high-mobility targets, including the following modules:

[0057] The multi-source sensor module is used to obtain the target's motion information in real time, including position, velocity and acceleration, and transmit the data to the motion modeling module;

[0058] The motion modeling module includes an aircraft motion modeling unit and a target motion modeling unit; the aircraft motion modeling unit constructs the aircraft motion model based on the line of sight coordinate system at the initial moment; the target motion modeling unit constructs the target's random maneuver model based on the inertial coordinate system and in combination with the target's motion information;

[0059] an area calculation module, configured to calculate, based on the output of the motion modeling module, the interceptable area of ​​the aircraft at the predicted impact moment and the predicted maneuverable escape area of ​​the target;

[0060] The projection and probability division module includes a three-dimensional projection unit and a probability division unit; the three-dimensional projection unit projects the interceptable area and the maneuverable escape area from three-dimensional space to a two-dimensional plane; the probability division unit divides the bounded two-dimensional maneuverable escape area into high, medium, and low probability areas according to the landing point probability, wherein the high probability area is the center area of ​​the ellipse, and the medium and low probability areas are the annular areas expanding outwards respectively;

[0061] The collaborative interception zone generation module, based on the disk covering theory, analytically calculates the minimum number of interceptors required to cover the probability area, the coordinates of the center of each interceptor, and the coverage radius, and gives priority to covering high-probability areas;

[0062] The dynamic deployment optimization module updates the target motion information in real time according to the changes in the mission environment, adjusts the deployment strategy of the interceptor, and ensures full coverage of the maneuverable escape area.

[0063] Beneficial effects

[0064] The beneficial effects of the present invention are as follows: Based on geometric figure coverage theory, the present invention approximates the target maneuvering escape area and divides it into ellipses. Based on disk coverage theory, the low, middle, and high areas of the ellipse are selectively covered, which can stably achieve full coverage of the target's predicted maneuvering escape area. The specific effects are analyzed as follows:

[0065] 1. By projecting the three-dimensional target maneuvering escape area onto a two-dimensional plane and combining it with the geometric disk coverage theory to directly calculate the coverage parameters (such as the number of interceptors, center coordinates, and radius), the iterative optimization process of traditional intelligent algorithms (such as virtual force and Lloyd-Voronoi algorithm) is avoided. Simulation results show that the calculation time is significantly shortened compared with existing methods (see Figure 5 ), which can adapt to the real-time interception decision-making needs in a highly dynamic battlefield environment.

[0066] 2. Divide the target escape area into high, medium and low probability areas through probability stratification strategy, and give priority to covering the high probability area (see Figure 3 This approach prioritizes full coverage of areas where the target is most likely to occur, given limited resources (see Figure 4 ), thereby significantly improving the interception success rate and reducing the risk of missed interception.

[0067] 3. Based on disk coverage theory, we analytically calculate the minimum number of interceptors and dynamically adjust resource allocation through a prioritized coverage strategy. Compared with traditional methods, this approach reduces the number of interceptors deployed while ensuring effective coverage, thereby lowering system cost and complexity.

[0068] 4. By approximating the unbounded nature of the target's maneuvering escape region with a bounded region, and combining the covariance matrix and probability distribution to model the target's dynamic characteristics, the algorithm effectively addresses sensor measurement errors and the uncertainty of target maneuvers. Furthermore, projection and coordinate transformation methods enhance the algorithm's adaptability to dynamic switching between multiple coordinate systems.

[0069] 5. The technical solution is implemented through clear mathematical models and analytical formulas (such as the ellipse projection formula and the calculation formula for the coverage circle parameters), which can be directly encoded into a computer program. The algorithm's operation time is significantly reduced compared to using optimized area coverage methods, meeting the real-time requirements of actual missions and showing good application prospects. Simulation verification shows that this method can run stably in the MATLAB environment and has the potential for rapid porting to actual interception systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a schematic diagram of the overall flow of the method for quickly calculating the collaborative interception zone provided by the present invention.

[0071] Figure 2It is a two-dimensional plane projection schematic diagram of the aircraft interception area and the target maneuvering escape area provided by the present invention.

[0072] Figure 3 This is a schematic diagram of the division of low, medium and high probability areas provided by the present invention.

[0073] Figure 4 This is a high-probability area coverage result map provided by the present invention.

[0074] Figure 5 Schematic diagram of simulation time of two methods provided by the present invention. DETAILED DESCRIPTION

[0075] The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0076] The virtual force-based coverage method has the property of rapid convergence when solving the coverage problem, but its optimization effect needs to be improved. The coverage method based on the intelligent algorithm also has the problems of slow convergence and limited exploration ability, which reduces the real-time requirements in actual tasks. The present invention provides a method for quickly calculating the cooperative interception zone for highly maneuverable targets. The specific steps are as follows:

[0077] Step 1: Establish the aircraft motion model based on the initial line-of-sight coordinate system; build the target motion model in the inertial coordinate system;

[0078] Step 2: Based on the aircraft motion model and the target motion model, respectively calculating the interceptable area of ​​the aircraft at the predicted impact moment and the maneuverable escape area of ​​the target at the predicted impact moment;

[0079] Step 3: Project the maneuverable escape area and the aircraft interceptable area from three-dimensional space to a two-dimensional plane, and approximate the unbounded characteristics of the maneuverable escape area using bounded regions. The approximated bounded regions are divided into high-probability, medium-probability, and low-probability regions based on the probability of landing points.

[0080] Step 4: Based on the disk covering theory, the minimum number of interceptors required to cover the high probability area, medium probability area and low probability area, as well as the center coordinates and coverage radius of each interceptor are analytically calculated, and the high probability area is covered first.

[0081] The present invention provides a collaborative interception zone construction system for high-mobility targets, comprising the following modules:

[0082] The multi-source sensor module is used to obtain the target's motion information in real time, including position, velocity and acceleration, and transmit the data to the motion modeling module;

[0083] The motion modeling module includes an aircraft motion modeling unit and a target motion modeling unit; the aircraft motion modeling unit constructs the aircraft motion model based on the line of sight coordinate system at the initial moment; the target motion modeling unit constructs the target's random maneuver model based on the inertial coordinate system and in combination with the target's motion information;

[0084] an area calculation module, configured to calculate, based on the output of the motion modeling module, the interceptable area of ​​the aircraft at the predicted impact moment and the predicted maneuverable escape area of ​​the target;

[0085] The projection and probability division module includes a three-dimensional projection unit and a probability division unit; the three-dimensional projection unit projects the interceptable area and the maneuverable escape area from three-dimensional space to a two-dimensional plane; the probability division unit divides the bounded two-dimensional maneuverable escape area into high, medium, and low probability areas according to the landing point probability, wherein the high probability area is the center area of ​​the ellipse, and the medium and low probability areas are the annular areas expanding outwards respectively;

[0086] The collaborative interception zone generation module, based on the disk covering theory, analytically calculates the minimum number of interceptors required to cover the probability area, the coordinates of the center of each interceptor, and the coverage radius, and gives priority to covering high-probability areas;

[0087] The dynamic deployment optimization module updates the target motion information in real time according to the changes in the mission environment, adjusts the deployment strategy of the interceptor, and ensures full coverage of the maneuverable escape area.

[0088] The present invention solves the problems of poor real-time performance and low coverage efficiency in the prior art through innovative three-dimensional projection, probability stratification and disk coverage strategy.

[0089] The above technical solution will be further described below with reference to the accompanying drawings and embodiments:

[0090] In one embodiment, referring to Figure 1 As shown in the figure, a method for quickly calculating the cooperative interception zone for high-maneuverability targets is described. The specific steps are as follows:

[0091] Step 1: Establish the aircraft motion model based on the initial line-of-sight coordinate system; and assume the target motion model in the inertial coordinate system.

[0092] In the line-of-sight reference coordinate system, the position vector of the aircraft is The velocity vector is make The motion model of the aircraft is

[0093]

[0094] Where A m ,B m for

[0095]

[0096] 0 3×3 ,I 3×3 are 3×3 zero matrix and identity matrix respectively, is the acceleration vector of the aircraft.

[0097] Considering that target information needs to be obtained through external sensors such as satellites, early warning aircraft radars, or drone radars, the target motion model will be established in the inertial coordinate system. Assume that the target model is:

[0098]

[0099] Where A T ,B T Same as A m ,B m are the system matrix and input matrix of appropriate dimensions, as shown below:

[0100]

[0101] X T is the target position vector, U T is the acceleration vector of the target;

[0102] Step 2: Calculate the aircraft's interceptable area and the target's predicted maneuvering escape area based on the motion model.

[0103] Aircraft interceptable area: The aircraft is in the motion state at time t0 and under the control after time t0. e The set of positions that can be reached at any time is called the interceptable area of ​​the aircraft, denoted as M(t0) and expressed as:

[0104] The coordinates of the zero control terminal position of the aircraft are recorded as Assume that the initial motion state of the aircraft is According to the aircraft motion model:

[0105]

[0106] Where, C=[I 3×3 0 3×3 ],Φ m (t e ,t0) is the state transfer matrix of the aircraft motion model, that is,

[0107]

[0108] On input Under the constraints, the interceptable area of ​​the aircraft at time t0 can be expressed as

[0109]

[0110] Note: M(t0) is closely related to the initial time. If t0 is the handover point of mid-terminal guidance, it is the interceptable area when the mid-terminal guidance is handed over. Constrained, assuming |u mx (t)|≤a mx ,|u my (t)|≤a my ,|u mz (t)|≤a mz , then

[0111]

[0112] Note: The above formula is derived using the relationship between the norms ||·||2 and ||·||1, that is,

[0113]

[0114] Note a max =a mx +a my +a mz ,but

[0115]

[0116] Further, remember Therefore

[0117]

[0118] Therefore, the interceptable area of ​​the aircraft at time t0 is

[0119]

[0120] Where, t0 represents the initial time of the aircraft, t e Indicates the moment the aircraft hits the target.

[0121] The maneuverable escape area is denoted as R and is expressed as:

[0122]

[0123] That is, the estimated target maneuver escape area is state Obey the mean The variance is Infinite area. In the formula, X T (t e )and t e The mean and covariance matrix of the motion state at each moment.

[0124] The mean and covariance matrices are:

[0125]

[0126] Step 3: Approximate calculation of the target's maneuvering escape area

[0127] Since in actual engineering applications, the estimated target maneuvering escape area is usually taken as a certain bounded area with a certain probability, an approximate calculation is performed on the infinite area of ​​the estimated target maneuvering escape area in step 2.

[0128] Step 3-1: Reference Figure 2 As shown, the three-dimensional predicted target maneuver escape area and the aircraft interceptable area are projected into a two-dimensional plane.

[0129] and are the projections of the maneuverable escape area and the aircraft interceptable area on the plane EFGH, and are the velocity vectors of the aircraft and the target respectively.

[0130] The projection of the aircraft interceptable area on the plane EFGH can be expressed as

[0131]

[0132] That is, (p y ,p z ) is the center of the circle and the radius is R(t e ,t0) of the disk.

[0133] For the predicted target maneuver escape area in the inertial coordinate system, the projection of the area in the plane EFGH can be obtained after coordinate transformation:

[0134]

[0135] in,

[0136]

[0137] Among them, L(q ε ,q β ) is the transformation matrix from the inertial coordinate system to the line of sight coordinate system, is the coordinate of the origin of the reference sight coordinate system in the inertial coordinate system, [x T (t e ),y T (t e),z T (t e )] T is the coordinate of the mean point of the maneuvering escape area in the inertial coordinate system, is the covariance matrix of the maneuver escape region in the inertial coordinate system.

[0138] Step 3-2: Use bounded regions to approximate unbounded regions based on the actual environment.

[0139] use Nearly unbounded region

[0140]

[0141] Step 3-3: Reference Figure 3 As shown, the approximate area is divided according to the landing probability, and the range coordinate value is parsed.

[0142] Will Divided into three areas

[0143]

[0144] say is a high probability area, is the medium probability area, It is a low probability area.

[0145] therefore, is an ellipse on EFGH with its center at The semi-major axis is The minor axis is The three areas are as follows:

[0146] The semi-major axis is The minor axis is ellipse;

[0147] The semi-major axis is The minor axis is Subtract the ellipse

[0148] The semi-major axis is The minor axis is Subtract the ellipse

[0149] Step 4: Design a fast calculation method for the multi-aircraft coordinated interception zone

[0150] Since the target's maneuverable escape zone on a target-aircraft encounter platform can be approximated as an ellipse, while the aircraft's interceptable zone is a circle, the area coverage optimization problem is to cover the elliptical area with the fewest circles. Within the divided area, the high-probability zone is covered first. If medium- and low-probability zones are to be covered, the same method as above can be used to cover the top, bottom, left, and right areas.

[0151] Assume that the equation of the ellipse is

[0152]

[0153] The equation of a circle is

[0154] y 2 +z 2 =R 2 or (y-y0) 2 +(z-z0) 2 =R 2 (10)

[0155] Case 1.b≤R≤a(major axis)

[0156] Find the intersection of an ellipse and a circle

[0157]

[0158] have to

[0159] like Then use two more disks to cover it. The equation of the disk is

[0160] (y-y1) 2 +z 2 =R 2 ,

[0161] Further, if Similar to the previous step, use two more discs to cover:

[0162] (y-y2) 2 +z 2 =R 2 ,

[0163] Continue with the above steps:

[0164] when When , a total of 2(V-1)+1 disks are needed to cover the elliptical disk. And the coordinates of the centers of the 2(V-1)+1 disks are (0,0). The radius is R.

[0165] Case2.b=R;

[0166] (1) b=R;

[0167] The four circles are

[0168] That is, the centers of the four circles are

[0169] (2) b=R;

[0170] Based on the original four circles in Case 2, four more circles are added to cover them, for a total of eight circles.

[0171] That is, the other four centers are:

[0172] Note: When a meets certain conditions, it is also possible to cover with two circles. However, in this case, the intersection of the rightmost and leftmost ellipses from the previous covering must be calculated and then compared with the circle radius R to determine whether it can be covered with a single circle. The calculation of the circle center is very complicated. Therefore, this method is not used.

[0173] By analogy, when b=R; , four circles are still needed to cover the remaining part of the ellipse. The centers of the four circles are:

[0174] Therefore, for b = R; , 4 (V-1) circles are needed to cover, and their centers are:

[0175]

[0176] Case3.b>R; hour

[0177] (1) When R <b<2R; hour

[0178] At this time, 9 disks can be used to cover the ellipse, with the centers at (0,0), (0,R), (0,-R),

[0179] (2) When R <b<2R; hour

[0180] Then, three more discs are added to the original nine, which means 15 discs are needed. The six new discs are

[0181]

[0182] Similarly, if R <b<2R; When , six new disks are added. The center of the circle is

[0183] Therefore, when R <b; When , a total of 6(V-1)+3 disks are needed to cover the ellipse, whose center is:

[0184] (3)R <b<MR; hour

[0185] Then 2(M+1)(V-1)+M+1=(M+1)(2V-1) disks are needed to cover the ellipse, and its center is

[0186] Note 1: If the center of the ellipse is Then the center of the covering circle is also translated That's it, Other similar.

[0187] In one implementation, the fast calculation method for the collaborative interception zone for highly maneuverable targets proposed in this embodiment was verified in the MATLAB environment. The specific embodiment approximated the target's predicted maneuvering escape area by setting parameters such as the target's initial position, velocity, and acceleration to obtain low, medium, and high probability areas; and the coverage effect and calculation time of the high-probability area were used to verify the effectiveness of the designed algorithm.

[0188] The parameters are as follows:

[0189] Table 1 Initial parameters

[0190]

[0191] For the complete coverage of different methods, see Figure 4 , running time Figure 5 As shown in the figure, this method can stably achieve full coverage of the target's predicted maneuvering escape area, and the algorithm calculation time is greatly shortened.

[0192] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A method for quickly calculating the coordinated interception zone for high-maneuverability targets, characterized by The specific steps are as follows: The aircraft motion model is established based on the line-of-sight coordinate system at the initial moment; the target motion model is constructed in the inertial coordinate system; Based on the aircraft motion model and the target motion model, respectively calculating the interceptable area of ​​the aircraft at the predicted impact moment and the maneuverable escape area of ​​the target at the predicted impact moment; The maneuverable escape area and the aircraft interceptable area are projected from three-dimensional space to a two-dimensional plane, and the unbounded characteristics of the maneuverable escape area are approximated by a bounded area. The approximated bounded area is divided into a high probability area, a medium probability area, and a low probability area according to the probability of landing point; Based on the disk covering theory, the minimum number of interceptors required to cover the high probability area, medium probability area and low probability area, as well as the center coordinates and coverage radius of each interceptor are analytically calculated, and the high probability area is covered first.

2. The method for rapidly calculating a coordinated interception zone for a high-maneuverability target according to claim 1, characterized in that: The expression of the aircraft motion model is: Where A m ,B m for 0 3×3 ,I 3×3 are 3×3 zero matrix and identity matrix respectively; is the acceleration vector of the aircraft; in, is the position vector of the aircraft, is the velocity vector; The expression of the target motion model is: Where A T ,B T They are the system matrix and input matrix, as shown below: X T is the target position vector, U T is the acceleration vector of the target.

3. The method for rapidly calculating a coordinated interception zone for a high-maneuverability target according to claim 2, characterized in that: The interceptable area is recorded as M(t0), which represents the state of the aircraft at time t0 and the control effect after time t0. e The set of positions that can be reached at any time is called the aircraft interceptable area; the expression is as follows: Where, t0 represents the initial time of the aircraft, t e Indicates the moment when the aircraft hits, a max Represents acceleration and vector; Indicates the coordinates of the zero control terminal position of the aircraft; The maneuverable escape area is denoted as R and is expressed as: Where, X T (t e )and are the target hitting time t e The mean and covariance matrix of the motion state at each moment, N represents the normal distribution.

4. The method for rapidly calculating a coordinated interception zone for a high-maneuverability target according to claim 3, characterized in that: The specific method of projecting the maneuverable escape area and the aircraft interceptable area from three-dimensional space to a two-dimensional plane includes: converting the mean point and covariance matrix of the target maneuverable escape area to a plane coordinate system through a conversion matrix from an inertial coordinate system to a line of sight coordinate system; The projection of the aircraft interceptable area in the plane is expressed as: That is, (p y ,p z ) is the center of the circle and the radius is R(t e ,t0) disk; The projection of the maneuverable escape area in the plane is: Where, Among them, L(q ε ,q β ) is the transformation matrix from the inertial coordinate system to the line of sight coordinate system, is the coordinate of the origin of the reference sight coordinate system in the inertial coordinate system, [x T (t e ),y T (t e ),z T (t e )] T is the coordinate of the mean point of the maneuvering escape area in the inertial coordinate system, is the covariance matrix of the maneuver escape region in the inertial coordinate system.

5. The method for rapidly calculating a coordinated interception zone for a high-maneuverability target according to claim 4, characterized in that: The bounded area after the maneuver escape area is approximated is an ellipse, and the expression is as follows: Where, σ y (t e ) and σ z (t e ) represent the major and minor axes of the ellipse respectively.

6. The method for rapidly calculating a coordinated interception zone for a high-maneuverability target according to claim 5, characterized in that: The specific method of dividing the approximated bounded area into a high probability area, a medium probability area, and a low probability area is as follows: the bounded area is defined as an ellipse, and based on the 3 sigma principle of Gaussian distribution, the ellipse division principle is as follows: High probability area: a sub-ellipse with the center of the ellipse as the circle center, the major semi-axis as the first threshold, and the minor semi-axis as the second threshold; Medium probability area: the annular area with the center of the ellipse as the center, the major semi-axis at the third threshold and greater than the first threshold, and the minor semi-axis at the fourth threshold and greater than the second threshold, and the high probability area is deducted; Low probability area: an annular area with the center of the ellipse as the center, the major semi-axis of the ellipse as the major semi-axis of the bounded area, and the minor semi-axis as the minor semi-axis of the ellipse as the bounded area, and the medium probability area is deducted.

7. The method for rapidly calculating a coordinated interception zone for a high-maneuverability target according to claim 6, characterized in that: The division of the high probability area, medium probability area and low probability area is as follows: The semi-major axis is The minor axis is ellipse; The semi-major axis is The minor axis is Subtract the ellipse The semi-major axis is The minor axis is Subtract the ellipse 8. The method for rapidly calculating a coordinated interception zone for a high-maneuverability target according to claim 7, characterized in that: The specific process of analytically calculating the minimum number of interceptors required to cover the high probability area, the medium probability area, and the low probability area, as well as the center coordinates and coverage radius of each interceptor, is as follows: When the length of the major axis of the ellipse, the length of the minor axis and the radius of the disk satisfy b≤R≤a, 2(V-1)+1 disks are distributed equally along the major axis; the coordinates of the center of the 2(V-1)+1 disks are (0,0). …, Among them, it is necessary to meet R represents the radius of the disk, a represents the length of the major axis of the ellipse, b represents the length of the minor axis of the ellipse, and V represents the multiple of the radius of the circle to the major axis of the ellipse; the number of disks is the minimum number of interceptors; When the length of the major axis of the ellipse, the length of the minor axis and the radius of the disk satisfy b = R; , 4 (V-1) disks are used to cover the ellipse boundary and the central area; the center coordinates of the 4 (V-1) disks are i=1,2,…,V-1; When the length of the major axis, the minor axis and the radius of the disk satisfy R <b<MR; When , 2(M+1)(V-1)+M+1=(M+1)(2V-1) disks are used to cover the ellipse boundary and the central area; the coordinates of the centers of the 2(M+1)(V-1)+M+1=(M+1)(2V-1) disks are i=1,2,…,V,j=0,1,…,M-1;M represents the multiple of the circle radius to the minor axis of the ellipse; When the ellipse center is offset, the center of the covering disk is translated to the offset ellipse center.

9. The method for rapidly calculating a coordinated interception zone for a high-maneuverability target according to claim 8, characterized in that: The strategy of the disk covering ellipse includes: after covering the high probability area, if it is necessary to cover the medium and low probability areas, the full area coverage is achieved by increasing the number of disks or adjusting the distribution direction of the disks.

10. A system for constructing a cooperative interception zone for a high-maneuverability target, for implementing the method for quickly calculating a cooperative interception zone for a high-maneuverability target according to any one of claims 1 to 9; characterized in that: Includes the following modules: The multi-source sensor module is used to obtain the target's motion information in real time, including position, velocity and acceleration, and transmit the data to the motion modeling module; Motion modeling module, including aircraft motion modeling unit and target motion modeling unit; The aircraft motion modeling unit constructs the aircraft motion model based on the line-of-sight coordinate system at the initial moment; the target motion modeling unit constructs the target's random maneuver model based on the inertial coordinate system and in combination with the target's motion information; an area calculation module, configured to calculate, based on the output of the motion modeling module, the interceptable area of ​​the aircraft at the predicted impact moment and the predicted maneuverable escape area of ​​the target; Projection and probability partitioning module, including three-dimensional projection unit and probability partitioning unit; The three-dimensional projection unit projects the interceptable area and the maneuverable escape area from the three-dimensional space to a two-dimensional plane; The probability division unit divides the bounded two-dimensional maneuverable escape area into high, medium and low probability areas according to the landing point probability, wherein the high probability area is the center area of ​​the ellipse, and the medium and low probability areas are the annular areas expanding outwards respectively; The collaborative interception zone generation module, based on the disk covering theory, analytically calculates the minimum number of interceptors required to cover the probability area, the coordinates of the center of each interceptor, and the coverage radius, and gives priority to covering high-probability areas; The dynamic deployment optimization module updates the target motion information in real time according to the changes in the mission environment, adjusts the deployment strategy of the interceptor, and ensures full coverage of the maneuverable escape area.

Images