Method for designing configuration number of countermeasure device in unmanned aerial vehicle countermeasure system

Abstract

The application discloses a method for designing the number of countermeasure devices in an unmanned aerial vehicle countermeasure system, comprising the following steps: S1. constructing a queuing model of the unmanned aerial vehicle countermeasure system service and giving relevant conditions of the queuing model; S2. for the queuing model of the unmanned aerial vehicle countermeasure system service, establishing a target number state transition graph by using a Markov process and listing state transition equations, analyzing the relationship of the to-be-processed target number and the relationship of the number state probabilities; S3. solving the steady-state solution of the state transition equation, and analyzing the success probability of intercepting targets in a long-time interception process of the unmanned aerial vehicle countermeasure system; S4. determining the efficiency and cost ratio of the unmanned aerial vehicle countermeasure system; and S5. analyzing the total interception probability derivation formula in combination with the efficiency and cost ratio formula, and selecting the optimal number N of countermeasure devices. The application can determine the optimal number of sets of countermeasure devices when the unmanned aerial vehicle countermeasure system is designed and constructed, and provides conditions for the construction of the unmanned aerial vehicle countermeasure system.

Description

Technical Field

[0001] This invention relates to the interception and countermeasures of unmanned aerial vehicles (UAVs), and in particular to a method for designing the number of countermeasure devices in an unmanned aerial vehicle (UAV) countermeasure system. Background Technology

[0002] With the rapid development and application of unmanned aerial vehicles (UAVs) in aerial photography, performances, agriculture, disaster relief, and other fields, the security of key and confidential locations such as airports and research institutions has also been threatened. For example, if UAV intrusion around airports cannot be effectively controlled, it could interfere with aircraft navigation and potentially cause serious accidents; if UAV intrusion around important conference venues and research institutions cannot be effectively controlled, it could lead to the leakage of important secrets; if UAV intrusion around venues for major events and competitions cannot be effectively controlled, it could threaten the normal conduct of the events and competitions, and even pose a security threat. Currently, there is a lot of research on the detection and countermeasures against UAVs, but most of this research only targets single targets or a small number of targets. However, with the reduction in the cost of UAVs and breakthroughs in swarm technology, key locations are likely to face security threats from multi-target, multi-directional, swarm-like UAVs.

[0003] Therefore, a single countermeasure device is no longer sufficient to meet the protection requirements of an unmanned aerial vehicle (UAV) countermeasure system; multiple countermeasure devices need to work in coordination to counter multiple targets. Determining the optimal number of countermeasure devices to effectively meet these requirements while keeping construction costs within a reasonable range is a crucial issue to consider in the design and construction of an UAV countermeasure system. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for designing the number of countermeasures devices in an unmanned aerial vehicle (UAV) countermeasure system. This method can determine the optimal number of countermeasures devices during the design and construction of the UAV countermeasure system, thus providing conditions for the construction of UAV countermeasure systems.

[0005] The objective of this invention is achieved through the following technical solution: a method for designing the number of countermeasure devices in an unmanned aerial vehicle (UAV) countermeasure system, comprising the following steps:

[0006] S1. Construct a queuing model for the unmanned aerial vehicle countermeasure system service, and give the relevant conditions for the queuing model;

[0007] S2. For the queuing model of the unmanned aerial vehicle countermeasure system service, a Markov process is used to establish the target quantity state transition diagram and list the state transition equations to analyze the relationship between the number of targets to be processed and the relationship between the state probabilities of each quantity.

[0008] S3. Find the steady-state solution of the state transition equation and analyze the success probability of the unmanned aerial vehicle countermeasure system intercepting the target during a long-term interception process;

[0009] S4. Determine the cost-effectiveness ratio of the unmanned aerial vehicle countermeasure system;

[0010] S5. The derivation formula of the total interception probability is analyzed in conjunction with the cost-effectiveness ratio formula to select the optimal number of countermeasures N.

[0011] The beneficial effects of this invention are as follows: By applying queuing models and Markov processes to describe the target interception service flow of an unmanned aerial vehicle (UAV) countermeasure system, this invention enables quantitative analysis of the UAV interception process. From this, indices for evaluating the effectiveness of the UAV countermeasure system are derived: total interception probability and cost-effectiveness ratio. Further, by deriving formulas, the impact of various parameter changes on system effectiveness can be analyzed, and the system's target interception service process can be quantitatively simulated and analyzed. Ultimately, the impact of changes in the number of countermeasure devices on system indicators is obtained, enabling the effective design of the optimal number of countermeasure devices. Attached Figure Description

[0012] Figure 1 This is a flowchart of the method of the present invention;

[0013] Figure 2 Queueing model diagram for unmanned aerial vehicle countermeasure systems;

[0014] Figure 3 The target quantity state transition model diagram;

[0015] Figure 4 A graph showing the relationship between the total interception probability and the number of countermeasure devices;

[0016] Figure 5 A graph showing the relationship between cost-effectiveness and the number of countermeasures devices;

[0017] Figure 6 A three-dimensional graph showing the relationship between the total interception probability, the number of countermeasures devices, and the frequency of target occurrence. Detailed Implementation

[0018] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.

[0019] In this application, the UAV countermeasure system mainly targets "low, slow, and small" UAVs, and uses a queuing model to describe the target interception service process of the "low, slow, and small" UAV countermeasure system. A Markov process is used to analyze the target interception service process, and the total interception effectiveness of the "low, slow, and small" UAV countermeasure system is derived, using the interception effectiveness as the basis for selecting the number of countermeasure devices. The cost-effectiveness ratio is used to further obtain the constraints for determining the number of countermeasure devices. Then, MATLAB software is used to simulate and analyze the cost-effectiveness ratio and the constraints for determining the countermeasure devices, analyzing the trend of the total interception probability changing with the number of countermeasure devices, and analyzing the trend of the total interception probability changing with different numbers of countermeasure devices for different target frequencies. Specifically:

[0020] like Figure 1 As shown, a method for designing the number of countermeasures devices in an unmanned aerial vehicle (UAV) countermeasure system includes the following steps:

[0021] S1. Construct a queuing model for the unmanned aerial vehicle countermeasure system service, and give the relevant conditions for the queuing model;

[0022] like Figure 2 The diagram shows a service queuing model for a "low, slow, and small" unmanned aerial vehicle (UAV) countermeasure system. When the UAV target arrives at a frequency of ω, the parameter for breaking through interception without being intercepted is υ, the parameter for preparing for the next interception after one interception is μ, the number of countermeasure devices providing interception services is N, and the frequency of breaking through interception is ω. out Specifically, it is described as follows:

[0023] When an unmanned aerial vehicle (UAV) appears at a frequency of ω in a location requiring interception, the UAV targets will form a target queue over time. The UAV countermeasure system will then intercept the emerging UAV target queue, i.e., the interception service process:

[0024] Some targets will be assigned interception services, while others will not be assigned interception services in time due to insufficient interception service capabilities of the countermeasure system, thus breaking through the interception of the UAV countermeasure system. The frequency of these targets breaking through the interception is set as υ.

[0025] When an unmanned aerial vehicle (UAV) countermeasure system comprises N countermeasure devices for interception services, the average service rate of each device for intercepting assigned targets is μ. A portion of these targets will be successfully intercepted, while another portion will fail to be intercepted due to service failure. The targets not assigned interception services and those assigned services but failing to be intercepted together constitute the final group of targets that did not receive interception services. Their frequency of breaching the interception zone is denoted as ω. out ;

[0026] Combination Figure 2 The model makes the following assumptions:

[0027] (1) The number of incoming "low, slow, and small" unmanned aerial vehicle targets follows a Poisson distribution with parameter ω. The probability of k targets appearing is:

[0028]

[0029] (2) The time required for the countermeasure device of the "low, slow, and small" unmanned aerial vehicle (UAV) countermeasure system to prepare for the next interception after completing one interception follows an exponential distribution with parameter μ, where μ is the average interception preparation time t. T The reciprocal of, that is:

[0030]

[0031] (3) If an incoming "low, slow, and small" unmanned aerial vehicle (UAV) target is not intercepted within a certain time, it will breach the interception zone and cause damage to key protected areas. The dwell time of a target in the interception waiting queue of the countermeasure device follows an exponential distribution with parameter υ, where parameter υ is the average dwell time t of the target. L The reciprocal of, that is:

[0032]

[0033] (4) The number of countermeasures devices in the "low, slow and small" unmanned aerial vehicle countermeasure system is set to N.

[0034] S2. For the queuing model of the unmanned aerial vehicle countermeasure system service, a Markov process is used to establish the target quantity state transition diagram and list the state transition equations to analyze the relationship between the number of targets to be processed and the relationship between the state probabilities of each quantity.

[0035] For the queuing model described above, Markov process analysis is applied to determine the number of targets to be processed, and a state transition model diagram for the number of targets is established as shown in the figure below. Figure 3 As shown, the transformation relationships between the various quantities of the target to be processed are described. In the model, the numbers inside the circle represent the quantity of the target to be processed, and the circle represents the state of the number inside the circle; the arrows indicate the direction of the transition from one quantity state to another, and indicate the strength of this transition.

[0036] When the number of countermeasures devices in the UAV countermeasure system is N, and the number of targets to be processed is n = 0, 1, 2, ..., the corresponding target quantity states are 0, 1, 2, ... In the model, state transitions only occur between two adjacent quantity states. When the transition is from a low quantity state to a high quantity state, i.e., n → n+1, the transition intensity is ω. When the transition is from a high quantity state to a low quantity state, and the number of targets to be processed is less than or equal to the number of UAV countermeasures devices, i.e., n → n-1, 0 < n ≤ N, the transition intensity is n(μ + υ). When the transition is from a high quantity state to a low quantity state, and the number of targets to be processed is greater than the number of UAV countermeasures devices, i.e., n → n-1, n > N, the transition intensity is Nμ + nυ.

[0037] Based on the target quantity state transition model diagram, the state transition equations are established as follows:

[0038]

[0039] p n Let p represent the probability of a state when the number of targets within the interception area is n. The state transition equation gives the relationship between the probabilities of each state and other states when the number of targets to be processed within the interception area is 0 to n. The state transition equation states the following rule: for any state with the number of targets n, p n The time derivative of (t) is equal to the sum of the probabilities of all states that have transitioned to the target state of n multiplied by their state transition strengths, minus the sum of the probabilities of the target state of n multiplied by the state transition strengths that have transitioned out of the target state of n.

[0040] S3. Find the steady-state solution of the state transition equation and analyze the success probability of the unmanned aerial vehicle countermeasure system intercepting the target during a long-term interception process;

[0041] To analyze the success probability of a low, slow, and small unmanned aerial vehicle (UAV) countermeasure system intercepting a target during a long-term interception process, the state transition equation can be further derived to obtain its steady-state solution. This allows us to obtain the probability of each state when the number of targets to be processed within the interception area is different, i.e., as t→∞, let... available

[0042]

[0043] Substituting the above equation into... get:

[0044]

[0045] Furthermore, the average number of countermeasures required for a "low, slow, and small" unmanned aerial vehicle (UAV) countermeasure system is obtained through a desired method:

[0046]

[0047] The probability that a "low, slow, and small" unmanned aerial vehicle (UAV) countermeasure system can intercept the target is:

[0048]

[0049] The total interception probability of a "low, slow, and small" unmanned aerial vehicle (UAV) countermeasure system against a target is:

[0050] p H =pF·p D

[0051] p D The probability of a single unmanned aerial vehicle (UAV) countermeasure system successfully intercepting a single target in a single countermeasure operation.

[0052] S4. Determine the cost-effectiveness ratio of the unmanned aerial vehicle (UAV) countermeasure system as follows:

[0053]

[0054] C N Cost of constructing N sets of countermeasures devices (ten thousand yuan / set).

[0055] S5. The derivation formula of the total interception probability is analyzed in conjunction with the cost-effectiveness ratio formula to select the optimal number of countermeasures N.

[0056] The analysis is based on the constraint of combining the derivation formula of the total interception probability and the cost-effectiveness formula:

[0057]

[0058] We aim to maximize the overall interception probability and the cost-effectiveness ratio, thereby selecting the optimal number of countermeasures N.

[0059] Substituting the known parameters ω, μ, υ, C1 and N = 1, 2, 3, ... into the formula, we obtain the total interception probability and cost-effectiveness ratio for the corresponding number of countermeasures devices. Therefore, we obtain the one-to-one correspondence between the number of countermeasures devices and the total interception probability, and the one-to-one correspondence between the number of countermeasures devices and the cost-effectiveness ratio. Since we want the total interception probability to be as high as possible to meet the total interception rate threshold required by the mission, and on this basis, we want the cost-effectiveness ratio to be as high as possible to reduce economic costs, we combine the two conditions to first select a set of countermeasures device numbers N that allow the total interception probability to reach the total interception probability threshold required by the mission, and then select the final number of countermeasures device N that maximizes the cost-effectiveness ratio from among them, which is the optimal number of countermeasures devices.

[0060] The embodiments of this application primarily consider countermeasures against "low, slow, and small" unmanned aerial vehicles.

[0061] Assuming the "low, slow, and small" UAV countermeasure system is equipped with 90 capture nets, the maximum number of targets that can appear in the interception area is 90. If this number is exceeded, the countermeasure system cannot complete its mission. The time t is the time required for each countermeasure device to prepare for the next interception after completing one. T =16s, the probability of each countermeasure device intercepting a target is p. D =0.936. The average frequency of incoming targets is ω=10 / minute, and the average tL=2min for them to penetrate the interception zone of the countermeasures system.

[0062] The proposed method was used for computational simulation, and the results were as follows: Figure 4 The graph shows the relationship between the total interception probability and the number of countermeasures devices, where the number of simulated countermeasures devices ranges from 1 to 20. From... Figure 4 As can be seen, initially the total interception probability increases with the number of countermeasures devices. However, when the number of countermeasures devices is 9 and the total interception probability is 0.8259, the total interception probability no longer increases with the number of countermeasures devices.

[0063] Assume the cost of a countermeasure device is C1 = 20,000 yuan. Using the cost-effectiveness ratio formula for simulation, the results are as follows: Figure 5 The graph shows the relationship between cost-effectiveness and the number of countermeasures devices, with the number of simulated countermeasures devices ranging from 1 to 20. From... Figure 5 As can be seen, the cost-effectiveness ratio decreases continuously with the increase of the number of countermeasures devices. In actual system design, the higher the cost-effectiveness ratio, the better. Therefore, considering the cost, we obtain the design constraints of a "low, slow, and small" unmanned aerial vehicle countermeasure system where the number of countermeasures devices is as low as possible.

[0064] Assuming the average frequency ω of future attacks by "low, slow, and small" unmanned aerial vehicle targets is set to a variable value, taking integers from 1 to 20, simulations can be performed to obtain the following results: Figure 6 The diagram shows the three-dimensional relationship between the total interception probability, the number of countermeasures devices, and the frequency of target occurrence.

[0065] The graph shows that when the number of countermeasures devices is less than 5, the total interception probability continuously decreases as the target occurrence frequency increases. When the number of countermeasures devices is greater than or equal to 6, the total interception probability remains relatively stable with a minor decrease as the target occurrence frequency increases, forming a stable plane in the three-dimensional relationship graph. Based on the simulation results, if the threshold for the total interception probability is 0.8, and considering the cost-effectiveness design constraints mentioned earlier, under this assumption, a design of 6 countermeasures devices is considered optimal.

[0066] In other words, during the analysis and simulation of the system's target interception service process, when the frequency of aircraft target appearance is fixed, this invention can simulate the relationship curve between the total interception probability and the number of countermeasures devices. It can analyze how the total interception probability changes as the number of countermeasures devices increases, and find the number of countermeasures devices corresponding to the highest total interception probability. It can also simulate the relationship curve between the cost-effectiveness ratio and the number of countermeasures devices, analyzing how the cost-effectiveness ratio changes as the number of countermeasures devices increases, and obtaining the constraints for selecting the number of countermeasures devices. When the frequency of aircraft target appearance is not fixed, a three-dimensional relationship graph between the total interception probability, the number of countermeasures devices, and the target appearance frequency can be simulated. This allows analysis of how the total interception probability changes with the number of countermeasures devices and the target appearance frequency, and obtaining the number of countermeasures devices required to achieve the highest total interception probability when the target appearance frequency is not fixed.

[0067] The foregoing description illustrates and describes a preferred embodiment of the present invention. However, as previously stated, it should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the inventive concept described herein through the foregoing teachings or techniques or knowledge in related fields. Any modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for designing the number of countermeasure devices in an unmanned aerial vehicle (UAV) countermeasure system, characterized in that: Includes the following steps: S1. Construct a queuing model for the unmanned aerial vehicle countermeasure system service, and give the relevant conditions for the queuing model; In the queuing model, when an unmanned aerial vehicle (UAV) appears at a frequency of ω at a location requiring interception, the UAV targets will form a target queue over time. The UAV countermeasure system will then intercept the emerging UAV target queue, i.e., the interception service process: Some targets will be assigned interception services, while others will not be assigned interception services in time due to insufficient interception service capabilities of the countermeasure system, thus breaking through the interception of the UAV countermeasure system. The frequency of these targets breaking through the interception is set as v. When an unmanned aerial vehicle (UAV) countermeasure system comprises N countermeasure devices for interception services, the average service rate of each device for intercepting assigned targets is μ. A portion of these targets will be successfully intercepted, while another portion will fail to be intercepted due to service failure. The targets not assigned interception services and those assigned services but failing to be intercepted together constitute the final group of targets that did not receive interception services. Their frequency of breaching the interception zone is denoted as ω. out ; The relevant conditions for the queuing model include: (1) The number of incoming unmanned aerial vehicle targets follows a Poisson distribution with parameter ω, and the probability of k targets appearing is: (2) The time for the countermeasure device of the unmanned aerial vehicle countermeasure system to prepare for the next interception after completing one interception follows an exponential distribution with parameter μ, where μ is the average interception preparation time t. T The reciprocal of, that is: (3) If an incoming unmanned aerial vehicle target is not intercepted within a certain period of time, it will break through the interception zone and cause damage to the key protected areas. The dwell time of a target in the interception waiting queue of the countermeasure device follows an exponential distribution with parameter υ, where parameter υ is the average dwell time t of the target. L The reciprocal of, that is: (4) The number of countermeasures devices in the unmanned aerial vehicle countermeasures system is set to N; S2. For the queuing model of the unmanned aerial vehicle countermeasure system service, a Markov process is used to establish the target quantity state transition diagram and list the state transition equations to analyze the relationship between the number of targets to be processed and the relationship between the state probabilities of each quantity. S3. Find the steady-state solution of the state transition equation and analyze the success probability of the unmanned aerial vehicle countermeasure system intercepting the target during a long-term interception process; S4. Determine the cost-effectiveness ratio of the unmanned aerial vehicle countermeasure system; S5. The derivation formula of the total interception probability is analyzed in conjunction with the cost-effectiveness ratio formula to select the optimal number of countermeasures N.

2. The method for designing the number of countermeasure devices in an unmanned aerial vehicle countermeasure system according to claim 1, characterized in that: Step S2 includes: S201. Based on the queuing model, apply the Markov process to analyze the number of targets to be processed, establish a target quantity state transition model, and describe the transformation relationship between the various quantities of targets to be processed. The transformation relationships between the various quantities of the target to be processed are described as follows: When the number of countermeasure devices in the unmanned aerial vehicle countermeasure system is The number of targets to be processed is At that time, the corresponding target quantity state is In the model, state transitions only occur between two adjacent states of the same quantity. A transition occurs when a state of the same quantity moves from a lower quantity state to a higher quantity state. During migration, the migration intensity is always When the migration moves from a high-quantity state to a low-quantity state, and the number of targets to be processed is less than or equal to the number of unmanned aerial vehicle (UAV) countermeasure devices, i.e. At that time, the migration intensity was When the migration moves from a high-quantity state to a low-quantity state, and the number of targets to be processed is greater than the number of unmanned aerial vehicle (UAV) countermeasures devices, i.e. At that time, the migration intensity was ; S202. Based on the target quantity state transition model, the state transition equations are established as follows: ； p n Let p represent the probability of a state when the number of targets within the interception area is n. The state transition equation gives the relationship between the probabilities of each state and other states when the number of targets to be processed within the interception area is 0 to n. The state transition equation states the following rule: for any state with the number of targets n, p n The time derivative of (t) is equal to the sum of the probabilities of all states that have transitioned to the target state of n multiplied by their state transition strengths, minus the sum of the probabilities of the target state of n multiplied by the state transition strengths that have transitioned out of the target state of n.

3. The method for designing the number of countermeasure devices in an unmanned aerial vehicle countermeasure system according to claim 1, characterized in that: Step S3 includes: S301. By further deriving the state transition equation, the steady-state solution of the state transition equation is obtained, yielding the probabilities of each state when the number of targets to be processed within the interception area is different: when ,make ,get ； Substituting the above equation into... get: ； S302. Obtain the average number of countermeasures devices required by the unmanned aerial vehicle countermeasure system using a desired method: ； S303. The probability of obtaining the unmanned aerial vehicle (UAV) countermeasure system's interception service for the target is: ； S304. Obtain the total interception probability of the unmanned aerial vehicle (UAV) countermeasure system against the target, i.e.: ； in, The probability of a single unmanned aerial vehicle (UAV) countermeasure system successfully intercepting a single target in a single countermeasure operation.

4. The method for designing the number of countermeasure devices in an unmanned aerial vehicle countermeasure system according to claim 1, characterized in that: In step S4, the cost-effectiveness ratio of the unmanned aerial vehicle countermeasure system is: ； C N The cost of constructing N sets of countermeasures devices.

5. The method for designing the number of countermeasure devices in an unmanned aerial vehicle countermeasure system according to claim 1, characterized in that: In step S5, the derivation formula for the total interception probability is analyzed in conjunction with the constraint of the cost-effectiveness ratio formula: ； Substituting the known parameters ω, μ, υ, C1 and N = 1, 2, 3, ... into the formula, we obtain the total interception probability and cost-effectiveness ratio for the corresponding number of countermeasures devices. Therefore, we obtain the one-to-one correspondence between the number of countermeasures devices and the total interception probability, and the one-to-one correspondence between the number of countermeasures devices and the cost-effectiveness ratio. First, we select a set of countermeasures device numbers N that allow the total interception probability to reach the threshold required by the mission. Then, we select the final number of countermeasures devices N that maximizes the cost-effectiveness ratio from these numbers. This is the optimal number of countermeasures devices.

Images