Distributed multi-source passive localization method and system

Abstract

The embodiments of this application relate to the field of passive positioning technology, and particularly to a distributed multi-radiation source passive positioning method and system. The method includes: monitoring and sensing through distributed monitoring stations, approximating the signal strength values ​​of the received signals at each monitoring station to obtain approximate signal strength values ​​that follow a log-normal distribution; based on the approximate signal strength values, calculating the probability density function of each monitoring station containing the horizontal and vertical coordinates and transmission power of the radiation source as unknown vectors; combining the probability density functions of all monitoring stations to obtain the likelihood function of the entire positioning problem, and deriving the objective function of the maximum likelihood estimation of the entire positioning problem based on the likelihood function; improving the differential evolution algorithm, and performing global optimization based on the improved differential evolution algorithm and the objective function of the maximum likelihood estimation of the entire positioning problem to solve for the maximum likelihood estimate of the unknown vectors, effectively achieving high-precision passive positioning of multiple radiation sources.

Description

Technical Field

[0001] The embodiments of this application relate to the field of passive positioning technology in electronic warfare, and particularly to a distributed multi-radiation source passive positioning method and system. Background Technology

[0002] Passive electromagnetic radiation source localization technology is a technique that can locate electromagnetic radiation sources without actively emitting electromagnetic detection signals. This technology enables the localizer to covertly locate the source, which has significant practical implications in the military field. As one of the core technologies of electronic warfare, passive electromagnetic radiation source localization can obtain the location coordinates of electromagnetic radiation sources under covert conditions. Its guiding principle is to locate the radiation source by measuring the intensity of the received signals through distributed monitoring stations. To ensure higher positioning accuracy, the positioning algorithm needs to be improved. Therefore, designing a high-precision passive positioning method is essential.

[0003] Currently, research teams both domestically and internationally have proposed several passive positioning methods. Classical passive positioning methods include those based on Angle of Arrival (AOA), Time of Arrival (TOA), Time Difference of Arrival (TDOA), Frequency of Arrival (FOA), and Frequency Difference of Arrival (FDOA).

[0004] It is worth noting that location technology based on received signal strength achieves location through the path loss model of electromagnetic signals, which is simpler than location schemes based on other key parameters. Typical methods for passive location of a single radiation source based on received signal strength include passive location methods using spatial correlation shadowing least squares algorithm, passive location methods based on maximum likelihood estimation, and passive location methods based on semidefinite programming maximum likelihood estimation.

[0005] The passive positioning methods described above are mostly designed for positioning scenarios with a single radiation source. However, positioning scenarios with a single radiation source cannot cover all possibilities of real-world positioning scenarios, especially in scenarios with dense electromagnetic radiation sources where signal interference is more significant, inevitably reducing the effectiveness of single-radiation-source passive positioning methods. Therefore, positioning scenarios with multiple radiation sources can be considered, and a distributed multi-radiation-source passive positioning system can be designed to achieve synchronous positioning of multiple radiation sources.

[0006] The above analysis shows that the proposed passive localization methods still have the following shortcomings.

[0007] First, most current research focuses on passive localization of a single radiation source based on the strength of the received signal, while there is relatively little research on passive localization of multiple radiation sources based on the strength of the received signal.

[0008] Second, the current multi-radiation source passive positioning methods have low positioning accuracy or may even fail when the noise power is high. Summary of the Invention

[0009] To address the aforementioned technical problems, embodiments of this application propose a distributed multi-radiation source passive positioning method and system, which can effectively achieve high-precision passive positioning of multiple radiation sources in line-of-sight propagation environments and under conditions of significant noise interference.

[0010] To achieve the above objectives, embodiments of this application propose a distributed multi-radiation source passive localization method, the method comprising: monitoring and sensing through distributed monitoring stations, and analyzing the signal strength value R of the received signal at the m-th monitoring station. m The Fenton-Wilkinson approximation method is used to approximate the signal strength value, which follows a log-normal distribution. Based on the approximate signal strength value Calculate the probability density function corresponding to the m-th monitoring station, which contains an unknown vector φ representing the x and y coordinates of the radiation source and its emitted power. Combine the probability density functions of all monitoring stations to obtain the likelihood function for the entire localization problem, and derive the objective function for maximum likelihood estimation based on this likelihood function. Improve the differential evolution algorithm using opposition learning, adaptive redirection, and an improved multi-mutation strategy. Perform global optimization based on the improved differential evolution algorithm and the objective function for maximum likelihood estimation of the entire localization problem to solve for the maximum likelihood estimate of the unknown vector φ. Achieve passive localization of distributed multi-radiation sources.

[0011] To achieve the above objectives, embodiments of this application also propose a distributed multi-radiation source passive positioning system, the system comprising: a monitoring station sensing module, used for monitoring and sensing through distributed monitoring stations, and for monitoring the signal strength value R of the received signal at the m-th monitoring station. m The Fenton-Wilkinson approximation method is used to approximate the signal strength value, which follows a log-normal distribution. The probability density function calculation module is used to calculate the approximate signal strength value. The system calculates the probability density function corresponding to the m-th monitoring station, which contains an unknown vector φ representing the horizontal and vertical coordinates of the radiation source and its emitted power. A maximum likelihood estimation module is used to jointly construct the probability density functions of all monitoring stations to obtain the likelihood function for the entire localization problem, and derives the objective function for maximum likelihood estimation based on this likelihood function. A maximum likelihood estimation solution module utilizes a fusion of oppositional learning, adaptive redirection, and an improved multi-mutation strategy to improve the differential evolution algorithm. Based on the improved differential evolution algorithm and the objective function for maximum likelihood estimation of the entire localization problem, a global optimization is performed to solve for the maximum likelihood estimate of the unknown vector φ. Achieve passive localization of distributed multi-radiation sources.

[0012] To achieve the above objectives, embodiments of this application also propose an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform a distributed multi-radiation source passive localization method as described above.

[0013] To achieve the above objectives, embodiments of this application also propose a computer-readable storage medium storing a computer program that, when executed by a processor, enables a distributed multi-radiation source passive localization method as described above.

[0014] This application proposes a distributed multi-source passive localization method and system. It approximates the signal strength values ​​of received signals detected by distributed monitoring stations using the Fenton-Wilkinson approximation method, transforming them into signal strength values ​​following a log-normal distribution. This simplifies the mathematical model of the received signal strength for multi-source passive localization and facilitates obtaining the probability density function corresponding to the received signal strength of each monitoring station. By combining the probability density functions corresponding to the approximate received signal strength of all monitoring stations, the likelihood function of the entire localization problem can be constructed. From this, the maximum likelihood estimation problem of the entire localization problem can be derived, i.e., the objective function of the maximum likelihood estimation of the entire localization problem. This transforms the passive localization problem into a maximum likelihood estimation problem. By integrating opposition learning, adaptive redirection, and an improved multi-mutation strategy, the differential evolution algorithm is improved. The improved differential evolution algorithm is used to solve the objective function of the maximum likelihood estimation of the entire localization problem, thereby improving the search capability and convergence speed of the differential evolution algorithm. This allows for a more efficient solution to the maximum likelihood estimate of the unknown vector, estimating the horizontal and vertical coordinates and transmission power of the radiation source. Under line-of-sight propagation conditions and with significant noise interference, high-precision passive localization of multiple radiation sources is effectively achieved.

[0015] Optionally, the target location area is a rectangular area with length l and width w. Within the target location area, there are M distributed monitoring stations and K radiation sources, where M and K are both integers greater than 1. The electromagnetic signal emitted by the k-th radiation source is received by the m-th monitoring station, and the signal strength value R of the received signal at the m-th monitoring station is... m This can be expressed by the following formula:

[0016]

[0017] Where, d m，k P represents the distance between the k-th radiation source and the m-th monitoring station, α is the path loss exponent, and P is the distance between the k-th radiation source and the m-th monitoring station. k Let n represent the emitted power of the k-th radiation source. m，k The propagation noise is represented by a mean of 0 and a variance of . It is a Gaussian random distribution.

[0018] Optionally, the signal strength value R of the received signal at the m-th monitoring station m The Fenton-Wilkinson approximation method is used to approximate the signal strength value, which follows a log-normal distribution. include:

[0019] Using the Fenton-Wilkinson approximation method, Rm is approximated as... and, Follows the mean μ m The variance is The normal distribution, μ m and This can be expressed by the formula:

[0020]

[0021] Where E(·) is the function for calculating the expectation, and Var(·) is the function for calculating the variance.

[0022] Optionally, based on the approximate signal strength value The probability density function corresponding to the m-th monitoring station is calculated using the following formula:

[0023]

[0024] Where φ is an unknown vector representing the horizontal and vertical coordinates of the radiation source and its emitted power. Let f(m) represent the probability density function corresponding to the m-th monitoring station.

[0025] Optionally, by combining the probability density functions corresponding to all monitoring stations, the likelihood function of the entire localization problem can be obtained, which is achieved through the following formula:

[0026]

[0027] Where L(φ) represents the likelihood function of the entire localization problem;

[0028] Based on the likelihood function, the objective function for the maximum likelihood estimation of the entire localization problem is derived, and is achieved through the following formula:

[0029]

[0030] in, It is the maximum likelihood estimator of the unknown vector φ that needs to be solved;

[0031] The constraints of the objective function for the maximum likelihood estimation of the entire localization problem are expressed by the following formula:

[0032]

[0033] P low ≤P k ≤P high ;

[0034] Where, x k The x-coordinate of the k-th radiation source is represented by y. k Let P represent the ordinate of the k-th radiation source, g represent the iteration number, and P represent the position of the k-th radiation source. low P represents the minimum transmit power. high This indicates the maximum transmission power.

[0035] Optionally, global optimization is performed based on the improved differential evolution algorithm and the objective function of the maximum likelihood estimation of the entire localization problem to solve for the maximum likelihood estimate of the unknown vector φ. To achieve passive localization of distributed multi-radiation sources, including:

[0036] An improved differential evolution algorithm is used to solve the objective function of the maximum likelihood estimation of the entire localization problem, and each element in the unknown vector φ is used as the gene of the improved differential evolution algorithm.

[0037] H individuals are randomly generated as the initial population, resulting in a random initial population. An alternative initial population is then obtained using the alternative learning technique. From these two populations, the top H individuals that minimize the objective function value of the maximum likelihood estimation for the entire localization problem are selected as the original population. The random initial population, the alternative initial population, and the original population are represented as follows:

[0038]

[0039] Where D is the dimension of an individual, that is, the total number of genes;

[0040] An improved multi-mutation strategy is used to mutate and crossover the original population in the current iteration, resulting in three experimental populations, represented as follows:

[0041]

[0042] For individuals whose genes cross boundaries during the mutation crossover process, adaptive redirection is performed, resulting in three redirected populations, which are represented as follows:

[0043]

[0044] Applying the opposition learning technique to each redirected population yields three new opposition populations, represented as follows:

[0045]

[0046] The selection operation is performed among the original population, three redirected populations, and three new opposing populations in the current iteration to obtain the original population for the next iteration.

[0047] When the number of iterations reaches the preset maximum number of iterations G, the optimal individual I in the optimal population is obtained. great , will I great The optimal solution to the objective function of the maximum likelihood estimation of the entire localization problem, i.e., the maximum likelihood estimator of the unknown vector φ.

[0048] Optionally, the initial population is randomly generated by the operator. Calculations show that the opposing initial populations are determined by the operator. Calculations show that a d b represents the upper bound of the d-th gene. d r represents the lower bound of the d-th gene. h It is a random number that follows a uniform distribution from 0 to 1;

[0049] The improved multi-mutation strategy consists of two parts: a mutation crossover strategy candidate pool and a control parameter strategy candidate pool. In each iteration, each mutation crossover strategy selects a control parameter generation strategy from the control parameter strategy candidate pool to form a new mutation crossover strategy, thereby generating the experimental population. The mutation strategy candidate pool contains three operators:

[0050]

[0051] Where o, p, and q are all positive integers randomly selected from the set {1, 2, ..., H}, satisfying the conditions that they are all distinct and not equal to h; F is a scaling factor taking values ​​between (0, 1); and c... hIt is the crossover probability that takes the value between (0, 1). It is the best individual in the original population during the g-th iteration;

[0052] The adaptive relocation operator is:

[0053]

[0054] Where, ω d It is a random number that takes values ​​between [0, 1] and follows a uniform distribution. and These are the lower and upper bounds for the adaptive relocation operation, respectively.

[0055] The operator for generating opposite individuals is:

[0056] The operator is selected as:

[0057] Here, fit(·) is the fitting function. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies of this application will be briefly introduced below. Obviously, the following drawings 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. The drawings described herein are only used to explain this application and are not intended to limit this application.

[0059] Figure 1 This is a flowchart of a distributed multi-radiation source passive localization method provided in one embodiment of this application;

[0060] Figure 2 This is a comparison diagram of the relative positioning error between the distributed multi-radiation source passive positioning method provided in one embodiment of this application and the traditional passive positioning method;

[0061] Figure 3 This is a comparison chart of the relative maximum cumulative error distribution rate between the distributed multi-radiation source passive localization method provided in one embodiment of this application and the traditional passive localization method;

[0062] Figure 4 This is a schematic diagram of the structure of a distributed multi-radiation source passive positioning system provided in another embodiment of this application;

[0063] Figure 5 This is a schematic diagram of the structure of an electronic device provided in another embodiment of this application. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the various embodiments of this application will be described in detail below with reference to the accompanying drawings. Those skilled in the art will understand that many technical details are presented in the various embodiments of this application to facilitate a better understanding of the application. However, the technical solutions claimed in this application can be implemented even without these technical details and various variations and modifications based on the following embodiments. The division of the various embodiments below is for ease of description and should not constitute any limitation on the specific implementation of this application. The various embodiments can be combined with and referenced by each other without contradiction.

[0065] One embodiment of this application proposes a distributed multi-source passive localization method applied to an electronic device, wherein the electronic device can be a terminal or a server. This embodiment and the following embodiments will use a server as an example for description. The implementation details of the distributed multi-source passive localization method proposed in this embodiment will be described in detail below. The following content is only for the convenience of understanding and is not necessary for implementing this solution.

[0066] The specific process of the distributed multi-radiation source passive localization method proposed in this embodiment can be described as follows: Figure 1 Shown, including:

[0067] S1, monitoring and sensing are performed through distributed monitoring stations, and the signal strength value R of the received signal at the m-th monitoring station is measured. m The Fenton-Wilkinson approximation method is used to approximate the signal strength value, which follows a log-normal distribution.

[0068] In practical implementation, there are multiple radiation sources in the target positioning area. The server needs to perform passive positioning of these multiple radiation sources within the target positioning area. This requirement is achieved based on distributed monitoring stations. The server monitors and senses these sources through the distributed monitoring stations. Each monitoring station can monitor (collect and receive) the signals emitted by the radiation sources. The signal strength value of the received signal at the m-th monitoring station is denoted as R. m The server uses the Fenton-Wilkinson approximation method to obtain an approximate signal strength value that follows a log-normal distribution.

[0069] The Fenton-Wilkinson approximation method simplifies the estimation of the distribution function by approximating the sum of multiple log-normal random variables into a single log-normal random variable. In this embodiment, the server uses the Fenton-Wilkinson approximation method to approximate the received signal strength value R, which follows a log-normal distribution. mThe approximation is the signal strength value derived from the log-normal distribution.

[0070] In one example, assume the target location area is a rectangular region with length l and width w. Within this area, there are M distributed monitoring stations and K radiation sources, where M and K are both integers greater than 1. The electromagnetic signal emitted by the k-th radiation source is monitored (received) by the m-th monitoring station, and the signal strength value R of the received signal at the m-th monitoring station is... m This can be expressed by the following formula:

[0071]

[0072] Where, d m，k P represents the distance between the k-th radiation source and the m-th monitoring station, α is the path loss exponent, and P is the distance between the k-th radiation source and the m-th monitoring station. k Let n represent the emitted power of the k-th radiation source. m，k The propagation noise is represented by a mean of 0 and a variance of . Gaussian random distribution (Gaussian random variable).

[0073] In one example, the server uses the Fenton-Wilkinson approximation method to approximate R. m Approximately and, Follows the mean μ m The variance is The normal distribution of μ. m and This can be expressed by the formula:

[0074]

[0075] Where E(·) is the function for calculating the expectation, and Var(·) is the function for calculating the variance.

[0076] S2, based on the approximate signal strength value Calculate the probability density function corresponding to the m-th monitoring station. The probability density function contains the unknown vector φ representing the horizontal and vertical coordinates of the radiation source and the emitted power.

[0077] In the actual implementation, the server obtains an approximate signal strength value. Next, it is necessary to base the approximate signal strength value on... Calculate the probability density function corresponding to the m-th monitoring station (i.e., the approximate signal strength value corresponding to the m-th monitoring station). The probability density function contains an unknown vector φ representing the x and y coordinates and the emitted power of the radiation source. By solving for the unknown vector φ representing the x and y coordinates and the emitted power of the radiation source, passive localization of multiple radiation sources can be achieved.

[0078] In one example, the server bases the signal strength value on an approximate value. The probability density function corresponding to the m-th monitoring station can be calculated using the following formula:

[0079]

[0080] Where φ is an unknown vector representing the horizontal and vertical coordinates of the radiation source and its emitted power. Let f(m) represent the probability density function corresponding to the m-th monitoring station.

[0081] S3. By combining the probability density functions corresponding to all monitoring stations, the likelihood function of the entire positioning problem is obtained, and the objective function of the maximum likelihood estimation of the entire positioning problem is derived based on the likelihood function.

[0082] In the specific implementation, after obtaining the probability density function corresponding to each monitoring station, the server needs to combine the probability density functions corresponding to all monitoring stations to obtain the likelihood function of the entire positioning problem, and derive the objective function of the maximum likelihood estimation of the entire positioning problem (i.e. the maximum likelihood estimation problem of the entire positioning problem) based on the likelihood function.

[0083] In one example, the server combines the probability density functions of all monitoring stations to obtain the likelihood function for the entire localization problem, which can be achieved using the following formula:

[0084]

[0085] Here, L(φ) represents the likelihood function of the entire localization problem.

[0086] In one example, the server derives the objective function for the maximum likelihood estimation of the entire localization problem based on the likelihood function, which can be achieved using the following formula:

[0087]

[0088] in, Let φ be the maximum likelihood estimate of the unknown vector to be solved. The constraints of the objective function for the maximum likelihood estimation of the entire localization problem are expressed by the following formula:

[0089]

[0090] P low ≤P k ≤P high;

[0091] Where, x k The x-coordinate of the k-th radiation source is represented by y. k Let P represent the ordinate of the k-th radiation source, g represent the iteration number, and P represent the position of the k-th radiation source. low P represents the minimum transmit power. high This indicates the maximum transmission power.

[0092] S4 utilizes opposition learning, adaptive redirection, and an improved multi-mutation strategy to refine the differential evolution algorithm. Based on the improved differential evolution algorithm and the objective function of the maximum likelihood estimation for the entire localization problem, global optimization is performed to solve for the maximum likelihood estimate of the unknown vector φ. Achieve passive localization of distributed multi-radiation sources.

[0093] In the specific implementation, after the server constructs the objective function for the maximum likelihood estimation of the entire localization problem, it needs to improve the differential evolution algorithm using opposition learning, adaptive redirection, and an improved multi-mutation strategy. Then, based on the improved differential evolution algorithm and the objective function for the maximum likelihood estimation of the entire localization problem, global optimization is performed to solve for the maximum likelihood estimate of the unknown vector φ. Achieve passive localization of distributed multi-radiation sources.

[0094] Improving differential evolution algorithms using opposition learning techniques, adaptive redirection techniques, and improved multi-mutation strategies is not something that can be achieved overnight, but rather it is a process that runs through the entire differential evolution process.

[0095] The server performs global optimization based on the improved differential evolution algorithm and the objective function of maximum likelihood estimation for the entire localization problem, solving for the maximum likelihood estimate of the unknown vector φ. To achieve passive localization of distributed multi-radiation sources, an improved differential evolution algorithm is first used to solve the objective function of the maximum likelihood estimation of the entire localization problem, and each element in the unknown vector φ is used as the gene of the improved differential evolution algorithm.

[0096] H initial population individuals are then randomly generated to obtain a random initial population. Based on the random initial population, an oppositional initial population is obtained using the oppositional learning technique. From these two populations, the top H individuals with the smallest function value of the objective function that minimizes the maximum likelihood estimation of the entire localization problem are selected as the original population.

[0097] The random initial population, the opposing initial population, and the original population are expressed by the following formulas:

[0098]

[0099] Where D represents the dimension of an individual, i.e., the total number of genes.

[0100] Next, the server uses an improved multi-mutation strategy to mutate and crossover the original population in the current iteration, resulting in three experimental populations, which are represented by the following formula:

[0101]

[0102] Then, the server adaptively redirects individuals whose genes cross boundaries during the mutation crossover process, resulting in three redirected populations, which are represented by the following formula:

[0103]

[0104] After establishing the redirected populations, the server needs to apply the opposition learning technique to each redirected population to obtain three new opposition populations. These three new opposition populations are represented by the following formula:

[0105]

[0106] Once all populations are established, the server selects from the original population of the current iteration, the three redirected populations, and the three new opposing populations to obtain the original population for the next iteration.

[0107] When the number of iterations reaches the preset maximum number of iterations G, the optimal individual I in the optimal population is obtained. great , will I great The optimal solution to the objective function of the maximum likelihood estimation of the entire localization problem, i.e., the maximum likelihood estimator of the unknown vector φ.

[0108] In one example, the random initial population is determined by the operator. The calculations show that the opposing initial populations are determined by the operator. Calculations show that a d and b d R represents the upper and lower bounds of the d-th gene, respectively. h It is a random number that follows a uniform distribution from 0 to 1.

[0109] In one example, the improved multi-mutation strategy comprises two parts: a mutation crossover strategy candidate pool and a control parameter strategy candidate pool. In each iteration, each mutation crossover strategy selects a control parameter generation strategy from the control parameter strategy candidate pool to form a new mutation crossover strategy, thereby generating the experimental population. The mutation strategy candidate pool contains three operators:

[0110]

[0111] Where o, p, and q are all positive integers randomly selected from the set {1, 2, ..., H}, satisfying the conditions that they are all distinct and not equal to h, F is a scaling factor taking values ​​between (0, 1), and c h It is the crossover probability that takes the value between (0, 1). It is the best individual in the original population during the g-th iteration.

[0112] In one example, the control parameter policy candidate pool contains two policies, including F ~ N(0.9, 0.2). 2 And P c ~N(0.1, 0.2) 2 ), and F~N(0.9, 0.2 2 And P c ~N(0.9, 0.2) 2 The adaptive relocation operator is expressed by the following formula:

[0113]

[0114] Where, ω d It is a random number that takes values ​​between [0, 1] and follows a uniform distribution. and These are the lower and upper bounds for the adaptive relocation operation, respectively.

[0115] In one example, the operator for generating opposite individuals is:

[0116] The operator is selected as:

[0117] Here, fit(·) is the fitting function.

[0118] In this embodiment, the signal strength values ​​of the received signals detected by distributed monitoring stations are approximated using the Fenton-Wilkinson approximation method to be transformed into signal strength values ​​following a log-normal distribution. This greatly simplifies the mathematical model of the received signal strength in passive localization of multiple radiation sources, making it easier to obtain the probability density function corresponding to the received signal strength of each monitoring station. By combining the probability density functions corresponding to the approximate received signal strength of all monitoring stations, the likelihood function of the entire localization problem can be constructed, and the maximum likelihood estimation problem of the entire localization problem can be derived from this, i.e., the objective function of the maximum likelihood estimation of the entire localization problem. The passive localization problem is transformed into a process of solving a maximum likelihood estimation problem. By integrating opposition learning technology, adaptive redirection technology, and an improved multi-mutation strategy, the differential evolution algorithm is improved. The improved differential evolution algorithm is used to solve the objective function of the maximum likelihood estimation of the entire localization problem, thereby improving the search capability and convergence speed of the differential evolution algorithm, and thus more efficiently solving for the maximum likelihood estimate of the unknown vector, estimating the horizontal and vertical coordinates and transmission power of the radiation source. Under line-of-sight propagation environment and conditions with large noise interference, high-precision passive localization of multiple radiation sources is effectively achieved.

[0119] The steps described above are for clarity only. In practice, they can be combined into one step or some steps can be broken down into multiple steps, as long as they involve the same logical relationship, they are all within the scope of protection of this application. Adding insignificant modifications or introducing insignificant designs to the algorithm or process, without changing the core design of the algorithm and process, are also within the scope of protection of this application.

[0120] In one embodiment, to evaluate the performance of the distributed multi-radiation source passive localization method proposed in this application (hereinafter referred to as the method), we used Matlab software for simulation verification.

[0121] The target location area is defined as a rectangular region of 2000m × 2000m, in which distributed anchor nodes (monitoring stations) are uniformly distributed, while target nodes (radiation sources) are randomly distributed, with their position coordinates following a uniform distribution. The number of anchor nodes M is set to 36, and the number of radiation sources is set to 3. The path loss index α is set to 2.5, and the shadowing fading factor σ varies between [2, 12] dB. Furthermore, it is assumed that the target's radiated power value P... k The value is randomly set within the range of [2000, 3000] mW. Note that when the distance between the k-th target node and the m-th anchor node is less than 1m, the received signal strength value from the k-th target node received by the m-th anchor node can be considered as the transmit power P of that anchor node. k .

[0122] The comparison of the relative positioning error between this method and traditional passive positioning methods can be seen as follows: Figure 2 As shown, the comparison of the relative maximum cumulative error distribution rate between this method and the traditional passive positioning method can be seen as follows: Figure 3 As shown.

[0123] Simulation results show that the RMSE and RMEF of all algorithms decrease as the shadow fading intensity σ decreases, indicating an improvement in positioning accuracy. Our proposed method outperforms the traditional l1-MMSE and I-BLOOMP algorithms in positioning accuracy. Specifically, when the shadow fading intensity σ = 2 dB, the RMSEs of the l1-MMSE and I-BLOOMP methods are 139.6 m and 243.3 m, respectively, while our proposed method's RMSE is only 126.3 m. Furthermore, compared to the DE-MLE method, our proposed method also exhibits a lower positioning error, thanks to multi-strategy fusion and adaptive redirection strategies. Further analysis shows that our proposed method significantly outperforms other methods in positioning accuracy under high shadow fading intensity conditions. When the shadow fading intensity σ = 12 dB, our proposed method's RMSE is 263.1 m, which is better than the I-BLOOMP method's 329.7 m at σ = 6 dB.

[0124] Another embodiment of this application proposes a distributed multi-source passive positioning system. The details of this distributed multi-source passive positioning system are described below. The following content is merely for ease of understanding and is not essential for implementing this example. Figure 4 This is a schematic diagram of the structure of a distributed multi-radiation source passive positioning system proposed in this embodiment, including: a monitoring station sensing module M1, a probability density function calculation module M2, a maximum likelihood estimation establishment module M3, and a maximum likelihood estimation solution module M4.

[0125] The monitoring station sensing module M1 is used for monitoring and sensing through distributed monitoring stations, and for measuring the signal strength value R of the received signal at the m-th monitoring station. m The Fenton-Wilkinson approximation method is used to approximate the signal strength value, which follows a log-normal distribution.

[0126] The probability density function calculation module M2 is used to calculate the approximate signal strength value. Calculate the probability density function corresponding to the m-th monitoring station. The probability density function contains the unknown vector φ representing the horizontal and vertical coordinates of the radiation source and the emitted power.

[0127] The maximum likelihood estimation module M3 is used to combine the probability density functions corresponding to all monitoring stations to obtain the likelihood function of the entire positioning problem, and derive the objective function of the maximum likelihood estimation of the entire positioning problem based on the likelihood function.

[0128] The maximum likelihood estimation module M4 is used to improve the differential evolution algorithm by combining opposition learning, adaptive redirection, and an improved multi-mutation strategy. Based on the improved differential evolution algorithm and the objective function of the maximum likelihood estimation of the entire localization problem, it performs global optimization to solve for the maximum likelihood estimate of the unknown vector φ. Achieve passive localization of distributed multi-radiation sources.

[0129] It is not difficult to see that this embodiment is a system embodiment corresponding to the above method embodiments, and this embodiment can be implemented in conjunction with the above method embodiments. The relevant technical details and technical effects mentioned in the above embodiments are still valid in this embodiment, and will not be repeated here to reduce repetition. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above embodiments.

[0130] It is worth mentioning that all modules involved in this embodiment are logical modules. In practical applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. Furthermore, to highlight the innovative aspects of this application, this embodiment does not introduce units that are not closely related to solving the technical problems proposed in this application; however, this does not mean that other units are absent in this embodiment.

[0131] Another embodiment of this application provides an electronic device, the structure of which is specifically as follows: Figure 5 As shown, it includes: at least one processor C1; and a memory C2 communicatively connected to the at least one processor C1; wherein the memory C2 stores instructions executable by the at least one processor C1, the instructions being executed by the at least one processor C1 to enable the at least one processor C1 to perform a distributed multi-radiation source passive localization method as described in the above method embodiments.

[0132] The memory and processor are connected via a bus, which includes any number of interconnecting buses and bridges, connecting various circuits of one or more processors and the memory. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and will not be described further herein. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by the processor is transmitted over the wireless medium via an antenna, which further receives data and transmits it to the processor.

[0133] The processor manages the bus and general processing, and also provides various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory is used to store data used by the processor during operation.

[0134] Another embodiment of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, can implement a distributed multi-radiation source passive localization method as described in the above method embodiments.

[0135] That is, those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a device (such as a microcontroller, chip, etc.) or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The storage medium includes various media capable of storing program code, such as a USB flash drive, portable hard drive, read-only memory, random access memory, magnetic disk, or optical disk.

[0136] Those skilled in the art will understand that the above embodiments are specific implementations of this application, and in practical applications, various changes in form and detail can be made without departing from the spirit and scope of this application. For those skilled in the art, several improvements and modifications can be made without departing from the principles of this application, and these improvements and modifications are also considered to be within the scope of protection of this application.

Claims

1. A distributed multi-radiation source passive localization method, characterized in that, include: Monitoring and sensing are performed through distributed monitoring stations, and the signal strength value R of the received signal at the m-th monitoring station is measured. m The Fenton-Wilkinson approximation method is used to approximate the signal strength value, which follows a log-normal distribution. Based on the approximate signal strength value Calculate the probability density function corresponding to the m-th monitoring station. The probability density function contains an unknown vector φ representing the horizontal and vertical coordinates of the radiation source and the emitted power. By combining the probability density functions corresponding to all monitoring stations, the likelihood function of the entire localization problem is obtained, and the objective function of the maximum likelihood estimation of the entire localization problem is derived based on the likelihood function. By employing opposition learning, adaptive redirection, and an improved multi-mutation strategy, the differential evolution algorithm is improved. Global optimization is then performed based on the improved differential evolution algorithm and the objective function of the maximum likelihood estimation for the entire localization problem, yielding the maximum likelihood estimate of the unknown vector φ. Achieve passive localization of distributed multi-radiation sources.

2. The distributed multi-radiation source passive localization method according to claim 1, characterized in that, The target location area is a rectangular area with length l and width w. Within this area, there are M distributed monitoring stations and K radiation sources, where M and K are both integers greater than 1. The electromagnetic signal emitted by the k-th radiation source is received by the m-th monitoring station. The signal strength value R of the received signal at the m-th monitoring station is... m This can be expressed by the following formula: Where, d m,k P represents the distance between the k-th radiation source and the m-th monitoring station, α is the path loss exponent, and P is the distance between the k-th radiation source and the m-th monitoring station. k Let n represent the emitted power of the k-th radiation source. m,k The propagation noise is represented by a mean of 0 and a variance of . It is a Gaussian random distribution.

3. The distributed multi-radiation source passive localization method according to claim 2, characterized in that, The signal strength value R of the received signal at the m-th monitoring station m The Fenton-Wilkinson approximation method is used to approximate the signal strength value, which follows a log-normal distribution. include: Using the Fenton-Wilkinson approximation method, R... m Approximately and, Follows the mean μ m The variance is The normal distribution, μ m and This can be expressed by the formula: Where E(·) is the function for calculating the expectation, and Var(·) is the function for calculating the variance.

4. The distributed multi-radiation source passive localization method according to claim 3, characterized in that, Based on the approximate signal strength value The probability density function corresponding to the m-th monitoring station is calculated using the following formula: Where φ is an unknown vector representing the horizontal and vertical coordinates of the radiation source and its emitted power. Let f(m) represent the probability density function corresponding to the m-th monitoring station.

5. The distributed multi-radiation source passive localization method according to claim 4, characterized in that, By combining the probability density functions corresponding to all monitoring stations, the likelihood function for the entire localization problem is obtained, which is achieved through the following formula: Where L(φ) represents the likelihood function of the entire localization problem; Based on the likelihood function, the objective function for the maximum likelihood estimation of the entire localization problem is derived, and is achieved through the following formula: in, It is the maximum likelihood estimator of the unknown vector φ that needs to be solved; The constraints of the objective function for the maximum likelihood estimation of the entire localization problem are expressed by the following formula: P low ≤P k ≤P high ; Where, x k The x-coordinate of the k-th radiation source is represented by y. k Let P represent the ordinate of the k-th radiation source, g represent the iteration number, and P represent the position of the k-th radiation source. low P represents the minimum transmit power. high This indicates the maximum transmission power.

6. The distributed multi-radiation source passive localization method according to claim 5, characterized in that, Global optimization is performed based on the improved differential evolution algorithm and the objective function of maximum likelihood estimation for the entire localization problem to solve for the maximum likelihood estimate of the unknown vector φ. To achieve passive localization of distributed multi-radiation sources, including: An improved differential evolution algorithm is used to solve the objective function of the maximum likelihood estimation of the entire localization problem, and each element in the unknown vector φ is used as the gene of the improved differential evolution algorithm. H individuals are randomly generated as the initial population, resulting in a random initial population. An alternative initial population is then obtained using the alternative learning technique. From these two populations, the top H individuals that minimize the objective function value of the maximum likelihood estimation for the entire localization problem are selected as the original population. The random initial population, the alternative initial population, and the original population are represented as follows: Where D is the dimension of an individual, that is, the total number of genes; An improved multi-mutation strategy is used to mutate and crossover the original population in the current iteration, resulting in three experimental populations, represented as follows: For individuals whose genes cross boundaries during the mutation crossover process, adaptive redirection is performed, resulting in three redirected populations, which are represented as follows: Applying the opposition learning technique to each redirected population yields three new opposition populations, represented as follows: The selection operation is performed among the original population, three redirected populations, and three new opposing populations in the current iteration to obtain the original population for the next iteration. When the number of iterations reaches the preset maximum number of iterations G, the optimal individual I in the optimal population is obtained. great , will I great The optimal solution to the objective function of the maximum likelihood estimation of the entire localization problem, i.e., the maximum likelihood estimator of the unknown vector φ.

7. The distributed multi-radiation source passive localization method according to claim 6, characterized in that, Random initial population is determined by the operator Calculations show that the opposing initial populations are determined by the operator. Calculations show that a d b represents the upper bound of the d-th gene. d r represents the lower bound of the d-th gene. h It is a random number that follows a uniform distribution from 0 to 1; The improved multi-mutation strategy consists of two parts: a mutation crossover strategy candidate pool and a control parameter strategy candidate pool. In each iteration, each mutation crossover strategy selects a control parameter generation strategy from the control parameter strategy candidate pool to form a new mutation crossover strategy, thereby generating the experimental population. The mutation strategy candidate pool contains three operators: Where o, p, and q are all positive integers randomly selected from the set {1,2,…,H}, satisfying the conditions that they are all distinct and not equal to h, F is a scaling factor taking values ​​between (0,1), and c h It represents the crossover probability that takes values ​​between (0,1). It is the best individual in the original population during the g-th iteration; The adaptive relocation operator is: Where, ω d It is a random number that takes values ​​between [0,1] and follows a uniform distribution. and These are the lower and upper bounds for the adaptive relocation operation, respectively. The operator for generating opposite individuals is: The operator is selected as: Here, fit(·) is the fitting function.

8. A distributed multi-radiation source passive positioning system, characterized in that, include; The monitoring station sensing module is used for monitoring and sensing through distributed monitoring stations, and for measuring the signal strength value R of the received signal at the m-th monitoring station. m The Fenton-Wilkinson approximation method is used to approximate the signal strength value, which follows a log-normal distribution. The probability density function calculation module is used to calculate the approximate signal strength value. Calculate the probability density function corresponding to the m-th monitoring station. The probability density function contains an unknown vector φ representing the horizontal and vertical coordinates of the radiation source and the emitted power. The maximum likelihood estimation module is used to combine the probability density functions corresponding to all monitoring stations to obtain the likelihood function of the entire localization problem, and derive the objective function of the maximum likelihood estimation of the entire localization problem based on the likelihood function. The maximum likelihood estimation module utilizes a fusion of oppositional learning, adaptive redirection, and an improved multi-mutation strategy to enhance the differential evolution algorithm. Based on the improved differential evolution algorithm and the objective function of the maximum likelihood estimation for the entire localization problem, it performs global optimization to solve for the maximum likelihood estimate of the unknown vector φ. Achieve passive localization of distributed multi-radiation sources.

9. An electronic device, characterized in that, include: At least one processor; as well as, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform a distributed multi-radiation source passive localization method as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it can implement a distributed multi-radiation source passive localization method as described in any one of claims 1 to 7.

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