Multi-vehicle formation cooperative deception jamming optimization method based on genetic algorithm

Abstract

This invention discloses an optimization method for multi-aircraft formation cooperative deception jamming based on genetic algorithms, belonging to the field of electronic countermeasures technology. This method addresses the problems of discrete false targets generated by existing multi-aircraft deception jamming techniques, which are easily identified and filtered by radar networks. First, a system model including aircraft formation, radar network, and flight area is established. Then, a cooperative jamming evaluation model is constructed. By calculating the spatial distance between false target pairs generated by different aircraft against different radars and comparing it with radar resolution thresholds, the jamming effectiveness of the formation is quantified. Finally, using this evaluation model as the objective function, a genetic algorithm is used to iteratively optimize the spatial positions of multiple aircraft, searching for an aircraft formation scheme that maximizes the spatial overlap of false targets. This invention can automatically generate optimized aircraft formation positions, significantly improving the cooperative deception jamming effectiveness of multi-aircraft formations against radar networks.

Description

Technical Field

[0001] This invention relates to the field of radar electronic countermeasures and intelligent optimization technology, and in particular to a multi-aircraft formation cooperative deception and jamming optimization method based on genetic algorithms. Background Technology

[0002] In the field of radar electronic countermeasures, multi-aircraft coordinated deception jamming is an important means to improve the survivability and penetration capability of aircraft formations. Existing typical multi-aircraft coordinated radar jamming techniques usually rely on multiple aircraft flying in a pre-planned fixed formation (such as linear or diamond patterns). Each aircraft independently generates and radiates deception jamming signals based on its relative relationship with the radar, thus creating independent false target marks on the displays of each radar. However, this traditional method has two prominent technical drawbacks:

[0003] First, the interference effect lacks coordination and is easily detected by advanced radar networks. Because each aircraft operates independently, the false targets they generate are spatially discrete and unrelated. Modern radar network systems generally employ multi-site data fusion and cross-validation techniques, easily determining that these false points from different spatial locations cannot converge on the same real target trajectory, thus identifying them as interference and filtering them out. The fundamental reason is that existing technology lacks a quantitative, coordinated interference effectiveness evaluation model with the core objective of deceiving radar networks, and therefore cannot guide aircraft formations to generate false targets that can cause multiple radars to produce consistent spatial misjudgments.

[0004] Second, the formation strategy is rigid and cannot dynamically adapt to the battlefield environment. The preset fixed formation cannot be dynamically adjusted according to real-time changing battlefield elements (such as radar deployment location, number, resolution characteristics, and friendly flight constraint areas), resulting in insufficient adaptability and robustness of the jamming strategy.

[0005] The core challenge facing current technology is how to plan the optimal multi-aircraft spatial formation in real time and automatically under the constraints of a given battlefield environment (radar network, flight airspace), so that the false target group generated by all aircraft in the formation can "overlap" in space to the greatest extent under the multi-view observation of the radar network, and thus be misjudged as a large number or multiple real moving targets.

[0006] Therefore, how to effectively deceive radar networks, especially to make multiple radars mistakenly identify false targets generated by the coordinated flight of aircraft as real targets, is a technical problem that urgently needs to be solved in the field of radar jamming. Summary of the Invention

[0007] In view of this, the purpose of this invention is to provide a multi-machine formation cooperative deception interference optimization method based on genetic algorithm. This method constructs a model that can accurately quantify and evaluate the effectiveness of formation cooperative deception interference, thereby achieving efficient search for the optimal formation scheme in a complex constraint space.

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] The multi-machine formation cooperative deception and interference optimization method based on genetic algorithm provided by this invention includes the following steps:

[0010] Step S1: Establish the system model and define the parameters:

[0011] Definition includes The formation of aircraft, its set of position coordinates is as follows 1, 2, ..., ;

[0012] Definition includes The radar network of the radar system has the following set of location coordinates: = 1, 2, ..., ;

[0013] Define the flight area Ω; Ω = ;

[0014] in, Indicates the first The horizontal coordinate of the aircraft; Indicates the first The vertical coordinate of the aircraft; Indicates an aircraft index; Indicates radar index;

[0015] Represents the horizontal coordinate variable of the plane; Represents the vertical coordinate variable of the plane; Indicates the lower bound of the x-coordinate of the flight area; Indicates the upper bound of the horizontal coordinate of the flight area; Indicates the lower bound of the vertical coordinate of the flight area; Indicates the upper bound of the vertical coordinate of the flight area;

[0016] Step S2: Construct a cooperative interference assessment model:

[0017] For each aircraft With each radar A set of false targets is generated based on their relative positions:

[0018] ;

[0019] in, Indicates targeting aircraft With radar A set of generated fake targets; Indicates the first false target; This indicates the fourth false target;

[0020] Calculate the results from different aircraft ( , For different radars ( , The distance between the generated false target pairs;

[0021] in, Indicates the first An airplane; Indicates the first An airplane; Indicates the first Radar; Indicates the first Radar;

[0022] The subscripts a and b indicate that they belong to 1, 2, ..., The two airplanes inside are a and b;

[0023] The subscripts c and d indicate that they belong to 1, 2, ..., The two radars inside are C and D;

[0024] When the distance is less than or equal to the radar resolution threshold When this occurs, it is determined to be a valid instance of coordinated interference;

[0025] The objective function C is constructed using the total number of effective cooperative jamming combinations of all radars and all aircraft, and is used as an indicator to evaluate the jamming effectiveness of the formation.

[0026] Step S3: Optimize the formation positions based on the genetic algorithm:

[0027] Using the objective function C as the fitness function, The coordinates of an aircraft are encoded as a chromosome, and the population is initialized within the flight area Ω.

[0028] The population is iteratively optimized through selection, crossover, and mutation operations using a genetic algorithm until the termination condition is met. The output is the set of aircraft coordinates that maximizes the objective function C, which serves as the optimal cooperative interference formation scheme.

[0029] Furthermore, in step S2, the step for each aircraft With each radar Generate a set of fake targets The method is as follows:

[0030] On the plane With radar On the line, at the airplane On the left and right sides, along the radar Pointing at the airplane The unit vector direction, at equal intervals K false targets are generated in a distributed manner.

[0031] in, This represents the distance between false targets; K represents the number of false targets.

[0032] Furthermore, the false target The first in Coordinates of the false target:

[0033] ;

[0034] in, Indicates airplane With radar A set of generated fake targets; Indicates targeting aircraft With radar The generated first A false target coordinate; Indicates the first The location of the aircraft; Indicates the first The directional coefficient of a false target; Indicates the distance between adjacent false targets; For radar Pointing at the airplane The unit vector.

[0035] Furthermore, in step S2, the expression for the objective function C is:

[0036] = ;

[0037] in, This indicates an indicator function, when its argument is... Not greater than The value is 1 if the condition is met, otherwise it is 0.

[0038] ;in, This indicates the spacing between false targets; when the distance between two targets is less than or equal to the radar resolution threshold. At that time, the radar network will identify them as a cooperative target;

[0039] in, Indicates the first Radar index; Indicates the first Radar index; Indicates the first Aircraft index; Indicates the first Aircraft index; Indicates the first A fake target index. Indicates the first A fake target index; Indicates airplane With radar The generated first A false target; Indicates airplane With radar The generated first A false target.

[0040] Furthermore, in step S3, the step of... The coordinates of each aircraft are encoded as a chromosome, specifically: the two-dimensional coordinates of each aircraft are... Each of the aircraft's binary strings is converted to a single binary string, and then the binary strings of all the aircraft are concatenated sequentially to form a chromosome.

[0041] Furthermore, in step S3, the parameters of the genetic algorithm include: population size popsize, maximum number of iterations, crossover probability, and mutation probability.

[0042] Furthermore, step S3 includes the following sub-steps:

[0043] S31. Encoding: The two-dimensional coordinates of each aircraft... Each of the aircraft's binary strings is converted to a single binary string, and the binary strings of all the aircraft are then concatenated sequentially to form a chromosome.

[0044] S32. Initialization: Randomly generate an initial population of a preset size of popsize within the flight area Ω;

[0045] S33. Evaluation: Decode each chromosome to obtain the corresponding aircraft coordinates, and call the objective function C constructed in step S2 to calculate the fitness value of the current formation scheme;

[0046] S34. Evolution: Select individuals based on fitness values ​​and perform crossover and mutation operations on the selected individuals to produce a new generation of population.

[0047] S35. Iteration: Repeat steps S33 and S34 until the maximum number of iterations is reached. Output the set of aircraft coordinates corresponding to the chromosome with the largest fitness value as the optimal cooperative interference formation scheme.

[0048] Furthermore, in step S31, the specific method for converting the two-dimensional coordinates of each aircraft into a binary string is as follows: the coordinate values ​​are linearly normalized to the [0,1] interval, and multiplied by ( The integer is then rounded to the nearest integer and converted into a binary string of bits, where bits is the preset number of bits for encoding.

[0049] Furthermore, in step S34, the selection operation uses a tournament selection method, and the crossover operation uses a single-point crossover, with a crossover probability of... The mutation operation uses bitwise mutation, with a mutation probability of . .

[0050] Furthermore, it also includes step S4: generating cooperative jamming control commands based on the optimal cooperative jamming formation scheme, and sending the control commands to each aircraft in the formation; the control commands are used to control the airborne jammer to radiate deception jamming signals according to the false target parameters generated in step S2.

[0051] The beneficial effects of this invention are as follows:

[0052] The present invention provides a multi-machine formation cooperative deception and interference optimization method based on genetic algorithm.

[0053] This invention discloses a multi-aircraft formation cooperative deception jamming optimization method based on genetic algorithms, belonging to the field of electronic countermeasures technology. This method addresses the problems of discrete false targets generated by multi-aircraft deception jamming in existing technologies, which are easily identified and filtered by radar networks. First, a system model including aircraft formation, radar network, and flight area is established. Then, a cooperative jamming evaluation model is constructed. By calculating the spatial distance between false target pairs generated by different aircraft against different radars and comparing it with radar resolution thresholds, the jamming effectiveness of the formation is quantified. Finally, using this evaluation model as the objective function, a genetic algorithm is used to iteratively optimize the spatial positions of multiple aircraft, searching for an aircraft formation scheme that maximizes the spatial overlap of false targets. This invention can automatically generate optimized aircraft formation positions, significantly improving the cooperative deception jamming effectiveness of multi-aircraft formations against radar networks, mainly in the following three aspects:

[0054] First, at the methodological level, this invention proposes a model-driven, performance-oriented dynamic optimization method for multi-aircraft cooperative jamming. This method differs from empirical methods that rely on pre-set fixed formations; by establishing a cooperative jamming evaluation model, the abstract "deception effect" is transformed into a computable objective function, thereby enabling precise quantitative evaluation of the jamming effectiveness of any formation scheme. Furthermore, a genetic algorithm is used to automatically optimize this objective function, achieving a fundamental shift from "fixed formations" to dynamically generating optimal formations based on real-time battlefield situation (radar network, airspace constraints).

[0055] Secondly, at the system implementation level, an automated and intelligent collaborative jamming decision support tool is provided. This system integrates model building, performance evaluation, and intelligent optimization algorithms. Based on input battlefield environment parameters, it can automatically search for and output aircraft spatial configuration schemes that maximize the effectiveness of collaborative deception jamming, greatly improving the efficiency and scientific rigor of tactical decision-making and overcoming the limitations of manual planning in handling complex constraints and global optimization.

[0056] Third, at the overall tactical value level, it effectively solves the core coordination problem in multi-aircraft deception jamming. By taking maximizing the spatial overlap of false targets as the direct optimization objective, the formation scheme generated by this invention can "align" false targets generated by different aircraft for different radars within the radar resolution limit, thereby significantly increasing the probability that the radar network will misjudge them as real targets, fundamentally improving the success rate of coordinated deception jamming and overall combat effectiveness.

[0057] The above and other objects, advantages, and features of the present invention will be more fully set forth and demonstrated through the following detailed description of specific embodiments in conjunction with the accompanying drawings. Those skilled in the art, upon referring to the following detailed description and the accompanying drawings, will be able to better understand and realize the above advantages of the present invention. Other objects, features, and advantages of the present invention will become clearer after being described in detail in the detailed description section in conjunction with the accompanying drawings. Attached Figure Description

[0058] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following drawings are provided for illustration.

[0059] Figure 1 The flowchart shows the optimization method for multi-machine formation cooperative deception and interference based on genetic algorithm.

[0060] Figure 2 This is a schematic diagram of a multi-machine formation cooperative deception and interference optimization system based on genetic algorithms.

[0061] Figure 3 This is a schematic diagram of a coordinated deception and interference scenario.

[0062] Figure 4 A graph showing the relationship between the number of iterations and the fitness value;

[0063] Figure 5 The solution is not optimized for random grouping / random initialization;

[0064] Figure 6 The simulation results show the optimal formation positions and the distribution of false targets.

[0065] Figure 7 Optimization flowchart for genetic algorithm. Detailed Implementation

[0066] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0067] Example 1

[0068] like Figure 1 As shown, Figure 1 The flowchart illustrates a multi-machine formation cooperative deception and interference optimization method based on a genetic algorithm. This embodiment provides a multi-machine formation cooperative deception and interference optimization method based on a genetic algorithm, which includes the following steps:

[0069] Step S1: Establish the system model and define the parameters:

[0070] Definition includes The formation of aircraft, its set of position coordinates is as follows 1, 2, ..., ;

[0071] Definition includes The radar network of the radar system has the following set of location coordinates: = 1, 2, ..., ;

[0072] Define the flight area Ω; Ω = ;

[0073] in, Indicates the first The horizontal coordinate of the aircraft; Indicates the first The vertical coordinate of the aircraft; Indicates an aircraft index; Indicates radar index; Represents the horizontal coordinate variable of the plane; Represents the vertical coordinate variable of the plane; Indicates the lower bound of the x-coordinate of the flight area; Indicates the upper bound of the horizontal coordinate of the flight area; Indicates the lower bound of the vertical coordinate of the flight area; Indicates the upper bound of the vertical coordinate of the flight area;

[0074] Step S2: Construct a cooperative interference assessment model:

[0075] For each aircraft With each radar A set of false targets is generated based on their relative positions:

[0076] ;

[0077] in, Indicates targeting aircraft With radar A set of generated fake targets; Indicates the first false target; This indicates the fourth false target;

[0078] Calculate the results from different aircraft ( , For different radars ( , The distance between the generated false target pairs;

[0079] in, Indicates the first An airplane; Indicates the first An airplane; Indicates the first Radar; Indicates the first Radar;

[0080] The subscripts a and b indicate that they belong to 1, 2, ..., The two airplanes inside are a and b;

[0081] The subscripts c and d indicate that they belong to 1, 2, ..., The two radars inside are C and D;

[0082] When the distance is less than or equal to the radar resolution threshold When this occurs, it is determined to be a valid instance of coordinated interference;

[0083] The objective function C is constructed using the total number of effective cooperative jamming combinations of all radars and all aircraft, and is used as an indicator to evaluate the jamming effectiveness of the formation.

[0084] Step S3: Optimize the formation positions based on the genetic algorithm:

[0085] Using the objective function C as the fitness function, The coordinates of an aircraft are encoded as a chromosome, and the population is initialized within the flight area Ω.

[0086] The population is iteratively optimized through selection, crossover, and mutation operations using a genetic algorithm until the termination condition is met. The output is the set of aircraft coordinates that maximizes the objective function C, which serves as the optimal cooperative interference formation scheme.

[0087] In step S2 of this embodiment, the step of targeting each aircraft... With each radar Generate a set of fake targets The method is as follows:

[0088] On the plane With radar On the line, at the airplane On the left and right sides, along the radar Pointing at the airplane The unit vector direction, at equal intervals The d-distribution generates K false targets.

[0089] in, K represents the distance between false targets; K represents the number of false targets.

[0090] The false target described in this embodiment The first in Coordinates of the false target:

[0091] ;

[0092] in, Indicates airplane With radar A set of generated fake targets; Indicates targeting aircraft With radar The generated first A false target coordinate; Indicates the first The location of the aircraft; Indicates the first The directional coefficient of a false target; Indicates the distance between adjacent false targets;

[0093] For radar Pointing at the airplane , unit vector;

[0094] In step S2 of this embodiment, the expression for the objective function C is:

[0095] = ;

[0096] in, This indicates an indicator function, when its argument is... Not greater than The value is 1 if the condition is met, otherwise it is 0.

[0097] ;in, This indicates the spacing between false targets; when the distance between two targets is less than or equal to the radar resolution threshold. At that time, the radar network will identify them as a cooperative target;

[0098] in, Indicates the first Radar index; Indicates the first Radar index; Indicates the first Aircraft index; Indicates the first Aircraft index; Indicates the first A fake target index. Indicates the first A fake target index; Indicates airplane With radar The generated first A false target; Indicates airplane With radar The generated first A false target.

[0099] In step S3 of this embodiment, the step of... The coordinates of each aircraft are encoded as a chromosome, specifically: the two-dimensional coordinates of each aircraft are... Each of the aircraft's binary strings is converted to a single binary string, and then the binary strings of all the aircraft are concatenated sequentially to form a chromosome.

[0100] In step S3 of this embodiment, the parameters of the genetic algorithm include: population size popsize, maximum number of iterations, crossover probability, and mutation probability. Wherein, popsize represents the initial population size;

[0101] Step S3 in this embodiment includes the following sub-steps:

[0102] S31. Encoding: The two-dimensional coordinates of each aircraft... Each of the aircraft's binary strings is converted to a single binary string, and the binary strings of all the aircraft are then concatenated sequentially to form a chromosome.

[0103] S32. Initialization: Randomly generate an initial population of a preset size of popsize within the flight area Ω;

[0104] S33. Evaluation: Decode each chromosome to obtain the corresponding aircraft coordinates, and call the objective function C constructed in step S2 to calculate the fitness value of the current formation scheme;

[0105] S34. Evolution: Select individuals based on fitness values ​​and perform crossover and mutation operations on the selected individuals to produce a new generation of population.

[0106] S35. Iteration: Repeat steps S33 and S34 until the maximum number of iterations is reached. Output the set of aircraft coordinates corresponding to the chromosome with the largest fitness value as the optimal cooperative interference formation scheme.

[0107] In step S31 of this embodiment, the specific method for converting the two-dimensional coordinates of each aircraft into a binary string is as follows: the coordinate values ​​are linearly normalized to the [0,1] interval, and multiplied by ( The integer is then rounded to the nearest integer and converted into a binary string of bits, where bits is the preset number of bits for encoding.

[0108] In step S34 of this embodiment, the selection operation uses the tournament selection method, and the crossover operation uses single-point crossover, with a crossover probability of . The mutation operation uses bitwise mutation, with a mutation probability of . .

[0109] This embodiment also includes step S4: generating a cooperative jamming control command based on the optimal cooperative jamming formation scheme, and sending the control command to each aircraft in the formation; the control command is used to control the airborne jammer to radiate deception jamming signals according to the false target parameters generated in step S2.

[0110] like Figure 2 As shown, the multi-machine formation cooperative deception and interference optimization system based on genetic algorithm provided in this embodiment includes:

[0111] The model building module is used to create models containing... Airplane, The system model of the radar and flight area is defined, and relevant parameters are defined. It is also used to construct a cooperative interference assessment model, which generates false targets based on the positions of the aircraft and radar, and calculates the distance between different pairs of false targets and radar resolution thresholds. The comparison is used to quantify the cooperative interference effectiveness of the formation and generate the objective function C;

[0112] The genetic algorithm optimization module is used to encode the coordinates of all aircraft in the formation into chromosomes using the objective function C as the fitness function, and to search for the aircraft coordinate configuration that maximizes the objective function C within the flight area through the iterative optimization process of the genetic algorithm.

[0113] The scheme output module is used to output the optimal set of aircraft coordinates obtained by the genetic algorithm optimization module as a cooperative interference formation scheme.

[0114] The rule for generating false targets in the model building module described in this embodiment is as follows: for each pair of aircraft and radar On the line connecting the two, at the aircraft's position On the left and right sides, along the unit vector direction from the radar pointing to the aircraft, at a fixed interval Generate multiple fake targets.

[0115] The genetic algorithm optimization module described in this embodiment includes:

[0116] The encoding unit is used to convert the two-dimensional coordinates of each aircraft into binary strings and splice them into a chromosome;

[0117] An initialization unit is used to randomly generate an initial population of a preset size within the flight area Ω;

[0118] The evaluation unit is used to decode the chromosome to obtain the aircraft coordinates and call the model building module to calculate the objective function C value of the current formation scheme as the fitness.

[0119] Evolutionary units are used to perform selection operations based on fitness and to perform crossover and mutation operations on selected individuals to produce a new generation of population.

[0120] Example 2

[0121] This embodiment details the implementation process of the multi-machine formation cooperative deception and interference optimization method based on genetic algorithms, as follows:

[0122] Step 1: System Model Establishment and Parameter Definition

[0123] Airplane: Yes An aircraft, a set of aircraft position coordinates { };

[0124] The position of the i-th aircraft 1, 2, ..., ;

[0125] Radar networking: Yes Radar, radar location coordinate set { };

[0126] Location of radar unit j = 1, 2, ..., ;

[0127] Flight area: Ω= ;

[0128] False target: Aircraft radar The generated set of false targets ;

[0129] No. A false target in ;

[0130] Four false targets are positioned on the left and right sides of the aircraft, at equal intervals ∆d along the line connecting the aircraft and the radar. Pointing at the airplane unit vector = ;

[0131] Step 2: Cooperative Interference Assessment Model

[0132] When the distance between two false targets is less than or equal to the radar resolution threshold At that time, the radar network will identify it as a single target;

[0133] Assuming an airplane Radars in a radar network Generate a set of false targets ,airplane Radars in a radar network Generate a set of false targets ;

[0134] Choose a fake target , Choose a fake target Calculate the distance between the two false targets:

[0135] ( )= ;

[0136] if ( )≤ Therefore, the two false targets constitute a coordinated interference;

[0137] like Figure 3 As shown, Figure 3 This is a schematic diagram of a coordinated deception and jamming scenario; the circular radar icon represents the radar position, the green icon represents the real aircraft position, the star-shaped mark represents the false target, the hollow circle represents the cooperative target, and the dashed line represents the radar-aircraft line of sight.

[0138] Construct the objective function:

[0139] = ;

[0140] Among them, the outer loop It involves traversing all combinations of two radars;

[0141] Intermediate loop It involves iterating through all the aircraft and pairing them up.

[0142] This embodiment uses an inner loop. Selected aircraft and airplane In the case of traversing the radar The generated false targets;

[0143] Indicates airplane radar The first A false target;

[0144] Indicates airplane radar The first A false target;

[0145] Indicates the spacing between dummy targets;

[0146] Function definition I ;

[0147] When the distance between two targets is less than or equal to the radar resolution threshold At that time, the radar network will identify it as a cooperative target.

[0148] In this embodiment, the objective function C is used to count the total number of cooperative interference events: outer layer summation. Iterate through all radars and combine them pairwise; sum the results in the middle. It iterates through all pairs of aircraft; the inner layer sums up. Iterate through the pairs of false targets generated by the two radars for each aircraft. For each pair of false targets, calculate the distance. = , and is indicated by the function; I Determine if the value is not greater than the discrimination threshold dr. If it is, count it as 1; otherwise, count it as 0. Sum all the counts to get C. The larger C is, the more times the coordinated interference is performed and the better the deception effect.

[0149] Step 3: Genetic Algorithm Optimization

[0150] Encoding: The coordinates of the aircraft are encoded into a chromosome using binary. ;

[0151] Population initialization: Set the population size popsize, and randomly generate popsize groups of flight formation schemes in the flight area Ω;

[0152] Fitness function evaluation: Decoding each chromosome ;

[0153] get Aircraft coordinates { },

[0154] Calculate all false target pairs and substitute them into the objective function Fitness = (A),

[0155] Calculate the Fitness score.

[0156] The higher the score, the better the interference effect.

[0157] The selection, crossover, and mutation processes are used to obtain a new population. The process is then iterated until the maximum number of iterations is reached. The result is then output to obtain the optimal cooperative interference formation scheme.

[0158] The binary encoding rules in this embodiment are as follows:

[0159] Mapping method (actual coordinates mapped to binary):

[0160] First, the aircraft is within the coordinate range [ ], , Linear normalization is performed on each coordinate. (where c is the coordinate, which can be either the x-coordinate or the y-coordinate);

[0161] Then quantize to integers: scaled=round(normalized*( ));

[0162] Finally, the quantized integer scaled is converted into binary code according to the length of bits. If the number of bits is insufficient, zeros are padded to the high bits to obtain a fixed-length binary string (with bits).

[0163] Binary coordinates mapped to actual coordinates:

[0164] First, convert the bit-sized binary string to an integer scaled (range 0~). );

[0165] Then backmap to coordinates ;

[0166] Number of bits per coordinate encoding (precision): Each coordinate has... The position, the step length is ;

[0167] Total chromosome length .

[0168] In this embodiment, the fitness function value is Fitness = (A) equals the total number of effective cooperative interference events. The larger C is, the more cooperative interference events there are and the better the deception effect.

[0169] The genetic algorithm operations (selection, crossover, mutation) in this embodiment are performed as follows:

[0170] Selection: Tournament selection is used. A fixed number of individuals are randomly selected from the population each time, their fitness is compared, and the one with the highest fitness is selected to enter the next generation.

[0171] Crossover: Single-point crossover is used. Crossover probability is applied to two adjacent parent individuals. Perform crossover by randomly selecting a crossover point on a chromosome and exchanging gene segments at the crossover point to generate two offspring; if the random number is greater than the crossover probability... Then the parent generation is directly retained.

[0172] Mutation: Position-by-position mutation is used. For each gene locus, a mutation probability is calculated. Flipping (0 becomes 1, 1 becomes 0) is performed to maintain population diversity and avoid premature convergence.

[0173] In this embodiment, the fitness function is Fitness = (A) Used to characterize the number of successful matches (or the number of effective interference events) in collaborative interference. For example... Figure 4 As shown, Figure 4 This is a graph showing the relationship between the number of iterations and the fitness value.

[0174] When the optimal solution is C=40, it means that under the current radar layout and formation parameters, a total of 40 cooperative interference matching events that meet the range threshold are achieved, and the cooperative interference effect reaches the optimal level of this optimization.

[0175] Compared to the baseline method, this optimization significantly increases the number of effective cooperative interference events, thereby improving the overall interference effect and stability. For example... Figure 5 As shown, Figure 5 This is a non-optimized scheme for random grouping / random initialization.

[0176] Example 3

[0177] This embodiment further illustrates the method with specific illustrations and implementation details. Specifically:

[0178] like Figure 6 and Figure 7 As shown, Figure 6The figure shows the simulation results of the optimal formation position and the distribution of false targets. Figure 7 Optimize the flowchart for the genetic algorithm; Figure 6 The diagram displays the optimized formation positions and the corresponding distribution of false targets. The x-axis represents X / m, and the y-axis represents Y / m. In the legend: solid red circles represent the actual aircraft positions; hollow blue circles represent the positions of false targets generated by each radar; solid black circles represent cooperative false targets that meet the cooperative matching conditions. The lines in the diagram represent the distribution relationship of false targets along the radar-aircraft direction; the dashed boxes represent the flight area boundaries; G is the preset maximum number of iterations, i.e., the maximum number of generations that can be evolved; g is the current iteration number, i.e., the number of generations that have been iterated.

[0179] In this embodiment, the aircraft formation consists of 4 aircraft, and the radar network consists of 3 radars.

[0180] Flight area Ω= ;

[0181] Radar network locations: Radar 1 coordinates (6000, 0), Radar 2 coordinates (7000, 0), Radar 3 coordinates (8000, 0);

[0182] Radar resolution threshold =50m; distance between false targets d=2000m;

[0183] Genetic algorithm parameters: Population size popsize=100, Number of iterations 2000, Crossover probability 0.8, mutation probability 0.05, in binary, is 10 bits;

[0184] Simulation results: Optimal formation positions of the four aircraft:

[0185] (32317, 32890), (32406, 32836);

[0186] (32495, 32766), (32587, 32720);

[0187] The optimal fitness value is C=40.

[0188] The embodiments described above are merely preferred embodiments for fully illustrating the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A multi-machine formation cooperative deception and interference optimization method based on genetic algorithm, characterized in that, Includes the following steps: Step S1: Establish the system model and define the parameters: Definition includes The formation of aircraft, its set of position coordinates is as follows 1, 2, ..., ; Definition includes The radar network of the radar system has the following set of location coordinates: = 1, 2, ..., ; Define the flight area Ω; Ω = ; in, Indicates the first The horizontal coordinate of the aircraft; Indicates the first The vertical coordinate of the aircraft; Indicates an aircraft index; Indicates radar index; Represents the horizontal coordinate variable of the plane; Represents the vertical coordinate variable of the plane; Indicates the lower bound of the x-coordinate of the flight area; Indicates the upper bound of the horizontal coordinate of the flight area; Indicates the lower bound of the vertical coordinate of the flight area; Indicates the upper bound of the vertical coordinate of the flight area; Step S2: Construct a cooperative interference assessment model: For each aircraft With each radar A set of false targets is generated based on their relative positions: ； in, Indicates targeting aircraft With radar A set of generated fake targets; Indicates the first false target; This indicates the fourth false target; Calculate the results from different aircraft ( , For different radars ( , The distance between the generated false target pairs; in, Indicates the first An airplane; Indicates the first An airplane; Indicates the first Radar; Indicates the first Radar; The subscripts a and b indicate that they belong to 1, 2, ..., The two airplanes inside are a and b; The subscripts c and d indicate that they belong to 1, 2, ..., The two radars inside are C and D; When the distance is less than or equal to the radar resolution threshold When this occurs, it is determined to be a valid instance of coordinated interference; The objective function C is constructed using the total number of effective cooperative jamming combinations of all radars and all aircraft, and is used as an indicator to evaluate the jamming effectiveness of the formation. Step S3: Optimize the formation positions based on the genetic algorithm: Using the objective function C as the fitness function, The coordinates of an aircraft are encoded as a chromosome, and the population is initialized within the flight area Ω. The population is iteratively optimized through selection, crossover, and mutation operations using a genetic algorithm until the termination condition is met. The output is the set of aircraft coordinates that maximizes the objective function C, which is the optimal cooperative interference formation scheme. In step S2, the step for each aircraft With each radar Generate a set of fake targets The method is as follows: On the plane With radar On the line, at the airplane On the left and right sides, along the radar Pointing at the airplane The unit vector direction, at equal intervals K false targets are generated in a distributed manner; in, This represents the distance between false targets; K represents the number of false targets.

2. The multi-machine formation cooperative deception interference optimization method based on genetic algorithm as described in claim 1, characterized in that, The false target The first in Coordinates of the false target: ； in, Indicates airplane With radar A set of generated fake targets; Indicates targeting aircraft With radar The generated first A false target coordinate; Indicates the first The location of the aircraft; Indicates the first The directional coefficient of a false target; Indicates the distance between adjacent false targets; For radar Pointing at the airplane The unit vector.

3. The multi-machine formation cooperative deception interference optimization method based on genetic algorithm as described in claim 1, characterized in that, In step S2, the expression for the objective function C is: = ； in, This indicates an indicator function, when its argument is... Not greater than The value is 1 if the condition is met, otherwise it is 0. ;in, This indicates the spacing between false targets; when the distance between two targets is less than or equal to the radar resolution threshold. At that time, the radar network will identify them as a cooperative target; in, Indicates the first Radar index; Indicates the first Radar index; Indicates the first Aircraft index, Indicates the first Aircraft index; Indicates the first A fake target index. Indicates the first A fake target index; Indicates airplane With radar The generated first A false target; Indicates airplane With radar The generated first A false target.

4. The multi-machine formation cooperative deception interference optimization method based on genetic algorithm as described in claim 1, characterized in that, In step S3, the step of... The coordinates of each aircraft are encoded as a chromosome, specifically: the two-dimensional coordinates of each aircraft are... Each of the aircraft's binary strings is converted to a single binary string, and then the binary strings of all the aircraft are concatenated sequentially to form a chromosome.

5. The multi-machine formation cooperative deception interference optimization method based on genetic algorithm as described in claim 1, characterized in that, In step S3, the parameters of the genetic algorithm include: population size popsize, maximum number of iterations, crossover probability, and mutation probability.

6. The multi-machine formation cooperative deception interference optimization method based on genetic algorithm as described in claim 1, characterized in that, Step S3 includes the following sub-steps: S31. Encoding: The two-dimensional coordinates of each aircraft... Each of the aircraft's binary strings is converted to a single binary string, and the binary strings of all the aircraft are then concatenated sequentially to form a chromosome. S32. Initialization: Randomly generate an initial population of a preset size of popsize within the flight area Ω; S33. Evaluation: Decode each chromosome to obtain the corresponding aircraft coordinates, and call the objective function C constructed in step S2 to calculate the fitness value of the current formation scheme; S34. Evolution: Select individuals based on fitness values ​​and perform crossover and mutation operations on the selected individuals to produce a new generation of population. S35. Iteration: Repeat steps S33 and S34 until the maximum number of iterations is reached. Output the set of aircraft coordinates corresponding to the chromosome with the largest fitness value as the optimal cooperative interference formation scheme.

7. The multi-machine formation cooperative deception interference optimization method based on genetic algorithm as described in claim 6, characterized in that, In step S31, the specific method for converting the two-dimensional coordinates of each aircraft into a binary string is as follows: linearly normalize the coordinate values ​​to the [0,1] interval, and multiply by ( The integer is then rounded to the nearest integer and converted into a binary string of bits, where bits is the preset number of bits for encoding.

8. The multi-machine formation cooperative deception interference optimization method based on genetic algorithm as described in claim 6, characterized in that, In step S34, the selection operation uses a tournament selection method, and the crossover operation uses a single-point crossover with a crossover probability of . The mutation operation uses bitwise mutation, with a mutation probability of . .

9. The multi-machine formation cooperative deception interference optimization method based on genetic algorithm as described in any one of claims 1 to 8, characterized in that, It also includes step S4: generating cooperative jamming control commands based on the optimal cooperative jamming formation scheme, and sending the control commands to each aircraft in the formation; the control commands are used to control the airborne jammer to radiate deception jamming signals according to the false target parameters generated in step S2.

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