An unmanned aerial vehicle assisted low observable communication method based on game theory and genetic algorithm

Abstract

This application discloses a UAV-assisted low-observable communication method based on game theory and genetic algorithms, relating to the field of communication technology. The method includes: using multiple flight paths as multiple individuals in an initial population; processing various strategy combinations between the two players using an iterative algorithm to determine the optimal observer's observation strategy probability distribution; adjusting the weights of the fitness function based on a fuzzy cognitive graph and entropy weight method according to the optimal observer's observation strategy probability distribution and fitness function to determine the updated fitness value of each individual; performing genetic operations on each individual using a genetic algorithm based on the updated fitness value to determine the final individuals; and using the flight path corresponding to the final individuals as the optimal flight path to control the UAV's flight. This application can effectively adapt to changes in the observer's observation strategy, significantly reduce the observation probability, and improve the robustness of low-observable communication.

Description

Technical Field

[0001] This application relates to the field of communication technology, and in particular to a UAV-assisted low-observable communication method based on game theory and genetic algorithms. Background Technology

[0002] In today's digital age, communication technologies have permeated all sectors, making information security increasingly important. Low-observable communication (LOC) is a core technology for ensuring information security, aiming to achieve secure information transmission by reducing the detectability of communication signals. It plays a crucial role in civilian scenarios such as the transportation of high-value assets (e.g., financial escort, medical sample delivery) and the transmission of sensitive data (e.g., trade secrets, patient privacy). However, traditional LOC methods (such as spread spectrum communication) struggle to balance the multi-objective conflict between communication quality, anti-observation capability, and low observability under complex urban electromagnetic environments or dynamic interference conditions, leading to problems such as poor communication stability and insufficient concealment in practical applications.

[0003] With the rapid development of UAV technology, its flexible deployment capabilities and maneuverability have provided new opportunities for low-observable communication. UAVs can serve as mobile relay nodes, quickly establishing communication links in complex terrains and environments, expanding coverage and enhancing communication flexibility. Meanwhile, genetic algorithms, as powerful global optimization tools, have demonstrated excellent performance in UAV path planning and communication parameter optimization by simulating selection, crossover, and mutation operations in the natural evolutionary process. However, existing research on UAV-based low-observable communication still has the following key shortcomings:

[0004] First, path planning suffers from insufficient static and dynamic countermeasure capabilities. Existing methods are mostly based on the assumption of static optimization, meaning the observer's strategy remains fixed. However, in real-world scenarios, the observer dynamically adjusts its strategy based on the UAV's flight path (e.g., changing the observation direction, adjusting the scanning cycle) to maximize the probability of observing the UAV. If only genetic algorithms are used for single-step optimization, the UAV strategy may converge to a local optimum for a fixed observation strategy, failing to adapt to the observer's dynamic countermeasures, thus reducing communication stealth and system robustness. Second, there is a lack of multi-objective conflict coordination mechanisms. Low-observable communication requires a dynamic balance between communication quality (e.g., bit error rate, signal strength), anti-observation capability (e.g., path avoidance risk), and low observability (e.g., signal detection probability). Existing methods generally use fixed weight mechanisms, making it difficult to dynamically adjust the priority of optimization objectives based on real-time environmental conditions (e.g., risk level, channel quality, data priority), leading to optimization results that easily get trapped in local optima and cannot cope with multi-objective conflicts in complex scenarios. Third, there is insufficient synergy between game theory and evolutionary algorithms. While game theory can effectively model the policy interactions between the communicating and observing parties, its solution efficiency is highly dependent on the rationality of the policy space and it is difficult to directly guide the dynamic optimization of UAV paths. Genetic algorithms, while adept at global search, lack the ability to evaluate the observer's countermeasures in real time. Existing research often applies these two methods independently, failing to establish a dynamic coupling mechanism to achieve the co-evolution of policy iterative optimization and path planning.

[0005] In summary, there is an urgent need for a UAV-assisted low-observable communication method that can adapt to dynamic changes in the observer's strategy, coordinate multi-objective conflicts, and integrate the advantages of game theory and evolutionary algorithms. The aforementioned shortcomings of existing technologies limit the communication stealth and system stability of UAVs in highly adversarial scenarios, becoming a pressing technical challenge that needs to be addressed. Summary of the Invention

[0006] The purpose of this application is to provide a UAV-assisted low-observable communication method based on game theory and improved genetic algorithm. It aims to solve the technical problem in the prior art that it is difficult to balance the global optimization capability and the dynamic game requirements of the UAV and the observer, which leads to the inability to efficiently solve the optimal flight path of the UAV, thus affecting its safe execution of low-observable communication tasks.

[0007] To achieve the above objectives, this application provides the following solution.

[0008] Firstly, this application provides a UAV-assisted low-observability communication method based on game theory and genetic algorithms, comprising: using multiple flight paths as multiple individuals in an initial population; each individual representing a flight path; each flight path including multiple path points; using the UAV path strategy of the communicating party and the observation strategy of the observing party as the two sides of the game; using an iterative algorithm to process the various strategy combinations existing between the two sides of the game to determine the optimal observation strategy probability distribution; each strategy combination is determined based on the UAV path strategy and the observation strategy of the observing party; according to the optimal observation strategy probability distribution and fitness function, adjusting the weights of the fitness function based on fuzzy cognitive graph and entropy weight method to determine the updated fitness value of each individual; the fitness function is constructed based on anti-observation ability score, low observability score and communication quality score; according to the updated fitness value of each individual, using a genetic algorithm to perform genetic operations on each individual to determine the final individuals; using the flight path corresponding to the final individuals as the optimal flight path to control the flight of the UAV.

[0009] Based on the specific embodiments provided in this application, the following technical effects are disclosed.

[0010] This application uses multiple combinations of UAV flight paths as the initial population of individuals. Then, it treats the UAV path strategy of the communicating party and the observation strategy of the observing party as two players in a game. For each strategy combination, an iterative algorithm is used to process the strategy combinations to determine the probability distribution of the optimal observing party's observation strategy. This allows for accurate prediction of the observing party's observation strategy based on the optimal observation strategy probability distribution. Furthermore, based on the optimal observing party's strategy probability and the fitness function, the updated fitness value of each individual is determined. The fitness function, constructed based on anti-observation capability score, low observability score, and communication quality score, dynamically adjusts its weights using a fuzzy cognitive graph and entropy weight method. This allows the individual fitness value calculated based on the fitness function to dynamically balance the UAV's low observability, communication quality, and anti-observation capability, ensuring accurate and reliable fitness value calculation. Further, based on the updated fitness value of each individual and a genetic algorithm, the final individuals are determined, and the corresponding flight paths of these final individuals are used as the optimal flight paths to control the UAV's flight. This application alternately applies game theory and genetic algorithms, enabling the UAV to dynamically optimize its path based on the observer's latest strategy. This achieves dynamic coupling between game theory and genetic algorithms, avoiding the lag in UAV strategy caused by single optimization and maintaining the robustness of the UAV strategy in a wider range of adversarial scenarios. Through alternating iteration, the optimal flight path of the UAV is determined efficiently and accurately, significantly improving the adaptability and reliability of the UAV in complex adversarial environments. This, in turn, enhances the security and flexibility of UAV communication, enabling UAV-assisted low-observable communication. Attached Figure Description

[0011] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0012] Figure 1 This is a flowchart illustrating a UAV-assisted low-observable communication method based on game theory and genetic algorithms provided in an embodiment of this application. Detailed Implementation

[0013] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0014] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0015] Example 1

[0016] like Figure 1 As shown, this application provides a UAV-assisted low-observable communication method based on game theory and genetic algorithm, including steps 101-105.

[0017] Step 101: Use multiple flight paths as multiple individuals in the initial population; each individual represents a flight path; each flight path includes multiple waypoints.

[0018] Step 102: Treat the drone path strategy of the communicating party and the observation strategy of the observing party as the two sides of the game, and use an iterative algorithm to process the various strategy combinations that exist between the two sides to determine the probability distribution of the optimal observation strategy of the observing party; the strategy combination includes each entity as the drone path strategy and each observation strategy of the observing party; the probability distribution of the optimal observation strategy of the observing party represents the frequency of each observation strategy of the observing party being selected in the entire iteration process.

[0019] In some embodiments, step 102 specifically includes: constructing a payoff function based on the strategy combinations corresponding to the two sides of the game; and processing each strategy combination using an iterative algorithm based on the payoff function and the Nash equilibrium point to determine the probability distribution of the optimal observer's observation strategy.

[0020] In some embodiments, before step 102, the method further includes: constructing a fitness function; the process of constructing the fitness function specifically includes:

[0021] Assuming that the observer has multiple observation strategies for observing the UAV, for any individual in the initial population, the probability that the observer will observe the individual using any observation strategy is defined as the comprehensive observation probability. Based on the comprehensive observation probability, the individual's anti-observation capability score is determined. Based on the distance between the various flight paths and the observer's observation area, the individual's low observability score is determined. Based on the signal strength and bit error rate of the communication link, the individual's communication quality score is determined. Based on the anti-observation capability score, the low observability score, and the communication quality score, a fitness function is constructed.

[0022] In this process, after constructing the fitness function, the weights of the fitness function are corrected based on the fuzzy cognitive graph and the entropy weight method to determine the updated fitness value of each individual.

[0023] In some embodiments, the low observability score is: .

[0024] in, Indicates flight path The Middle The shortest distance from each path point to the observation area of ​​the observer; The number of path points; Flight path The low observability score.

[0025] In some embodiments, the communication quality score is: .

[0026] in, ; ; Flight path The Middle Signal strength at each path point For transmission power, and These represent the antenna gains at the transmitting and receiving ends, respectively. For carrier wavelength, Flight path The Middle The distance between each path point and the receiver Flight path The Middle Bit error rate per path point; The function is the Gaussian error function. For noise power spectral density, For signal bandwidth; Flight path The communication quality score.

[0027] In some embodiments, the anti-observation capability score is as follows.

[0028] .

[0029] in, Flight path The Middle Each path point is observed in the observation strategy. The probability of being detected. Selecting an observation strategy for the observer from the probability distribution of the optimal observer's observation strategy The probability, The number of observation strategies employed by the observer; Flight path The score for resistance to observation, i.e., the flight path of the drone. Observation strategy of the observer The ability to withstand observation.

[0030] In some embodiments, the fitness function is as follows.

[0031] .

[0032] in, Flight path fitness value; Flight path Communication quality score; Flight path The score for resistance to observation; Flight path The low observability score; and They are respectively and The corresponding weights.

[0033] Step 103: Based on the probability distribution of the optimal observer's observation strategy and the fitness function, the weights of the fitness function are corrected using the fuzzy cognitive graph and entropy weight method to determine the updated fitness value for each individual; the fitness function is constructed based on the anti-observation ability score, the low observability score, and the communication quality score.

[0034] Step 104: Based on the updated fitness value of each individual, perform genetic operations on each individual using a genetic algorithm to determine the final individuals.

[0035] Step 105: Use the flight paths corresponding to each of the final entities as the optimal flight paths to control the UAV flight.

[0036] In some embodiments, step 103 specifically includes steps 201-202.

[0037] Step 201: Based on the fuzzy cognitive graph and the entropy weight method, the weights of the fitness function are corrected to determine the updated weights.

[0038] Step 202: Determine the updated fitness function based on the updated weights and the probability distribution of the optimal observer's observation strategy, and determine the updated fitness value for each individual based on the updated fitness function.

[0039] In some embodiments, step 201 specifically includes: constructing a threat level, a channel quality index, and a data priority; performing fuzzy inference mapping on the threat level, the channel quality index, and the data priority, and determining the activation intensity corresponding to each preset fuzzy rule based on multiple preset fuzzy rules; the multiple preset fuzzy rules are determined based on prior knowledge; determining the weights of the fitness function according to each activation intensity and the centroid method for defuzzification; introducing information entropy according to the entropy weight method, correcting the weights based on the information entropy, and determining the updated weights.

[0040] In some embodiments, the threat level for: .

[0041] in, The shortest distance from the path point to the observation area. This is the critical distance for risk. The distance sensitivity coefficient, It is a natural exponential function.

[0042] Channel Quality Index : .

[0043] in, For the first Bit error rate per path point For the target bit error rate, This is the maximum tolerance value; This represents the number of waypoints in the flight path.

[0044] The data priority is The Includes multiple preset values.

[0045] Specifically, there is an inherent conflict between the optimization objectives of low observability, communication quality, and anti-observation capability. To overcome the limitations of fixed weights, a collaborative strategy of fuzzy cognitive graphs and entropy weighting is adopted to dynamically update the weights of the fitness function, as detailed below.

[0046] 1) Quantification of environmental parameters.

[0047] Threat Level as follows.

[0048]

[0049] in, The shortest distance from the path point to the observation area. , This is the critical distance for risk. Radius of the observation equipment; This is the distance sensitivity coefficient; It is a natural exponential function.

[0050] Channel Quality Index :

[0051]

[0052] in, path point (i.e., the first) The bit error rate of (each path point), For the target bit error rate, This is the maximum tolerance value; This represents the number of path points.

[0053] Data Priority , Static allocation based on the data type transmitted by the drone: regular monitoring data, encrypted business data, and emergency control commands are respectively assigned to... .

[0054] For example, in a medical supplies transportation mission: patient vital signs telemetry data is regarded as routine monitoring data, and DPR=0.3; encrypted electronic medical records are regarded as encrypted business data, and DPR=0.5; emergency instructions are regarded as emergency control instructions, and DPR=0.7.

[0055] 2) Fuzzy inference mapping.

[0056] Normalization Mapping to fuzzy semantics (low / medium / high), the three membership functions are defined as follows.

[0057] .

[0058] in, The low membership function for fuzzy inference is used to map the normalized input parameters to the membership degree of the fuzzy semantic variable "low". The medium membership function for fuzzy inference is used to map the normalized input parameters to the membership degree of the fuzzy semantic variable "medium". The high membership function for fuzzy inference is used to map the normalized input parameters to the membership degree of the fuzzy semantic variable "high".

[0059] 3) Preset activation of the fuzzy rule base and weight calculation.

[0060] Examples of preset fuzzy rules are as follows.

[0061] Rule 1: When the fuzzy semantics of the threat level is "high" (i.e., the membership degree mapped by the high membership function dominates), the fuzzy semantics of the channel quality index is "medium" (the membership degree mapped by the medium membership function dominates), and the fuzzy semantics of the data priority is "low" (the membership degree mapped by the low membership function dominates).

[0062] Set the weight assignment: the weight of the low observability score is "high"; the weight of the communication quality score is "medium"; the weight of the anti-observability ability score is "low".

[0063] Rule 2: When the fuzzy semantics of the threat level is "low" (i.e., the membership degree mapped by the low membership function dominates), the fuzzy semantics of the channel quality index is "high" (i.e., the membership degree mapped by the high membership function dominates), and the fuzzy semantics of the data priority is "medium" (i.e., the membership degree mapped by the medium membership function dominates).

[0064] Set the weight assignment: the weight of the low observability score is "low"; the weight of the communication quality score is "high"; the weight of the anti-observability ability score is "medium" (the safe area focuses on reliable transmission).

[0065] The weights are generated by defuzzification using the centroid method, and at this time the weights are the initial values: .

[0066] Among them, is the rule index of each preset fuzzy rule in the fuzzy rule base (a total of 27 rules, ); is the activation intensity corresponding to the r-th preset fuzzy rule; The index of the weight (values ​​are 1, 2, 3). For the r-th preset fuzzy rule The preset weights.

[0067] .

[0068] in, For the first In each preset fuzzy rule Fuzzy semantic levels; For the r-th preset fuzzy rule The fuzzy semantic level; For the r-th preset fuzzy rule The level of fuzzy semantics.

[0069] 4) Dynamic correction using entropy weight method.

[0070] To reduce reliance on subjective opinions, information entropy is introduced. Adjust the initial value of the weights ( ), determine the updated weights , , .

[0071] .

[0072] in, The values ​​are 1, 2, and 3. For the first In the preset fuzzy rules Preset weights; for The sum of preset weights among all preset fuzzy rules; for In the The weighting percentage in a pre-defined fuzzy rule; Information entropy is assigned to the weights corresponding to low observability, communication quality, and anti-observation capability, respectively, to quantify the disorder (i.e. uncertainty) of the weight distribution.

[0073] The fitness function is updated based on the corrected weights.

[0074] In some embodiments, step 104 specifically includes steps 301-303.

[0075] Step 301: Based on the updated fitness value of each individual, perform genetic operations on each individual using a genetic algorithm to determine each new individual.

[0076] Step 302: Replace each individual with the new individuals, return to step "treat the drone and the observer as two sides in a game in game theory, use an iterative algorithm to process each strategy combination, determine the probability distribution of the optimal observer's observation strategy", and determine the fitness value of each new individual.

[0077] Step 303: Based on the preset threshold, the updated fitness value of each individual, and the fitness value of each new individual, determine the final individuals.

[0078] In some embodiments, step 303 specifically includes: determining the difference between the fitness value of each new individual and the updated fitness value of each individual; determining whether the difference is less than or equal to the preset threshold, and determining a first determination result; if the first determination result is yes, taking each new individual as the final individual; if the first determination result is no, taking each new individual as the individual in the initial population, and returning to step "based on the updated fitness value of each individual, performing genetic operations on each individual using a genetic algorithm to determine each new individual", until the difference is less than or equal to the preset threshold.

[0079] Example 2.

[0080] In practical applications, the UAV-assisted low-observable communication method based on game theory and genetic algorithms provided in this application includes the following steps.

[0081] Step 1: Communication scenario modeling and genetic algorithm population initialization.

[0082] In the communication scenario, the positions of both communicating parties include the (three-dimensional) coordinates of the sending end as the starting point. (3D) coordinates of the receiving end as the endpoint The (3D) coordinates of the vertices of the observation area. .

[0083] The initialized genetic algorithm population, where each individual contains a flight path. The flight path consists of multiple discrete waypoints; the number of waypoints is... .

[0084] The specific process is as follows.

[0085] 3D path generation: The flight path of each individual must satisfy the following condition in the Cartesian coordinate system: the starting coordinates are... The endpoint coordinates are The intermediate path points are randomly distributed in three-dimensional space as follows.

[0086]

[0087] The minimum width range is The maximum width range is The minimum length range is The maximum length range is Minimum height range Minimum height range (Δh is the preset height fluctuation value). Wherein, It is uniformly distributed.

[0088] Step 2: Modeling the observation strategy and calculating the observation probability.

[0089] Input: Set of observation strategies for the observer Observation equipment parameters (observation radius) Azimuth Beamwidth Scan cycle Observation point height ), drone flight speed .

[0090] Output: The p-th path point in the observation strategy The overall probability of being observed .

[0091] The technical details are as follows.

[0092] 1. Physical layer observation probability: For UAVs With observation strategy Define instantaneous observation probability .

[0093] .

[0094] in, For distance attenuation; For azimuth attenuation; This affects signal quality.

[0095] in, ; For the p-th path point to the observation device j The three-dimensional Euclidean distance; ; The absolute azimuth of the p-th path point With the direction of the main beam The minimum included angle deviation between them; The beamforming factor, also known as the directional attenuation index; The main direction of observation; ; For observation equipment j The signal-to-noise ratio received at the p-th path point, For transmission power, For antenna gain, For wavelength, For noise power spectral density, The bandwidth is defined as follows: the observation equipment is the observer.

[0096] Azimuth coverage angle constraint: The observation probability is calculated only if the following condition is met: .in, This is the azimuth coverage angle (half-power beamwidth). Otherwise: combined observation probability. .

[0097] 2. Time-domain observation probability .

[0098] Considering the impact of scan cycle: .

[0099] Constraints: .

[0100] in: The scan cycle; This refers to the flight speed of the drone.

[0101] 3. Overall Observation Probability .

[0102] .

[0103] in: This represents the strategy type coefficient. Weighted average (routine observation) was used. The principle of selecting the largest value should be adopted (applicable to alert observation). and All are physical layer / temporal domain observation weights, satisfying .

[0104] Step 3: Fitness function design and dynamic weight update mechanism.

[0105] Input: Flight path of each individual ; Observer's observation strategy probability distribution (From step four output); Environmental dynamic parameters (threat level) Channel quality index Data priority );

[0106] Output: Fitness value for each individual And dynamic weights.

[0107] The specific process is as follows.

[0108] 1. Low observability score : .

[0109] in, Indicates flight path The Middle The shortest distance from each path point to the observation area of ​​the observer; The number of path points; Flight path The low observability score.

[0110] The larger the value, the further the drone's flight path is from the observer's observation area, and the better its communication concealment.

[0111] 2. Communication Quality Score : .

[0112] in, ; ; Flight path The Middle Signal strength at each path point For transmission power, and These represent the antenna gains at the transmitting and receiving ends, respectively. For carrier wavelength, Flight path The Middle The distance between each path point and the receiver Flight path The Middle Bit error rate per path point; The function is the Gaussian error function. For noise power spectral density, For signal bandwidth; Flight path Communication quality score; The number of path points; Flight path Communication quality score under the observer's observation strategy; The higher the value, the better the communication quality.

[0113] 3. Score for resistance to observation : .

[0114] in, Flight path The Middle The path point is at the _ The probability of being detected under each observer's observation strategy For the first The probability of each observer's observation strategy. The number of observation strategies employed by the observer; Flight path The score for the ability to resist observation under the observer's observation strategy. The larger the value, the lower the probability of the drone being observed when facing various observation strategies of the observer, and the stronger its counter-observation capability.

[0115] 4. Definition of fitness function.

[0116] Taking into account stealth, communication quality, and ability to counter observation, the fitness function The definition is as follows.

[0117] .

[0118] in, Flight path Fitness value; Flight path Communication quality score; Flight path The score for resistance to observation; Flight path The low observability score.

[0119] in, 、 and They are respectively and The corresponding weights, i.e., the weight coefficients of the fitness function, and These weighting coefficients are adjusted according to actual needs; if greater emphasis is placed on concealment, then... The value is relatively large; if communication quality is of greater importance, then... The value is relatively large; if more emphasis is placed on the ability to counter observation, then The value is relatively large.

[0120] 5. Adaptive weight update mechanism.

[0121] In dynamic game environments, the optimization objectives of low observability, communication quality, and anti-observation capability inherently conflict. To overcome the limitations of fixed weights, a collaborative strategy combining fuzzy cognitive graphs and entropy weighting is employed to dynamically update the weight vector.

[0122] 1) Quantification of environmental parameters.

[0123] Threat Level : .

[0124] in, is the shortest distance from the path point to the observation area, , is the risk critical distance; is the radius of the observation device; is the distance sensitivity coefficient; is the natural exponential function.

[0125] Channel Quality Index : .

[0126] Among them, is the path point (i.e., the th path point) bit error rate, is the target bit error rate, is the maximum tolerance value; is the number of path points.

[0127] Data Priority , is statically allocated according to the data types transmitted by the UAV: regular data, encrypted data, and emergency instructions respectively correspond to .

[0128] Exemplarily, in the medical supply transportation task: the patient's vital sign telemetry data is regarded as regular monitoring data (DPR = 0.3); the encrypted electronic medical record is regarded as encrypted service data (DPR = 0.5); the emergency instruction is regarded as an emergency control instruction (DPR = 0.7).

[0129] 2) Fuzzy inference mapping.

[0130] Map the normalized to fuzzy semantics (low / middle / high), and three membership functions are defined as: .

[0131] Among them, is the low membership function of fuzzy inference, which is used to map the normalized input parameter to the membership degree of the fuzzy semantic variable "low"; is the middle membership function of fuzzy inference, which is used to map the normalized input parameter to the membership degree of the fuzzy semantic variable "middle"; is the high membership function of fuzzy inference, which is used to map the normalized input parameter to the membership degree of the fuzzy semantic variable "high".

[0132] 3) Activation of the preset fuzzy rule base and weight calculation.

[0133] Examples of preset fuzzy rules are as follows.

[0134] Rule 1: When the fuzzy semantics of the threat level (TQ) is "high" (i.e., through the high membership function The membership degree of the mapping is dominant, and the fuzzy semantics of the Channel Quality Index (CQI) is "neutral" (through the neutral membership function). The fuzzy semantics of the mapping's membership degree (which is dominant) and data priority (DPR) is "low" (through low membership functions). When the membership degree of the mapping is dominant.

[0135] Set weight allocation: weight for low observability scores. "High" is the weighting for the communication quality score. The score is "medium"; weighting of the anti-observation capability score. It is "low".

[0136] Rule 2: When the fuzzy semantics of the threat level (TQ) is "low" (i.e., through a low membership function) The fuzzy semantics of the Channel Quality Index (CQI), which is dominated by the membership degree of the mapping, is "high" (i.e., through a high membership function). The fuzzy semantics of the mapping's membership degree as dominant and data priority (DPR) is "medium" (i.e., through the medium membership function). When the membership degree of the mapping is dominant.

[0137] Weighting is set as follows: Low observability score weight w1 is "low"; communication quality score weight w2 is "high"; and anti-observation ability score weight w3 is "medium" (the security zone emphasizes reliable transmission).

[0138] Weights are generated by unfuzzing using the centroid method: .

[0139] in, For each preset fuzzy rule in the fuzzy rule base, there is a rule index (a total of 27 rules). ); The activation intensity corresponding to the r-th preset fuzzy rule; The index of the weight (values ​​are 1, 2, 3). For the r-th preset fuzzy rule The preset weights.

[0140] .

[0141] in, For the first In each preset fuzzy rule Fuzzy semantic levels; For the r-th preset fuzzy rule The fuzzy semantic level; For the r-th preset fuzzy rule The level of fuzzy semantics.

[0142] 5) Dynamic correction using entropy weight method.

[0143] To reduce reliance on subjective opinions, information entropy is introduced. The corrected weights determine the updated weights as follows, where, The values ​​are 1, 2, and 3.

[0144] .

[0145] in, For the first In the preset fuzzy rules Preset weights; for The sum of the preset weights in all preset fuzzy rules (27 fuzzy rules); for In the The weighting percentage in the preset fuzzy rules; Information entropy is assigned to the weights corresponding to low observability, communication quality, and anti-observation capability, respectively, to quantify the disorder (i.e. uncertainty) of the weight distribution.

[0146] Based on the updated weights , and Update the fitness function.

[0147] Step 4: Solve for Nash equilibrium based on game theory, as follows.

[0148] Input: Drone strategy space (Individuals in the genetic algorithm population, each) Corresponding to a path ); set of observation strategies for the observer Profit Matrix .

[0149] Output: Probability distribution of the optimal observer's observation strategy (Observer selects each strategy) The probability of ( ).

[0150] Define the drone policy space (i.e., the set of drone policies) as follows: Each strategy A corresponding flight path for a drone Defined as: in For strategy (i.e., flight path) The starting point three-dimensional coordinates, For strategy The endpoint three-dimensional coordinates.

[0151] Population size: (Number of candidate solutions generated by the genetic algorithm).

[0152] Observer's set of observation strategies: .

[0153] For the first The observation strategy includes the parameters of the observation equipment: ,in For the first The effective observation radius of this observation strategy For the first The main observation direction of this observation strategy For the first Beamwidth of the observation strategy For the first The scanning cycle of the observation strategy For the first The observation point height for each observation strategy.

[0154] definition: That is, the observation strategy of the observer. Below, drone strategy The fitness value (from step three). This indicates that when using a drone strategy and observation strategy The revenue of the drone. The revenue function of the communicating party. This can be mapped to evaluating flight paths in a genetic algorithm. Fitness function Each strategy A corresponding flight path for a drone .

[0155] Assume the strategy combination corresponding to the Nash equilibrium is ,in, The optimal drone strategy (flight path). This is the optimal observation strategy.

[0156] Nash equilibrium condition: This means that neither party can increase its profits by unilaterally changing its strategy.

[0157] Example:

[0158] 1. Game theory model construction.

[0159] Participants: Communicator (Player 1): Choose Strategy In order to maximize their own benefits.

[0160] Observer (Player 2): Choose a strategy To maximize the probability of observing drones.

[0161] Strategy Space: Drone Strategy Space (i.e., the set of drone strategies), defined by a genetic algorithm population.

[0162] Observer's observation strategy space That is, the set of observation strategies of the observer.

[0163] Profit Matrix That is, based on the drone revenue matrix A definite set of returns.

[0164] .

[0165] 2. Fictional game theory algorithm.

[0166] Since directly solving for Nash equilibrium can be quite complex, iterative algorithms can be used for approximate solutions. For example, a hypothetical game algorithm can be employed.

[0167] Objective: To approximate the Nash equilibrium point through iterative strategy updates.

[0168] 1) Initialization: Initial strategy for drones: Randomly select an individual .

[0169] Initial observation strategy: Randomly select an observation strategy. .

[0170] Historical strategy frequency: (Uniform distribution) (Uniformly distributed).

[0171] N The total number of individuals; k The number of observation strategies employed by the observer; For the first A drone strategy The corresponding initial policy frequency; For the first j Individual observation strategy The corresponding initial policy frequency.

[0172] 2) Iterative process (the first) (nth iteration).

[0173] Drone strategy update: Calculation of the first Expected return under the observer's observation strategy distribution corresponding to the current iteration: .in, For the first The iteration of the ... jThe initial strategy frequency corresponding to the observation strategy of each observer; For the first Distribution of observation strategies for the next iteration.

[0174] Choose the drone strategy that yields the highest expected returns. : .

[0175] The observer's observation strategy has been updated as follows.

[0176] Calculate the expected observation probability under the current policy distribution of the UAV:

[0177] The observer strategy distribution corresponding to the maximum value in the expected observation probability is selected as the first... The distribution of the observer's observation strategy corresponding to the next iteration (next iteration) is used as follows: express:

[0178] The frequency of updating historical strategies is as follows.

[0179] Drone strategy frequency: in This is an indicator function (1 if the condition is true, 0 otherwise). For the first The policy frequency corresponding to the next iteration of the drone policy; For the first The current iteration of the drone strategy corresponds to the strategy frequency.

[0180] Observer's observation strategy frequency: . Let the frequency of the observation strategy of the j-th observer be the policy frequency corresponding to the next iteration of the observation strategy. Let be the policy frequency corresponding to the current iteration of the observation policy of the j-th observer.

[0181] 3) Convergence criterion: When continuous The iteration terminates when the policy change is less than the threshold. Output Nash equilibrium strategy combination .

[0182] 4) Update the observation strategy probability distribution of the observer. (i.e., the corresponding time to determine convergence) ).

[0183] Specifically, the set of observation strategies of the observer. Probability distribution of the observer's observation strategy The relationship is as follows.

[0184] Observer's observation strategy set ,definition: , representing the set of all observation strategies available to the observer. Each strategy This represents a specific observation method, for example: High-frequency scanning and fixed-direction observation; Low-frequency scanning and dynamic orientation adjustment; Random scanning and highly sensitive observation. In other words, It is the "action library" of all possible choices for the observer.

[0185] The observer uses a probability distribution selection strategy. .

[0186] definition: , representing the probability distribution of each observer's choice of observation strategy under Nash equilibrium. Wherein, , To select a strategy The probability of; The sum of all probabilities is 1.

[0187] For example, if This indicates that the observer has a 60% probability of choosing... 40% probability of choosing .

[0188] effect: It is the optimal hybrid strategy formulated by the observer to maximize its own benefits (observation drones).

[0189] After multiple iterations, the observer's policy frequency will converge to a certain distribution, which is the observer's optimal policy probability distribution. , j∈K. Specifically, the observer's observation strategy probability It is based on the strategy chosen by the observer during the game. It is calculated based on historical frequency. For example, if the observer has a total of T games... The next strategy was chosen. ,but = / T.

[0190] Where S*=( S is the probability distribution of the observer's optimal strategy combination, representing the set of observation strategies S={ when the game reaches Nash equilibrium. The probability corresponding to each strategy in}.

[0191] By iteratively approximating the Nash equilibrium point, the... The probability of the observer's observation strategy corresponding to the next iteration Calculated based on historical selection frequency. The specific formula for the observer's observation strategy probability corresponding to the next iteration is: .

[0192] Where: the number of historical choices represents the number of strategies chosen by the observer during game iterations. The total number of times.

[0193] The total number of game rounds is the total number of iterations of the game. .

[0194] For example, if the observer chooses in 10 rounds of the game 7 times 3 times, then: .

[0195] If the Nash equilibrium is a mixed-policy equilibrium (where the observer chooses a policy based on a probability distribution), then It is given directly from the equilibrium solution. For example, the equilibrium solution might be: .

[0196] At this point, the observer chooses with an 80% probability. 20% choice .

[0197] Updated The fitness function is used to calculate the overall performance of the UAV strategy under different observer strategies. The fitness function formula is: .

[0198] Step 5: Iterative optimization using genetic algorithm (coupling with step 4).

[0199] Input: Observer's observation strategy probability distribution Genetic algorithm parameters (crossover probability) Probability of mutation Maximum number of iterations Variable Asynchronous Length Output: New generation population .

[0200] 1. Select the action (roulette).

[0201] Calculate the total fitness of the population:

[0202] Individual choice probability: .

[0203] Generate random numbers Individuals are selected to enter the mating pool based on probability.

[0204] 2. Cross operation (single-point cross).

[0205] Randomly select two parent individuals and Randomly select intersection points .

[0206] The path for generating offspring is as follows.

[0207] .

[0208] Among them, two parent individuals are randomly selected. and Randomly select intersection points ( ), For path points, child Inheritance from the father The former path points (i.e.) ) and parent generation After path points (i.e.) )composition, Similarly, offspring by father The former Point (i.e.) ) and parent generation After Point (i.e.) )composition,

[0209] 3. Mutation operation (Gaussian perturbation).

[0210] Path point coordinate variation: .

[0211] in, Representing path points The original horizontal coordinates (longitude, latitude, altitude); Indicates the new coordinates after the mutation; Represents the random perturbation values ​​of the coordinates (following a uniform distribution); Indicates a variable length in the horizontal direction; Indicates a variable length in the vertical direction. It follows a uniform distribution.

[0212] Variable Asynchronous Length The following adjustments will be made dynamically based on the threat level.

[0213] .

[0214] .

[0215] in, The adjustment coefficient controls the sensitivity of the step size adjustment. For the first The horizontal variation of the generation is asynchronous; For the first The vertical variable asynchronous length of the generation; For the first The adjusted horizontal variable asynchronous length; For the first The adjusted vertical variable asynchronous length; The maximum detection probability represents the current optimal path. In all observation strategies The highest probability of being observed; The radius is the observation radius.

[0216] 4. Elite retention strategy.

[0217] Retain the most fit individuals of the present generation Replace the individual with the lowest fitness in the new population.

[0218] .

[0219] in, For the first The new population of the next generation, that is, the new set of paths generated by the genetic algorithm; The worst path is the one with the lowest fitness in the new population. Current generation (the first generation) The individual with the highest fitness in a generation represents the optimal path. This is a set difference operation, representing the removal of elements from the new population. ; For set union operations, it means to combine sets. Joining a new population.

[0220] 5. Game theory feedback update (closed-loop coupling).

[0221] New population Enter the information in step four to update the observer's observation strategy probability. .

[0222] According to the new and threat level Channel quality CQI Data priority DPR Dynamically adjust variable asynchronous length and weight .

[0223] Example: Setting initial parameters: Population size: ; Number of path points: ; Initial change asynchronous length: Initial observer's observation strategy probability: .

[0224] 1. Assume the initial population consists of:

[0225] individual :path: .

[0226] individual :path: .

[0227] 2. First iteration ( ).

[0228] Fitness calculation:

[0229] individual : .

[0230] individual : .

[0231] Selection Operation: Select Twice (due to higher adaptability).

[0232] Crossover operation: The parent is the same, and no new individuals are generated.

[0233] Mutation operation: Individual Mutation Path points Disturbance is Other parameters remain unchanged.

[0234] Elite retention: Retention Replace the mutated The new population is: .

[0235] Step 4 (Game Theory Feedback Update): Input the new population Observer's set of observation strategies .

[0236] Solving for Nash Equilibrium: Observer Selection (Higher observation probability), update strategy probability:

[0237] Adjusting the variable asynchronous length: .

[0238] 3. Second iteration ( ).

[0239] 1) Fitness calculation (using the updated version) ).

[0240] individual Path points To the observation point ,

[0241] Communication quality (Assuming the channel is good).

[0242] Overall observation probability: Down .

[0243] Down , .

[0244] Dynamic weights (assuming) ) .

[0245] individual Path points to the observation point , Communication quality (The greater the distance, the slightly higher the error rate).

[0246] Observation probability: Down , Down ,

[0247] Fitness is calculated as follows.

[0248] 2) Selection operation: Total fitness: .

[0249] Selection probability: .

[0250] Random number generation: hypothetical generation (Selected) ), (Selected) ).

[0251] 3) Crossover operation: Parent selection: and Intersection: (Third path point).

[0252] Offspring generation: Offspring :path: Communication parameters: , Offspring :path: .

[0253] 4) Mutation operation: offspring Variation: Path point Disturbance is ( ).

[0254] offspring Variation: Path point Disturbance is .

[0255] 5) Elite Preservation: Current Best Individual: (Fitness 0.616). Replace the worst individual: Assuming the mutated individual... The one with the lowest fitness is replaced. New population:

[0256] 6) Call step four (game feedback update): Input the new population :Include and Solving a hypothetical game: Observer selection (because exist (The probability of observation is higher in the next observation). Update the observation strategy probability: Adjusting the variable asynchronous length: .

[0257] 4. Third iteration ( (and subsequent events)

[0258] Repeat the above steps until the termination condition is met (e.g., the change in fitness is less than a threshold). Or reach the maximum number of iterations ).

[0259] The final output is the optimal number. The most adaptable UAV configuration. Observer's observation strategy probability: converges to... .

[0260] After generating the new population in step five, the observation strategy and parameters of the observer are updated in step four. The output of step four ( and This directly affects the fitness calculation and mutation operation in step five. Dynamic adjustment mechanism: Observer's observation strategy probability: reflects the observer's countermeasure strategy against UAV behavior. Variable timing: dynamically adjusted according to observation risk, enhancing global search capability in high-risk situations. Elite retention: ensures the optimal solution of each generation is not eliminated, accelerating convergence. Through this closed-loop iteration, the UAV strategy is gradually optimized, ultimately achieving an optimal balance between stealth, communication quality, and anti-observation capability. This application dynamically couples game theory with genetic algorithms, achieving closed-loop optimization of "strategy generation" and "strategy evolution" through alternating execution. This dynamic coupling has the following core advantages.

[0261] 1. Dynamic adversarial requirements: The observer's observation strategy will be adjusted in real time according to the behavior of the UAV. Alternating the execution of game theory and genetic algorithm can enable the UAV to dynamically optimize the path and communication parameters according to the latest strategy of the observer, avoiding the strategy lag caused by single optimization.

[0262] 2. Avoiding local optima: Genetic algorithms may get stuck in local optima under a fixed observer strategy, while game theory, by introducing multi-strategy equilibrium solutions for the observer, forces the drone strategy to remain robust in a wider range of adversarial scenarios.

[0263] 3. Mathematical Complementarity: Genetic algorithms excel at global searches in complex solution spaces but lack adversarial evaluation; game theory provides adversarial payoff calculations but relies on the completeness of the strategy space. Combining the two can compensate for their respective theoretical limitations, forming a synergistic mechanism of "optimization-feedback-re-optimization".

[0264] Specifically, the game theory module provides real-time feedback on the observer's strategy to the genetic algorithm through Nash equilibrium solutions, redefining the optimization weights and directions of the fitness function. Meanwhile, the new generation of the genetic algorithm expands the strategy space for game theory, enhancing the diversity of equilibrium solutions. Through alternating iterations, the UAV strategy gradually approaches a dynamic optimal balance between stealth, communication quality, and anti-observation capabilities, thereby significantly improving the system's adaptability and reliability in complex adversarial environments.

[0265] This application constructs a UAV flight path as the initial population for a genetic algorithm; it builds a dynamic game model between the communicator and the observer; based on the new path population generated by the genetic algorithm, it iteratively solves the Nash equilibrium through the game algorithm to update the probability distribution of the observer's observation strategy; the observer's observation strategy probability output from the game is fed back to the genetic algorithm, and combined with an adaptive weighting mechanism based on fuzzy cognitive graphs and entropy weighting, the weights of stealth, communication quality, and anti-observation capability in the fitness function are dynamically adjusted according to real-time threat level, channel quality, and data priority; the selection, crossover, and mutation operations of the genetic algorithm are performed based on the updated fitness values ​​to generate a new generation of path populations; through the alternating iteration of the genetic algorithm and the game theory module, a closed-loop system of "genetic optimization-game feedback-weight adjustment" is formed, outputting the optimal flight path. Through the dynamic coupling mechanism and adaptive weight allocation of the fitness function, this application can effectively adapt to changes in the observer's observation strategy, significantly reduce the observation probability, and improve the robustness of low-observable communication.

Claims

1. A UAV-assisted low-observable communication method based on game theory and genetic algorithms, characterized in that, include: Multiple flight paths are used as multiple individuals in the initial population; each individual represents a flight path. Each flight path includes multiple waypoints; The drone path strategy of the communicating party and the observation strategy of the observing party are regarded as the two sides of the game. An iterative algorithm is used to process the various strategy combinations between the two sides to determine the probability distribution of the optimal observation strategy of the observing party. Each strategy combination is determined based on the drone path strategy and the observation strategy of the observing party. Based on the probability distribution of the optimal observer strategy and the fitness function, the weights of the fitness function are corrected using fuzzy cognitive graphs and entropy weighting method to determine the updated fitness value for each individual. The fitness function is constructed based on the anti-observation capability score, the low observability score, and the communication quality score; Based on the updated fitness value of each individual, a genetic algorithm is used to perform genetic operations on each individual to determine the final individuals; The flight paths corresponding to each of the final entities are used as the optimal flight paths to control the drone's flight.

2. The UAV-assisted low-observable communication method based on game theory and genetic algorithm according to claim 1, characterized in that, The drone path strategy of the communicating party and the observation strategy of the observing party are treated as the two sides of a game. An iterative algorithm is used to process the various strategy combinations between the two sides to determine the probability distribution of the optimal observation strategy of the observing party. Specifically, this includes: Based on the various strategy combinations for both sides in the game, construct the payoff function; Based on the aforementioned payoff function and Nash equilibrium point, an iterative algorithm is used to process each strategy combination to determine the probability distribution of the optimal observer's observation strategy.

3. The UAV-assisted low-observable communication method based on game theory and genetic algorithm according to claim 1, characterized in that, Based on the probability distribution of the optimal observer strategy and the fitness function, the weights of the fitness function are adjusted using fuzzy cognitive graphs and entropy weighting method to determine the updated fitness value for each individual, specifically including: The weights of the fitness function are corrected based on the fuzzy cognitive graph and the entropy weight method to determine the updated weights; Based on the updated weights and the probability distribution of the optimal observer's observation strategy, an updated fitness function is determined, and based on the updated fitness function, an updated fitness value for each individual is determined.

4. The UAV-assisted low-observable communication method based on game theory and genetic algorithm according to claim 3, characterized in that, The weights of the fitness function are corrected based on fuzzy cognitive graphs and entropy weight method to determine the updated weights, specifically including: Construct threat levels, channel quality indices, and data priorities; The threat level, the channel quality index, and the data priority are subjected to fuzzy inference mapping, and the activation intensity corresponding to each preset fuzzy rule is determined based on multiple preset fuzzy rules; the multiple preset fuzzy rules are determined based on prior knowledge. The weights of the fitness function are determined based on the activation intensities and the centroid method for fuzzy resolution. Information entropy is introduced according to the entropy weight method, and the weight is adjusted based on the information entropy to determine the updated weight.

5. The UAV-assisted low-observable communication method based on game theory and genetic algorithm according to claim 1, characterized in that, Before treating the drone path strategy of the communicating party and the observation strategy of the observing party as the two sides of a game, and using an iterative algorithm to process the various strategy combinations existing between the two sides to determine the probability distribution of the optimal observation strategy of the observing party, the following steps are also included: Construct the fitness function; The construction process of the fitness function specifically includes: Assuming that the observer has multiple observation strategies for observing the UAV, for any individual in the initial population, the probability that the observer observes the individual using any observation strategy is defined as the comprehensive observation probability. Based on the comprehensive observation probability, the individual's anti-observation ability score is determined; The low observability score of the individual is determined based on the distance between various flight paths and the observation area of ​​the observer; The communication quality score of the individual is determined based on the signal strength and bit error rate of the communication link; A fitness function is constructed based on the anti-observation capability score, the low observability score, and the communication quality score.

6. The UAV-assisted low-observable communication method based on game theory and genetic algorithm according to claim 1, characterized in that, Based on the updated fitness value of each individual, a genetic algorithm is used to perform genetic operations on each individual to determine the final individuals, specifically including: Based on the updated fitness value of each individual, a genetic algorithm is used to perform genetic operations on the population individuals to determine each new individual; Replace each individual with the new individuals, return to step "treat the UAV path strategy of the communicating party and the observation strategy of the observing party as the two sides of the game, use an iterative algorithm to process the strategy combinations that exist between the two sides of the game, and determine the probability distribution of the optimal observation strategy of the observing party", and determine the fitness value of each new individual. Based on a preset threshold, the updated fitness value of each individual, and the fitness value of each new individual, the final individuals are determined.

7. The UAV-assisted low-observable communication method based on game theory and genetic algorithm according to claim 6, characterized in that, Based on a preset threshold, the updated fitness value of each individual, and the fitness value of each new individual, the final individuals are determined, specifically including: Determine the difference between the fitness value of each new individual and the updated fitness value of each individual; Determine whether the difference is less than or equal to the preset threshold, and determine the first determination result; If the first determination result is yes, then each new individual is taken as the final individual; If the first judgment result is negative, each new individual is taken as an individual in the initial population, and the process returns to the step "Based on the updated fitness value of each individual, genetic operations are performed on each individual using a genetic algorithm to determine each new individual" until the difference is less than or equal to the preset threshold.

8. The UAV-assisted low-observable communication method based on game theory and genetic algorithm according to claim 1, characterized in that, The low observability score is: ； in, Indicates flight path The Middle The shortest distance from each path point to the observation area of ​​the observer; The number of path points; Flight path The low observability score; The communication quality score is: ； in, ; ; Flight path The Middle Signal strength at each path point For transmission power, and These represent the antenna gains at the transmitting and receiving ends, respectively. For carrier wavelength, Flight path The Middle The distance between each path point and the receiver Flight path The Middle Bit error rate per path point; The function is the Gaussian error function. For noise power spectral density, For signal bandwidth; Flight path Communication quality score; The number of path points; Flight path Communication quality score under the observer's observation strategy; The score for resistance to observation is: ； in, Flight path The Middle The path point is at the _ The probability of being detected under each observer's observation strategy The probability distribution of the optimal observer's observation strategy is the th The probability of each observer's observation strategy. The number of observation strategies employed by the observer; Flight path The score for the ability to resist observation under the observer's observation strategy.

9. The UAV-assisted low-observable communication method based on game theory and genetic algorithm according to claim 1, characterized in that, The fitness function is: ； in, Flight path fitness value; Flight path Communication quality score; Flight path The score for resistance to observation; Flight path The low observability score; and They are respectively and The corresponding weights.

10. The UAV-assisted low-observable communication method based on game theory and genetic algorithm according to claim 4, characterized in that, The threat level for: ； in, The shortest distance from the path point to the observation area. This is the critical distance for risk. Here, exp(·) is the distance sensitivity coefficient, and exp(·) is the natural exponential function; The channel quality index for: ； in, For the first Bit error rate per path point For the target bit error rate, This is the maximum tolerance value; The number of waypoints in the flight path; The data priority is The Includes multiple preset values.

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