Radar emitter weak signal detection method based on cooperation of unmanned aerial vehicle group

Abstract

The application discloses a radar radiation source weak signal detection method based on cooperation of a UAV group, first establishes a single-UAV detection model based on energy detection, considers Rayleigh fading characteristics of a channel, establishes a Rayleigh channel model and analyzes false alarm probability and detection probability, then proposes a method for cooperative detection of a radar radiation source by multiple UAVs based on a local detection + information fusion architecture, establishes a global detection performance evaluation model, analyzes performance of the detection system and realizes signal detection.The model and method of the application effectively improve the detection probability of the UAV group on the radiation source target in a low signal-to-noise ratio scene, not only enrich the technical framework of the multi-UAV cooperative reconnaissance field in theory, but also provide an effective technical means in practical application to cope with the reconnaissance challenge in a low signal-to-noise ratio environment, and have wide application prospects for improving the reliability and accuracy of the reconnaissance system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar target detection, and particularly relates to a radar radiation source weak signal detection method based on cooperation of a UAV swarm. BACKGROUND

[0002] In the field of civilian monitoring, UAV swarms play an increasingly important role. They greatly enhance the depth and breadth of intelligence collection by providing real-time, high-mobility air surveillance. However, the execution of monitoring tasks is often constrained by low signal-to-noise ratio (SNR) environments, where target signals are often obscured by background noise, leading to decreased detection performance. This challenge has prompted researchers to explore more efficient cooperative reconnaissance strategies to improve reconnaissance effectiveness in complex signal environments.

[0003] Multi-UAV cooperative reconnaissance is a method that improves reconnaissance efficiency through the joint action of multiple UAVs. Compared with a single UAV, a multi-UAV system has significant advantages in target detection, data collection, and information processing. First, multiple UAVs can observe targets from different angles and distances simultaneously, increasing the diversity and reliability of information. Second, through information sharing and cooperative processing, the false alarm rate of individual UAVs can be effectively reduced, improving the overall system's detection capability. In addition, multi-UAV systems have strong anti-interference ability and flexibility, capable of adapting to dynamically changing environments.

[0004] In low signal-to-noise ratio environments, target signals are often overwhelmed by background noise, and existing signal detection methods are difficult to effectively identify targets. In this case, the detection of weak signals from radar radiation sources becomes a major problem. The Rayleigh fading characteristics of the channel further exacerbate this challenge, making signal propagation and reception more unstable. In addition, due to changes in position and speed during flight, the channel conditions also change, which puts higher requirements on the robustness of the detection algorithm.

[0005] Energy detection is a commonly used signal detection method that is widely used in low signal-to-noise ratio conditions due to its simplicity and efficiency. This method detects whether the signal energy exceeds a set threshold to determine the presence of a target. However, single energy detection is easily affected by noise in low signal-to-noise ratio environments. To this end, information fusion technology is introduced, which integrates the detection results of multiple UAVs to form a more accurate global decision. Information fusion can significantly improve the detection probability and reduce the false alarm rate, and is one of the key technologies for improving multi-UAV cooperative monitoring tasks.

[0006] Currently, researchers are actively exploring new models and algorithms for multi-UAV cooperative monitoring to address reconnaissance challenges in complex environments. Key research directions include: optimizing UAV cooperation strategies, enhancing the intelligence and adaptability of information fusion algorithms, developing detection technologies adapted to time-varying channels, and utilizing advanced simulation and numerical methods to improve the accuracy and efficiency of algorithms. Simultaneously, with the introduction of artificial intelligence and machine learning technologies, the intelligence level of multi-UAV cooperative reconnaissance systems will be further enhanced, providing stronger technical support for radar emission source signal detection.

[0007] This multi-layered and multi-faceted technological advancement not only enriches the theoretical framework of UAV collaborative reconnaissance but also provides a solid technological foundation for practical applications, demonstrating broad application prospects. In the future, multi-UAV collaborative reconnaissance technology will continue to play a crucial role in complex and ever-changing environments, driving reconnaissance technology towards greater efficiency and intelligence. Summary of the Invention

[0008] To address the aforementioned technical problems, this invention proposes a radar radiation source weak signal detection method based on UAV swarm collaboration, which addresses the reconnaissance challenges in low signal-to-noise ratio environments and improves the reliability and accuracy of reconnaissance systems.

[0009] The technical solution adopted in this invention is: a method for detecting weak signals of radar radiation sources based on UAV swarm cooperation, the steps of which are as follows:

[0010] S1. Establish a single UAV detection probability model based on energy detection and output local decision results;

[0011] S2. Establish a Rayleigh channel model and use Monte Carlo experiments to observe and analyze the impact of time-varying and time-invariant channels on detection performance;

[0012] S3. Based on the channel model established in step S2, construct a local detection performance evaluation model;

[0013] S4. Based on the local detection results of step S3, a collaborative detection method for weak signals of multiple UAV radar radiation sources with a local detection + decision fusion architecture is proposed.

[0014] S5. Based on step S4, establish a global detection performance evaluation model, analyze the performance of the detection system, and realize signal detection.

[0015] Furthermore, step S1 is specifically as follows:

[0016] Set a by A network of drones, with a sampling point count within a detection interval of [number] points. , No. Observations received by a drone The expression is as follows:

[0017] (1)

[0018] where, , represents a complex Gaussian white noise with mean 0 and variance , represents a target signal, represents a transmission channel gain, .

[0019] When an energy detector is used, the energy statistics at the first UAV are expressed as follows:

[0020] (2)

[0021] Let represent a decision threshold, and let represent a local decision, the decision rule for each UAV is expressed as follows:

[0022] (3)

[0023] When the number of sampling points in the detection interval is large enough, according to the central limit theorem, the energy statistics in equation (2) are represented by a Gaussian distribution under the assumption and . The expression of the target signal energy is as follows:

[0024] (4)

[0025] The corresponding expectation and variance expressions are as follows:

[0026] (5)

[0027] where, , represent the corresponding expectation and variance under the assumption , , represent the corresponding expectation and variance under the assumption , represents the instantaneous signal-to-noise ratio of the received signal of the first UAV, and the specific expression is as follows:

[0028] (6)

[0029] where, , represents the average signal-to-noise ratio.​

[0030] Then the first A drone is at a given threshold False alarm probability at time Detection probability The expressions are as follows:

[0031] (7)

[0032] in, Represents probability. Representation Standard The function, expressed as follows:

[0033] (8)

[0034] in, Indicates the lower limit of integration. Let the integral variable be represented. Then consider the transmission channel gain. It is time-invariant within the perception interval, that is... The resulting expression is as follows:

[0035] (9)

[0036] The final expression for the detection probability model of a single UAV based on energy detection is as follows:

[0037] (10)

[0038] in,

[0039] (11)

[0040] in, This represents a given false alarm probability value.

[0041] Furthermore, step S2 is specifically as follows:

[0042] The Rayleigh channel model is used to simulate the process of transmitting the decision results of drones to the decision center. It is assumed that the signals received by each drone are independent of each other. The probability density model expression of the Rayleigh channel is as follows:

[0043] (12)

[0044] in, Indicates the signal amplitude.

[0045] Then, the Monte Carlo method was used to perform numerical simulations to estimate the average detection probability under the influence of time-varying channels. .set up Indicates the first The results transmitted by the reconnaissance aircraft to the decision center, The decoding results of the content transmitted by the unmanned aircraft, The decoding results of the content transmitted by the unmanned aircraft,

[0046] (13)

[0047] wherein, , represents a Gaussian variable with zero mean and variance , represents the channel gain between the decision center and each unmanned aircraft, and the probability density function of is expressed as follows:

[0048] (14)

[0049] Further, the step S3 is specifically as follows:

[0050] The local detection performance evaluation model evaluation indexes include a local detection probability and a local false alarm probability.

[0051] First, the conditional probability density function expression is set as follows:

[0052] (15)

[0053] (16)

[0054] wherein, The expression is defined as follows:

[0055] (17)

[0056] wherein, represents a positive part.

[0057] By using the signal detection theory derivation, the expectation and variance expressions of the detection results under various conditions are respectively as follows:

[0058] (18)

[0059] (19)

[0060] wherein, According to the formula (19), the received local decision result depends on the local false alarm probability and the detection probability, and the local false alarm probability and the detection probability are expressed as , then The distribution expression of

[0061] (20)

[0062] Then, the equivalent probability expressions of false alarm probability and detection probability are derived as follows:

[0063] (21)

[0064] (22)

[0065] Since , we have:

[0066] (23)

[0067] Then, the expressions of and are substituted into equation (23) under the condition of local decision , and the conditional probability density of received observation is obtained as follows:

[0068] (24)

[0069] Let be a variable substitution, and the integral property of function is used to obtain the expression as follows:

[0070] (25)

[0071] where , , and the integral of both sides of equation (25) with respect to is obtained as follows:

[0072] (26)

[0073] Similarly, when , we have:

[0074] (27)

[0075] The expressions of and are substituted into and , and the local false alarm probability and detection probability are obtained by calculation as follows:

[0076] (28)

[0077] (29)

[0078] where,​ SNR represents the signal-to-noise ratio of the transmission channel between each UAV and the decision center.

[0079] Further, the step S4 is specifically as follows:

[0080] S41, based on the local detection result of step S3, evaluating and optimizing the detection performance of the UAV;

[0081] In local detection, the first When the UAV is at a given threshold The false alarm and detection probability expressions are as follows:

[0082] (30)

[0083] (31)

[0084] The relationship between the detection probability and the instantaneous signal-to-noise ratio The expression is as follows:

[0085] (32)

[0086] Wherein, The inverse function of the standard function, The instantaneous signal-to-noise ratio of the received signal of the UAV.

[0087] S42, using the Bayesian global decision method for decision fusion to obtain the global detection result;

[0088] In decision fusion, it is assumed that the receiving channels of each UAV to the decision center are independent and not interfered, and the delay in the information transmission process is ignored. After the decision center receives the decision results of each UAV , the local decision results are decoded to obtain , which are independent of each other.

[0089] Then, the decision center uses the Bayesian global decision method. The Bayesian global decision rule determines the global detection result by calculating the posterior probability, which represents the probability of the target existing under the condition of the detection result of each UAV. The expression is as follows:

[0090] (33)

[0091] Wherein, The prior probability, The joint probability of the detection result of each UAV under the condition of the target existing, The marginal probability.

[0092] Finally, the global decision rule expression is as follows:

[0093] (34)

[0094] Since and are constants, the expression is simplified as follows:

[0095] (35)

[0096] If there are ones in the local decision result obtained by decoding, and , then

[0097] (36)

[0098] Further, the step S5 is specifically as follows:

[0099] The global detection performance evaluation model comprises a global false alarm probability evaluation model and a detection probability evaluation model.

[0100] The global false alarm probability evaluation model of the decision center is and the detection probability evaluation model is The expressions are as follows:

[0101] (37)

[0102] (38)

[0103] Wherein, represents the decision threshold of the decision center.

[0104] Finally, based on the global detection performance evaluation model, signal detection is realized, and the target detection probability is improved.

[0105] The method of the present application first establishes a single unmanned aerial vehicle detection model based on energy detection, considers the Rayleigh fading characteristics of the channel, establishes a Rayleigh channel model and analyzes the false alarm probability and the detection probability, then proposes a method of multi-unmanned aerial vehicle cooperative detection of radar radiation sources based on local detection + information fusion architecture, establishes a global detection performance evaluation model, analyzes the performance of the detection system, and realizes signal detection. The model and method of the method of the present application effectively improve the detection probability of the unmanned aerial vehicle group cooperative detection of the radiation source target in the low signal-to-noise ratio scene, not only enrich the technical framework of the multi-unmanned aerial vehicle cooperative reconnaissance field in theory, but also provide an effective technical means in practical application to cope with the reconnaissance challenge in the low signal-to-noise ratio environment. It has a wide application prospect for improving the reliability and accuracy of the reconnaissance system. BRIEF DESCRIPTION OF DRAWINGS

[0106] Figure 1 A flow chart of a radar emitter weak signal detection method based on UAV swarm cooperation.

[0107] Figure 2 A signal processing flow chart in the embodiment of the application.

[0108] Figure 3 A global detection probability and UAV quantity relationship graph in the embodiment of the application.

[0109] Figure 4 A detection probability comparison graph under time-varying channel and time-invariant channel in the embodiment of the application. DETAILED DESCRIPTION

[0110] The method of the application will be further described below in combination with the drawings and embodiments.

[0111] As shown in the flow chart of the radar emitter weak signal detection method based on UAV swarm cooperation of the application, the specific steps are as follows: Figure 1 S1, a single-UAV detection probability model based on energy detection is established, and a local decision result is output.

[0112] S2, a Rayleigh channel model is established, and Monte Carlo experiments are used to observe and analyze the influence of time-varying channel and time-invariant channel on detection performance.

[0113] S3, based on the channel model established in step S2, a local detection performance evaluation model is constructed.

[0114] S4, based on the local detection result of step S3, a multi-UAV radar emitter weak signal cooperative detection method of local detection + decision fusion architecture is proposed.

[0115] S5, based on step S4, a global detection performance evaluation model is established, the performance of the detection system is analyzed, and signal detection is realized.

[0116] In this embodiment, the step S1 is specifically as follows:

[0117] A network composed of N UAVs is set, the number of sampling points in a detection interval is N, the observation value received by the i-th UAV is X i, and the expression is as follows:

[0118]

[0119] (1)

[0120] wherein, , ​​​​​This indicates that both the real and imaginary parts have a mean of 0 and a variance of . Complex Gaussian white noise, Indicates the target signal. Indicates the transmission channel gain. .

[0121] When using an energy detector, the first Energy statistics at each drone The expression is as follows:

[0122] (2)

[0123] set up Indicates the decision threshold. To represent local decision-making, the decision rule expression for each drone is as follows:

[0124] (3)

[0125] When the number of sampling points in the detection interval Large enough, according to the central limit theorem, the energy statistics in equation (2) In the assumption and The following are all represented using a Gaussian distribution. Then the target signal energy... The expression is as follows:

[0126] (4)

[0127] The corresponding expressions for expectation and variance are as follows:

[0128] (5)

[0129] in, , Indicates a hypothesis The corresponding expected value and variance are as follows. , Indicates a hypothesis The corresponding expected value and variance are as follows. Indicates the first The instantaneous signal-to-noise ratio of the signal received by the drone is expressed as follows:

[0130] (6)

[0131] in, , which represents the average signal-to-noise ratio.

[0132] Then the first A drone is at a given threshold False alarm probability at time Detection probability The expressions are as follows, respectively:

[0133] (7)

[0134] wherein, denotes a probability, denotes a standard function, the expression is as follows:

[0135] (8)

[0136] wherein, denotes an integral lower limit, denotes an integral variable. Then, considering that the transmission channel gain is time-invariant within the sensing interval, i.e. , the expression is as follows:

[0137] (9)

[0138] Finally, the expression of the detection probability model of the single unmanned aerial vehicle based on energy detection is as follows:

[0139] (10)

[0140] wherein,

[0141] (11)

[0142] wherein, denotes a given false alarm probability value.

[0143] In the embodiment, the step S2 is specifically as follows:

[0144] In the process of transmitting the decision result of the unmanned aerial vehicle to the decision center, noise and attenuation exist, and the Rayleigh channel model is used to simulate the process. It is assumed that the signals received by each unmanned aerial vehicle are independent of each other, and the expression of the probability density model of the Rayleigh channel is as follows:

[0145] (12)

[0146] wherein, denotes a signal amplitude.

[0147] In the case of facing time-varying channel conditions, due to the dynamic change of the channel state, it is extremely challenging to obtain an analytical solution of the detection probability according to the existing probability density function. In view of this, the Monte Carlo method is used for numerical simulation to estimate the average detection probability under the influence of the time-varying channel The method simulates the random change of channel state by a large number of random sampling, and then statistically analyzes the detection performance under different signal-to-noise ratio conditions, thereby providing an effective numerical solution for radar emitter signal detection under time-varying channels.

[0148] Considering that the decision encoding received at the decision center from each UAV may have bit error problems, the decoding error is defined to quantify this phenomenon. Let denote the result transmitted by the frame reconnaissance aircraft to the decision center, denote the decoding result of the fusion center to the transmission content of the frame UAV, and the expression is defined as follows:

[0149] (13)

[0150] wherein, , denotes a Gaussian variable with zero mean and variance , and denotes the channel gain between the decision center and each UAV, and the probability density function of the expression is as follows:

[0151] (14)

[0152] In this embodiment, the step S3 is specifically as follows:

[0153] The local detection performance evaluation model is described by the local detection probability and the local false alarm probability. The expressions of the two probabilities are derived as follows.

[0154] First, the conditional probability density function expression is set as follows:

[0155] (15)

[0156] (16)

[0157] wherein, the expression is defined as follows:

[0158] (17)

[0159] wherein, denotes the positive part.

[0160] Using the signal detection theory derivation, the expressions of the expectation and variance of the detection result under various conditions are as follows:

[0161] (18)

[0162] (19)

[0163] where, From equation (19), it can be seen that the received local decision depends on the local false alarm probability and detection probability. For convenience, the local false alarm probability and detection probability are denoted as , The distribution expression of is as follows:

[0164] (20)

[0165] Then, the equivalent probability expression of the false alarm probability and detection probability under the condition that is derived as follows:

[0166] (21)

[0167] (22)

[0168] Since , it can be obtained that:

[0169] (23)

[0170] Then, under the condition that the local decision is given, the expression of and is substituted into equation (23) to obtain the conditional probability density of the received observation , which is expressed as follows:

[0171] (24)

[0172] Let be a variable substitution, and the expression is obtained by using the integral property of function as follows:

[0173] (25)

[0174] where, , , the integral of both sides of equation (25) with respect to is obtained as follows:

[0175] (26)

[0176] Similarly, when , it is derived that:

[0177] (27)

[0178]

[0179] (28)

[0180] (29)

[0181]

[0182] In this embodiment, the step S4 is specifically as follows:

[0183] S41, based on the local detection result of step S3, evaluating and optimizing the detection performance of the unmanned aerial vehicle;

[0184] In the local detection, the first The false alarm probability and the detection probability of the unmanned aerial vehicle at a given threshold are respectively as follows:

[0185] (30)

[0186] (31)

[0187] In the radar radiation source target detection problem of the unmanned aerial vehicle, the instantaneous signal-to-noise ratio is a key parameter, which directly affects the distribution characteristics of the detection statistic. Therefore, the detection threshold can be expressed analytically, so as to deduce the relationship between the missed detection probability and the expected false alarm probability under the given false alarm probability constraint. Specifically, by setting the false alarm probability, the detection threshold can be determined, and then based on the signal detection theory, the missed detection probability and the detection probability under the threshold are calculated. This process provides an analytical method for the target detection problem, which can evaluate and optimize the detection performance of the unmanned aerial vehicle while meeting the specific false alarm probability requirement, and the relationship between the detection probability and the instantaneous signal-to-noise ratio is as follows:

[0188] (32)

[0189]

[0190] S42, adopting the Bayesian global decision method for decision fusion to obtain the global detection result;​​​​​​​​​​​

[0191] like Figure 2 As shown in the signal processing flowchart, in the decision fusion process, the receiving channels from each UAV to the decision center are set to be independent and interference-free, while the delay in information transmission is ignored. The decision center receives the decision results from each UAV. Then, based on the local decision results, the following is decoded: , These detections are independent of each other. Based on this, the decision center adopts a Bayesian global decision method. The Bayesian global decision rule determines the global detection result by calculating the posterior probability. The posterior probability represents the probability of the target existing given the detection results of each UAV, and its expression is as follows:

[0192] (33)

[0193] in, Represents the prior probability. This represents the joint probability of detection results from all drones, assuming the target exists. This represents the marginal probability.

[0194] The final global decision rule expression is as follows:

[0195] (34)

[0196] because and If it is a constant, then the simplified expression is as follows:

[0197] (35)

[0198] The local decision result obtained from the decoding is set to include One, and ,but

[0199] (36)

[0200] In this embodiment, step S5 is specifically as follows:

[0201] The global detection performance evaluation model includes: a global false alarm probability evaluation model and a detection probability evaluation model.

[0202] The global false alarm probability assessment model of the decision center and detection probability evaluation model The expressions are as follows:

[0203] (37)

[0204] (38)

[0205] wherein, represents a decision threshold of a decision center.

[0206] Finally, based on the global detection performance evaluation model, signal detection is realized, and the target detection probability is improved.

[0207] The embodiment is further simulated and analyzed, and the specific embodiments are as follows:

[0208] Any parameter set in the simulation of the embodiment , , and are applicable to the derived local or global detection probability, so some classic parameters are used to draw the detection probability and false alarm probability curve to observe their influence on the system detection performance. Without loss of generality, the positions of each unmanned aerial vehicle are fixed, and the number of samples in one observation time is , the channel adopts the Rayleigh channel model, and for all simulation cases, the channel vector can be modeled as a complex Gaussian random vector with zero mean. In addition, the average signal-to-noise ratio of all unmanned aerial vehicle receiving channels is the same, that is, , the error probability of the channel is set to 0.1, and at this time .

[0209] Figure 3 It is disclosed in the embodiment that under different instantaneous signal-to-noise ratio conditions, the increase of the number of unmanned aerial vehicles has a positive effect on the global detection probability. The results show that the increase of the number of unmanned aerial vehicles significantly improves the detection accuracy, especially in a high signal-to-noise ratio environment, the detection probability is improved more significantly.

[0210] Figure 4 The detection probability of the unmanned aerial vehicle group under the time-varying channel is estimated by the Monte Carlo simulation method. The results show that the Monte Carlo simulation can provide accurate detection probability estimation for the unmanned aerial vehicle group under complex channel conditions, and provide important data support for the decision of the actual reconnaissance task. The effectiveness of this method provides a feasible solution for the reconnaissance problem under the time-varying channel.

[0211] In summary, the method of the present application establishes a single unmanned aerial vehicle reconnaissance model based on energy detection, analyzes the false alarm probability, detection probability and missed detection probability in the Rayleigh fading channel in detail, discusses the influence of instantaneous signal-to-noise ratio on the detection performance, and further develops a multi-unmanned aerial vehicle cooperative detection strategy. Through the calculation of local and global false alarm probability and detection probability, the significant improvement of the overall detection performance of the unmanned aerial vehicle group with the increase of the number of unmanned aerial vehicles is revealed. The effectiveness of the model and method of the present embodiment is verified through the above simulation, and the results show that the global detection probability is significantly improved with the increase of the number of unmanned aerial vehicles. At the same time, the influence of time-varying channel and time-invariant channel on the detection probability is simulated, and the detection probability under the time-varying channel is successfully estimated by using the Monte Carlo method. The model and method of the present application effectively improve the detection probability of the unmanned aerial vehicle group in the low signal-to-noise ratio scene.

[0212] Those skilled in the art will realize that the embodiments described herein are for the purpose of illustration and should not be construed as limiting the scope of the present application. Those skilled in the art can make various modifications and combinations according to the technical spirit of the present application disclosed herein without departing from the scope of the present application.

Claims

1. A method for detecting weak signals from radar radiation sources based on UAV swarm collaboration, comprising the following steps: S1. Establish a single UAV detection probability model based on energy detection and output local decision results; S2. Establish a Rayleigh channel model and use Monte Carlo experiments to observe and analyze the impact of time-varying and time-invariant channels on detection performance; S3. Based on the channel model established in step S2, construct a local detection performance evaluation model; S4. Based on the local detection results of step S3, a collaborative detection method for weak signals of multiple UAV radar radiation sources with a local detection + decision fusion architecture is proposed. S5. Based on step S4, establish a global detection performance evaluation model, analyze the performance of the detection system, and realize signal detection; The specific steps of S1 are as follows: Set a network consisting of a number of unmanned vehicles, a sampling point in a detection interval is , the observation value received by the unmanned vehicle expressed as follows: （1）； in, , represents a complex Gaussian white noise with mean 0 and variance , represents a target signal, represents a transmission channel gain, ; When an energy detector is used, the energy statistics at the first drone are The expression is as follows: （2）； set up Indicates the decision threshold. To represent local decision-making, the decision rule expression for each drone is as follows: （3）； When the number of sampling points in the detection interval Large enough, according to the central limit theorem, the energy statistics in equation (2) In the assumption and The following are all represented by a Gaussian distribution; then the target signal energy The expression is as follows: （4）； The corresponding expressions for expectation and variance are as follows: （5）； in, , Indicates a hypothesis The corresponding expected value and variance are as follows. , Indicates a hypothesis The corresponding expected value and variance are as follows. Indicates the first The instantaneous signal-to-noise ratio of the signal received by the drone is expressed as follows: （6）； in, , representing the average signal-to-noise ratio; Then the first A drone is at a given threshold False alarm probability at time Detection probability The expressions are as follows: （7）； in, Represents probability. Representation Standard The function, expressed as follows: （8）； in, Indicates the lower limit of integration. Represent the integral variable; then consider the transmission channel gain. It is time-invariant within the perception interval, that is... The resulting expression is as follows: （9）； The final expression for the detection probability model of a single UAV based on energy detection is as follows: （10）； in, （11）； in, This represents a given false alarm probability value.

2. The method for detecting weak radar radiation sources based on UAV swarm collaboration according to claim 1, characterized in that, Step S2 is as follows: The Rayleigh channel model is used to simulate the process of transmitting the decision results of drones to the decision center. It is assumed that the signals received by each drone are independent of each other. The probability density model expression of the Rayleigh channel is as follows: （12）； in, Indicates signal amplitude; Then, the Monte Carlo method was used to perform numerical simulations to estimate the average detection probability under the influence of time-varying channels. ;set up Indicates the first The results transmitted from the reconnaissance aircraft to the decision-making center Indicates the integration center's position on the first The decoding result of the content transmitted by the drone is defined by the following expression: （13）； in, , This indicates zero mean and variance. Gaussian variables, The probability density function represents the channel gain between the decision center and each UAV. The expression is as follows: （14）。 3. The method for detecting weak radar radiation sources based on UAV swarm collaboration according to claim 2, characterized in that, Step S3 is as follows: The evaluation metrics of the local detection performance evaluation model include: local detection probability and local false alarm probability; First, the conditional probability density function expression is defined as follows: （15）； （16）； in, The expression is defined as follows: （17）； in, Indicates the positive part; Using signal detection theory, the expressions for the expectation and variance of the detection results under various conditions are derived as follows: （18）； （19）； in, As can be seen from equation (19), the received local decision result Depending on the local false alarm probability and the detection probability, the local false alarm probability and the detection probability are expressed as... ,but The distribution expression is as follows: （20）； Then it is derived that, in setting The equivalent probability expressions for the false alarm probability and the detection probability are as follows: （21）； （22）； because Then we can obtain: （23）； Then, in a given local decision Under the conditions, and Substituting the expression into equation (23), we obtain the received observations. The conditional probability density is expressed as follows: （24）； make Variable substitution, and utilize The integral property of a function yields the following expression: （25）； in, , Equation (25) is applied to both sides. Integrating, we obtain the following expression: （26）； Similarly, when At that time, the derivation yielded: （27）； Will and Substituting the expression and In the calculation, the local false alarm probability and detection probability are obtained, and the expressions are as follows: （28）； （29）； in, This represents the signal-to-noise ratio of the transmission channel between each drone and the decision-making center.

4. The method for detecting weak radar radiation sources based on UAV swarm collaboration according to claim 3, characterized in that, Step S4 is as follows: S41. Based on the local detection results of step S3, evaluate and optimize the detection performance of the UAV; In local detection, the first The drone is at a given threshold The expressions for false alarm and detection probability at time are as follows: （30）； （31）； The relationship between detection probability and instantaneous signal-to-noise ratio The expression is as follows: （32）； in, Representation Standard The inverse function of the function, This represents the instantaneous signal-to-noise ratio of the signal received by the drone; S42. The Bayesian global decision method is used to perform decision fusion to obtain the global detection results; In decision fusion, the receiving channels from each UAV to the decision center are set to be independent and interference-free, and the delay in information transmission is ignored. The decision center receives the decision results from each UAV. Then, based on the local decision results, the following is decoded: , They are independent of each other; Then, the decision center adopts the Bayesian global decision method. The Bayesian global decision rule determines the global detection result by calculating the posterior probability. The posterior probability represents the probability that the target exists given the detection results of each UAV, and the expression is as follows: （33）； in, Represents the prior probability. This represents the joint probability of detection results from all drones, assuming the target exists. Represents marginal probability; The final global decision rule expression is as follows: （34）； because and If it is a constant, then the simplified expression is as follows: （35）； The local decision result obtained from the decoding is set to include One, and ,but （36）。 5. The method for detecting weak radar radiation sources based on UAV swarm collaboration according to claim 4, characterized in that, Step S5 is as follows: The global detection performance evaluation model includes: a global false alarm probability evaluation model and a detection probability evaluation model; The global false alarm probability assessment model of the decision center and detection probability evaluation model The expressions are as follows: （37）； （38）； in, This indicates the decision threshold of the decision-making center; Finally, based on the global detection performance evaluation model, signal detection is achieved, thereby improving the target detection probability.

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