Electromagnetic spectrum map generation method

Abstract

The invention relates to the technical field of electromagnetic spectrum map completion, and particularly discloses an electromagnetic spectrum map generation method, which comprises the following steps: dividing a two-dimensional geographic space of a to-be-measured electromagnetic environment into grids, and constructing a three-dimensional original map according to multiple pieces of spectrum data in the grids; complementing the original map by using an inverse distance weighted interpolation (IDW) algorithm to obtain an initial map; dividing the area of the initial map by using a k-means clustering algorithm K-means to obtain a strong radiation area and a weak radiation area; respectively complementing the intense radiation area and the weak radiation area, and replacing the original map with the complemented intense radiation area and weak radiation area to obtain a complete electromagnetic spectrum map; determining the number of radiation sources and the positions of the radiation sources according to the signal intensity difference value and the path loss of the radiation center of the intense radiation area and each point in the area; and when the position of the radiation source is not changed, the electromagnetic spectrum map and the position of the radiation source are output as a final electromagnetic spectrum map and a final position of the radiation source respectively.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetic spectrum map completion, and particularly to a method for generating an electromagnetic spectrum map. Background Art

[0002] With the rapid development of electronic and communication technologies and the continuous increase in the number of radio devices, the electromagnetic environment faced by people is becoming increasingly complex, and the regulatory requirements for the electromagnetic spectrum and electromagnetic radiation sources are also increasing. In order to achieve efficient electromagnetic space management and control, it is necessary to master the location information of each radiation source in the area through radiation source positioning. Radiation source positioning refers to the process of estimating the geographical location of a radiation source using the positioning parameters measured by detection equipment, and has broad application prospects. In the civilian field, radiation source positioning can obtain the location information of abnormal interference sources, which is beneficial for relevant departments to combat illegal activities using radio stations. At the same time, it can provide location-related services to ensure the normal progress of social production and life.

[0003] In recent years, driven by technologies such as cognitive radio, the concept of an electromagnetic spectrum map has been proposed and widely studied. The electromagnetic spectrum map combines the actual geographical environment and describes the electromagnetic environment of the target area from dimensions such as time domain, frequency domain, and electromagnetic signal intensity. Among them, the distribution of electromagnetic signal intensity can reflect the number and location of radiation sources. Therefore, based on the electromagnetic spectrum map, radiation sources in the target area can be located.

[0004] In reality, when using sensors to conduct electromagnetic mapping of a specific area, it is difficult to collect complete and accurate data. Therefore, it is necessary to first generate an electromagnetic spectrum map. The construction methods of electromagnetic spectrum maps are divided into indirect construction methods and direct construction methods. The indirect construction method requires parameters such as the location and power of known radiation sources as prior information, and thus cannot locate unknown radiation sources. The direct construction method, also known as the spatial interpolation method, is a method that directly uses the data collected by sensing nodes for interpolation to obtain an electromagnetic spectrum map.

[0005] In the radiation source positioning technology based on the electromagnetic spectrum map, the quality of the electromagnetic spectrum map directly determines the accuracy of the final radiation source positioning, and the spectrum map generation process and the positioning process are separated from each other. When using known nodes to complete the spectrum map, the information related to radiation sources cannot be effectively utilized, resulting in a low map accuracy, which in turn affects the positioning accuracy. Summary of the Invention

[0006] Aiming at the problem that it is difficult to obtain the complete electromagnetic situation of the area and it is difficult to directly locate radiation sources, the purpose of the present invention is to provide a method for generating an electromagnetic spectrum map, which extracts radiation area information for sub-region tensor completion, and while improving the accuracy of spectrum map generation, synchronously realizes the precise positioning of radiation sources.

[0007] The present invention provides a method for generating an electromagnetic spectrum map, including: Dividing the two-dimensional geographical space of the electromagnetic environment to be measured into grids, and constructing a three-dimensional original map according to multiple spectrum data in the grids; the spectrum data is the average received signal strength of one time slot in the grid; Using the inverse distance weighted interpolation algorithm IDW to complement the original map to obtain an initial map; Using the k-means clustering algorithm K-means to divide the area of the initial map to obtain a strong radiation area and a weak radiation area; Complementing the strong radiation area and the weak radiation area respectively, and using the complemented strong radiation area and weak radiation area to replace the original map to obtain a complete electromagnetic spectrum map; Determining the number of radiation sources and the positions of the radiation sources according to the signal strength difference and path loss between the radiation center of the strong radiation area and each point in the area; When the positions of the radiation sources do not change, outputting the electromagnetic spectrum map and the positions of the radiation sources as the final electromagnetic spectrum map and the final positions of the radiation sources respectively; When the positions of the radiation sources change, using the inverse distance weighted interpolation algorithm IDW to complement the original map again.

[0008] In a possible implementation manner, the dividing the two-dimensional geographical space of the electromagnetic environment to be measured into grids and constructing a three-dimensional original map according to multiple spectrum data in the grids includes: Representing the original map according to the following formula : ; wherein, is a tensor element, is a grid index, is the abscissa of the grid, is the ordinate of the grid, is the number of the time slot, is the th grid and the average received signal strength of the rd time slot, is the set of all grids and the average received signal strength.

[0009] In a possible implementation manner, the using the inverse distance weighted interpolation algorithm IDW to complement the original map to obtain an initial map includes: Performing interpolation calculation on a preset number of known grids closest to the unknown grid to obtain an interpolation grid; Calculate the path loss from each point in the interpolation grid to the unknown grid according to the free space proximity path loss model, and calculate the grid weight of the unknown grid based on the path loss. Determine the signal reception strength of the unknown grid according to the grid weight of the unknown grid and the signal reception strength of the known grid, and complete the original map according to the signal reception strength of the unknown grid to obtain an initial map.

[0010] In a possible implementation, the calculating the path loss from each point in the interpolation grid to the unknown grid according to the free space proximity path loss model and calculating the grid weight of the unknown grid based on the path loss includes: Calculate the path loss from each point in the interpolation grid to the unknown grid according to the following formula: ; ; where represents the signal frequency, is a variable affected by the environment, is the spatial distance from the unknown grid to the known grid, is a typical lognormal random variable, represents the speed of light, is the free space path loss at 1m, is the path loss between the two points being calculated; Calculate the grid weight of the following interpolation calculation grid as : ; where is the parameter regarding the rate of decrease of the grid weight with the path loss, is the preset quantity, is the number of the interpolation grid, is up to the th grid's path loss.

[0011] In a possible implementation, the determining the signal reception strength of the unknown grid according to the grid weight of the unknown grid and the signal reception strength of the known grid includes: Calculate the signal reception strength of the unknown grid according to the following formula: ; where is the signal reception strength of the unknown grid , is the grid weight of the unknown grid, is a preset quantity, is the number of the interpolation grid, is the known interpolation grid signal reception strength.

[0012] In a possible implementation, the step of using the K-means clustering algorithm to divide the area of the initial map to obtain a strong radiation area and a weak radiation area includes: Convert the initial map into a set of data points, and determine a signal strength difference matrix according to the absolute value of the signal strength difference between any two data points in the set of data points; Use the Ward algorithm to perform agglomerative hierarchical clustering on any two data points to obtain an initial number of clusters; Use the K-means algorithm according to the initial number of clusters to obtain a strong radiation area and a weak radiation area.

[0013] In a possible implementation, the step of using the Ward algorithm to perform agglomerative hierarchical clustering on any two data points to obtain an initial number of clusters includes: Calculate the Ward distance between any two data points in the set of data points; Merge the two data points with the smallest total variance increment, and calculate the Ward distance between the two data points with the smallest total variance increment until all data points are merged into one cluster; Use the number of clusters corresponding to the points greater than the average merging distance as the clustering candidate value of the K-means algorithm; Use the elbow method to calculate the sum of squared errors of K-means clustering under all the clustering candidate values, draw a relationship graph between the clustering candidate values and the sum of squared errors, and use the clustering candidate value corresponding to the elbow point of the relationship graph as the initial number of clusters.

[0014] In a possible implementation, the step of calculating the Ward distance between any two data points in the set of data points includes: Calculate the Ward distance between any two data points and according to the following formula : ; where and represent the sizes of two clusters respectively, and represent the mean vectors of two clusters respectively.

[0015] In a possible implementation, the step of determining the number and location of radiation sources according to the signal strength difference and path loss between the radiation center of the strong radiation area and each point in the area includes: Determine the number of radiation sources and their locations according to the following formula: ; where, is the average of the absolute errors between the theoretical path loss and the actual path loss for point , is the number of radiation sources, is the minimum of the absolute errors between the theoretical path loss and the actual path loss for point , is the minimum value among all , is the number of all grid points, is the multiple relationship between and when there are currently k clustering centers, is when there are currently clustering centers and the multiple relationship of, is the set threshold.

[0016] In a possible implementation, the separately complementing the strong radiation area and the weak radiation area, and replacing the original map with the complemented strong radiation area and weak radiation area to obtain a complete electromagnetic spectrum map includes: Calculate the missing values of the strong radiation area to be complemented and the weak radiation area to be complemented according to the following formula: ; where, is the spectral tensor, is the mask tensor of the observation area, , , , , , are all auxiliary variables, is a parameter introduced when solving using the ADMM algorithm, is the observed spectral tensor; Complement the strong radiation area to be complemented and the weak radiation area to be complemented respectively according to the missing values, and replace the original map with the complemented strong radiation area and weak radiation area to obtain a complete electromagnetic spectrum map.

[0017] The electromagnetic spectrum map generation method provided by the present invention makes full use of the low-rank characteristics of the surrounding area of the radiation source. During the spectrum map generation process, the radiation source area is confirmed, and then the spectrum map is completed using the radiation source characteristics. It realizes the simultaneous generation of the spectrum map and the positioning of the radiation source, which not only makes full use of the radiation source information to improve the accuracy of the spectrum map but also enables the accurate positioning of the radiation source. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic flowchart of the electromagnetic spectrum map generation method provided by the embodiment of the present invention; Figure 2 It is a schematic diagram of electromagnetic environment measurement provided by the embodiment of the present invention; Figure 3 It is a schematic diagram of the modeling of the electromagnetic spectrum map provided by the embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0019] The following further describes the embodiments of the present invention in detail with reference to the drawings and embodiments. The detailed description and drawings of the following embodiments are used to exemplarily illustrate the principle of the present invention, but cannot be used to limit the scope of the present invention, that is, the present invention is not limited to the described preferred embodiments, and the scope of the present invention is defined by the claims.

[0020] In the description of the present invention, it should be noted that unless otherwise specified, the meaning of "a plurality of" is two or more; the terms "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying relative importance; for those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0021] Figure 1 It is a schematic flowchart of the electromagnetic spectrum map generation method provided by the embodiment of the present invention, as Figure 1 shown, the present invention provides an electromagnetic spectrum map generation method, including: Step S1, dividing the two-dimensional geographical space of the electromagnetic environment to be measured into grids, and constructing a three-dimensional original map according to multiple spectrum data in the grids; In a possible implementation manner, the two-dimensional geographical space of the electromagnetic environment to be measured is divided into a group of grids, the spectrum data is the average received signal strength in one time slot in the grid, and the historical spectrum data measured continuously for T time slots can be modeled as a three-dimensional spectrum map tensor . Figure 2 It is a schematic diagram of electromagnetic environment measurement provided by the embodiment of the present invention, Figure 3 It is a schematic diagram of the modeling of the electromagnetic spectrum map provided by the embodiment of the present invention.

[0022] The original map is represented according to the following formula : ; Among them, is a tensor element, , is a grid index, is the abscissa of the grid, is the ordinate of the grid, is the number of the time slot, is the grid and the th time slot's average received signal strength, is the set of all grids and average received signal strengths.

[0023] Step S2, use the inverse distance weighted interpolation algorithm IDW to complete the original map to obtain the initial map; In a possible implementation, for the collected original map, limited by the sampling rate and detection range, it is necessary to use the improved IDW algorithm to preliminarily complete the original map to obtain the initial map.

[0024] Specifically, perform interpolation calculation on a preset number of known grids closest to the unknown grid to obtain the interpolation grid; For any unknown data in the spectrum map tensor, calculate the spatial distance L from all known points to this unknown point, and select the grids with the closest spatial distance as 's interpolation grid, denoted as , where .

[0025] Calculate the path loss from each point in the interpolation grid to the unknown grid according to the free space proximity path loss model, and calculate the grid weight of the unknown grid according to the path loss; According to the theory of electromagnetic wave propagation, the received signal strength at a certain point in space is essentially determined by the transmission power of all radiation sources in this area and the propagation path loss. Among them, the path loss characteristic is significantly affected by multi-dimensional environmental parameters such as terrain and obstacles.

[0026] In a possible implementation, calculate the path loss from each point in the interpolation grid to the unknown grid according to the following formula: ; ; Among them, represents the signal frequency, is a variable affected by the environment, is the spatial distance from the unknown grid to the known grid, is a typical lognormal random variable with a mean of 0 dB and a standard deviation is , represents the speed of light, is the free space path loss at 1 m, is the path loss between the two calculated points; Calculate the grid weights of the following interpolation grid of the grid : ; wherein, is the parameter regarding the rate of decrease of the grid weight with respect to the path loss, usually , is the preset quantity, is the number of the interpolation grid, is the path loss to the th grid.

[0027] Determine the signal reception intensity of the unknown grid according to the grid weight of the unknown grid and the signal reception intensity of the known grid, and complete the original map according to the signal reception intensity of the unknown grid to obtain the initial map.

[0028] Calculate the signal reception intensity of the unknown grid according to the following formula: ; wherein, is the signal reception intensity of the unknown grid , is the grid weight of the unknown grid, is the preset quantity, is the number of the interpolation grid, is the signal reception intensity of the known interpolation grid .

[0029] Step S3, use the K-means clustering algorithm to divide the area of the initial map to obtain the strong radiation area and the weak radiation area; K-Means clustering is the most commonly used clustering algorithm, originally originating from signal processing. Its goal is to divide data points into K clusters, find the center of each cluster and minimize its metric. The biggest advantage of this algorithm is simplicity, easy to understand, and relatively fast operation speed. The disadvantage is that it can only be applied to continuous data and the number of clusters to be aggregated needs to be specified before clustering.

[0030] The following is the analysis process of the K-Means clustering algorithm, and the steps are as follows: The first step is to determine the value of K, that is, to cluster the data into K clusters or groups.

[0031] In the second step, randomly select K data points from the dataset as centroids or data centers.

[0032] In the third step, calculate the distance between each point and each centroid respectively, and divide each point into the group closest to the centroid, following the determined centroid.

[0033] In the fourth step, after each centroid has gathered some points, re - define the algorithm to select new centroids.

[0034] In the fifth step, compare the new centroids with the old centroids. If the distance between the new centroids and the old centroids is less than a certain threshold, it means that the position change of the recalculated centroids is not significant, the convergence is stable, and it is considered that the clustering has achieved the desired result, and the algorithm terminates.

[0035] In the sixth step, if the change between the new centroids and the old centroids is large, that is, the distance is greater than the threshold, continue to iteratively execute the third step to the fifth step until the algorithm terminates.

[0036] In a possible implementation, convert the initial map into a set of data points D, and determine the signal strength difference matrix according to the absolute value of the signal strength difference between any two data points in the set of data points ; The signal strength difference matrix is a symmetric matrix, and the diagonal elements are 0.

[0037] ; The total number of the set D is , and each data point in the set D is a quadruple , is the geographical location coordinate, q represents the time slot, is the signal strength at this position.

[0038] Use the Ward algorithm to perform agglomerative hierarchical clustering on any two data points to obtain the initial number of clusters; The Ward method is a linkage criterion based on variance minimization, and its goal is to minimize the total variance increment after merging clusters. In the initialization stage, each data point is regarded as a separate cluster, According to the initial number of clusters, use the K - means algorithm to obtain the strong radiation area and the weak radiation area.

[0039] Calculate the Ward distance between any two data points in the set of data points; Specifically, calculate the Ward distance between any two data points and according to the following formula : ; Among them, and represent the sizes of two clusters, i.e., the number of data points they contain, and represent the mean vectors of the two clusters respectively.

[0040] Merge the two data points with the smallest total variance increment, and calculate the Ward distance between the two data points with the smallest total variance increment until all data points are merged into one cluster; Take the number of clusters corresponding to the points greater than the average merging distance as the clustering candidate value of the K-means algorithm; Using the elbow method, calculate the sum of squared errors of K-means clustering under all clustering candidate values, draw the relationship diagram between the clustering candidate values and the sum of squared errors, and take the clustering candidate value corresponding to the elbow point of the relationship diagram as the initial number of clusters.

[0041] According to the determined K value, use the K-means algorithm, and the spectral map will be segmented into K classes, which will contain K - 1 peripheral regions of radiation sources (i.e., strong radiation regions), denoted as , and a background region (i.e., weak radiation region), denoted as , and each strong radiation region will contain at least one radiation source.

[0042] Step S4, complement the strong radiation region and the weak radiation region respectively, and replace the original map with the complemented strong radiation region and weak radiation region to obtain a complete electromagnetic spectrum map; In a possible implementation, in the spectral map, the strong radiation source region shows stronger low-rankness and has obvious advantages in tensor completion. Therefore, in the process of generating a complete spectral map, a step-by-step complementation method for the strong radiation region and the weak radiation region is adopted.

[0043] For the divided strong radiation regions, map them to the original map to obtain the strong radiation regions to be complemented . The complementation problem of each strong radiation region can be simplified into a tensor completion problem: ; where represents the truncated nuclear norm, which is defined as , is n-mode expansion, represents a tensor of the same size as , the elements of are known values in the subset , and the elements not belonging to this subset are missing values.

[0044] Introduce auxiliary variables Satisfy , then for a third-order tensor, the completion problem is equivalent to: ; Using the ADMM algorithm to solve, the augmented Lagrangian function can be constructed as follows: ; The solution is obtained as: ; ; ; Among them, means that the matrix is folded into a tensor according to the modulus k, represents the wide-area singular value threshold operator related to truncated nuclear norm minimization.

[0045] Calculate the missing values of the strong radiation area to be completed and the weak radiation area to be completed according to the following formula: ; Among them, is the spectral tensor, is the mask tensor of the observation area, , , , , , are all auxiliary variables, is the parameter introduced when using the ADMM algorithm to solve, is the observed spectral tensor; Complete the strong radiation area to be completed and the weak radiation area to be completed according to the missing values respectively, and replace the original map with the completed strong radiation area and weak radiation area to obtain a complete electromagnetic spectrum map.

[0046] In an example, after sequentially completing the strong radiation area , replace the corresponding area in the original map with the completed data. At this time, only the weak radiation area has missing values. Adopt the same tensor completion scheme as the strong radiation area to complete the global map, and a complete spectrum map can be obtained.

[0047] Step S5, determine the number of radiation sources and the positions of radiation sources according to the signal intensity difference and path loss between the radiation center of the strong radiation area and each point in the area; In a possible implementation, select the point with the maximum signal reception intensity in the strong radiation area as the radiation center; Define is a set of radiation sources, and the radiation center is denoted as .

[0048] Calculate the path loss from each of the remaining points in the strong radiation area to the radiation center according to the following formula : ; Calculate the signal strength difference between each of the remaining points in the strong radiation area and the radiation center according to the following formula : ; records the theoretical path loss between two points, records the actual path loss between two points. Calculate the absolute error between each of the remaining points in the strong radiation area and the radiation center according to the following formula : ; Define , then is the point with the largest error between the two: ; Repeat the above calculations and update synchronously.

[0049] When the following inequality is satisfied, the number of radiation sources and the positions of the radiation sources are obtained: ; where is the average value of the absolute errors between the theoretical path loss and the actual path loss for point , is the number of radiation sources, is the minimum value of the absolute errors between the theoretical path loss and the actual path loss for point , is the minimum value among all , is the number of all grid points, is the multiple relationship between and when there are currently k clustering centers, is when there are currently clustering centers and the multiple relationship, is the set threshold.

[0050] Step S6, determine whether the positions of the radiation sources have changed; When the position of the radiation source does not change, execute step S7, and output the electromagnetic spectrum map and the radiation source position as the final electromagnetic spectrum map and the final radiation source position respectively; when the position of the radiation source changes, return to execute step S2.

[0051] The electromagnetic spectrum map generation method proposed in the present invention has the following significant beneficial effects: (1) Breakthrough improvement in positioning accuracy: By establishing a collaborative optimization mechanism for spectrum map generation and radiation source positioning, and using the tensor completion algorithm to dynamically integrate the spatial distribution characteristics of the radiation source during the completion process, the error in spectrum map reconstruction is reduced.

[0052] (2) Innovation in multi-dimensional information fusion: Creatively introduce low-rank constraints in the radiation source region, build a joint optimization model through tensor nuclear norm regularization, effectively explore the potential correlation characteristics of electromagnetic signals in the three-dimensional space-frequency-time, and break through the limitation of traditional interpolation methods that only consider spatial correlation.

[0053] (3) Significant improvement in computing efficiency: The alternating direction multiplier method is used to efficiently solve the joint model. The variable splitting technology is used to decompose complex optimization problems into sub-problem modules that can be calculated in parallel, reducing the computational complexity and meeting the real-time requirements of scenarios such as battlefield reconnaissance.

[0054] (4) Enhanced anti-interference capability: By introducing a robust tensor completion mechanism with prior constraints on radiation source characteristics, radiation source positioning can still be achieved under conditions of a high data missing rate, which is suitable for complex electromagnetic environments.

[0055] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for generating an electromagnetic spectrum map, characterized in that, Including: Dividing the two-dimensional geographical space of the electromagnetic environment to be measured into grids, and constructing a three-dimensional original map based on multiple spectrum data in the grids; the spectrum data is the average received signal strength in one time slot in the grid; Using the Inverse Distance Weighted (IDW) interpolation algorithm to complement the original map to obtain an initial map; Using the K-means clustering algorithm to divide the regions of the initial map to obtain strong radiation regions and weak radiation regions; Complementing the strong radiation region and the weak radiation region respectively, and replacing the original map with the complemented strong radiation region and weak radiation region to obtain a complete electromagnetic spectrum map; Determining the number of radiation sources and the positions of radiation sources according to the signal strength difference and path loss between the radiation center of the strong radiation region and each point in the region; When the positions of the radiation sources do not change, outputting the electromagnetic spectrum map and the positions of the radiation sources as the final electromagnetic spectrum map and the final positions of the radiation sources respectively; When the positions of the radiation sources change, using the Inverse Distance Weighted (IDW) interpolation algorithm again to complement the original map.

2. The electromagnetic spectrum map generation method according to claim 1, wherein The step of dividing the two-dimensional geographical space of the electromagnetic environment to be measured into grids and constructing a three-dimensional original map based on multiple spectrum data in the grids includes: Represent the original map according to the following formula : ； Among them, is a tensor element, is a grid index, is the abscissa of the grid, is the ordinate of the grid, is the number of the time slot, is the grid and the average received signal strength of the time slot, and is the set of all grids and the average received signal strength.

3. The electromagnetic spectrum map generation method according to claim 1, wherein The step of using the Inverse Distance Weighted (IDW) interpolation algorithm to complement the original map to obtain an initial map includes: Performing interpolation calculation on a preset number of known grids closest to the unknown grid to obtain an interpolation grid; Calculating the path loss from each point in the interpolation grid to the unknown grid according to the free space proximity path loss model, and calculating the grid weight of the unknown grid according to the path loss; Determining the signal reception strength of the unknown grid according to the grid weight of the unknown grid and the signal reception strength of the known grid, and complementing the original map according to the signal reception strength of the unknown grid to obtain an initial map.

4. The electromagnetic spectrum map generation method according to claim 3, characterized in that, The step of calculating the path loss from each point in the interpolation grid to the unknown grid according to the free space proximity path loss model and calculating the grid weight of the unknown grid according to the path loss includes: Calculating the path loss from each point in the interpolation grid to the unknown grid according to the following formula: ； ； Among them, represents the signal frequency, is a variable affected by the environment, is the spatial distance from the unknown grid to the known grid, is a typical lognormal random variable, represents the speed of light, is the free space path loss at 1m, is the path loss between the two calculated points; Interpolate the mesh according to the following mesh weights : ； Among them, is a parameter regarding the rate of decrease of the grid weight with respect to the path loss, is a preset quantity, is the number of the interpolation grid, is up to the th grid's path loss.

5. The electromagnetic spectrum map generation method according to claim 3, characterized in that, The step of determining the signal reception strength of the unknown grid according to the grid weight of the unknown grid and the signal reception strength of the known grid includes: Calculating the signal reception strength of the unknown grid according to the following formula: ； Among them, is the signal reception strength of the unknown grid , is the grid weight of the unknown grid is the preset quantity is the number of the interpolation grid is the known interpolation grid 's signal reception strength.

6. The electromagnetic spectrum map generation method according to claim 1, wherein The step of using the K-means clustering algorithm to divide the regions of the initial map to obtain strong radiation regions and weak radiation regions includes: Converting the initial map into a set of data points, and determining a signal strength difference matrix according to the absolute value of the signal strength difference between any two data points in the set of data points; Using the Ward algorithm to perform agglomerative hierarchical clustering on the any two data points to obtain an initial number of clusters; Using the K-means algorithm according to the initial number of clusters to obtain strong radiation regions and weak radiation regions.

7. The electromagnetic spectrum map generation method according to claim 6, wherein The step of using the Ward algorithm to perform agglomerative hierarchical clustering on the any two data points to obtain an initial number of clusters includes: Calculating the Ward distance between any two data points in the set of data points; Merge the two data points with the smallest total variance increment, and calculate the Ward distance between the two data points with the smallest total variance increment until all data points are merged into one cluster; Use the number of clusters corresponding to the points greater than the average merging distance as the clustering candidate value for the K-means algorithm; Using the elbow method, calculate the sum of squared errors of K-means clustering under all the clustering candidate values, draw a relationship graph between the clustering candidate values and the sum of squared errors, and use the clustering candidate value corresponding to the elbow point of the relationship graph as the initial number of clusters.

8. The electromagnetic spectrum map generation method according to claim 7, wherein The calculation of the Ward distance between any two data points in the data point set includes: Calculate the Ward distance between any two data points according to the following formula and as follows : ； Among them, and respectively represent the sizes of two clusters, and respectively represent the mean vectors of two clusters.

9. The electromagnetic spectrum map generation method according to claim 1, wherein The determination of the number of radiation sources and the positions of radiation sources according to the signal intensity difference and path loss between the radiation center of the strong radiation area and each point in the area includes: Determine the number of radiation sources and the positions of radiation sources according to the following formula: ； Among them, is the average value of the absolute error between the theoretical path loss and the actual path loss for point , is the number of radiation sources, is the minimum value of the absolute error between the theoretical path loss and the actual path loss for point , is the minimum value among all , is the number of all grid points, is the multiple relationship between and when there are currently k clustering centers, is when there are currently clustering centers and the multiple relationship of, is the set threshold value.

10. The electromagnetic spectrum map generation method according to claim 1, characterized in that, The respective completion of the strong radiation area and the weak radiation area, and the replacement of the original map with the completed strong radiation area and weak radiation area to obtain a complete electromagnetic spectrum map includes: Calculate the missing values of the to-be-completed strong radiation area and the to-be-completed weak radiation area according to the following formula: ； Among them, is the spectral tensor, is the mask tensor of the observation area, , , , , , are all auxiliary variables, is the parameter introduced when solving using the ADMM algorithm, is the observed spectral tensor; Respectively complete the to-be-completed strong radiation area and the to-be-completed weak radiation area according to the missing values, and replace the original map with the completed strong radiation area and weak radiation area to obtain a complete electromagnetic spectrum map.

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