Electromagnetic map reconstruction system and method based on propagation model

Abstract

The invention provides an electromagnetic map reconstruction system and method based on a propagation model, and belongs to the technical field of electromagnetic map reconstruction. Randomly selecting a grid in the target area, and utilizing a signal power value received by a sensor in the grid; calculating a semi-variation value and a distance between each point pair by using data received by the sensor and the position of the sensor, grouping according to the distance, and removing an abnormal value to obtain a distance and semi-variation value two-dimensional array; modeling a variation function by using a radio wave propagation rule, and solving an undetermined coefficient of the function by using a particle swarm optimization algorithm to obtain the variation function; and calculating a semi-variation value between the unknown grid and the known grid by using the variation function, obtaining a signal receiving power value of the unknown grid by combining the signal receiving power of the known grid, and finally obtaining a complete electromagnetic map. According to the method, the variation function is modeled by using the radio wave propagation model from the variation function, spatial interpolation is completed to obtain reconstruction of the electromagnetic map, and the precision of the electromagnetic map is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic map reconstruction, and in particular relates to an electromagnetic map reconstruction system and method based on a propagation model. Background Art

[0002] With the development of information technology, the competition for electromagnetic space in the military field has become increasingly fierce. Therefore, it is of great significance to improve the electromagnetic situational awareness capability in complex environments and gain control of the electromagnetic spectrum. Communication energy consumption has increased significantly and spectrum resources are becoming increasingly scarce. Therefore, how to analyze and manage the electromagnetic spectrum and optimize the design of network and communication resource configuration is of great significance. Electromagnetic maps can quantitatively describe the electromagnetic environment from multiple dimensions such as signal frequency, spatial distribution, and intensity. High-precision electromagnetic maps can provide electromagnetic situation information of the target area to guide spectrum management, network optimization, and base station deployment.

[0003] The prior arts closest to the present invention are "a method for realizing electromagnetic spectrum map based on improved inverse distance interpolation" and "a method, device and equipment for constructing electromagnetic spectrum map based on residual kriging". Among them, "a method for realizing electromagnetic spectrum map based on improved inverse distance interpolation" realizes the construction of electromagnetic spectrum map by improving the inverse distance interpolation method; "a method, device and equipment for constructing electromagnetic spectrum map based on residual kriging" combines the Bayesian hierarchical model with the residual kriging method to realize the construction of electromagnetic spectrum map.

[0004] like Figure 1 As shown in the figure, "A method for implementing an electromagnetic spectrum map based on improved inverse distance interpolation" first collects and preprocesses spectrum data at spatial positions, then determines a variable search radius, eliminates data that are far away from the point to be interpolated, increases the weights of points that are closer, and then calculates the weight coefficient according to the weight formula. Finally, the electromagnetic spectrum map is calculated by combining the weight coefficient with known data points.

[0005] like Figure 2As shown, the "electromagnetic spectrum map construction method, device and equipment based on residual kriging method" decomposes the construction of electromagnetic map into path attenuation component estimation and shadow fading component estimation according to the theory of radio wave propagation. First, the electromagnetic environment monitoring data and the position of the point to be estimated are obtained, and then the Bayesian hierarchical model is used to obtain the posterior distribution of the model parameters based on the model parameter distribution and the likelihood function of the parameters constructed according to the electromagnetic environment monitoring data. The model parameter estimation value is obtained using the Giles distribution, and then combined with the path attenuation model, the path attenuation component estimation value of the point to be estimated is obtained; then the received power is subtracted from the path attenuation component estimation value of the corresponding position to obtain the residual monitoring data, and then the residual kriging interpolation of the exponential model is used according to the residual monitoring data to obtain the shadow fading component estimation value of the point to be estimated; finally, the path attenuation component estimation value is summed with the shadow fading component estimation value to obtain the received power estimation value of the point to be estimated.

[0006] "A method for implementing electromagnetic spectrum maps based on improved inverse distance interpolation" has poor accuracy in reconstructing electromagnetic maps when the sampling grid accounts for a small proportion, and the electromagnetic distribution of the reconstructed electromagnetic map is disordered, which is not conducive to guiding practical applications such as base station deployment and network optimization. "Method, device and equipment for constructing electromagnetic spectrum maps based on residual kriging" requires sampling of specific grid positions, and requires early electromagnetic detection data as the data basis for subsequent electromagnetic map construction. Although the reconstruction accuracy is high, it is difficult to construct and apply electromagnetic maps in areas lacking prior information and non-cooperative areas. Summary of the invention

[0007] In view of the deficiencies in the prior art, the present invention proposes an electromagnetic map reconstruction scheme based on a propagation model.

[0008] A first aspect of the present invention provides a method for reconstructing an electromagnetic map based on a propagation model, the method comprising:

[0009] Step S1, sparse data collection;

[0010] A certain number of grids are randomly selected in the target area, and the signal power values ​​received by the sensor in the grids are used as the collected sample data;

[0011] Step S2, sample data processing;

[0012] The sample data collected by the sensor and the location of the sensor are used to calculate the semi-variation value and distance between each pair of sampling nodes. The nodes are grouped according to the distance and outliers are removed to obtain a two-dimensional array of distance and semi-variation value.

[0013] Step S3, constructing a variation function;

[0014] Based on the two-dimensional array, the variation function is modeled using the law of radio wave propagation, and the particle swarm optimization algorithm is used to solve the unknown coefficients of the function to obtain the variation function;

[0015] Step S4: spatial interpolation processing;

[0016] The semi-variance value between the unknown grid and the known grid is calculated using the variation function. The signal receiving power value of the unknown grid is obtained by weighted summation based on the calculated semi-variance value and the known grid, thus obtaining a complete electromagnetic map.

[0017] According to the method of the first aspect of the present invention, in step S1:

[0018] Divide the target area into grids, and use the coordinates of each grid center point as grid coordinates. The grid size is used to represent the resolution of the electromagnetic map. The smaller the grid area, the higher the resolution of the electromagnetic map.

[0019] The equipment for data collection is: an unmanned mobile platform equipped with a radio signal sensor and a positioning system, the unmanned mobile platform is a drone or an unmanned vehicle;

[0020] The grids in the target area are randomly sampled using randomly placed fixed-position radio signal sensors or wearable devices with radio signal receiving capabilities, or by dropping radio signal sensors in the air to sample the target area.

[0021] According to the method of the first aspect of the present invention, in step S2, sample data processing refers to using the collected sample data to establish a variogram cloud and process it to provide a data basis for subsequent variogram modeling; wherein:

[0022] Take Z=[z(x1),z(x2),...,z(x n )] represents the electromagnetic data of the sampling grid in the target area, x1, x2, ..., x n Represents the position parameter of the grid. The semi-variance value and distance between each pair of sampling nodes are calculated based on the position information and signal power value in the sampled grid electromagnetic data:

[0023]

[0024] Establish a variogram cloud based on the calculation results;

[0025] The samples are grouped, outliers and outliers in each group are removed, and the mean of the groups is summed to obtain the distance and semi-variation value scatter point set. When grouping, the basic lag distance S and distance tolerance R are selected according to the number of samples and the characteristics of the attribute value. According to KS-R≤d ij≤KS+R, (K=1, 2, …, n) divide the set into n groups according to the distance; when removing outliers and outliers, in the case of unknown data distribution, use the box plot to identify outliers and define the interquartile range (IQR) indicator:

[0026] IQR=Q3-Q1

[0027] Where Q3 represents the upper quartile, Q1 represents the lower quartile, and IQR represents the distance between the upper quartile and the lower quartile; the reasonable interval is defined as [Q1-K×IQR,Q3+K×IQR], where K is a positive number that controls the length of the interval; after removing the outliers, the average distance h within each group after grouping is calculated. m (m = 1, 2, ..., n), as the lag distance of the independent variable of the semivariogram; the number of point pairs involved in the calculation of each group N (h m ) is called the point pair, and the calculation formula of the semivariogram value corresponding to the lag distance is:

[0028]

[0029] γ mi Indicates that the lag distance is h m The ith semivariogram value in the group of , thus obtaining a two-dimensional discrete point set of hysteresis distance and semivariogram function value {(h1, γ1), (h2, γ2), …, (h n , γ n )}.

[0030] According to the method of the first aspect of the present invention, in step S3, a set of discrete points is fitted to obtain the semivariogram value of a pair of points at any distance, and the variogram is modeled according to the law of radio wave propagation; wherein:

[0031] The signal expression in the target area is:

[0032]

[0033] P T represents the transmit power, w represents the receive matrix, h represents the channel, x represents the transmit symbol, and n represents the noise; calculate the semi-variance value between the two grids:

[0034] γ ij =P T (||h i || 2 -||h j || 2 )+(σ i 2 -σ j 2 )

[0035] ||·|| represents the calculation of the second norm, σ i 2 represents the noise power; the channel h follows a complex Gaussian distribution, and σ i 2 -σ j 2 Obey the chi-square distribution; introduce the loss model of radio wave propagation:

[0036] L=32.45+20logf+20logd

[0037] The frequency of the signal propagating in the target area is known, and the path loss of the signal in the target area is proportional to the logarithm of the distance. The functional relationship between the distance and the semi-variance value is:

[0038] γ ij =P T (32.45+20logf+20logd)+σ ij

[0039] σ ij Represents σ i -σ j The variance of ; the model of the variogram is constructed as:

[0040] γ(h)=alogbh+c

[0041] a, b, c are the unknown coefficients; solve the unknown coefficients to get the accurate expression of the variation function; use the particle swarm optimization algorithm to solve the unknown coefficients of the function expression, and the fitness function is:

[0042]

[0043] F(i) represents fitness, γ i (h) is the semi-variance value actually calculated, is the semivariate value estimated according to the model, Represents the weight factor; defines the position and velocity of the particle:

[0044]

[0045] D i represents the set of particle positions, a i , b i , c i represents the current solution of the function's undetermined coefficients, V i represents the velocity set of the particle, v ai , v bi , v ciIndicates the change size of the three solutions, and its positive and negative are the direction of change; in order to find the global optimal solution, the particle swarm algorithm continuously updates the speed and position of the particles in an iterative manner, and records the global optimal solution and the individual optimal solution; the speed and position update formula is:

[0046]

[0047] i=1,2,…,N,N represents the size of the particle swarm, i represents the i-th particle; d=1,2,…,D,D represents the dimension of the particle swarm, d represents the d-th dimension of the particle position, and its dimension is 3 in the undetermined coefficients of the optimal variation function; k represents the current number of iterations; ω represents the inertia weight; b1 represents the individual learning factor; b2 represents the group learning factor; r1 and r2 are random numbers in the interval [0,1]; represents the historical optimal position of the d-th dimension position of the ith particle in the k-th iteration, that is, the optimal solution obtained by the ith particle after the k-th iteration; represents the historical optimal position of the particle swarm in the d-th dimension in the k-th iteration, that is, the optimal solution obtained by the entire particle swarm search after the k-th iteration. represents the d-dimensional updated position of the ith particle in the k+1th iteration, represents the d-th dimension historical optimal position of the ith particle in the k-th iteration, Update the velocity of the dth dimension of the ith particle at the k+1th iteration; use a linearly decreasing inertia weight adjustment strategy to obtain better search performance:

[0048]

[0049] ω max Indicates the maximum inertia weight value set, ω min Indicates the minimum inertia weight value set, k is the current iteration number, and K is the total iteration number; the optimal solution of the variation function parameters is obtained.

[0050] According to the method of the first aspect of the present invention, in step S4, the attribute values ​​of the space are uniform, and there are the same expectation and variance for any point in the space. The attribute value of the unknown point is obtained by linearly weighting the attribute values ​​of the known points:

[0051]

[0052] x0 represents the position to be estimated, represents the attribute value of the point to be estimated, λ i Represents the weight coefficient of each known point;

[0053] Confirming the weight coefficients will get the attribute values ​​of the points to be estimated, which meet two standard conditions: unbiasedness and minimum variance; combined with the solution of the variance function, the coefficient determination problem is further transformed into a nonlinear constrained minimum problem:

[0054]

[0055] Constructing the objective function using the Lagrange multiplier method Let J′ be the parameter Φ, λ i The partial derivative is found to be 0, and the complete electromagnetic map is obtained.

[0056] A second aspect of the present invention provides an electromagnetic map reconstruction system based on a propagation model, the system comprising a processing unit, the processing unit being configured to perform the following steps:

[0057] Step S1, sparse data collection;

[0058] A certain number of grids are randomly selected in the target area, and the signal power values ​​received by the sensor in the grids are used as the collected sample data;

[0059] Step S2, sample data processing;

[0060] The sample data collected by the sensor and the location of the sensor are used to calculate the semi-variation value and distance between each pair of sampling nodes. The nodes are grouped according to the distance and outliers are removed to obtain a two-dimensional array of distance and semi-variation value.

[0061] Step S3, constructing a variation function;

[0062] Based on the two-dimensional array, the variation function is modeled using the law of radio wave propagation, and the particle swarm optimization algorithm is used to solve the unknown coefficients of the function to obtain the variation function;

[0063] Step S4: spatial interpolation processing;

[0064] The semi-variance value between the unknown grid and the known grid is calculated using the variation function. The signal receiving power value of the unknown grid is obtained by weighted summation based on the calculated semi-variance value and the known grid, thus obtaining a complete electromagnetic map.

[0065] The third aspect of the present invention discloses an electronic device. 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 in the electromagnetic map reconstruction method based on the propagation model described in the first aspect of the present disclosure are implemented.

[0066] The fourth aspect of the present invention discloses a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps in the electromagnetic map reconstruction method based on a propagation model described in the first aspect of the present disclosure are implemented.

[0067] In summary, the present invention starts from the variation function, uses the radio wave propagation model to model the variation function and completes the reconstruction of the electromagnetic map by spatial interpolation, thereby effectively improving the accuracy of the electromagnetic map. The present invention mainly solves the problems that the existing technology has low accuracy in non-cooperative complex environments, and the existing methods require a lot of data collection and fixed collection locations. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0069] Figure 1 The present invention is a flowchart of a method for realizing an electromagnetic spectrum map based on improved inverse distance interpolation in the prior art.

[0070] Figure 2 The present invention is a flowchart of a method for constructing an electromagnetic spectrum map based on residual kriging in the prior art.

[0071] Figure 3 4 is a flow chart of an electromagnetic map reconstruction method based on a propagation model according to an embodiment of the present invention.

[0072] Figure 4 Heat map of the real electromagnetic map.

[0073] Figure 5 This is a thermal map of the electromagnetic map reconstructed using the method proposed in the present invention.

[0074] Figure 6 Heat map of the electromagnetic map obtained using the Kriging method.

[0075] Figure 7 Heat map of the electromagnetic map obtained using the inverse distance weighted method.

[0076] Figure 8 Heat map of the electromagnetic map obtained using the nearest neighbor method.

[0077] Fig. 9 Heat map of the electromagnetic map obtained using random forest. DETAILED DESCRIPTION

[0078] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in 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 work are within the scope of protection of the present invention.

[0079] Electromagnetic maps can quantitatively describe the electromagnetic environment from multiple dimensions such as the operating frequency, spatial distribution and signal strength of electromagnetic signals, and visualize the electromagnetic energy distribution and spectrum resource distribution of the area of ​​interest in combination with geographic information. The electromagnetic map of the present invention is used to characterize the signal receiving power value of each point in the area of ​​interest, and can reflect the geographical location attributes and electromagnetic energy attributes of each point.

[0080] like Figure 3 As shown. The scheme described in the present invention needs to go through the steps of sparse data collection, sample data processing, variation function modeling and solution, spatial interpolation processing, etc. Sparse data collection is to randomly select a certain number of grids in the target area and use the signal power value received by the sensor in the grid as the data support for the subsequent steps; sample data processing is to use the data received by the sensor and the location of the sensor to calculate the semi-variance value and distance between each point pair and group them according to the distance, and after removing the abnormal values, obtain the distance and semi-variance value two-dimensional array as the basis for variation function modeling; variation function modeling and solution is to use the law of radio wave propagation to model the variation function and use the particle swarm optimization algorithm to solve the unknown coefficients of the function to obtain the variation function; spatial interpolation is to use the variation function to calculate the semi-variance value between the unknown grid and the known grid, and the signal receiving power value of the unknown grid can be obtained by weighted summation based on the calculated semi-variance value combined with the signal receiving power of the known grid, and finally a complete electromagnetic map is obtained.

[0081] 1. Data Collection

[0082] First, the area of ​​interest is divided into grids, and the coordinates of each grid center point are used as grid coordinates, that is, the geographical location of the grid. In the actual measurement process, since radio waves can be approximately considered to be uniformly reduced or even unchanged when propagating over a small distance, the data at the center of the grid can be used as the representative of the entire grid data. The size of the grid can be used to represent the resolution of the electromagnetic map. The smaller the area of ​​the grid, the higher the resolution of the electromagnetic map, the more detailed the electromagnetic situation it depicts, and the greater the computational overhead. Therefore, the size of the grid division needs to be set according to actual needs.

[0083] When collecting data, unmanned mobile platforms equipped with radio signal sensors and GPS / Beidou antennas, i.e., drones or unmanned vehicles, can be used to randomly sample grids in the target area. Randomly deployed fixed-position radio signal sensors or wearable devices with radio signal receiving functions, such as mobile phones, can also be used to randomly collect data. Similarly, low-cost radio signal sensors can be dropped from aircraft to sample the target area.

[0084] 2. Sample data processing

[0085] Sample data processing is to use the collected data to establish a variogram cloud and process it to provide data for subsequent variogram modeling.

[0086] Let Z = [z(x1),z(x2),...,z(x n )] represents the electromagnetic data of the sampling grid in the target area, x1, x2, ..., x n Represents the position parameter of the grid. The semi-variance value and distance between each pair of sampling nodes are calculated based on the position information and signal power value in the sampled grid electromagnetic data. The calculation formula is:

[0087]

[0088] According to the calculation results, the variation function cloud can be established. However, it can be found that under the same distance, the number of samples is not the same, and the distance between some point pairs is too large, and the correlation between their attribute values ​​is too poor. Therefore, considering the number of samples and the quality of samples, the samples are first grouped and then the outliers and outliers in each group are removed. Finally, the means of the groups are summed to obtain the distance and semi-variance value scatter point set.

[0089] When grouping, it is necessary to select the basic lag distance S and distance tolerance R according to the number of samples and the characteristics of the attribute value. And according to KS-R≤d ij ≤KS+R, (K=1, 2, …, n) divide the set into n groups according to the distance. When removing outliers and outliers, considering the unknown data distribution, the box plot does not make any restrictive requirements on the data distribution, so the result of using the box plot to identify outliers will be more objective. When using the box plot to identify outliers, the interquartile range (IQR) indicator needs to be defined first, that is:

[0090] IQR=Q3-Q1 (2)

[0091] Q3 represents the upper quartile, Q1 represents the lower quartile, and IQR represents the distance between the upper quartile and the lower quartile. Then the reasonable interval is defined as: [Q1-K×IQR,Q3+K×IQR], where K is a positive number for the control interval length, and K is usually 1.5. After removing the outliers, the average distance h within each group after grouping is calculated. m (m = 1, 2, ..., n), which is the lag distance of the independent variable of the semivariogram function. The number of point pairs involved in the calculation of each group is N (h m ) is called the point pair. The calculation formula for the semivariogram value corresponding to the lag distance is:

[0092]

[0093] where γ mi Indicates that the lag distance is h m The ith semivariance value in the group of . Thus, we can obtain a two-dimensional discrete point set of lag distance and semivariance function value {(h1, γ1), (h2, γ2), …, (h n , γ n )}.

[0094] 3. Modeling and solving the variation function

[0095] By selecting a suitable model to fit a set of discrete points, the semivariogram value of any distance point pair can be obtained. Commonly used fitting models include Gaussian model, exponential model, power function model and spherical model. However, the commonly used fitting models have poor accuracy and do not conform to the law of radio wave propagation. Therefore, it is necessary to model the variogram according to the law of radio wave propagation.

[0096] Assume that the signal expression in the target area is:

[0097]

[0098] Where P T represents the transmit power, w represents the receive matrix, h represents the channel, x represents the transmit symbol, and n represents the noise. Calculating the semivariance between the two grids yields:

[0099] γ ij =P T (||h i || 2 -||h j || 2 )+(σ i 2 -σ j 2 ) (5)

[0100] where ||·|| represents the calculation of the second norm, σ i2 represents the noise power. Since the channel h follows a complex Gaussian distribution and σ i 2 -σ j 2 Obey the chi-square distribution. Introduce the loss model of radio wave propagation:

[0101] L=32.45+20logf+20logd (6)

[0102] Since the frequency of the signal propagating in the target area is known, it can be considered that the path loss of the signal in the target area is proportional to the logarithm of the distance. The functional relationship between the distance and the semi-variance value can be obtained as follows:

[0103] γ ij =P T (32.45+20logf+20logd)+σ ij (7)

[0104] where σ ij Represents σ i 2 -σ j 2 In view of this, we can construct the model of the variogram as:

[0105] γ(h)=alogbh+c (8)

[0106] Where a, b, and c are unknown coefficients. Solving the unknown coefficients can get the accurate expression of the variation function. When solving the unknown coefficients of the function expression, the particle swarm optimization algorithm is used to define the fitness function as:

[0107]

[0108] Where F(i) represents fitness, γ i (h) is the semi-variance value actually calculated, is the semivariate value estimated according to the model, Represents the weight factor, which is used to adjust and optimize the problem of uneven distribution of sample data. After obtaining the fitness function, the position and speed of the particle are defined as:

[0109]

[0110] Where D i represents the set of particle positions, a i , b i , c i represents the current solution of the function's undetermined coefficients, V i represents the velocity set of the particle, v ai , v bi , vci Indicates the change size of the three solutions, and its positive and negative are the direction of change. The position of the particle can be updated through the speed. In order to find the global optimal solution, the particle swarm algorithm continuously updates the speed and position of the particle through iteration, and records the global optimal solution and the individual optimal solution. The speed and position update formula is:

[0111]

[0112] Where i = 1, 2, ..., N, N represents the size of the particle swarm, i represents the i-th particle; d = 1, 2, ..., D, D represents the dimension of the particle swarm, d represents the d-th dimension of the particle position, and its dimension is 3 in the undetermined coefficient of the optimal variation function; k represents the current number of iterations; ω is the inertia weight; b1 is the individual learning factor; b2 is the group learning factor; r1 and r2 are random numbers in the interval [0, 1] to increase the randomness of the search; represents the historical optimal position of the d-th dimension position of the ith particle in the k-th iteration, that is, the optimal solution obtained by the ith particle after the k-th iteration; It represents the historical optimal position of the particle swarm in the d-th dimension in the k-th iteration, that is, the optimal solution obtained by the entire particle swarm search after the k-th iteration. represents the d-dimensional updated position of the ith particle in the k+1th iteration, represents the d-th dimension historical optimal position of the ith particle in the k-th iteration, is the d-dimensional update speed of the ith particle in the k+1th iteration. A linearly decreasing inertia weight adjustment strategy is used here to obtain better search performance, and its formula is:

[0113]

[0114] Among them, ω max Indicates the maximum inertia weight value set, ω min Indicates the minimum inertia weight value set, k is the current iteration number, and K is the total iteration number. From this, the optimal solution of the variation function parameters can be obtained.

[0115] 4. Spatial interpolation

[0116] Since the attribute values ​​of the space are uniform, there is the same expectation and variance for any point in the space, so the attribute value of the unknown point can be obtained by linear weighting the attribute value of the known point, that is:

[0117]

[0118] Among them, x0 represents the position to be estimated, represents the attribute value of the point to be estimated, λ iRepresents the weight coefficient of each known point. Only the weight coefficient needs to be confirmed to obtain the attribute value of the point to be estimated, and the coefficient needs to meet two standard conditions, namely: unbiasedness and minimum variance. Combined with the solution of the variance function, the coefficient determination problem can be further transformed into a nonlinear constrained minimum problem, namely:

[0119]

[0120] Then use the Lagrange multiplier method to construct the objective function Let J′ be the parameter Φ, λ i Find the partial derivative to be 0, and finally we can get:

[0121]

[0122] This allows for a complete electromagnetic map.

[0123] 5. Evaluation indicators

[0124] (1) Quality of electromagnetic map restoration

[0125] Considering the actual application, the reconstructed electromagnetic map needs to represent the relevant information in the target area with high quality. The quality of the reconstruction can be judged by comprehensively considering whether there is a bull's eye phenomenon and abnormal isomagnetic line morphology, which can qualitatively indicate the accuracy of the reconstructed electromagnetic map.

[0126] (2) Root mean square error

[0127] The root mean square error (RMSE) is often used as an indicator to measure the prediction accuracy of the prediction model on continuous data. In the reconstruction of electromagnetic maps, it can effectively measure the average deviation between each predicted value and the true value, and can quantitatively express the accuracy of the reconstructed electromagnetic map. Its expression is:

[0128]

[0129] Where N represents the number of points to be predicted, Z(x0) represents the true value, Represents the predicted value.

[0130] 6. Specific Experiments

[0131] (1) Experimental scenario construction

[0132] In order to fully consider the complexity of real conditions, the simulation experiment uses AOTOLL software to select a 4km×4km square area in the Brussels map and then rasterize it, and define the base station parameters. The base station height is set to 30m, the equivalent height of the receiving end is 1.5m, the frequency is set to 2.6GHz, and there are 3 base stations in total. After rasterization, a total of 40,000 grids are obtained, that is, each grid size is 20m×20m. Then 4,000 sampling nodes are randomly deployed in the area to collect electromagnetic data in the grid.

[0133] (2) Effect analysis

[0134] As mentioned above, the root mean square error is used as an indicator for performance evaluation in the simulation experiment. In order to verify the effectiveness of the method proposed in the present invention, the Kriging method, the inverse distance weighted method, the nearest neighbor method, and the random forest method commonly used in constructing spectrum maps are selected for comparison.

[0135] (2.1) Quality of electromagnetic map restoration

[0136] 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 Figure 4-9 As shown in the figure, it can be seen that the electromagnetic map reconstructed by the inverse distance weighted method and the random forest method has a serious bull's eye phenomenon, the distribution of isomagnetic lines is relatively messy, and the reconstruction effect is poor; the electromagnetic map reconstructed by the nearest neighbor method has a serious bull's eye phenomenon, and the description of the electromagnetic distribution is not detailed enough; the electromagnetic map reconstructed by the Kriging interpolation method has a relatively messy distribution of isomagnetic lines; and the electromagnetic map restored by the method proposed in the present invention is smooth and continuous, can better reflect the detailed information around the radiation source, and has a higher construction quality.

[0137] (2.2) Root mean square error comparison

[0138] Under the condition that the sampling grid accounts for 1%, the RMSE of the electromagnetic map constructed by each method and the benchmark data is calculated as shown in Table 1. It can be seen that the RMSE of the method proposed in the present invention is the lowest. In addition, it can be seen that under the condition that the sampling grid accounts for 1% and the environment is more complex, the RMSE of the method proposed in the present invention can achieve better RMSE than other literatures, which shows the effectiveness of the method proposed in the present invention.

[0139] Table 1: Comparison of root mean square error of each algorithm

[0140]

[0141] Please note that the technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, all possible combinations of the technical features in the above embodiments are not 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-mentioned embodiments only express several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention. It should be pointed out that for ordinary technicians in this field, without departing from the concept of the present invention, several variations and improvements can be made, which all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the attached claims.

Claims

1. A method for reconstructing an electromagnetic map based on a propagation model, characterized in that: The method comprises: Step S1, sparse data collection; A certain number of grids are randomly selected in the target area, and the signal power values ​​received by the sensor in the grids are used as the collected sample data; Step S2, sample data processing; The sample data collected by the sensor and the location of the sensor are used to calculate the semi-variation value and distance between each pair of sampling nodes. The nodes are grouped according to the distance and outliers are removed to obtain a two-dimensional array of distance and semi-variation value. Step S3, constructing a variation function; Based on the two-dimensional array, the variation function is modeled using the law of radio wave propagation, and the particle swarm optimization algorithm is used to solve the unknown coefficients of the function to obtain the variation function; Step S4: spatial interpolation processing; The semi-variance value between the unknown grid and the known grid is calculated using the variation function. The signal receiving power value of the unknown grid is obtained by weighted summation based on the calculated semi-variance value and the known grid, thus obtaining a complete electromagnetic map.

2. The electromagnetic map reconstruction method based on the propagation model according to claim 1, characterized in that: In step S1: Divide the target area into grids, and use the coordinates of each grid center point as grid coordinates. The grid size is used to represent the resolution of the electromagnetic map. The smaller the grid area, the higher the resolution of the electromagnetic map. The equipment for data collection is: an unmanned mobile platform equipped with a radio signal sensor and a positioning system, the unmanned mobile platform is a drone or an unmanned vehicle; The grids in the target area are randomly sampled using randomly placed fixed-position radio signal sensors or wearable devices with radio signal receiving capabilities, or by dropping radio signal sensors in the air to sample the target area.

3. The electromagnetic map reconstruction method based on the propagation model according to claim 2, characterized in that: In step S2, sample data processing refers to using the collected sample data to establish a variogram cloud and process it to provide a data basis for subsequent variogram modeling; wherein: With Z = [z(x1),z(x2),...,z(x n )] represents the electromagnetic data of the sampling grid in the target area, x1, x2, ..., x n Represents the position parameter of the grid. The semi-variance value and distance between each pair of sampling nodes are calculated based on the position information and signal power value in the sampled grid electromagnetic data: Establish a variogram cloud based on the calculation results; The samples are grouped, outliers and outliers in each group are removed, and the mean of the groups is summed to obtain the distance and semi-variation value scatter point set. When grouping, the basic lag distance S and distance tolerance R are selected according to the number of samples and the characteristics of the attribute value. According to KS-R≤d ij ≤KS+R, (K=1,2,…,n) Divide the set into n groups according to the distance; when removing outliers and outliers, in the case of unknown data distribution, use the box plot to identify outliers and define the interquartile range (IQR) indicator: IQR=Q3-Q1 Where Q3 represents the upper quartile, Q1 represents the lower quartile, and IQR represents the distance between the upper quartile and the lower quartile; the reasonable interval is defined as [Q1-K×IQR,Q3+K×IQR], where K is a positive number that controls the length of the interval; after removing the outliers, the average distance h within each group after grouping is calculated. m (m=1,2,…,n), as the lag distance of the independent variable of the semivariogram; the number of point pairs involved in the calculation of each group N (h m ) is called the point pair, and the calculation formula of the semivariogram value corresponding to the lag distance is: γ mi Indicates that the lag distance is h m The ith semivariogram value in the group of , thus obtaining a two-dimensional discrete point set of hysteresis distance and semivariogram function value {(h1,γ1),(h2,γ2),…,(h n ,γ n )}.

4. The electromagnetic map reconstruction method based on the propagation model according to claim 3 is characterized in that: In step S3, the discrete point set is fitted to obtain the semivariogram value of the point pair at any distance, and the variogram is modeled according to the law of radio wave propagation; wherein: The signal expression in the target area is: P T represents the transmit power, w represents the receive matrix, h represents the channel, x represents the transmit symbol, and n represents the noise; calculate the semi-variance value between the two grids: ||·|| represents the calculation of the second norm, σ i 2 represents the noise power; the channel h follows a complex Gaussian distribution, and σ i 2 -σ j 2 Obey the chi-square distribution; introduce the loss model of radio wave propagation: L=32.45+20logf+20logd The frequency of the signal propagating in the target area is known, and the path loss of the signal in the target area is proportional to the logarithm of the distance. The functional relationship between the distance and the semi-variance value is: γ ij =P T (32.45+20logf+20logd)+σ ij σ ij Represents σ i 2 -σ j 2 The variance of ; the model of the variogram is constructed as: γ(h)=a log bh+c a, b, c are the unknown coefficients; solve the unknown coefficients to get the accurate expression of the variation function; use the particle swarm optimization algorithm to solve the unknown coefficients of the function expression, and the fitness function is: F(i) represents fitness, γ i (h) is the semi-variance value actually calculated, is the semivariate value estimated according to the model, Represents the weight factor; defines the position and velocity of the particle: D i represents the set of particle positions, a i , b i , c i represents the current solution of the function's undetermined coefficients, V i represents the velocity set of the particle, v ai , v bi , v ci Indicates the change size of the three solutions, and its positive and negative are the direction of change; in order to find the global optimal solution, the particle swarm algorithm continuously updates the speed and position of the particles in an iterative manner, and records the global optimal solution and the individual optimal solution; the speed and position update formula is: i=1,2,…,N, N represents the size of the particle swarm, i represents the i-th particle; d=1,2,…,D, D represents the dimension of the particle swarm, d represents the d-th dimension of the particle position, and its dimension is 3 in the undetermined coefficients of the optimal variation function; k represents the current number of iterations; ω is the inertia weight; b1 is the individual learning factor; b2 is the group learning factor; r1 and r2 are random numbers in the interval [0, 1]; represents the historical optimal position of the d-th dimension position of the ith particle in the k-th iteration, that is, the optimal solution obtained by the ith particle after the k-th iteration; represents the historical optimal position of the particle swarm in the d-th dimension in the k-th iteration, that is, the optimal solution obtained by the entire particle swarm search after the k-th iteration. represents the d-dimensional updated position of the ith particle in the k+1th iteration, represents the d-th dimension historical optimal position of the ith particle in the k-th iteration, Update the velocity of the dth dimension of the ith particle at the k+1th iteration; use a linearly decreasing inertia weight adjustment strategy to obtain better search performance: ω max Indicates the maximum inertia weight value set, ω min Indicates the minimum inertia weight value set, k is the current iteration number, and K is the total iteration number; the optimal solution of the variation function parameters is obtained.

5. The electromagnetic map reconstruction method based on the propagation model according to claim 4, characterized in that: In step S4, the attribute values ​​of the space are uniform, and there is the same expectation and variance for any point in the space. The attribute value of the unknown point is obtained by linearly weighting the attribute value of the known point: x0 represents the position to be estimated, represents the attribute value of the point to be estimated, λ i Represents the weight coefficient of each known point; Confirming the weight coefficients will get the attribute values ​​of the points to be estimated, which meet two standard conditions: unbiasedness and minimum variance; combined with the solution of the variance function, the coefficient determination problem is further transformed into a nonlinear constrained minimum problem: Constructing the objective function using the Lagrange multiplier method Let J′ be the parameter Φ, λ i The partial derivative is found to be 0, and the complete electromagnetic map is obtained.

6. An electromagnetic map reconstruction system based on a propagation model, characterized in that: The system comprises a processing unit configured to perform the following steps: Step S1, sparse data collection; A certain number of grids are randomly selected in the target area, and the signal power values ​​received by the sensor in the grids are used as the collected sample data; Step S2, sample data processing; The sample data collected by the sensor and the location of the sensor are used to calculate the semi-variation value and distance between each pair of sampling nodes. The nodes are grouped according to the distance and outliers are removed to obtain a two-dimensional array of distance and semi-variation value. Step S3, constructing a variation function; Based on the two-dimensional array, the variation function is modeled using the law of radio wave propagation, and the particle swarm optimization algorithm is used to solve the unknown coefficients of the function to obtain the variation function; Step S4: spatial interpolation processing; The semi-variance value between the unknown grid and the known grid is calculated using the variation function. The signal receiving power value of the unknown grid is obtained by weighted summation based on the calculated semi-variance value and the known grid, thus obtaining a complete electromagnetic map.

7. 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 in the electromagnetic map reconstruction method based on the propagation model described in any one of claims 1 to 5 are implemented.

8. 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 in the electromagnetic map reconstruction method based on a propagation model described in any one of claims 1 to 5 are implemented.

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