A method for locating radiation sources in a direction-finding cross system with power-assisted arrival.

Abstract

This invention discloses a radiation source localization method for a direction finding cross system assisted by arrival power, comprising the following steps: (1) establishing a multi-source, multi-station direction finding model containing M direction finding stations and Q radiation sources; (2) using arrival power to initially eliminate false points and obtain a coarse correlation point set Γ; (3) removing outliers from the coarse correlation point set Γ to obtain a clustered correlation point set Γ. c (4) Remove clustered related point set Γ c For intersections outside the detection area, a set of associated points is obtained (5). K-means clustering is performed on the associated point set to obtain the cluster center as the positioning result. This invention utilizes the power arrival information obtained simultaneously by direction finding to effectively eliminate false points, reduce the minimum number of direction finding stations required, increase the probability of correct association, and thus improve the positioning accuracy of the direction finding intersection system.

Description

Technical Field

[0001] This invention relates to radiation source localization, and in particular to a radiation source localization method for a direction finding cross system with wave arrival power assisted. Background Technology

[0002] Electromagnetic radiation source localization technology has been widely applied in numerous fields such as navigation, reconnaissance, rescue, counter-drone operations, and radio spectrum monitoring. Among these, direction-finding cross-location is a commonly used method. This method uses multiple direction-finding stations at known locations to determine the direction of the radiation source, and then intersects the direction-finding lines to obtain the target location. This method is simple in principle, easy to implement, and because the angular information of the radiation source is relatively stable in complex scenarios, it has higher reliability than other methods, making it a key research focus for scholars both domestically and internationally.

[0003] In single-source, dual-station scenarios, the direction-finding cross-location method can directly obtain the location from the intersection point. In single-source, multi-station scenarios, the location can be obtained by clustering the intersection points. However, in multi-source, multi-station scenarios, the direction-finding station cannot distinguish which radiation source the direction-finding line belongs to. False intersection points (spurious points) are generated when direction-finding lines from two different radiation sources to two different direction-finding stations intersect; associated intersection points (associated points) are generated when direction-finding lines from the same radiation source to two different direction-finding stations intersect. When there is no direction-finding error, the associated point represents the radiation source location; when the direction-finding error is small, the associated point remains near the radiation source location. Increasing the number of direction-finding stations can usually improve the accuracy of single-source positioning. However, multiple radiation sources may exist simultaneously within the detection band. As the number of sources and stations increases, the number of false points increases quadratically, which will seriously affect the radiation source positioning accuracy. This is a problem that must be solved when applying direction-finding cross-location to multi-source, multi-station positioning. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a radiation source localization method for a direction finding cross system with arrival power assisted. By utilizing the arrival power information obtained simultaneously during direction finding, false points can be effectively eliminated, the minimum number of direction finding stations required can be reduced, the probability of correct association can be increased, and thus the positioning accuracy of the direction finding cross system can be improved.

[0005] The objective of this invention is achieved through the following technical solution: a method for locating radiation sources in a direction-finding cross system with power-assisted arrival, comprising the following steps:

[0006] (1) Establish a multi-source, multi-station direction finding cross model

[0007] Let M represent the number of direction finding stations and Q represent the number of radiation sources. Let the i-th direction finding station be the base station (1≤i≤M), the m-th direction finding station be the reference station (1≤m≤M, m≠i), the j-th direction finding line of the base station be the baseline (1≤j≤Q), and the n-th reference line of the reference station be the reference line (1≤n≤Q). The true position coordinates of the i-th direction finding station are represented as (x... s (i),y s (i)), the orientation of the normal is represented by Φ. i The true location of the q-th radiation source is represented as (x... e (i),y e (i)), 1≤q≤Q, the transmit power is expressed as P t (q).

[0008] Each direction-finding station uses an array signal processing method to simultaneously detect the angle of arrival (DOA) and power of arrival (HPA) of each radiation source. It is assumed that all direction-finding stations can detect the DOA and HPA of every radiation source, with no missed or false detections, and that the direction-finding lines do not overlap. θ(i,j), 1≤j≤Q represents the DOA of the j-th direction-finding line at the i-th direction-finding station, and P(i,j) represents the HPA on the j-th direction-finding line at the i-th direction-finding station. It should be noted that the direction-finding line number j and the radiation source number q are not necessarily the same; in reality, the radiation source number corresponding to the direction-finding line is unknown.

[0009] (2) Using the power of arrival (HA) to initially eliminate spurious points, we obtain the coarsely correlated point set Γ.

[0010] (2a) Parameter initialization: Let i = 1, j = 1, m = 2, n = 1. Given parameters M, Q, (x... s ,y s ),Φ i Step (2) takes θ and P as inputs and outputs Γ as output.

[0011] (2b) Calculate the slope k(i,j) and intercept b(i,j) of the baseline and the slope k(m,n) and intercept b(m,n) of the reference line:

[0012]

[0013] b(i,j)=y s (i)-k(i,j)x s (i)

[0014]

[0015] b(m,n)=y s (m)-k(m,n)x s (m)

[0016] (2c) Calculate the coordinates of the intersection point of the baseline and the reference line:

[0017]

[0018] y(i,j,m,n)=k(i,j)x(i,j,m,n)+b(i,j)

[0019] (2d) Calculate the Euclidean distances between the intersection point and the base station and the reference station respectively:

[0020]

[0021]

[0022] (2e) Calculate the confidence level of the intersection:

[0023] Using Friis's formula in the electromagnetic wave free-space propagation model, the power of arrival of the q-th radiation source at the i-th direction-finding station can be obtained:

[0024]

[0025] Among them G t (q) represents the antenna gain of the q-th radiation source, G r Let λ represent the antenna gain of the direction-finding station, λ represent the carrier wavelength, L represent the system loss factor of the direction-finding station, and d(i,q) represent the distance between the i-th direction-finding station and the q-th radiation source.

[0026]

[0027] Similarly, the arrival power P of the q-th radiation source at the m-th direction-finding station can be obtained. r (m,q), the ratio of the wave power received by two direction finding stations at the same radiation source is

[0028]

[0029] If the correlation point is located near the radiation source, and the direction finding is accurate, the ratio of the squares of the distances from the correlation point to the two survey stations is equal to the reciprocal of the ratio of the wave power received.

[0030]

[0031] Where P(i,j) represents the power of arrival detected by the base station on the reference line, and P(m,n) represents the power of arrival detected by the reference station on the reference line. Even with slight errors in direction finding, the associated points still approximately satisfy the above proportional relationship. False points, however, have no physical meaning and therefore do not satisfy the above proportional relationship. A confidence level C(i,j,m,n) is defined to describe the degree to which the intersection points satisfy the above proportional relationship:

[0032]

[0033] Ideally, the confidence level of a correlated point is ∞, while the confidence level of a false point is typically lower than that of a correlated point. By iterating through each reference line index n of the reference station, the Q intersection points on the baseline and their corresponding confidence levels can be calculated.

[0034] (2f) If n = Q, then execute step (2g); otherwise, let n = n + 1 and execute step (2b).

[0035] (2g) Determine relevant and false points based on confidence level:

[0036] Obtain the reference line number that maximizes the confidence level from the Q intersection points.

[0037]

[0038] Then the baseline and the first The intersection of the reference lines is identified as a related point and added to the coarse related point set Γ. The intersection of this baseline with the remaining Q-1 reference lines is identified as a false point and is not considered in subsequent positioning processes.

[0039] (2h) If m = M, then execute step (2i); otherwise, let m = m + 1, n = 1, and execute step (2b).

[0040] (2i) If j = Q, then execute step (2j); otherwise, let j = j + 1, m = i + 1, n = 1, and execute step (2b).

[0041] (2j) If i = M-1, then execute step (3); otherwise, let i = i+1, j = 1, m = i+1, n = 1, and execute step (2b).

[0042] (4) Remove outliers from the coarsely correlated point set Γ to obtain the clustered correlated point set Γ. c .

[0043] Outliers are points that are significantly different from other points in the set. This invention uses distance-based outlier detection, where D... T Dis[·] represents the distance threshold, and Dis[·] represents the Euclidean distance between two points. For a point Γ(u) in the coarsely correlated point set Γ, if There exists Dis[Γ(u),Γ(v)]>D T If the condition is met, then Γ(u) is determined to be an outlier. Using this as the criterion, all outliers in Γ are found, and after removing them, the clustered set of related points Γ is obtained. c .

[0044] (4) Remove clustered related point sets Γ cThe intersection points located outside the detection area are used to obtain the set of associated points.

[0045] In practical applications, only radiation sources in a specific area need to be detected, and each direction-finding station may have a certain blind zone, within which the positioning error is relatively large. Therefore, according to the task requirements, a detection area is defined, and when the coordinates of the intersection point are within the detection area (excluding the area boundary), it is added to the associated point set. If the intersection point is outside the detection area, discard it. Find Γ. c The set of associated points is obtained by finding all intersections within the detection area.

[0046] (5) For the set of related points Perform K-means clustering and use the cluster centers as the location results.

[0047] In multi-station positioning with M direction finding stations, the bi-station direction finding lines intersect pairwise to obtain intersection points, and each radiation source has... These are the associated points, assuming no direction finding error. All Q correlation points coincide with the actual locations of the radiation sources. In the presence of direction-finding errors, these Q radiation sources... The associated points are distributed around the actual location of the radiation source. Some of these associated points may have been removed in steps (3) and (4), leaving the remaining associated points in... In the middle. Using K-means clustering to... The points in the cluster are grouped into Q-classes, and the cluster centers are used as the localization results.

[0048] The beneficial effects of this invention are: by utilizing the power arrival information obtained simultaneously from direction finding, this invention effectively eliminates false points, reduces the minimum number of direction finding stations required, increases the probability of correct association, and thus improves the positioning accuracy of the direction finding cross system. Attached Figure Description

[0049] Figure 1 This is a flowchart of the method of the present invention;

[0050] Figure 2 A schematic diagram illustrating the specific process of using wave power to initially eliminate spurious points and obtain a coarse correlation point set;

[0051] Figure 3 This is a schematic diagram of a multi-source, multi-station direction finding cross-positioning model;

[0052] Figure 4 A graph showing the correlation coefficient as a function of the standard deviation of DOA;

[0053] Figure 5 This is a graph showing the variation of average positioning error with the standard deviation of DOA. Detailed Implementation

[0054] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.

[0055] like Figure 1 As shown, a method for locating radiation sources in a direction-finding cross system with power-assisted arrival includes the following steps:

[0056] (1) Establish a multi-source, multi-station direction finding cross model

[0057] Suppose the number of direction finding stations is M = 4, and their location coordinates are (50,0), (0,50), (50,100), (100,50), with the normal direction Φ. i The radiation sources are located at 90°, 0°, -90°, and 180°, with Q = 3 sources and coordinates (50,0), (0,50), and (50,100), respectively. The emission power is P. t Both are 1W. To simplify the calculation, let the antenna gain of the radiation source be G. t Both are 1, and the antenna gain G of the direction-finding station is 1. r =1, carrier wavelength λ = 0.6928m, system loss factor L = 1.

[0058] Each direction-finding station uses an array signal processing method to simultaneously obtain the angle of arrival (DOA) and power of arrival of the radiation source. Under ideal conditions with no errors, the DOA and power of arrival obtained by each direction-finding station are shown in Table 1 and Table 2, respectively.

[0059] Table 1. Actual Angle of Arrival (unit: degrees) for each direction finding station

[0060]

[0061] Table 2. Actual power of arrival at each direction finding station (unit: microwatts)

[0062]

[0063] Assume that the angle of arrival estimation of the direction finding station has a standard deviation of σ. θ With zero-mean Gaussian noise, the power-at-arrival estimate has a standard deviation of σ. P The zero-mean Gaussian noise. For ease of demonstration in this example, we assume there are no errors in the estimation of angle of arrival and power of arrival, i.e., σ θ =0,σ P =0. In addition, in practical applications, the angle of arrival and the power of arrival are in one-to-one correspondence, but it is unknown which radiation source each direction finding line corresponds to. In this example, the angles of arrival of each direction finding station are arranged in descending order, and the power of arrival is also corresponding accordingly. For example, θ(1,1)=123.69, P(1,1)=2.3383, θ(2,1)=164.05, P(1,1)=2.2942.

[0064] (2) Using the power of arrival (HA) to initially eliminate spurious points, a coarsely correlated point set is obtained, such as... Figure 2 As shown, the specific process includes:

[0065] (2a) Parameter initialization: Let i = 1, j = 1, m = 2, n = 1. Given parameters M, Q, (x... s ,y s ),Φ i The input is θ, P, and the output is Γ.

[0066] (2b) Calculate the slope k(i,j) and intercept b(i,j) of the baseline and the slope k(m,n) and intercept b(m,n) of the reference line:

[0067]

[0068] b(i,j)=y s (i)-k(i,j)x s (i)

[0069]

[0070] b(m,n)=y s (m)-k(m,n)x s (m)

[0071] Specifically, in the first cycle, the slope of the baseline k(1,1) = -1.5, the intercept b(1,1) = 75, the slope of the reference line k(2,1) = 3.5, and the intercept b(2,1) = 50 can be calculated.

[0072] (2c) Calculate the coordinates of the intersection point of the baseline and the reference line:

[0073]

[0074] y(i,j,m,n)=k(i,j)x(i,j,m,n)+b(i,j)

[0075] Specifically, in the first cycle, the coordinates of the intersection point can be calculated as x(1,1,2,1)=5, y(1,1,2,1)=67.5.

[0076] (2d) Calculate the Euclidean distances between the intersection point and the base station and the reference station respectively:

[0077]

[0078]

[0079] Specifically, in the first cycle, d1(1,1,2,1)=81.1249 and d2(1,1,2,1)=18.2003 can be calculated.

[0080] (2e) Calculate the confidence level of the intersection:

[0081]

[0082] Specifically, in the first round of iterations, the confidence level of the crossover point can be calculated as C(1,1,2,1) = 4673.

[0083] (2f) If n = Q, then execute step (2g); otherwise, let n = n + 1 and execute step (2b).

[0084] (2g) Determine relevant and false points based on confidence level:

[0085] Obtain the reference line number that maximizes the confidence level from the Q intersection points.

[0086]

[0087] Then the baseline and the first The intersection of this baseline with the remaining Q-1 reference lines is identified as a correlated point and added to the coarse correlated point set. The intersection of this baseline with the remaining Q-1 reference lines is identified as a false point and will not be considered in subsequent positioning processes.

[0088] Specifically, in the first iteration, step (2f) yields the confidence levels of the three intersection points on the baseline: C(1,1,2,1) = 4673, C(1,1,2,2) = 52557, and C(1,1,2,3) = ∞. The intersection point with the highest confidence level is the intersection of the first direction finding line of direction finding station 1 and the third direction finding line of direction finding station 2. This intersection point is identified as a correlated point and added to the coarse correlated point set Γ. Since it is assumed that there are no errors in the measurement of the angle of arrival and power of arrival, the confidence level of this intersection point is ∞. The other two intersection points are identified as false points.

[0089] (2h) If m = M, then execute step (2i); otherwise, let m = m + 1, n = 1, and execute step (2b).

[0090] (2i) If j = Q, then execute step (2j); otherwise, let j = j + 1, m = i + 1, n = 1, and execute step (2b).

[0091] (2j) If i = M-1, then execute step (3); otherwise, let i = i+1, j = 1, m = i+1, n = 1, and execute step (2b).

[0092] During the entire loop of step (2), steps (2b)-(2e) are executed times, step (2g) is executed times, and a total of associated points and false points are determined. Specifically, in this example, 18 associated points and 36 false points are determined.

[0093] (3) Remove the outlier points from the rough associated point set Γ to obtain the aggregated associated point set Γ c .

[0094] An outlier point refers to a point that is significantly different from other points in the point set. In this invention, distance-based outlier detection is used. Let D T represent the distance threshold. In this example, D T is set to 20. Dis[·] represents the Euclidean distance between two points. For a certain point Γ(u) in the rough associated point set Γ, if Dis[Γ(u),Γ(v)] > D T holds, then Γ(u) is determined as an outlier point. Based on this determination criterion, all outlier points in Γ are found, and after removal, the aggregated associated point set Γ c is obtained. In this example, there are no outlier points in Γ, so Γ c = Γ.

[0095] (4) Remove the intersection points outside the detection area in the aggregated associated point set Γ c to obtain the associated point set

[0096] In practical applications, only the radiation sources in a specific area need to be detected, and each direction-finding station may have a certain blind area where the positioning error is relatively large. Therefore, the detection area is defined. Remove the intersection points outside the detection area in the aggregated associated point set to obtain the associated point set In this example, it is assumed that the area where 5 < x < 95 and 5 < y < 95 is the detection area. There are no intersection points outside the detection area in Γ c , so

[0097] (5) Cluster the associated point set to obtain the cluster center as the positioning result.

[0098] In the multi-station positioning of M direction-finding stations, the direction-finding lines of two stations intersect pairwise to obtain intersection points. Each radiation source has associated points. In the case of no direction-finding error, these associated points all coincide with the true position of the radiation source. In the case of direction-finding error, for these Q radiation sources The associated points are distributed around the actual location of the radiation source. Some of these associated points may have been removed in steps (3) and (4), leaving the remaining associated points in... In the middle. Using K-means clustering to... The points in the cluster are grouped into Q-classes, and the cluster centers are used as the localization results.

[0099] This example uses the K-Means clustering method based on Euclidean distance to cluster related point sets. The points in the data are clustered into Q=3 classes, with cluster centers at (10,85), (70,15), and (30,30). Compared with the actual location of the radiation source, the location is accurate.

[0100] The technical effects of the present invention will be explained in detail below with reference to simulation experiments.

[0101] 1. Simulation conditions:

[0102] The positioning error of the radiation source is expressed as the Euclidean distance between the true coordinates of the radiation source and the nearest cluster center. The association accuracy is calculated as the ratio of the number of intersection points between the coarse association point set and the true association point set to the number of coarse association points. In comparison, prior art 1 uses an angle-based data association method, and prior art 2 uses the baseline minimum distance method. The remaining simulation parameters are set the same as in the specific embodiment.

[0103] Hardware and software environment during simulation:

[0104] Hardware environment: CPU is Intel Core i7-8750H with a clock speed of 2.2GHz, RAM is 24GB with a frequency of 2666MHz.

[0105] Software environment: The system environment is Windows 11 Education Edition 21H2, and the simulation software is MATLAB R2021a.

[0106] 2. Simulation content and result analysis:

[0107] In the presence of small direction-finding errors, the multi-source, multi-station direction-finding cross-positioning model is as follows: Figure 3 As shown. The baseline, reference lines, and their intersections in the first cycle are marked. Figure 3 middle.

[0108] Let the standard deviation of the angle of arrival estimate be given by σ. θ =0 degrees change to σ θ =5 degrees, intervals of 0.2 degrees, 1000 Monte Carlo experiments were performed at each standard deviation. The correlation accuracy between the present invention and two prior art techniques as a function of DOA standard deviation is shown in the curves. Figure 4 As shown in the figure, the average positioning error of the three radiation sources varies with the standard deviation of DOA. Figure 5As shown in Table 3, the average single run time for each method is as follows.

[0109] Reference Figure 4 Because this invention utilizes wave arrival power information, it has a higher correlation accuracy rate compared to existing technologies. In particular, this invention can still maintain a high correlation accuracy rate when the direction finding error is large.

[0110] Reference Figure 5 Compared to existing technologies, this invention exhibits lower positioning errors, especially when direction-finding errors are significant. It's important to note that the number of associated points estimated by this invention and existing technology 1 matches the actual number of associated points, while existing technology 2 estimates a slightly higher number. Therefore, existing technology 2 has a lower association accuracy but a smaller positioning error than existing technology 1. In contrast, this invention achieves advantages in both positioning error and accurate association rate.

[0111] Table 3. Average single run time for each method

[0112]

[0113] Referring to Table 3, the computational complexity of this invention is slightly higher than that of prior art 1, but significantly lower than that of prior art 2, and it is engineering feasible.

[0114] Compared with the traditional multi-source, multi-station direction finding cross method, this invention utilizes the arrival power information of the radiation source, reducing the minimum number of direction finding stations required from three to two, thereby improving the correlation accuracy and positioning precision, while reducing the computational load.

[0115] The above description represents preferred embodiments of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technical or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for locating radiation sources in a direction-finding cross system with power-assisted arrival, characterized in that: Includes the following steps: (1) Establish a multi-source, multi-station direction finding model containing M direction finding stations and Q radiation sources; (2) Use the power of arrival to initially eliminate false points and obtain the coarse correlation point set Γ; Step (2) includes the following sub-steps: (2a) Parameter initialization: Let i = 1, j = 1, m = 2, n = 1. Given parameters M, Q, (x s ,y s ),Φ i Step (2) takes θ and P as inputs and outputs Γ. (2b) Calculate the slope k(i,j) and intercept b(i,j) of the baseline and the slope k(m,n) and intercept b(m,n) of the reference line: b(i,j)=y s (i)-k(i,j)x s (i) b(m,n)=y s (m)-k(m,n)x s (m) (2c) Calculate the coordinates of the intersection point of the baseline and the reference line: y(i,j,m,n)=k(i,j)x(i,j,m,n)+b(i,j) (2d) Calculate the Euclidean distances between the intersection point and the base station and the reference station respectively: (2e) Calculate the confidence level of the intersection: Where P(i,j) represents the power of arrival detected by the base station on the baseline, and P(m,n) represents the power of arrival detected by the reference station on the reference line; (2f) If n = Q, then execute step (2g); otherwise, let n = n + 1 and execute step (2b). (2g) Determine relevant and false points based on confidence level: Obtain the reference line number that maximizes the confidence level from the Q intersection points. Then the baseline and the first The intersection of the reference lines is determined to be a related point and added to the coarse related point set Γ; the intersection of the baseline with the remaining Q-1 reference lines is determined to be a false point. (2h) If m = M, then execute step (2i); otherwise, let m = m + 1, n = 1, and execute step (2b). (2i) If j = Q, then execute step (2j); otherwise, let j = j + 1, m = i + 1, n = 1, and execute step (2b). (2j) If i = M-1, then proceed to step (3); otherwise, let i = i+1, j = 1, m = i+1, n = 1, and execute step (2b). (3) Remove outliers from the coarsely correlated point set Γ to obtain the clustered correlated point set Γ. c ; (4) Remove clustered related point sets Γ c The intersection points located outside the detection area are used to obtain the set of associated points. (5) For the set of related points Perform K-means clustering and use the cluster centers as the location results.

2. The method for locating radiation sources in a direction-finding cross system with power-assisted arrival as described in claim 1, characterized in that: Step (1) includes: Let the i-th direction finding station be the base station, 1≤i≤M, and the m-th direction finding station be the reference station, 1≤m≤M, m≠i. Let the j-th direction finding line of the base station be the baseline, 1≤j≤Q, and the n-th reference line of the reference station be the reference line, 1≤n≤Q. The true position coordinates of the i-th direction finding station are represented as (x... s (i),y s (i)), the orientation of the normal is represented by Φ. i The true location of the q-th radiation source is represented as (x e (i),y e (i)), 1≤q≤Q, the transmit power is expressed as P t (q); Each direction finding station uses an array signal processing method to simultaneously detect the angle of arrival and power of arrival of each radiation source: Assume that all direction finding stations can detect the angle of arrival and power of arrival of every radiation source, with no missed or false detections, and that the direction finding lines do not coincide. θ(i,j) represents the DOA corresponding to the j-th direction finding line of the i-th direction finding station, where DOA represents the angle of arrival, and P(i,j) represents the power of arrival on the j-th direction finding line of the i-th direction finding station. The radiation source number q corresponding to the direction finding line number j is unknown.

3. The method for locating radiation sources in a direction-finding cross system with power-assisted arrival as described in claim 1, characterized in that: In step (3), outlier detection and removal based on distance includes: Let D T Dis[·] represents the distance threshold, and Dis[·] represents the Euclidean distance between two points. For a point Γ(u) in the coarsely correlated point set Γ, if There exists Dis[Γ(u),Γ(v)]>D T If the condition is met, then Γ(u) is determined to be an outlier; using this as the criterion, all outliers in Γ are found, and after removing them, the clustered associative point set Γ is obtained. c .

4. The method for locating the radiation source of a direction-finding cross system with power-assisted arrival as described in claim 1, characterized in that: In step (4), a detection area is pre-defined according to task requirements. When the coordinates of an intersection point are within the detection area, it is added to the associated point set. If the coordinates of the intersection point are outside the detection area, the intersection point will be discarded; the detection area does not include the area boundary. Find Γ c The set of associated points is obtained by finding all intersections within the detection area.

5. The method for locating radiation sources in a direction-finding cross system with power-assisted arrival as described in claim 1, characterized in that: Step (5) includes: In multi-station positioning with M direction finding stations, the bi-station direction finding lines intersect pairwise to obtain intersection points, and each radiation source has... These are the associated points, assuming no direction finding error. All the associated points coincide with the actual location of the radiation source; In the presence of direction-finding errors, these Q radiation sources The associated points are distributed around the actual location of the radiation source. Some of these associated points were removed in steps (3) and (4), and the remaining associated points are... In the middle, K-means clustering is used to... The points in the cluster are grouped into Q-classes, and the cluster centers are used as the localization results.

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