A method for generating electromagnetic spectrum map

Abstract

The present invention relates to the technical field of electromagnetic spectrum map completion, and specifically discloses a method for generating an electromagnetic spectrum map, comprising: dividing a two-dimensional geographic space of an electromagnetic environment to be measured into grids, and constructing a three-dimensional original map based on multiple spectrum data in the grids; completing the original map using an inverse distance weighted interpolation algorithm (IDW) to obtain an initial map; dividing the regions of the initial map using a K-means clustering algorithm (K-means) to obtain strong radiation regions and weak radiation regions; completing the strong radiation regions and weak radiation regions respectively, and replacing the original map with the completed strong radiation regions and weak radiation regions to obtain a complete electromagnetic spectrum map; determining the number and positions of radiation sources based on the difference in signal strength between the radiation center of the strong radiation region and each point in the region and the path loss; and outputting the electromagnetic spectrum map and the radiation source positions as the final electromagnetic spectrum map and the final radiation source positions, respectively, when the radiation source positions do not change.

Description

Technical Field

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

[0002] With the rapid development of electronics and communications technology and the increasing number of radio devices, the electromagnetic environment we face is becoming increasingly complex, and the need for regulation of the electromagnetic spectrum and electromagnetic radiation sources is also increasing. To achieve efficient electromagnetic space management and control, it is necessary to obtain the location information of each radiation source within a region through radiation source positioning. Radiation source positioning, which uses positioning parameters measured by detection equipment to estimate the geographic location of a radiation source, has broad application prospects. In the civilian sector, radiation source positioning can obtain the location information of abnormal interference sources, helping relevant departments to combat illegal activities using radio stations. It can also provide location-related services to ensure the normal operation of social production and life.

[0003] In recent years, driven by technologies like cognitive radio, the concept of electromagnetic spectrum mapping has been proposed and widely researched. Electromagnetic spectrum mapping, incorporating the actual geographical context, describes the electromagnetic environment of a target area from various dimensions, including the time domain, frequency domain, and electromagnetic signal strength. The distribution of electromagnetic signal strength can reveal the number and location of radiation sources. Therefore, using electromagnetic spectrum mapping, radiation sources within a target area can be located.

[0004] In reality, it's difficult to collect complete and accurate data when using sensors to conduct electromagnetic mapping of a specific area. Therefore, it's necessary to first generate an electromagnetic spectrum map. There are two methods for constructing electromagnetic spectrum maps: indirect and direct. Indirect methods require prior knowledge of radiation source parameters such as location and power, making it impossible to locate unknown radiation sources. Direct methods, also known as spatial interpolation, directly interpolate data collected by sensing nodes to obtain an electromagnetic spectrum map.

[0005] In emitter location technology based on electromagnetic spectrum maps, the quality of the electromagnetic spectrum map directly determines the accuracy of the final emitter location. Furthermore, the spectrum map generation process is separate from the location process. When using known nodes to complete the spectrum map, information about the emitter cannot be effectively utilized, resulting in low map accuracy, which in turn affects location accuracy. Summary of the Invention

[0006] In view of the problems that it is difficult to obtain the complete electromagnetic situation of a region and difficult to directly locate the radiation source, the purpose of the present invention is to provide a method for generating an electromagnetic spectrum map. By extracting radiation area information and performing regional tensor completion, the accuracy of spectrum map generation is improved while simultaneously achieving accurate positioning of the radiation source.

[0007] The present invention provides a method for generating an electromagnetic spectrum map, comprising:

[0008] Divide the two-dimensional geographic space of the electromagnetic environment to be measured into grids, and construct a three-dimensional original map based on multiple spectrum data in the grids; the spectrum data is the average received signal strength of a time slot in the grid;

[0009] The original map is completed using an inverse distance weighted interpolation algorithm (IDW) to obtain an initial map;

[0010] Using a K-means clustering algorithm (K-means) to divide the region of the initial map into strong radiation regions and weak radiation regions;

[0011] Completing the strong radiation area and the weak radiation area respectively, and replacing the original map with the completed strong radiation area and weak radiation area to obtain a complete electromagnetic spectrum map;

[0012] Determine the number and location of radiation sources based on the signal strength difference and path loss between the radiation center and each point in the strong radiation area;

[0013] When the position of the radiation source does not change, outputting the electromagnetic spectrum map and the radiation source position as the final electromagnetic spectrum map and the final radiation source position, respectively;

[0014] When the position of the radiation source changes, the inverse distance weighted interpolation algorithm IDW is used again to complete the original map.

[0015] In a possible implementation, dividing the two-dimensional geographic 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:

[0016] The original map is represented by the following formula :

[0017] ;

[0018] in, is a tensor element, is the grid index, is the horizontal coordinate of the grid, is the vertical coordinate of the grid, is the number of the time slot, For the Grid and The average received signal strength of each time slot is is the set of all grids and the average received signal strength.

[0019] In a possible implementation, the using of the inverse distance weighted interpolation algorithm IDW to complete the original map to obtain the initial map includes:

[0020] Perform interpolation calculation on a preset number of known grids closest to the unknown grid to obtain an interpolated grid;

[0021] Calculating the path loss from each point in the interpolation grid to the unknown grid according to a free space proximity path loss model, and obtaining a grid weight of the unknown grid according to the path loss calculation;

[0022] The signal reception strength of the unknown grid is determined according to the grid weight of the unknown grid and the signal reception strength of the known grid, and the original map is completed according to the signal reception strength of the unknown grid to obtain an initial map.

[0023] In a possible implementation, calculating the path loss from each point in the interpolation grid to the unknown grid according to a free space proximity path loss model, and obtaining the grid weight of the unknown grid according to the path loss includes:

[0024] The path loss from each point in the interpolation grid to the unknown grid is calculated according to the following formula:

[0025] ;

[0026] ;

[0027] in, represents the signal frequency, are variables 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 1 m, is the calculated path loss between the two points;

[0028] The grid is calculated based on the following interpolation The grid weight :

[0029] ;

[0030] in, For the mesh weight The parameter of the rate at which the path loss decreases, For the preset number, is the number of the interpolation grid, To the The path loss of a grid.

[0031] In a possible implementation, 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:

[0032] The signal reception strength of the unknown grid is calculated according to the following formula:

[0033] ;

[0034] in, For unknown grid Signal reception strength, is the grid weight of the unknown grid, For the preset number, is the number of the interpolation grid, For a known interpolation grid signal reception strength.

[0035] In a possible implementation, dividing the area of ​​the initial map using a K-means clustering algorithm to obtain strong radiation areas and weak radiation areas includes:

[0036] Converting the initial map into a set of data points, and determining a signal strength difference matrix based on the absolute value of the difference in signal strength between any two data points in the set of data points;

[0037] Use the Ward algorithm to perform agglomerative hierarchical clustering on any two data points to obtain the initial number of clusters;

[0038] A K-means algorithm is used according to the initial number of clusters to obtain strong radiation areas and weak radiation areas.

[0039] In a possible implementation, performing agglomerative hierarchical clustering on the arbitrary two data points using the Ward algorithm to obtain the initial number of clusters includes:

[0040] Calculate the Ward distance between any two data points in the data point set;

[0041] 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;

[0042] The number of clusters corresponding to the points with a distance greater than the average merge distance is used as the candidate cluster value of the K-means algorithm;

[0043] The elbow method is used to calculate the sum of square errors of K-means clustering under all the cluster candidate values, and a relationship graph between the cluster candidate values ​​and the sum of square errors is drawn. The cluster candidate value corresponding to the elbow point of the relationship graph is used as the initial number of clusters.

[0044] In a possible implementation, calculating the Ward distance between any two data points in the data point set includes:

[0045] Calculate any two data points according to the following formula and Ward distance :

[0046] ;

[0047] in, and Represent the sizes of the two clusters, and Represent the mean vectors of the two clusters respectively.

[0048] In a possible implementation, determining the number and positions of radiation sources based on the signal strength difference and path loss between the radiation center of the strong radiation area and each point in the area includes:

[0049] The number and location of radiation sources are determined according to the following formula:

[0050] ;

[0051] in, For the point The average absolute error between the theoretical path loss and the actual path loss, is the number of radiation sources, For the point The minimum absolute error between the theoretical path loss and the actual path loss, For all The minimum value in is the number of all grid points, When there are k cluster centers and The multiple relationship For the present Cluster centers and The multiple relationship is the set threshold.

[0052] In a possible implementation, the respectively completing the strong radiation area and the weak radiation area, and replacing the original map with the completed strong radiation area and weak radiation area to obtain a complete electromagnetic spectrum map includes:

[0053] The missing values ​​of the strong radiation area to be completed and the weak radiation area to be completed are calculated according to the following formula:

[0054] ;

[0055] in, is the spectrum tensor, is the mask tensor of the observation area, 、 、 、 、 、 are auxiliary variables, is the parameter introduced when solving the problem using the ADMM algorithm, is the observed spectrum tensor;

[0056] The strong radiation areas to be completed and the weak radiation areas to be completed are completed respectively according to the missing values, and the original map is replaced with the completed strong radiation areas and weak radiation areas to obtain a complete electromagnetic spectrum map.

[0057] The electromagnetic spectrum map generation method provided by this invention fully utilizes the low-rank characteristics of the area surrounding the radiation source. During the spectrum map generation process, the radiation source area is identified and then the radiation source characteristics are used to complete the spectrum map. This enables the simultaneous generation of the spectrum map and the localization of the radiation source, fully utilizing the radiation source information to improve the accuracy of the spectrum map and accurately locate the radiation source. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A schematic flow chart of a method for generating an electromagnetic spectrum map according to an embodiment of the present invention;

[0059] Figure 2 A schematic diagram of electromagnetic environment measurement provided by an embodiment of the present invention;

[0060] Figure 3 A schematic diagram of modeling of an electromagnetic spectrum map provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The following detailed description of the embodiments of the present invention is provided in conjunction with the accompanying drawings and examples. The following detailed description of the embodiments and the accompanying drawings are intended to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention. That is, the present invention is not limited to the preferred embodiments described, and the scope of the present invention is defined by the claims.

[0062] In the description of the present invention, it should be noted that, unless otherwise specified, “plurality” means two or more; the terms “first”, “second”, etc. are used for descriptive purposes only and cannot be understood as indicating or implying relative importance; for ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances.

[0063] Figure 1 A flow chart of a method for generating an electromagnetic spectrum map according to an embodiment of the present invention is provided. Figure 1 As shown, the present invention provides a method for generating an electromagnetic spectrum map, comprising:

[0064] Step S1, dividing the two-dimensional geographic 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;

[0065] In one possible implementation, the two-dimensional geographic space of the electromagnetic environment to be measured is divided into a group The grid, the spectrum data is the average received signal strength of a time slot in the grid, and the historical spectrum data of T time slots can be modeled as a three-dimensional spectrum map tensor. . Figure 2 A schematic diagram of electromagnetic environment measurement provided by an embodiment of the present invention, Figure 3 A schematic diagram of modeling of an electromagnetic spectrum map provided in an embodiment of the present invention.

[0066] The original map is represented by the following formula :

[0067] ;

[0068] in, is a tensor element, 、 is the grid index, is the horizontal coordinate of the grid, is the vertical coordinate of the grid, is the number of the time slot, For the Grid and The average received signal strength of each time slot is is the set of all grids and the average received signal strength.

[0069] Step S2, using the inverse distance weighted interpolation algorithm IDW to complete the original map to obtain the initial map;

[0070] In a possible implementation, due to the limitations of sampling rate and detection range, the original map collected needs to be preliminarily completed using an improved IDW algorithm to obtain an initial map.

[0071] Specifically, interpolation calculation is performed on a preset number of known grids closest to the unknown grid to obtain an interpolated grid;

[0072] For any unknown data in the spectrum map tensor , calculate the spatial distance L from all known points to the unknown point, and select the one with the closest spatial distance Grid As The interpolation grid is denoted as ,in .

[0073] The path loss from each point in the interpolation grid to the unknown grid is calculated based on the free space proximity path loss model, and the grid weight of the unknown grid is calculated based on the path loss;

[0074] According to electromagnetic wave propagation theory, the received signal strength at a certain point in space is essentially determined by the transmission power of all radiation sources in the area and the propagation path loss. Among them, the path loss characteristics are significantly affected by multi-dimensional environmental parameters such as terrain and obstacles.

[0075] In one possible implementation, the path loss from each point in the interpolation grid to the unknown grid is calculated according to the following formula:

[0076] ;

[0077] ;

[0078] in, represents the signal frequency, are variables 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 0dB and a standard deviation of for , Represents the speed of light, is the free space path loss at 1 m, is the calculated path loss between the two points;

[0079] The grid is calculated based on the following interpolation The grid weight :

[0080] ;

[0081] in, For the mesh weight The parameter of the rate at which path loss decreases, usually , For the preset number, is the number of the interpolation grid, To the The path loss of a grid.

[0082] The signal reception strength of the unknown grid is determined according to the grid weight of the unknown grid and the signal reception strength of the known grid, and the original map is completed according to the signal reception strength of the unknown grid to obtain the initial map.

[0083] The signal reception strength of the unknown grid is calculated according to the following formula:

[0084] ;

[0085] in, For unknown grid Signal reception strength, is the grid weight of the unknown grid, For the preset number, is the number of the interpolation grid, For a known interpolation grid signal reception strength.

[0086] Step S3, using the K-means clustering algorithm to divide the area of ​​the initial map into strong radiation areas and weak radiation areas;

[0087] K-Means clustering is the most commonly used clustering algorithm, originally developed in signal processing. Its goal is to partition data points into K clusters, find the center of each cluster, and minimize its metric. The algorithm's greatest advantages are its simplicity, ease of understanding, and high computational speed. However, its disadvantages are that it can only be applied to continuous data and that the number of clusters must be specified before clustering.

[0088] The following is the analysis process of the K-Means clustering algorithm. The steps are as follows:

[0089] The first step is to determine the K value, that is, to cluster the data set into K clusters or groups.

[0090] In the second step, K data points are randomly selected from the dataset as centroids or data centers.

[0091] The third step is to calculate the distance between each point and each centroid, and divide each point into the group closest to the centroid, and stick to that centroid.

[0092] In the fourth step, after each centroid has gathered some points, redefine the algorithm to select a new centroid.

[0093] The fifth step is to compare the new centroid with the old centroid. If the distance between the new centroid and the old centroid is less than a certain threshold, it means that the recalculated centroid position has not changed much and the convergence is stable. It is considered that the clustering has achieved the desired result and the algorithm terminates.

[0094] In the sixth step, if the new centroid and the old centroid change greatly, that is, the distance is greater than the threshold, continue to iterate the third to fifth steps until the algorithm terminates.

[0095] In one possible implementation, the initial map Convert it into a data point set D, and determine the signal strength difference matrix based on the absolute value of the signal strength difference between any two data points in the data point set ; The signal strength difference matrix is ​​a symmetric matrix with all diagonal elements being zero.

[0096] ;

[0097] The total number of sets D is , each data point in set D is a four-tuple , is the geographic location coordinate, q represents the time slot, is the signal strength at that location.

[0098] Use Ward algorithm to perform agglomerative hierarchical clustering on any two data points to obtain the initial number of clusters;

[0099] The Ward method is a link criterion based on variance minimization, whose goal is to minimize the total variance increment after merging clusters. In the initialization phase, each data point is regarded as a separate cluster.

[0100] The K-means algorithm is used according to the initial number of clusters to obtain strong radiation areas and weak radiation areas.

[0101] Calculate the Ward distance between any two data points in the data point set;

[0102] Specifically calculate any two data points according to the following formula and Ward distance :

[0103] ;

[0104] in, and Respectively represent the size of the two clusters, that is, the number of data points contained, and Represent the mean vectors of the two clusters respectively.

[0105] 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;

[0106] The number of clusters corresponding to the points with a distance greater than the average merge distance is used as the candidate cluster value of the K-means algorithm;

[0107] Using the elbow method, the sum of squared errors of K-means clustering under all cluster candidate values ​​is calculated, and a relationship graph between cluster candidate values ​​and the sum of squared errors is drawn. The cluster candidate value corresponding to the elbow point of the relationship graph is used as the initial number of clusters.

[0108] Using the K-means algorithm based on the determined K value, the spectrum map will be divided into K categories, which will include K-1 radiation source surrounding areas (i.e., strong radiation areas), recorded as , and a background region (i.e., weak radiation region), denoted as , each strong radiation area will contain at least one radiation source.

[0109] Step S4: completing the strong radiation area and the weak radiation area respectively, and replacing the original map with the completed strong radiation area and weak radiation area to obtain a complete electromagnetic spectrum map;

[0110] In one possible implementation, in the spectrum map, the strong radiation source area exhibits stronger low-rank properties and shows obvious advantages when performing tensor completion. Therefore, in the process of generating a complete spectrum map, the strong radiation area and the weak radiation area are completed step by step.

[0111] For the divided strong radiation area, map it to the original map In the example, we get the strong radiation area to be completed The completion problem of each strong radiation region can be simplified into a tensor completion problem:

[0112] ;

[0113] in, represents the truncated nuclear norm, which is defined as , for n-mode expansion, Represents a Tensors of the same size, The elements in the subset The ones in represent known values, and the elements that do not belong to the subset are missing values.

[0114] Introducing auxiliary variables satisfy , then for a third-order tensor, the completion problem is equivalent to:

[0115] ;

[0116] Using the ADMM algorithm to solve, the augmented Lagrangian function can be constructed as follows:

[0117] ;

[0118] The solution is:

[0119] ;

[0120] ;

[0121] ;

[0122] in, represents the matrix folded into a tensor modulo k, represents the wide-area singular value threshold operator associated with minimization of the truncated nuclear norm.

[0123] The missing values ​​of the strong radiation area to be completed and the weak radiation area to be completed are calculated according to the following formula:

[0124] ;

[0125] in, is the spectrum tensor, is the mask tensor of the observation area, 、 、 、 、 、 are auxiliary variables, is the parameter introduced when solving the problem using the ADMM algorithm, is the observed spectrum tensor;

[0126] The strong radiation areas to be completed and the weak radiation areas to be completed are completed according to the missing values, and the original map is replaced by the completed strong radiation areas and weak radiation areas to obtain a complete electromagnetic spectrum map.

[0127] In one example, the strong radiation area After completing them one by one, replace the original map with the completed data In the corresponding area in , only the weak radiation area has missing values. The global map is completed using the same tensor completion scheme as the strong radiation area to obtain a complete spectrum map.

[0128] Step S5, determining the number and location of radiation sources based on the signal strength difference and path loss between the radiation center of the strong radiation area and each point in the area;

[0129] In a possible implementation, a point with the largest signal reception intensity within the strong radiation area is selected as the radiation center;

[0130] definition is the set of radiation sources, and the radiation center is denoted as .

[0131] Calculate the distance from other points in the strong radiation area to the radiation center according to the following formula Path loss :

[0132] ;

[0133] Calculate the distance between the remaining points in the strong radiation area and the radiation center according to the following formula Signal strength difference :

[0134] ;

[0135] What is recorded in is the theoretical path loss between two points. The actual path loss of the two points is recorded in the figure. The path loss of the remaining points in the strong radiation area and the radiation center is calculated according to the following formula: The absolute error :

[0136] ;

[0137] definition ,but The point with the largest error between the two:

[0138] ;

[0139] Repeat the above calculations and update synchronously.

[0140] When the following inequalities are satisfied, the number and position of radiation sources are obtained:

[0141] ;

[0142] in, For the point The average absolute error between the theoretical path loss and the actual path loss, is the number of radiation sources, For the point The minimum absolute error between the theoretical path loss and the actual path loss, For all The minimum value in is the number of all grid points, When there are k cluster centers and The multiple relationship For the present existence Cluster centers and The multiple relationship is the set threshold.

[0143] Step S6, determining whether the position of the radiation source changes;

[0144] When the radiation source position 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 radiation source position changes, return to execute step S2.

[0145] The electromagnetic spectrum map generation method proposed in the present invention has the following significant beneficial effects:

[0146] (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 spectrum map reconstruction error is reduced.

[0147] (2) Innovation in multi-dimensional information fusion: Creatively introduce low-rank constraints on 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 space, and break through the limitation of traditional interpolation methods that only consider spatial correlation.

[0148] (3) Significant optimization of computing efficiency: The alternating direction multiplier method is used to achieve efficient solution of 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.

[0149] (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.

[0150] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for generating an electromagnetic spectrum map, characterized in that: include: The two-dimensional geographic space of the electromagnetic environment to be measured is divided into grids, and a three-dimensional original map is constructed based on multiple spectrum data in the grids; the spectrum data is the average received signal strength of a time slot in the grid; The original map is completed using an inverse distance weighted interpolation algorithm (IDW) to obtain an initial map; Using a K-means clustering algorithm (K-means) to divide the region of the initial map into strong radiation regions and weak radiation regions; Completing the strong radiation area and the weak radiation area in sequence respectively, and replacing the original map with the completed strong radiation area and weak radiation area to obtain a complete electromagnetic spectrum map; Determine the number and location of radiation sources based on the signal strength difference and path loss between the radiation center and each point in the strong radiation area; When the position of the radiation source does not change, outputting 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, the original map is supplemented again using the inverse distance weighted interpolation algorithm IDW; The method of using the inverse distance weighted interpolation algorithm IDW to complete the original map to obtain the initial map includes: Perform interpolation calculation on a preset number of known grids closest to the unknown grid to obtain an interpolated grid; Calculating the path loss from each point in the interpolation grid to the unknown grid according to a free space proximity path loss model, and obtaining a grid weight of the unknown grid according to the path loss calculation; The signal reception strength of the unknown grid is determined according to the grid weight of the unknown grid and the signal reception strength of the known grid, and the original map is completed according to the signal reception strength of the unknown grid to obtain an initial map.

2. The electromagnetic spectrum map generation method according to claim 1, characterized in that: The step of dividing the two-dimensional geographic 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: The original map Y is expressed according to the following formula: Y=P Ω (X) Among them, x m,n,t is the tensor element, Ω is the grid index, m is the horizontal coordinate of the grid, n is the vertical coordinate of the grid, t is the number of the time slot, (P Ω (X) m,n,t is the average received signal strength of the (m,n)th grid and the tth time slot, P Ω (X) is the set of all grids and the average received signal strength.

3. The electromagnetic spectrum map generation method according to claim 1, characterized in that: Calculating the path loss from each point in the interpolation grid to the unknown grid according to a free space proximity path loss model, and obtaining the grid weight of the unknown grid according to the path loss includes: The path loss from each point in the interpolation grid to the unknown grid is calculated according to the following formula: Among them, f represents the signal frequency, n is the variable affected by the environment, and d is the spatial distance from the unknown grid to the known grid. is a typical lognormal random variable, c represents the speed of light, FSPL(f,1m) is the free space path loss at 1m, and PL i (f,d)[dB] is the calculated path loss between the two points; The grid s is calculated according to the following interpolation 0i The grid weight ω i : Where p is the grid weight ω i The parameter of the rate at which the path loss decreases, r is the preset number, i is the number of the interpolation grid, is the path loss to the i-th grid.

4. The method for generating an electromagnetic spectrum map according to claim 1, wherein: 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: The signal reception strength of the unknown grid is calculated according to the following formula: in, is the signal receiving strength of the unknown grid t0, ω i is the grid weight of the unknown grid, r is the preset number, i is the number of the interpolation grid, For a known interpolation grid S 0i signal reception strength.

5. The method for generating an electromagnetic spectrum map according to claim 1, wherein: The K-means clustering algorithm is used to divide the area of ​​the initial map to obtain the strong radiation area and the weak radiation area, including: Converting the initial map into a set of data points, and determining a signal strength difference matrix based on the absolute value of the difference in signal strength 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 the initial number of clusters; A K-means algorithm is used according to the initial number of clusters to obtain strong radiation areas and weak radiation areas.

6. The method for generating an electromagnetic spectrum map according to claim 5, wherein: The Ward algorithm is used to perform agglomerative hierarchical clustering on any two data points to obtain the initial number of clusters: Calculate the Ward distance between any two data points in the data point set; 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; The number of clusters corresponding to the points with a distance greater than the average merge distance is used as the candidate cluster value of the K-means algorithm; The elbow method is used to calculate the sum of square errors of K-means clustering under all the cluster candidate values, and a relationship graph between the cluster candidate values ​​and the sum of square errors is drawn. The cluster candidate value corresponding to the elbow point of the relationship graph is used as the initial number of clusters.

7. The method for generating an electromagnetic spectrum map according to claim 6, wherein: Calculating the Ward distance between any two data points in the data point set includes: The Ward distance d(C1, C2) between any two data points C1 and C2 is calculated according to the following formula: Among them, |C1| and |C2| represent the sizes of the two clusters, and μC1 and μC2 represent the mean vectors of the two clusters.

8. The method for generating an electromagnetic spectrum map according to claim 1, wherein: Determining the number and location of radiation sources based on the signal strength difference and path loss between the radiation center of the strong radiation area and each point in the area includes: The number and location of radiation sources are determined according to the following formula: in, For point C q The average absolute error between the theoretical path loss and the actual path loss, K is the number of radiation sources, For point C q The minimum absolute error between the theoretical path loss and the actual path loss, For all The minimum value in , N is the number of all grid points, When there are k cluster centers and The multiple relationship When there are K-1 cluster centers and The multiple relationship is σ, and σ is the set threshold.

9. The method for generating an electromagnetic spectrum map according to claim 1, wherein: The step of respectively completing the strong radiation area and the weak radiation area, and replacing the original map with the completed strong radiation area and weak radiation area to obtain a complete electromagnetic spectrum map includes: The missing values ​​of the strong radiation area to be completed and the weak radiation area to be completed are calculated according to the following formula: in, is the spectrum tensor, Z is the mask tensor of the observation area, M 1. M 2. M 3. Y 1. Y 2. Y 3 are auxiliary variables, ρ is the parameter introduced when solving the problem using the ADMM algorithm, X max(n) is the observed spectrum tensor; The strong radiation areas to be completed and the weak radiation areas to be completed are completed respectively according to the missing values, and the original map is replaced with the completed strong radiation areas and weak radiation areas to obtain a complete electromagnetic spectrum map.

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