A system and method for reconstructing electromagnetic maps based on graph structure data

Abstract

The present invention proposes a system and method for electromagnetic map reconstruction based on graph-structured data, belonging to the field of electromagnetic situational awareness technology. The method comprises: utilizing sensors to receive signal strength data from randomly selected grids to complete sparse data acquisition; performing interpolation and completion processing on the signal strength data to preliminarily predict the received signal strength values ​​of grids where no signals were collected; wherein, after the interpolation and completion processing, each grid has both geographic location attributes and electromagnetic strength attributes; constructing a feature matrix based on the electromagnetic strength attributes of the grids, and constructing an adjacency matrix based on the geographic location attributes of the grids, thereby completing the construction of the graph-structured data; using the constructed feature matrix, adjacency matrix, and signal strength data received from the grids as inputs to a graph convolutional neural network, and outputting a new predicted received signal strength value.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic situational awareness, and in particular relates to an electromagnetic map reconstruction system and method based on graph structure data. Background Art

[0002] Military: In the context of modern information warfare, the competition in the electromagnetic space is becoming increasingly fierce. Comprehensive and accurate perception of the electromagnetic situation within the battlefield is crucial for gaining electromagnetic superiority and providing commanders with situational information to support operations.

[0003] Civilian applications: With the increasing number of frequency-using devices, spectrum resource scarcity and poor network coverage are becoming increasingly prominent. Electromagnetic maps can intuitively display electromagnetic situational information from multiple dimensions, including time, space, and frequency domains.

[0004] Therefore, constructing high-precision electromagnetic maps to provide electromagnetic situation information for the battlefield, guide the deployment of civilian base stations and network optimization, and improve spectrum reuse efficiency is a feasible technical solution with important application value and development prospects in both military and civilian fields.

[0005] Existing technologies similar to the present invention are generally: (1) using a convolutional neural network model to construct a spectrum map; or (2) using a graph neural network to construct a spectrum map.

[0006] like Figure 1 As shown in FIG, for (1), the incomplete data is completed by interpolation and the numerical data is mapped to obtain a low-resolution spectrum map, the low-resolution spectrum map is used as the input of the convolutional neural network, and finally a high-resolution spectrum map is output.

[0007] During the training phase, the method first collects incomplete spectral data from the region of interest. Then, it extracts varying amounts of data multiple times and uses Kriging interpolation to complete and map the resulting low-resolution and high-resolution spectral maps. The low-resolution and high-resolution spectral maps are then transformed into a training sample set through steps such as sparse dictionary construction, image feature extraction, and sparse matrix representation. This sample set is used to train a convolutional neural network model that can process low-resolution spectral maps into high-resolution ones.

[0008] In the application stage, a small amount of spectrum data in the area of ​​interest is first collected and the data is completed using the Kriging interpolation method. The low-resolution spectrum map obtained by mapping the completed data is input into the trained convolutional neural network model, and a high-resolution spectrum map is output.

[0009] like Figure 2As shown in (2), the region of interest is divided into blocks, different data collection strategies are used for different blocks, and a dataset is constructed to train the graph neural network. The spectrum map is constructed through the graph neural network.

[0010] During the training phase, the method first divides the region of interest into several equal-sized subregions, divided into subregion set A and subregion set B. All subregions are then rasterized to equal areas. For subregion set A, spectral data is collected for a portion of the grid within each subregion; for subregion set B, spectral data is continuously collected for the grids. The data sampled from subregion set B is used to construct a training set, and a graph neural network is trained.

[0011] In the application stage, partial spectrum data in each sub-region in the sub-region set A is input into the trained graph neural network model, and a complete spectrum map is output.

[0012] In (1), the conditions set do not consider the impact of buildings, ground objects, etc. on radio wave propagation in real environments. The conditions are too idealized and may not be applicable in complex propagation environments. In addition, the high-resolution spectrum map that can be constructed by this method is small in area, and it fails to provide a quantitative indicator to describe the change from low resolution to high resolution, which is not conducive to real-world application needs.

[0013] In (2), it is necessary to continuously collect spectrum data of the grid within a certain sub-region. This signal acquisition method is too costly and difficult to use in dense urban environments. In addition, this method is an inductive learning method, and the spectrum data of a certain sub-region may not fully represent the data distribution characteristics of the entire region. Summary of the Invention

[0014] The present invention mainly solves the technical problems that the existing technology needs to collect many data points, considers the environment to be relatively ideal, resulting in high signal acquisition costs and is difficult to apply to complex real environments.

[0015] The first aspect of the present invention provides a method for reconstructing an electromagnetic map based on graph structure data. The method comprises:

[0016] Step S1: Using sensors to receive signal strength data from randomly selected grids to complete sparse data collection;

[0017] Step S2: performing interpolation and completion processing on the signal strength data to preliminarily predict the received signal strength value of the grid where no signal is collected;

[0018] Among them, after interpolation and completion processing, each grid has geographical location attributes and electromagnetic intensity attributes;

[0019] Step S3: construct a feature matrix based on the electromagnetic intensity attributes of the grid, and construct an adjacency matrix based on the geographical location attributes of the grid, thereby completing the construction of the graph structure data;

[0020] Step S4: Use the constructed feature matrix, adjacency matrix, and signal strength data received from the grid as inputs to the graph convolutional neural network, and output a new predicted value of the received signal strength value.

[0021] According to the method of the first aspect of the present invention, in step S1: the area of ​​interest is rasterized into equal areas, the geographical location of each grid is represented by the geographical coordinates of the center point of the grid, which is defined as the geographical location attribute value of the grid and represented by a two-dimensional column vector; the received signal strength obtained at any point in the grid is the electromagnetic strength attribute of the grid, which is represented by a real number.

[0022] According to the method of the first aspect of the present invention, in step S1: the collection of sparse data is carried out in a road test manner, and the basic equipment used includes a movable loading platform, a radio signal sensor, and a data storage and processing device; or a crowdsourcing method is adopted, using randomly arranged fixed-position radio signal sensors or wearable devices with radio signal receiving functions.

[0023] According to the method of the first aspect of the present invention, in step S2, the received signal strength value of the grid where no signal is collected is preliminarily predicted by interpolation and completion processing; specifically, the method includes:

[0024] With Z=[z(x1),z(x2),...,z(x n )] T represents the received signal strength vector of the sampling grid in the region of interest, x1,x2,...,x n Represents the position parameter of the grid. The received signal strength z(x) at any point x in Z has the same expected μ and variance σ 2 , its spatial properties are uniform;

[0025] During the interpolation process, the received signal strength of the unknown grid is expressed as the linear weighted sum of the received signal strengths of all known grids. The basic interpolation formula is:

[0026]

[0027] Where Λ=[λ1,λ2,...,λ n ] T , represents the weight vector of linear summation, which transforms the data interpolation problem into the problem of solving the optimal weight vector Λ;

[0028] The optimization goal of weight solution is to make the true value and the predicted value satisfy the statistical unbiased estimation and minimum variance. The solution of the optimal weight vector Λ is further transformed into a nonlinear constrained minimum problem:

[0029] min{J=2Λ T Γ0-Λ T ΓΛ-γ 00}

[0030] st||Λ||1=1

[0031] in, Γ0=[γ 10 ,γ 20 ,...,γ n0 ],Γ[γ ij ] n×n ;

[0032] The Lagrange multiplier method is used to construct the objective function J'=J+φ(||σ||1-1). The partial derivative of J' with respect to the parameters Λ and φ is 0, and the matrix form is:

[0033]

[0034] The optimal weight matrix Λ is obtained by solving.

[0035] According to the method of the first aspect of the present invention, in step S3, constructing the feature matrix specifically includes:

[0036] The interpolated completed data is normalized to the minimum and maximum values. The minimum and maximum normalization formula is as follows:

[0037]

[0038] The result of the minimum and maximum normalization of the data is converted into a 60-bit binary representation, embedded as the feature vector of the corresponding grid, and written in the matrix form H m×n , where m represents the number of grids and n represents the dimension of each grid embedding feature, n=60.

[0039] According to the method of the first aspect of the present invention, in step S3, constructing the adjacency matrix specifically includes: if there is a connection relationship between two grid points, it is represented by 1; if there is no connection relationship, it is represented by 0; the connection relationship between the two grids is represented by the adjacency matrix A m×m express.

[0040] According to the method of the first aspect of the present invention, in step S4:

[0041] Define the Laplace matrix L = DA, where D is a diagonal matrix, The regularized form of the Laplace matrix is This matrix is ​​used as the input of the graph convolutional neural network, and a trainable parameter matrix is ​​introduced. The received signal strength of the known grid is used as the label for semi-supervised training.

[0042] By updating the parameter matrix in several layers of graph convolutional layers, the input feature matrix of size m×n is compressed into a feature column vector of size m×1. This column vector is the predicted output of the received signal strength of the corresponding grid.

[0043] A loss function is constructed based on the received signal strength at the known grid and the received signal strength of the predicted output at the corresponding grid, and the parameter matrix in the graph convolutional neural network is continuously updated to obtain the final output;

[0044] Among them, the basic operation of graph convolution is:

[0045] H (l+1) =σ(L′H (l) W (l) )

[0046] H (l) and H (l+1) They represent the feature matrices of the lth layer and the l+1th layer respectively, W represents the trainable parameter matrix, and σ represents the activation function.

[0047] A second aspect of the present invention provides an electromagnetic map reconstruction system based on graph structure data. The system comprises:

[0048] The first processing unit is configured to: Step S1, use a sensor to receive signal strength data from a randomly selected grid to complete the collection of sparse data;

[0049] The second processing unit is configured to: perform interpolation and completion processing on the signal strength data to preliminarily predict the received signal strength value of the grid where no signal is collected;

[0050] Among them, after interpolation and completion processing, each grid has geographical location attributes and electromagnetic intensity attributes;

[0051] The third processing unit is configured to: construct a feature matrix based on the electromagnetic intensity attributes of the grid, and construct an adjacency matrix based on the geographical location attributes of the grid, thereby completing the construction of the graph structure data;

[0052] The fourth processing unit is configured to: use the constructed feature matrix, the adjacency matrix and the signal strength data received from the grid as inputs of the graph convolutional neural network, and output a predicted value of a new received signal strength value.

[0053] According to the system of the second aspect of the present invention, the first processing unit is specifically configured to: rasterize the area of ​​interest into equal areas, and the geographical location of each grid is represented by the geographical coordinates of the center point of the grid, which is defined as the geographical location attribute value of the grid and represented by a two-dimensional column vector; the received signal strength obtained at any point in the grid is the electromagnetic strength attribute of the grid, which is represented by a real number.

[0054] According to the system of the second aspect of the present invention, the first processing unit is specifically configured as follows: the collection of sparse data adopts the road test method, and the basic equipment used includes a movable loading platform, a radio signal sensor, and a data storage and processing device; or adopts a crowdsourcing method, using randomly arranged fixed-position radio signal sensors or wearable devices with radio signal receiving functions.

[0055] According to the system of the second aspect of the present invention, the second processing unit is specifically configured to: preliminarily predict the received signal strength value of the grid where no signal is collected through interpolation and completion processing; specifically including:

[0056] With Z=[z(x1),z(x2),...,z(x n )] T represents the received signal strength vector of the sampling grid in the region of interest, x1,x2,...,x n Represents the position parameter of the grid. The received signal strength z(x) at any point x in Z has the same expected μ and variance σ 2 , its spatial properties are uniform;

[0057] During the interpolation process, the received signal strength of the unknown grid is expressed as the linear weighted sum of the received signal strengths of all known grids. The basic interpolation formula is:

[0058]

[0059] Where Λ=[λ1,λ2,...,λ n ] T , represents the weight vector of linear summation, which transforms the data interpolation problem into the problem of solving the optimal weight vector Λ;

[0060] The optimization goal of weight solution is to make the true value and the predicted value satisfy the statistical unbiased estimation and minimum variance. The solution of the optimal weight vector Λ is further transformed into a nonlinear constrained minimum problem:

[0061] min{J=2Λ T Γ0-Λ T ΓΛ-γ 00}

[0062] st||Λ||1=1

[0063] in, Γ0=[γ 10 ,γ 20 ,...,γ n0 ], Γ=[γ ij ] n×n ;

[0064] The Lagrange multiplier method is used to construct the objective function J'=J+φ(||Λ||1-1). The partial derivative of J' with respect to the parameters Λ and φ is 0, and the matrix form is:

[0065]

[0066] The optimal weight matrix Λ is obtained by solving.

[0067] According to the system of the second aspect of the present invention, the third processing unit is specifically configured to: construct a feature matrix; specifically including:

[0068] The interpolated completed data is normalized to the minimum and maximum values. The minimum and maximum normalization formula is as follows:

[0069]

[0070] The result of the minimum and maximum normalization of the data is converted into a 60-bit binary representation, embedded as the feature vector of the corresponding grid, and written in the matrix form H m×n , where m represents the number of grids and n represents the dimension of each grid embedding feature, n=60.

[0071] According to the system of the second aspect of the present invention, the third processing unit is specifically configured to: construct an adjacency matrix; specifically including: if there is a connection relationship between two grid points, it is represented by 1; if there is no connection relationship, it is represented by 0; the connection relationship between the two grids is represented by the adjacency matrix A m×m express.

[0072] According to the system of the second aspect of the present invention, the fourth processing unit is specifically configured to:

[0073] Define the Laplace matrix L = DA, where D is a diagonal matrix, The regularized form of the Laplace matrix is This matrix is ​​used as the input of the graph convolutional neural network, and a trainable parameter matrix is ​​introduced. The received signal strength of the known grid is used as the label for semi-supervised training.

[0074] By updating the parameter matrix in several layers of graph convolutional layers, the input feature matrix of size m×n is compressed into a feature column vector of size m×1. This column vector is the predicted output of the received signal strength of the corresponding grid.

[0075] A loss function is constructed based on the received signal strength at the known grid and the received signal strength of the predicted output at the corresponding grid, and the parameter matrix in the graph convolutional neural network is continuously updated to obtain the final output;

[0076] Among them, the basic operation of graph convolution is:

[0077] H (l+1) =σ(L'H (l) W (l) )

[0078] H (l) and H (l+1) They represent the feature matrices of the lth layer and the l+1th layer respectively, W represents the trainable parameter matrix, and σ represents the activation function.

[0079] A third aspect of the present invention discloses an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the electromagnetic map reconstruction method based on graph structure data disclosed in the present invention are implemented.

[0080] A fourth aspect of the present invention discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the electromagnetic map reconstruction method based on graph structure data disclosed herein.

[0081] In summary, the technical solution of this invention, based on both battlefield requirements and social applications, proposes a method for constructing high-precision electromagnetic maps in complex urban environments. Building on existing interpolation techniques, the data is modeled as a graph structure, a trainable parameter matrix is ​​introduced, and a graph convolutional neural network (GCN) is used to effectively improve accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0083] Figure 1 A flowchart of a spectrum map construction method based on a convolutional neural network in the prior art;

[0084] Figure 2 A flowchart of a spectrum map construction method based on graph neural network in the prior art;

[0085] Figure 3 is a flowchart of a method for reconstructing an electromagnetic map based on graph structure data according to an embodiment of the present invention;

[0086] Figure 4(a) shows the real electromagnetic map;

[0087] FIG4( b ) is an electromagnetic map obtained using the method of the present invention;

[0088] Figure 4(c) shows the electromagnetic map obtained using the Kriging method;

[0089] Figure 4(d) shows the electromagnetic map obtained using the inverse distance weighted method;

[0090] Figure 4(e) shows the electromagnetic map obtained using the nearest neighbor method;

[0091] Figure 4(f) shows the electromagnetic map obtained using the radial basis function method;

[0092] Figure 5 is a structural diagram of an electronic device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0093] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0094] Electromagnetic maps are used to represent electromagnetic information of interest within a radio communication environment, such as received signal strength, radio wave attenuation, and channel gain at each point within a geographic area. They can intuitively describe and display the electromagnetic characteristics of the area of ​​interest in the time, energy, and spatial domains. The electromagnetic map described in the present invention represents the received signal strength at each point within the area of ​​interest, reflecting both the geographic location and electromagnetic energy properties of each point.

[0095] The first aspect of the present invention provides a method for reconstructing an electromagnetic map based on graph structure data. The method comprises:

[0096] Step S1: Using sensors to receive signal strength data from randomly selected grids to complete sparse data collection;

[0097] Step S2: performing interpolation and completion processing on the signal strength data to preliminarily predict the received signal strength value of the grid where no signal is collected;

[0098] Among them, after interpolation and completion processing, each grid has geographical location attributes and electromagnetic intensity attributes;

[0099] Step S3: construct a feature matrix based on the electromagnetic intensity attributes of the grid, and construct an adjacency matrix based on the geographical location attributes of the grid, thereby completing the construction of the graph structure data;

[0100] Step S4: Use the constructed feature matrix, adjacency matrix, and signal strength data received from the grid as inputs to the graph convolutional neural network, and output a new predicted value of the received signal strength value.

[0101] According to the method of the first aspect of the present invention, in step S1: the area of ​​interest is rasterized into equal areas, the geographical location of each grid is represented by the geographical coordinates of the center point of the grid, which is defined as the geographical location attribute value of the grid and represented by a two-dimensional column vector; the received signal strength obtained at any point in the grid is the electromagnetic strength attribute of the grid, which is represented by a real number.

[0102] According to the method of the first aspect of the present invention, in step S1: the collection of sparse data is carried out in a road test manner, and the basic equipment used includes a movable loading platform, a radio signal sensor, and a data storage and processing device; or a crowdsourcing method is adopted, using randomly arranged fixed-position radio signal sensors or wearable devices with radio signal receiving functions.

[0103] According to the method of the first aspect of the present invention, in step S2, the received signal strength value of the grid where no signal is collected is preliminarily predicted by interpolation and completion processing; specifically, the method includes:

[0104] With Z=[z(x1),z(x2),...,z(x n )] T represents the received signal strength vector of the sampling grid in the region of interest, x1,x2,...,x n Represents the position parameter of the grid. The received signal strength z(x) at any point x in Z has the same expected μ and variance σ 2 , its spatial properties are uniform;

[0105] During the interpolation process, the received signal strength of the unknown grid is expressed as the linear weighted sum of the received signal strengths of all known grids. The basic interpolation formula is:

[0106]

[0107] Where Λ=[λ1,λ2,...,λ n ] T , represents the weight vector of linear summation, which transforms the data interpolation problem into the problem of solving the optimal weight vector Λ;

[0108] The optimization goal of weight solution is to make the true value and the predicted value satisfy the statistical unbiased estimation and minimum variance. The solution of the optimal weight vector Λ is further transformed into a nonlinear constrained minimum problem:

[0109] min{J=2Λ T Γ0-Λ T ΓΛ-γ 00}

[0110] st||Λ||1=1

[0111] in, Γ0=[γ 10 ,γ 20 ,...,γ n0 ], Γ=[γ ij ] n×n ;

[0112] The Lagrange multiplier method is used to construct the objective function J'=J+φ(||Λ||1-1). The partial derivative of J' with respect to the parameters Λ and φ is 0, and the matrix form is:

[0113]

[0114] The optimal weight matrix Λ is obtained by solving.

[0115] According to the method of the first aspect of the present invention, in step S3, constructing the feature matrix specifically includes:

[0116] The interpolated completed data is normalized to the minimum and maximum values. The minimum and maximum normalization formula is as follows:

[0117]

[0118] The result of the minimum and maximum normalization of the data is converted into a 60-bit binary representation, embedded as the feature vector of the corresponding grid, and written in the matrix form H m×n , where m represents the number of grids and n represents the dimension of each grid embedding feature, n=60.

[0119] According to the method of the first aspect of the present invention, in step S3, constructing the adjacency matrix specifically includes: if there is a connection relationship between two grid points, it is represented by 1; if there is no connection relationship, it is represented by 0; the connection relationship between the two grids is represented by the adjacency matrix A m×m express.

[0120] According to the method of the first aspect of the present invention, in step S4:

[0121] Define the Laplace matrix L = DA, where D is a diagonal matrix, The regularized form of the Laplace matrix is This matrix is ​​used as the input of the graph convolutional neural network, and a trainable parameter matrix is ​​introduced. The received signal strength of the known grid is used as the label for semi-supervised training.

[0122] By updating the parameter matrix in several layers of graph convolutional layers, the input feature matrix of size m×n is compressed into a feature column vector of size m×1. This column vector is the predicted output of the received signal strength of the corresponding grid.

[0123] A loss function is constructed based on the received signal strength at the known grid and the received signal strength of the predicted output at the corresponding grid, and the parameter matrix in the graph convolutional neural network is continuously updated to obtain the final output;

[0124] Among them, the basic operation of graph convolution is:

[0125] H (l+1) =σ(L'H (l) W (l) )

[0126] H (l) and H (l+1) They represent the feature matrices of the lth layer and the l+1th layer respectively, W represents the trainable parameter matrix, and σ represents the activation function.

[0127] The following combination Figure 3 The method of the first aspect of the present invention will be described in detail.

[0128] like Figure 3 As shown. The solution described in this patent needs to go through the steps of sparse data collection, data pre-interpolation, graph structure data construction, and graph convolutional neural network processing. Sparse data collection is to randomly select a grid and use a sensor to measure the received signal strength in the grid as the basic data support for subsequent steps. Data pre-interpolation is to interpolate and complete the collected data to preliminarily predict the received signal strength of the grid where the signal is not collected. After the data pre-interpolation processing, each grid has geographic location attributes and electromagnetic intensity attributes. Secondly, a feature matrix is ​​constructed based on the electromagnetic intensity attributes of the grid, and an adjacency matrix is ​​constructed based on the geographic location attributes of the grid. This step is called graph structure data construction. Finally, the constructed feature matrix, adjacency matrix and received signal strength of the sampled grid are used as inputs to the graph convolutional neural network to obtain the predicted value output of the new received signal strength reception value.

[0129] 1. Data Collection

[0130] First, the area of ​​interest is rasterized to an equal area. The geographic location of each grid cell is represented by the geographic coordinates of the grid center point, which is called the geographic location attribute value of the grid and is usually represented by a two-dimensional column vector. In actual measurement, the received signal strength obtained at any point within the grid is called the electromagnetic intensity attribute of the grid, usually represented by a real number. Because radio waves propagate over extremely small distances, they can be considered to be uniform and experience almost no attenuation over this distance. Therefore, the received signal strength at any point within the grid can be used to represent the received signal strength of the entire grid. Therefore, the area of ​​the grid can be used to represent the resolution of the electromagnetic map. The smaller the grid area, the higher the resolution of the electromagnetic map, and the more detailed the electromagnetic situation. However, high resolution inevitably increases computational overhead, so the resolution of the electromagnetic map needs to be set according to actual needs.

[0131] Data collection can be done through road testing. The basic equipment used should include a mobile platform, such as an unmanned vehicle or drone; radio signal sensors, such as software-defined radio peripherals (SRPs) and radio signal measurement receivers; data storage and processing equipment; and location information acquisition devices, such as GPS / Beidou antennas. Alternatively, crowdsourcing can be employed. Data can be collected randomly using randomly deployed fixed-position radio signal sensors or wearable devices with radio signal reception capabilities, such as mobile phones.

[0132] 2. Data pre-interpolation

[0133] Data pre-interpolation is to use the interpolation method to preliminarily estimate the received signal strength at unknown grid points.

[0134] Let Z = [z(x1),z(x2),...,z(x n )] T represents the received signal strength vector of the sampling grid in the region of interest, x1,x2,...,x n In order to simplify the modeling conditions and obtain a solvable mathematical problem, we consider the ideal case where the received signal strength z(x) at any point x in Z has the same expected μ and variance σ. 2 , that is, the spatial attributes are uniform. Therefore, during the interpolation process, the received signal strength of the unknown grid can be expressed as the linear weighted sum of the received signal strengths of all known grids, and the basic formula for interpolation can be obtained as:

[0135]

[0136] where Λ=[λ1,λ2,...,λ n ] T , represents the weight vector of linear summation, and the data interpolation problem is transformed into the problem of solving the optimal weight vector Λ.

[0137] The unbiased estimation and minimum variance of the true value and the predicted value are taken as the optimization goal of the weight solution. The solution of the optimal weight vector Λ is further transformed into a nonlinear constrained minimum problem, namely:

[0138] min{J=2Λ T Γ0-Λ T ΓΛ-γ 00}

[0139] st||Λ||1=1

[0140] In this process, where Γ0=[γ 10 ,γ 20 ,...,γ n0 ], Γ=[γ ij ] n×n .

[0141] Use the Lagrange multiplier method to construct the objective function J'=J+φ(||Λ||1-1), let the partial derivative of J' with respect to the parameters Λ and φ be 0, and write it in matrix form, we get:

[0142]

[0143] The optimal weight matrix Λ can be obtained.

[0144] 3. Construction of high-precision electromagnetic maps

[0145] (1) Feature matrix construction

[0146] Perform minimum and maximum normalization on the pre-interpolated completed data. The minimum and maximum normalization calculation formula is as follows:

[0147]

[0148] The result of the minimum and maximum normalization of the data is converted into a 60-bit binary representation and embedded as the feature vector of the corresponding grid. And written in matrix form H m×n . Where m represents the number of grids, and n represents the dimension of the embedded features of each grid, that is, n = 60. This feature matrix will serve as one of the inputs of the subsequent graph convolutional neural network. Considering that the feature vector embedded for each grid should simultaneously reflect the similarity of grids with similar attribute values ​​and the difference of grids with large attribute values, and that sparse representation matrices are conducive to accelerating neural network operations, the data is converted into binary representation after minimum and maximum normalization as feature vector embedding.

[0149] (2) Adjacency matrix construction

[0150] Taking into account the influence of building occlusion in the real environment, it is considered that if there is a building occlusion between the straight line connecting two grid points, there is no connection relationship between the grid points; considering that if the distance between the two grid points is too far, the correlation between the grid points is weak and this influence can be ignored, and in this case it is also considered that there is no connection relationship between the grid points. If there is a connection relationship between the two grid points, it is represented by "1", and if there is no connection relationship, it is represented by "0". The connection relationship between the two grids is represented by the adjacency matrix A. m×m In addition, it is considered that there is a connection between the grids themselves.

[0151] (3) Image signal processing

[0152] Graph Signal Processing (GSP) theory is the basic theory for processing graph-structured data. The most important feature of processing graph-structured data is that messages are transmitted between nodes through the connection relationships between nodes to achieve the purpose of updating node features. The purpose of constructing the feature matrix and adjacency matrix mentioned above is to achieve batch processing through matrix operations. In graph signal processing, the Laplace matrix L = DA is defined. Where D is a diagonal matrix, From the calculation method of matrix D, it can be seen that the D obtained by nodes with more connections and nodes with fewer connections is ii Therefore, the regularized form of the Laplace matrix is ​​usually considered. This matrix serves as the input to the graph convolutional neural network.

[0153] (4) Construction of high-precision electromagnetic data

[0154] The constructed regularized Laplacian matrix is ​​used as the input of the graph convolutional neural network, and a trainable parameter matrix is ​​introduced. The received signal strength of the known grid is used as a label for semi-supervised training. By updating the parameter matrix in several layers of graph convolutional neural layers, the input m×n feature matrix is ​​finally compressed into a feature column vector of size m×1. This column vector is the predicted output of the received signal strength of the corresponding grid. By constructing a loss function by combining the received signal strength at the known grid with the received signal strength of the predicted output at the corresponding grid, the parameter matrix in the graph convolutional neural network is continuously updated to obtain the final output. The basic operation of graph convolution is:

[0155] H (l+1) =σ(L'H (l) W (l) )

[0156] Among them, H (l) and H (l+1) They represent the feature matrices of the lth layer and the l+1th layer respectively, W represents the trainable parameter matrix, and σ represents the activation function.

[0157] From the above process, it can be seen that, unlike the inductive learning method adopted in the prior art, the method proposed in the present invention is a direct learning method, which mainly realizes the prediction of unknown grid point data by mining the inherent laws between the data.

[0158] For the method of the first aspect, the present invention provides several evaluation indicators.

[0159] 1. Root mean square error

[0160] The construction of an electromagnetic map is essentially the prediction of electromagnetic data at unknown points. Therefore, the root mean square error (RMSE) is a commonly used indicator to quantitatively measure the average deviation between the predicted data and the actual data to evaluate the quality of the electromagnetic map constructed by this algorithm. Its expression is:

[0161]

[0162] Among them, N represents the number of points to be predicted, y i represents the true value, Represents the predicted value.

[0163] 2. Electromagnetic map restoration quality

[0164] A common problem in electromagnetic map construction is that the predicted data is mostly distributed near the overall mean of the training data, while predictions are often poor near the data extremes. The RMSE describes the average accuracy of all data recovered within the entire area and does not accurately describe the accuracy of local map reconstruction. Therefore, it is also necessary to evaluate points near the data extremes from an observational perspective.

[0165] For the method of the first aspect, the present invention provides a simulation experiment example.

[0166] 1. Experimental scene construction

[0167] To fully account for the complexity of real-world environments, this paper selected a real-world city map and building information within a 5 km × 5 km square area, rasterized it, and defined base station parameters. The grid size was 5 m × 5 m, the base station height was set to 50 m, the number of sectors was 3, the downtilt angle was 5°, the radio frequency was 3.5 GHz, commonly used for mobile phone communications, and the transmit power was 40 dBm. Ray tracing was used to calculate the electromagnetic distribution within this area as baseline data. In the CGCS2000_3_Degree_GK_Zone_38 projection coordinate system, the map center point was located at (38426150, 2556712).

[0168] 2. Effect Analysis

[0169] As mentioned above, the root mean square error (RMS) is used as the performance evaluation metric in the simulation experiment. To verify the effectiveness of the proposed method, the Kriging method, inverse distance weighted method, nearest neighbor method, and radial basis function method, which are commonly used to construct spectrum maps, are selected for comparison.

[0170] (1) Root mean square error comparison

[0171] Assuming random sampling, simulation experiments were conducted under the condition that the number of sampled grids accounted for 1% of the total number of grids. Existing algorithms for data recovery, such as tensor completion and compressed sensing, usually require that the number of sampled grids account for more than 10% to achieve good results, which shows the effectiveness of the method proposed in this patent. The RMSE of the electromagnetic maps and benchmark data constructed by each method are shown in Table 1. It can be seen that the RMSE of the method proposed in this invention is the lowest. In addition, it can be seen that under the conditions where the sampling grid accounts for 1% and the environment is more complex, the RMSE of the method proposed in this patent can achieve better results than the RMSE of methods in other literature or patents, which shows the effectiveness of the method proposed in this patent.

[0172] Table 1: Comparison of the root mean square error of each algorithm

[0173]

[0174] (2) Comparison of electromagnetic map restoration quality

[0175] Under the condition that the sampling grid accounts for 1%, the original data and the restored complete data are mapped into a heat map, such as Figures 4(a)-4(f) As shown in the figure, the electromagnetic map constructed by the Kriging interpolation method has many discontinuities in both the horizontal and vertical directions, and the quality of the restoration is relatively rough around the radiation source; the electromagnetic maps restored by the inverse distance weighted method and the radial basis function method are discontinuous, and the electromagnetic situation of certain areas is blurred with point-like color blocks, and the quality of the constructed electromagnetic maps is not high; the electromagnetic map constructed by the nearest neighbor method is relatively continuous, but tends to be homogenized. The electromagnetic map restored by the method proposed in this patent is smoother and more continuous, can better reflect the detailed information around the radiation source, and is of higher quality.

[0176] A second aspect of the present invention provides an electromagnetic map reconstruction system based on graph structure data. The system comprises:

[0177] The first processing unit is configured to: Step S1, use a sensor to receive signal strength data from a randomly selected grid to complete the collection of sparse data;

[0178] The second processing unit is configured to: perform interpolation and completion processing on the signal strength data to preliminarily predict the received signal strength value of the grid where no signal is collected;

[0179] Among them, after interpolation and completion processing, each grid has geographical location attributes and electromagnetic intensity attributes;

[0180] The third processing unit is configured to: construct a feature matrix based on the electromagnetic intensity attributes of the grid, and construct an adjacency matrix based on the geographical location attributes of the grid, thereby completing the construction of the graph structure data;

[0181] The fourth processing unit is configured to: use the constructed feature matrix, the adjacency matrix and the signal strength data received from the grid as inputs of the graph convolutional neural network, and output a predicted value of a new received signal strength value.

[0182] According to the system of the second aspect of the present invention, the first processing unit is specifically configured to: rasterize the area of ​​interest into equal areas, and the geographical location of each grid is represented by the geographical coordinates of the center point of the grid, which is defined as the geographical location attribute value of the grid and represented by a two-dimensional column vector; the received signal strength obtained at any point in the grid is the electromagnetic strength attribute of the grid, which is represented by a real number.

[0183] According to the system of the second aspect of the present invention, the first processing unit is specifically configured as follows: the collection of sparse data adopts the road test method, and the basic equipment used includes a movable loading platform, a radio signal sensor, and a data storage and processing device; or adopts a crowdsourcing method, using randomly arranged fixed-position radio signal sensors or wearable devices with radio signal receiving functions.

[0184] According to the system of the second aspect of the present invention, the second processing unit is specifically configured to: preliminarily predict the received signal strength value of the grid where no signal is collected through interpolation and completion processing; specifically including:

[0185] With Z=[z(x1),z(x2),...,z(x n )] T represents the received signal strength vector of the sampling grid in the region of interest, x1,x2,...,x n Represents the position parameter of the grid. The received signal strength z(x) at any point x in Z has the same expected μ and variance σ 2 , its spatial properties are uniform;

[0186] During the interpolation process, the received signal strength of the unknown grid is expressed as the linear weighted sum of the received signal strengths of all known grids. The basic interpolation formula is:

[0187]

[0188] Where Λ=[λ1,λ2,...,λ n ] T, represents the weight vector of linear summation, which transforms the data interpolation problem into the problem of solving the optimal weight vector Λ;

[0189] The optimization goal of weight solution is to make the true value and the predicted value satisfy the statistical unbiased estimation and minimum variance. The solution of the optimal weight vector Λ is further transformed into a nonlinear constrained minimum problem:

[0190] min{J=2Λ T Γ0-Λ T ΓΛ-γ 00}

[0191] st||Λ||1=1

[0192] in, Γ0=[γ 10 ,γ 20 ,...,γ n0 ], Γ=[γ ij ] n×n ;

[0193] The Lagrange multiplier method is used to construct the objective function J'=J+φ(||Λ||1-1). The partial derivative of J' with respect to the parameters Λ and φ is 0, and the matrix form is:

[0194]

[0195] The optimal weight matrix Λ is obtained by solving.

[0196] According to the system of the second aspect of the present invention, the third processing unit is specifically configured to: construct a feature matrix; specifically including:

[0197] The interpolated completed data is normalized to the minimum and maximum values. The minimum and maximum normalization formula is as follows:

[0198]

[0199] The result of the minimum and maximum normalization of the data is converted into a 60-bit binary representation, embedded as the feature vector of the corresponding grid, and written in the matrix form H m×n , where m represents the number of grids and n represents the dimension of each grid embedding feature, n=60.

[0200] According to the system of the second aspect of the present invention, the third processing unit is specifically configured to: construct an adjacency matrix; specifically including: if there is a connection relationship between two grid points, it is represented by 1; if there is no connection relationship, it is represented by 0; the connection relationship between the two grids is represented by the adjacency matrix A m×m express.

[0201] According to the system of the second aspect of the present invention, the fourth processing unit is specifically configured to:

[0202] Define the Laplace matrix L = DA, where D is a diagonal matrix, The regularized form of the Laplace matrix is This matrix is ​​used as the input of the graph convolutional neural network, and a trainable parameter matrix is ​​introduced. The received signal strength of the known grid is used as the label for semi-supervised training.

[0203] By updating the parameter matrix in several layers of graph convolutional layers, the input feature matrix of size m×n is compressed into a feature column vector of size m×1. This column vector is the predicted output of the received signal strength of the corresponding grid.

[0204] A loss function is constructed based on the received signal strength at the known grid and the received signal strength of the predicted output at the corresponding grid, and the parameter matrix in the graph convolutional neural network is continuously updated to obtain the final output;

[0205] Among them, the basic operation of graph convolution is:

[0206] H (l+1) =σ(L'H (l) W (l) )

[0207] H (l) and H (l+1) They represent the feature matrices of the lth layer and the l+1th layer respectively, W represents the trainable parameter matrix, and σ represents the activation function.

[0208] A third aspect of the present invention discloses an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the steps of the electromagnetic map reconstruction method based on graph structure data disclosed in the present invention are implemented.

[0209] Figure 5 FIG. 1 is a structural diagram of an electronic device according to an embodiment of the present invention. Figure 5As shown, the electronic device includes a processor, a memory, a communication interface, a display screen and an input device connected via a system bus. The processor of the electronic device is used to provide computing and control capabilities. The memory of the electronic device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the electronic device is used to communicate with an external terminal in a wired or wireless manner, and the wireless manner can be achieved through WIFI, an operator network, near field communication (NFC) or other technologies. The display screen of the electronic device can be a liquid crystal display or an electronic ink display screen, and the input device of the electronic device can be a touch layer covering the display screen, or a button, trackball or touchpad provided on the electronic device housing, or an external keyboard, touchpad or mouse.

[0210] Those skilled in the art will understand that Figure 5 The structure shown in the figure is only a structural diagram of the part related to the technical solution of the present disclosure, and does not constitute a limitation on the electronic device to which the solution of the present application is applied. The specific electronic device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0211] A fourth aspect of the present invention discloses a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for electromagnetic signal distribution reconstruction based on data completion disclosed herein.

[0212] In summary, the technical solution of the present invention realizes the reconstruction of the electromagnetic signal distribution map based on data completion, which can not only accurately obtain the electromagnetic signal distribution map of the wireless communication network, but can also be widely used in military fields such as battlefield spectrum management and electronic warfare, and civilian fields such as radio supervision and network optimization. It has important military significance and social application value.

[0213] Please note that the technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification. The above embodiments only express several implementation methods of the present application. The description is relatively specific and detailed, but it cannot be understood as a limitation on the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, without departing from the concept of this application, several variations and improvements can be made, which all fall within the scope of protection of this application. Therefore, the scope of protection of the patent in this application shall be based on the attached claims.

Claims

1. A method for reconstructing an electromagnetic map based on graph structure data, characterized in that: The method comprises: Step S1: Using sensors to receive signal strength data from randomly selected grids to complete sparse data collection; Step S2: performing interpolation and completion processing on the signal strength data to preliminarily predict the received signal strength value of the grid where no signal is collected; Among them, after interpolation and completion processing, each grid has geographical location attributes and electromagnetic intensity attributes; Step S3: construct a feature matrix based on the electromagnetic intensity attributes of the grid, and construct an adjacency matrix based on the geographical location attributes of the grid, thereby completing the construction of the graph structure data; Step S4: Using the constructed feature matrix, adjacency matrix, and signal strength data received from the grid as inputs to the graph convolutional neural network, and outputting a new predicted value of the received signal strength value; Wherein, in the step S2, the received signal strength value of the grid where no signal is collected is preliminarily predicted by interpolation and completion processing; specifically, the method includes: With Z=[z(x1),z(x2),...,z(x n )] T represents the received signal strength vector of the sampling grid in the region of interest, x1,x2,...,x n Represents the position parameter of the grid. The received signal strength z(x) at any point x in Z has the same expected μ and variance σ 2 , its spatial properties are uniform; During the interpolation process, the received signal strength of the unknown grid is expressed as the linear weighted sum of the received signal strengths of all known grids. The basic interpolation formula is: Where Λ=[λ1,λ2,...,λ n ] T , represents the weight vector of linear summation, which transforms the data interpolation problem into the problem of solving the optimal weight vector Λ; The optimization goal of weight solution is to make the true value and the predicted value satisfy the statistical unbiased estimation and minimum variance. The solution of the optimal weight vector Λ is further transformed into a nonlinear constrained minimum problem: min{J=2Λ T G0-L T GL-g 00 } st||Λ||1=1 Among them, Γ0=[γ 10 ,c 20 ,...,c n0 ],Γ=[γ ij ] n×n ; The Lagrange multiplier method is used to construct the objective function J'=J+φ(||Λ||1-1). The partial derivative of J' with respect to the parameters Λ and φ is 0, and the matrix form is: The optimal weight matrix Λ is obtained by solving.

2. The electromagnetic map reconstruction method based on graph structure data according to claim 1, characterized in that: In step S1: the area of ​​interest is rasterized into equal areas, the geographical location of each grid is represented by the geographical coordinates of the center point of the grid, which is defined as the geographical location attribute value of the grid and represented by a two-dimensional column vector; the received signal strength obtained at any point in the grid is the electromagnetic intensity attribute of the grid, which is represented by a real number.

3. The electromagnetic map reconstruction method based on graph structure data according to claim 2, characterized in that: In step S1: sparse data is collected by road testing, and the basic equipment used includes a movable loading platform, a radio signal sensor, and a data storage and processing device; or a crowdsourcing method is adopted, using randomly arranged fixed-position radio signal sensors or wearable devices with radio signal receiving functions.

4. The electromagnetic map reconstruction method based on graph structure data according to claim 3, characterized in that: In step S3, constructing the feature matrix specifically includes: The interpolated completed data is normalized to the minimum and maximum values. The minimum and maximum normalization formula is as follows: The result of the minimum and maximum normalization of the data is converted into a 60-bit binary representation, embedded as the feature vector of the corresponding grid, and written in the matrix form H m×n , where m represents the number of grids and n represents the dimension of each grid embedding feature, n=60.

5. The electromagnetic map reconstruction method based on graph structure data according to claim 4, characterized in that: In step S3, constructing the adjacency matrix specifically includes: if there is a connection relationship between two grid points, it is represented by 1; if there is no connection relationship, it is represented by 0; the connection relationship between two grids is represented by the adjacency matrix A m×m express.

6. The electromagnetic map reconstruction method based on graph structure data according to claim 5, characterized in that: In step S4: Define the Laplace matrix L = DA, where D is a diagonal matrix, The regularized form of the Laplace matrix is This matrix is ​​used as the input of the graph convolutional neural network, and a trainable parameter matrix is ​​introduced. The received signal strength of the known grid is used as the label for semi-supervised training. By updating the parameter matrix in several layers of graph convolutional layers, the input feature matrix of size m×n is compressed into a feature column vector of size m×1. This column vector is the predicted output of the received signal strength of the corresponding grid. A loss function is constructed based on the received signal strength at the known grid and the received signal strength of the predicted output at the corresponding grid, and the parameter matrix in the graph convolutional neural network is continuously updated to obtain the final output; Among them, the basic operation of graph convolution is: H (l+1) =σ(L'H (l) W (l) ) H (l) and H (l+1) They represent the feature matrices of the lth layer and the l+1th layer respectively, W represents the trainable parameter matrix, and σ represents the activation function.

7. An electromagnetic map reconstruction system based on graph structure data, characterized in that: The system comprises: The first processing unit is configured to: Step S1, use a sensor to receive signal strength data from a randomly selected grid to complete the collection of sparse data; The second processing unit is configured to: perform interpolation and completion processing on the signal strength data to preliminarily predict the received signal strength value of the grid where no signal is collected; Among them, after interpolation and completion processing, each grid has geographical location attributes and electromagnetic intensity attributes; The third processing unit is configured to: construct a feature matrix based on the electromagnetic intensity attributes of the grid, and construct an adjacency matrix based on the geographical location attributes of the grid, thereby completing the construction of the graph structure data; a fourth processing unit configured to: use the constructed feature matrix, the adjacency matrix, and the signal strength data received from the grid as inputs to a graph convolutional neural network, and output a predicted value of a new received signal strength value; The second processing unit is specifically configured to: preliminarily predict the received signal strength value of the grid where no signal is collected through interpolation and completion processing; including: With Z=[z(x1),z(x2),...,z(x n )] T represents the received signal strength vector of the sampling grid in the region of interest, x1,x2,...,x n Represents the position parameter of the grid. The received signal strength z(x) at any point x in Z has the same expected μ and variance σ 2 , its spatial properties are uniform; During the interpolation process, the received signal strength of the unknown grid is expressed as the linear weighted sum of the received signal strengths of all known grids. The basic interpolation formula is: Where Λ=[λ1,λ2,...,λ n ] T , represents the weight vector of linear summation, which transforms the data interpolation problem into the problem of solving the optimal weight vector Λ; The optimization goal of weight solution is to make the true value and the predicted value satisfy the statistical unbiased estimation and minimum variance. The solution of the optimal weight vector Λ is further transformed into a nonlinear constrained minimum problem: min{J=2Λ T G0-L T GL-g 00 } st||Λ||1=1 Among them, Γ0=[γ 10 ,c 20 ,...,c n0 ],Γ=[γ ij ] n×n ; The Lagrange multiplier method is used to construct the objective function J'=J+φ(||Λ||1-1). The partial derivative of J' with respect to the parameters Λ and φ is 0, and the matrix form is: The optimal weight matrix Λ is obtained by solving.

8. An electronic device, characterized in that: The electronic device includes a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the steps of the electromagnetic map reconstruction method based on graph structure data according to any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the electromagnetic map reconstruction method based on graph structure data according to any one of claims 1 to 6 are implemented.

Images