Frequency spectrum situation generation method based on compressed sensing and thin-plate spline

Abstract

The invention provides a spectrum situation generation method based on compressed sensing and thin-plate splines, and relates to the technical field of construction schemes of magnetic spectrum maps. The method specifically comprises the following steps: constructing a region model based on a frequency spectrum situation generation algorithm, comprising L radiation sources, H sensors and a plurality of data processing centers, and respectively collecting a received signal strength (RSS) value of the position of each sensor; constructing a TPS function according to the received signal strength RSS value of the position of each sensor; optimizing the TPS function by establishing a limiting condition of the TPS function; and generating a spectrogram of the region model based on the spectrum situation generation algorithm by using the optimized TPS function. According to the method, the compressed sensing algorithm and the TPS algorithm in the spectrum map generation algorithm are reasonably combined, and the problems that the generated spectrum map is not clear, large errors are generated, and many abnormal value points are generated are effectively solved.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetic spectrum map construction solutions, and in particular to a spectrum situation generation method based on compressed sensing and thin plate splines. Background Art

[0002] In recent years, using limited sensing nodes to collect spectrum data and extract spectrum situation information in a wide geographic space has become an important means to maintain the order and safety of airborne radio waves. Improving the efficiency of spectrum utilization has become an urgent need in the increasingly complex electromagnetic environment and the growing demand for spectrum. Spectrum maps are the top priority of drone data collection. They not only show the strength of collected signals at different time and frequency, but also reflect whether there are available channels to use, as well as the distribution of radiation sources and the location of data centers. The spectrum situation generation technology based on spatial interpolation estimates the received signal strength (RSS) value of the unknown location by analyzing the spatial domain after grid discretization, and finally generates a spectrum map using the spatial dependency of the data, thereby constructing an interpolation model.

[0003] Based on the traditional spatial spectrum construction, a spatial spectrum estimation method based on finite samples is proposed. Among them, the encrypted grid interpolation method and the number of samples are important factors affecting the mapping accuracy. Commonly used interpolation methods include Kriging interpolation method, Thin Plate Spline (TPS) method and polynomial method.

[0004] Although the final spectrum map can be generated by RSS data of different time frequencies and different positions in the commonly used interpolation method, the spectrum map generated in this way cannot be fully evaluated and used. Therefore, the method based on spatial sparse sampling is particularly critical. This method uses limited sampling data to reconstruct the spectrum map, reveal the number and location of radiation sources, and realize the visualization of the electromagnetic spectrum. In the absence of prior information, Kriging and TPS interpolation methods are usually used to complete the data and generate maps. However, in the case of unknown electromagnetic environment information and sparse distribution of radiation sources, the spectrum situation generation method based on compressed sensing (CS) is more convenient and advantageous. Based on the theory of compressed sensing, discrete grid points in space are used as candidate points of radiation sources, and a compressed sensing model is constructed based on this, which is used as a complete dictionary for sparse expression of radiation sources. However, compressed sensing is sensitive to noise and model errors, which may lead to unstable performance in practical applications. Especially in the presence of strong noise interference or model mismatch, the reconstruction accuracy of compressed sensing may be seriously affected. Summary of the invention

[0005] In view of the above-mentioned deficiencies of the prior art, the present invention proposes a spectrum situation generation method based on compressed sensing and thin plate splines by mixing sparse representation spectrum situation generation technologies such as compressed sensing and the TPS algorithm, thereby ensuring the accuracy and clarity of spectrum map production.

[0006] The present invention proposes a spectrum situation generation method based on compressed sensing and thin plate splines, the method comprising the following steps:

[0007] Step 1: Construct a regional model based on the spectrum situation generation algorithm, including: L radiation sources, H sensors and several data processing centers, and collect the received signal strength RSS value of each sensor location;

[0008] Step 2: Construct the TPS function based on the received signal strength RSS value at each sensor location;

[0009] Step 3: Divide the regional model based on the spectrum situation generation algorithm into T grids, establish the restriction conditions of the TPS function, and use the restriction conditions to optimize the TPS function to obtain the optimized TPS function;

[0010] Step 4: Calculate the received signal strength RSS estimation value of each grid point in the regional model based on the spectrum situation generation algorithm using the optimized TPS function, and generate the spectrum diagram of the regional model based on the spectrum situation generation algorithm using the received signal strength RSS estimation values ​​of all grid points;

[0011] The step 1 further comprises:

[0012] Step 1.1: Establish a three-dimensional target area (X, Y, Z); where X represents the horizontal axis; Y represents the vertical axis; and Z represents the vertical axis;

[0013] Step 1.2: Randomly set L radiation sources, H sensors and several data processing centers in the three-dimensional target area (X, Y, Z) to construct a spatial area scene graph;

[0014] Step 1.3: Get the positions of all sensors in the spatial region scene graph and construct a sensor position set Get the positions of all radiation sources in the spatial region scene graph and construct a radiation source position set in represents the position of the hth sensor; represents the position of the lth radiation source;

[0015] Step 1.4: Use the equidistant segmentation method to divide the spatial region scene graph into I grids, and ensure that no two or more radiation sources are located in the same grid, and obtain the regional model based on the spectrum situation generation algorithm;

[0016] Step 1.5: Calculate the received signal strength RSS value of each sensor location in the regional model based on the spectrum situation generation algorithm, and construct the RSS value set {W 1 ,W 2 ,...,W H}, where W 1 Indicates the RSS value collected by the first sensor; W 2 Indicates the RSS value collected by the second sensor; W H Represents the RSS value collected by the Hth sensor;

[0017] The calculation method of the received signal strength RSS value at the location of each sensor in step 1.5 is as follows: construct a simplified path loss model of the sensor when collecting the RSS value, and for any sensor, calculate the path loss of the sensor when receiving the signal from each radiation source, calculate the received signal strength received by the sensor from all radiation sources in each grid, and sum them up to obtain the received signal strength RSS value at the location of the sensor;

[0018] The received signal strength RSS value is expressed as:

[0019]

[0020] Where W h represents the RSS value collected by the hth sensor; P h represents the measurement error of the hth sensor; i represents the i-th grid; δ i represents the radiation power of the i-th radiation source; represents the simplified path loss model of the sensor when collecting RSS values, T 0 represents the reference distance between the radiation source and the sensor without considering the path loss, represents the distance between the sensor and the radiation source, represents the location of the sensor, represents the location of the radiation source, and when hour, when hour, Where μ represents the path loss factor;

[0021] The method for constructing the TPS function in step 2 is: for any sensor location (α, β, ε) in the regional model based on the spectrum situation generation algorithm, where α represents the horizontal axis coordinate of the data point; β represents the vertical axis coordinate of the data point; ε represents the vertical axis coordinate of the data point; construct the TPS function G (α, β, ε), expressed as:

[0022]

[0023] Where n represents the number of received signal strength RSS values; λ represents the received signal strength RSS value collected by the λth sensor; χ λ is the unknown coefficient, and λ=1,...,n; ω 1 ,ω 2 ,ω 3 ,ω 4 All are unknown coefficients; p λ represents the weight of the received signal strength RSS value collected by the λth sensor; α λ Indicates the horizontal axis coordinate of the position of the λth sensor; β λ Indicates the vertical coordinate of the position of the λth sensor; ε λ represents the vertical axis coordinate of the position of the λth sensor; p represents the weight of the received signal strength RSS value; U(·) is the radial basis function, and its complete form is:

[0024]

[0025] Where U(r ijk ) represents the radial basis function; r ijk represents the Euclidean distance between the location of the i-th sensor, the location of the j-th sensor, and the location of the k-th sensor; P i Represents the weight of the received signal strength RSS value collected by the i-th sensor; α i Indicates the horizontal axis coordinate of the location of the i-th sensor; β i Indicates the vertical coordinate of the location of the i-th sensor; ε i represents the vertical axis coordinate of the position of the i-th sensor; P j Represents the weight of the received signal strength RSS value collected by the jth sensor; α j Indicates the horizontal axis coordinate of the jth sensor location; β j Indicates the vertical coordinate of the jth sensor location; ε j represents the vertical axis coordinate of the jth sensor location; P k Represents the weight of the received signal strength RSS value collected by the kth sensor; α k Indicates the horizontal axis coordinate of the kth sensor location; β k Indicates the vertical coordinate of the kth sensor location; ε k Indicates the vertical axis coordinate of the location of the kth sensor;

[0026] The step 3 further comprises:

[0027] Step 3.1: Use the average equidistant method to re-divide the regional model based on the spectrum situation generation algorithm into T grids, and ensure that no two or more radiation sources are located in the same grid, and then re-obtain the position of each sensor in the regional model based on the spectrum situation generation algorithm;

[0028] Step 3.2: Construct the constraints of the TPS function based on the thin plate spline interpolation method, including:

[0029] The displacement of the TPS function under boundary conditions is zero;

[0030] The normal displacement of the TPS function on the boundary is zero;

[0031] The curvature of the TPS function at the boundary is zero;

[0032] The torque exerted by the TPS function on the boundary is zero;

[0033] Step 3.3: For any sensor in the regional model based on the spectrum situation generation algorithm after the grid is re-divided, the received signal strength RSS value of the sensor location is re-collected, and the received signal strength RSS value is transmitted to the data processing center closest to the sensor;

[0034] Step 3.4: After the received signal strength RSS values ​​of all sensors are transmitted to the data processing center, the data retrieved from each data processing center are calculated respectively;

[0035] Step 3.5: Optimize the TPS function using the constraints of the TPS function and the data collected by all data processing centers to obtain an optimized TPS function, which is used to calculate the RSS estimation value of each sensor location;

[0036] The optimized TPS function is expressed as:

[0037]

[0038] Where R * (x i ,y i ,z i ) indicates that the i-th sensor is at position (x i ,y i ,z i ) at the RSS estimate;

[0039] The step 4 further comprises:

[0040] Step 4.1: For the regional model based on the spectrum situation generation algorithm divided into T grids, the received signal strength RSS values ​​of all sensor locations in the regional model are interpolated to obtain the kernel matrix P;

[0041] Step 4.2: Obtain the distance between every two grid points in the regional model based on the spectrum situation generation algorithm, and use the distance between the grid points to calculate the matrix D and the kernel function matrix K;

[0042] Step 4.3: Transmit the received signal strength RSS values ​​of all sensor locations to the data processing center closest to the sensor, calculate the data received by each data processing center, and use the data received by each data processing center to construct a data vector r = [R 1 ,R 2 ,...,R M ] T ; where R 1 Indicates the data retrieved by the first data center; R 2 Indicates the data retrieved by the second data center; R M Indicates the data retrieved by the Mth data center;

[0043] Step 4.4: Use the kernel function of each grid point in the kernel function matrix K to replace the data vector r = [R 1 ,R 2 ,...,R M ] T The data collected by each data processing center is used to obtain a new data vector r′=[F 1 ,F 2 ,...,F Q ] T ; where F 1 represents the kernel function of the first grid point; F 2 represents the kernel function of the second grid point; F Q represents the kernel function of the Qth grid point;

[0044] Step 4.5: Set the new data vector r′=[F 1 ,F 2 ,...,F Q ] T Substitute the optimized TPS function and obtain the received signal strength RSS estimation value of each grid point by solving the unknown function value in the optimized TPS function;

[0045] Step 4.6: Generate a spectrum diagram of the regional model based on the spectrum situation generation algorithm using the received signal strength RSS estimates of all grid points.

[0046] The beneficial effects of adopting the above technical solution are:

[0047] Since there is no single method to clearly display the spectrum map in the field of spectrum construction, the method of the present invention proposes a spectrum situation generation algorithm based on CS-TPS, which mixes sparse representation spectrum situation generation technology such as compressed sensing and the TPS algorithm. The two algorithms complement each other, so that the accuracy and clarity of spectrum map production are guaranteed to the greatest extent.

[0048] Since the spectrum obtained by the TPS interpolation method is quite different from the actual spectrum of the radiation source and its surrounding space area, the method of the present invention combines the TPS interpolation method with the compressed sensing algorithm, and smoothly connects the abnormal value points generated by the compressed sensing algorithm by adding the TPS algorithm after the spectrum map generated by the compressed sensing algorithm to generate an accurate spectrum map. When the number of samples is sufficient, the spectrum obtained by the compressed sensing method can more accurately describe the radiation intensity and has a strong accuracy.

[0049] Since the TPS algorithm is superior to the Kriging interpolation method, the method of the present invention adopts the TPS algorithm to make up for the shortcomings of the compressed sensing algorithm. The TPS function is a fitting of the sample to approximate or smooth the surface and is unique. Therefore, when the number of interpolation points is not less than 3 and does not intersect, it can accurately characterize the nonlinear characteristics of data in discrete data surface interpolation. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is a flow chart of a spectrum situation generation method based on compressed sensing and thin plate splines in this implementation;

[0051] Figure 2 A spatial region scene diagram of a spectrum situation generation algorithm based on CS-TPS in this implementation mode;

[0052] Figure 3 This is a schematic diagram of a spectrum situation generation method based on compressed sensing and thin plate splines in this embodiment. DETAILED DESCRIPTION

[0053] In order to facilitate the understanding of the present application, the specific embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings and embodiments. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present application more thoroughly understood.

[0054] This implementation method effectively solves the problem of unclear spectrum map generation, large errors and many outlier points by reasonably combining two algorithms in the spectrum map generation algorithm, namely, the organic combination of the compressed sensing algorithm and the TPS algorithm. At the same time, it clarifies the good supplement of the TPS algorithm to the compressed sensing algorithm, better solves the problem of outlier points it brings, and makes the spectrum map clearer and more accurate.

[0055] A spectrum situation generation method based on compressed sensing and thin plate splines in this embodiment is as follows: Figure 1 As shown, the following steps are included:

[0056] Step 1: Construct a regional model based on the spectrum situation generation algorithm, including: L radiation sources, H sensors and several data processing centers, and collect the received signal strength RSS value of each sensor location;

[0057] In this embodiment, a regional model based on a spectrum situation generation algorithm is constructed according to the constructed spatial regional scene graph, that is, a system scene model is constructed in a three-dimensional target area (X, Y, Z).

[0058] Step 1.1: Establish a three-dimensional target area (X, Y, Z); where X represents the horizontal axis; Y represents the vertical axis; and Z represents the vertical axis.

[0059] Step 1.2: Randomly set L radiation sources, H sensors and several data processing centers in the three-dimensional target area (X, Y, Z) to construct a spatial area scene graph.

[0060] In this embodiment, if Figure 2 As shown in the figure, the spatial area scene diagram consists of L radiation sources, H sensors and several data processing centers, namely data acquisition pools. This area is divided into I grids and on this basis, the sensors cooperate with each other to estimate the RSS value of each discrete grid point, thereby obtaining the spectrum situation of the target area.

[0061] Step 1.3: Get the positions of all sensors in the spatial region scene graph and construct a sensor position set Get the positions of all radiation sources in the spatial region scene graph and construct a radiation source position set in represents the position of the hth sensor; Indicates the position of the lth radiation source.

[0062] In this embodiment, the coordinates of the positions of all sensors are expressed as Where i represents the i-th sensor; x i Represents the horizontal axis coordinate of the i-th sensor; y i represents the vertical coordinate of the i-th sensor; zi Represents the vertical axis coordinate of the i-th sensor.

[0063] Step 1.4: Use the equidistant segmentation method to divide the spatial area scene graph into I grids, and ensure that there are no two or more radiation sources located in the same grid, and obtain the regional model based on the spectrum situation generation algorithm.

[0064] Step 1.5: Calculate the received signal strength (RSS) value of each sensor location in the regional model based on the spectrum situation generation algorithm, and construct the RSS value set {W 1 ,W 2 ,...,W H}, where W 1 Indicates the RSS value collected by the first sensor; W 2 Indicates the RSS value collected by the second sensor; W H Indicates the RSS value collected by the Hth sensor.

[0065] In this embodiment, taking into account factors such as path loss and shadow attenuation in signal propagation, it is assumed that the correlation of shadow fading is known and the relationship between the sources is not affected.

[0066] The calculation method of the received signal strength RSS value at the location of each sensor is as follows: construct a simplified path loss model for the sensor when collecting the RSS value, and for any sensor, calculate the path loss of the sensor when receiving signals from each radiation source, calculate the received signal strengths received by the sensor from all radiation sources in each grid, and sum them up to obtain the received signal strength RSS value at the location of the sensor.

[0067] The received signal strength RSS value is expressed as:

[0068]

[0069] Where W h represents the RSS value collected by the hth sensor; P h represents the measurement error of the hth sensor. In this embodiment, the error is taken into account due to the drop of shadows and other factors; i represents the i-th grid; δ τ represents the radiation power of the τth radiation source; represents the sum of the signal strengths received by the sensor from all grids; a represents the ath grid; It represents the simplified path loss model of the sensor when collecting RSS value, T 0 represents the reference distance between the radiation source and the sensor without considering the path loss, represents the distance between the sensor and the radiation source, represents the location of the sensor, represents the location of the radiation source, and when hour, when hour, Where μ represents the path loss factor.

[0070] Step 2: Construct a TPS function based on the received signal strength RSS value at each sensor location.

[0071] The method for constructing the TPS function is as follows: for any position (α, β, ε) of a sensor in the regional model based on the spectrum situation generation algorithm, where α represents the horizontal axis coordinate of the data point; β represents the vertical axis coordinate of the data point; ε represents the vertical axis coordinate of the data point; construct the TPS function G (α, β, ε), which is expressed as:

[0072]

[0073] Where n represents the number of received signal strength RSS values; λ represents the received signal strength RSS value collected by the λth sensor; χ λ is the unknown coefficient, and λ=1,...,n; ω 1 ,ω 2 ,ω 3 ,ω 4 All are unknown coefficients; p λ represents the weight of the received signal strength RSS value collected by the λth sensor; α λ Indicates the horizontal axis coordinate of the position of the λth sensor; β λ Indicates the vertical coordinate of the position of the λth sensor; ε λ represents the vertical axis coordinate of the position of the λth sensor; p represents the weight of the received signal strength RSS value; U(·) is the radial basis function, and its complete form is:

[0074]

[0075] r ijk =|P i (α i ,β i ,ε i )-P j (α j ,β j ,ε j )-P k (α k ,β k ,ε k )| (4)

[0076] Where U(r ijk ) represents the radial basis function; r ijk represents the Euclidean distance between the location of the i-th sensor, the location of the j-th sensor, and the location of the k-th sensor; P i Represents the weight of the received signal strength RSS value collected by the i-th sensor; α i Indicates the horizontal axis coordinate of the location of the i-th sensor; β i Indicates the vertical coordinate of the location of the i-th sensor; ε i represents the vertical axis coordinate of the position of the i-th sensor; P j Represents the weight of the received signal strength RSS value collected by the jth sensor; α j Indicates the horizontal axis coordinate of the jth sensor location; β j Indicates the vertical coordinate of the jth sensor location; ε j represents the vertical axis coordinate of the jth sensor location; P k Represents the weight of the received signal strength RSS value collected by the kth sensor; α k Indicates the horizontal axis coordinate of the kth sensor location; β k Indicates the vertical coordinate of the kth sensor location; ε k Indicates the vertical coordinate of the location of the kth sensor.

[0077] In this embodiment, due to the continuity of the geographical location, the sensor cannot obtain RSS information from each location, and the RSS value of each location cannot be estimated through limited operations. In order to better display the RSS value of the target area, a spectrum diagram is often used to visualize it. On this basis, a multi-layer grid division method is proposed based on a genetic algorithm. When the grid division is sufficiently fine, the radiation source can be regarded as sparse. On this basis, based on the grid node, that is, the position vector of the sensor, a sparse representation of the radiation source position is achieved, and the compressed sensing theory is used to solve it. Assume that Ω is a one-dimensional space vector with a vector length of N, which can be represented by a set of N×N sparse basis matrices The linear representation is:

[0078]

[0079] in represents a set of sparse basis matrices; S represents an N-dimensional one-dimensional space vector;

[0080] On this basis, the convex optimization method is used to obtain relevant information such as the location of the radiation source and the transmission power. The TPS algorithm is introduced on the discrete outlier points to reduce the error of the spectrum map.

[0081] Step 3: Divide the regional model based on the spectrum situation generation algorithm into T grids, establish the restriction conditions of the TPS function, and use the restriction conditions to optimize the TPS function to obtain the optimized TPS function.

[0082] Step 3.1: Use the average equidistant method to re-divide the regional model based on the spectrum situation generation algorithm into T grids, and ensure that there are no two or more radiation sources located in the same grid, and then re-obtain the position of each sensor in the regional model based on the spectrum situation generation algorithm.

[0083] In this embodiment, the space is first divided evenly in the three-dimensional space according to the preset grid position coordinates, that is, the regional model based on the spectrum situation generation algorithm is evenly divided into T grids, and the position of each sensor in its corresponding grid is accurately determined, which is recorded as Where t represents the position of the t-th sensor, and t=1,...,H, to ensure that the segmentation result can accurately reflect the signal strength characteristics and radiation source power values ​​of the locations of these sensors.

[0084] Step 3.2: Construct the constraints of the TPS function based on the thin plate spline interpolation method, including:

[0085] The displacement of the TPS function under boundary conditions is zero;

[0086] The normal displacement of the TPS function on the boundary is zero;

[0087] The curvature of the TPS function at the boundary is zero;

[0088] The torque exerted by the TPS function at the boundary is zero.

[0089] In this embodiment, the deformation function, i.e., the TPS function model, is similar to the shape of a steel plate. The energy required to bend the steel plate on a two-dimensional surface by passing the steel plate through given n points can be expressed as:

[0090]

[0091] Where E(f) represents the energy required for bending the thin steel plate; f represents the measurement function; x represents the horizontal axis direction in the two-dimensional coordinate system; y represents the vertical axis direction in the two-dimensional coordinate system.

[0092] The TPS algorithm cannot find all the coefficients at the given F sample points because the number of unknown coefficients is F + 4. In a real thin plate bending environment, in order to prevent the thin plate from moving up and down or rotating on the surface, the load and moment acting on the thin plate must be zero, so four restrictions need to be added to the TPS function.

[0093] Step 3.3: For any sensor in the regional model based on the spectrum situation generation algorithm after the grid is re-divided, the received signal strength RSS value of the sensor location is re-collected and the received signal strength RSS value is transmitted to the data processing center closest to the sensor.

[0094] Step 3.4: After the received signal strength RSS values ​​of all sensors are transmitted to the data processing center, the data received by each data processing center are calculated separately.

[0095] In this embodiment, the data processing center complements and integrates all the collected data to fit the spatial correlation law of the signal strength data, and uses the TPS interpolation method to generalize the obtained spatial correlation law to the entire grid area.

[0096] Step 3.5: Optimize the TPS function using the constraints of the TPS function and the data collected by all data processing centers to obtain an optimized TPS function, which is used to calculate the RSS estimation value of each sensor location;

[0097] The optimized TPS function is expressed as:

[0098]

[0099] Where R * (x i ,y i ,z i ) indicates that the i-th sensor is at position (x i ,y i ,z i ) is the estimated RSS value at .

[0100] In this embodiment, based on the traditional algorithm, using the principle of compressed sensing, and based on the constraints, a new multi-objective optimization method is proposed. The spectrum situation generation method of compressed sensing is a convex optimization problem, but its calculation takes a long time. As the number of grid points increases, more grid vectors are required to implement, which leads to longer calculation time for each step. At this time, the TPS algorithm is needed to further improve the shortcomings of the compressed sensing algorithm. The radiation spectrum generated by the compressed sensing method can clearly show the spatial distribution of radiation when there are sufficient samples, and if there is no radiation source at the pre-set grid point, the radiation intensity will decrease. Or when the radiation source appears at other points, more outlier points will be generated, and these outlier points can be smoothly connected using the TPS spectrum generation algorithm, and the surface interpolation of discrete data can be estimated by processing the RSS value, and the RSS distribution of the compressed sensing algorithm can be combined to realize the construction of the overall spectrum map of the target area. The TPS algorithm can process the RSS value of the measuring point.

[0101] Step 4: Use the optimized TPS function to calculate the received signal strength RSS estimate of each grid point in the regional model based on the spectrum situation generation algorithm, and use the received signal strength RSS estimate of all grid points to generate a spectrum diagram of the regional model based on the spectrum situation generation algorithm.

[0102] In this embodiment, if Figure 3 As shown in the figure, by converting the spatial spectrum situation generation problem into the problem of sparse radiation source information estimation, the received signal strength RSS value of each sensor is obtained based on the compressed sensing algorithm, and then the received signal strength RSS value is used for interpolation calculation to obtain the kernel matrix P and construct the kernel function matrix K, and establish the sampling vector, that is, the data vector r. The RSS estimation value of each grid point can be obtained by calculating the thin plate spline function coefficients, and finally the spectrum diagram of the regional model based on the spectrum situation generation algorithm is generated.

[0103] Step 4.1: For the regional model based on the spectrum situation generation algorithm divided into T grids, the received signal strength RSS values ​​of all sensor locations in the regional model are interpolated to obtain the kernel matrix P.

[0104] The kernel matrix P is expressed as:

[0105]

[0106] Where m represents the mth grid point; Represents the kernel function of the mth grid point.

[0107] In this embodiment, a new TPS interpolation model is constructed, that is, according to the received signal strength RSS value at the position coordinates of each sensor, and an interpolation calculation is performed to obtain a kernel matrix P.

[0108] In this embodiment, the number of sensors is H. If the number of sensors is sufficient, the distances between the sensors can be used.

[0109] Step 4.2: Obtain the distance between every two grid points in the regional model based on the spectrum situation generation algorithm, and use the distance between the grid points to calculate the matrix D and the kernel function matrix K.

[0110] The matrix D and the kernel function matrix K are respectively expressed as:

[0111]

[0112] in represents the kernel function of the nth grid point; O represents the zero matrix.

[0113] By solving KW=r, we can get the coefficient vector W:

[0114]

[0115] Where W represents the coefficient vector; r represents the data vector; where χ 1x , χ 2x , χ nx 、w 1x 、w 2x 、w 3x , χ 1y , χ 2y , χ ny 、w 1y 、w 2y 、w 3y , χ 1z , χ 2z , χ nz , χ nz 、w 1z 、w 2z and w 3z All are undetermined coefficients.

[0116] Step 4.3: Transmit the received signal strength RSS values ​​of all sensor locations to the data processing center closest to the sensor, calculate the data received by each data processing center, and use the data received by each data processing center to construct a data vector r = [R 1 ,R 2 ,...,R M ] T ; where R 1 Indicates the data retrieved by the first data center; R 2 Indicates the data retrieved by the second data center; R M Indicates the data retrieved by the Mth data center.

[0117] Step 4.4: Use the kernel function of each grid point in the kernel function matrix K to replace the data vector r = [R 1 ,R 2 ,...,R M ] T The data collected by each data processing center is used to obtain a new data vector in Represents the kernel function of the first grid point; represents the kernel function of the second grid point; represents the kernel function of the Qth grid point.

[0118] Step 4.5: Transform the new data vector Substitute the optimized TPS function and obtain the received signal strength RSS estimation value of each grid point by solving the unknown function value in the optimized TPS function.

[0119] The calculation method of the received signal strength RSS estimation value of each grid point is: for any grid point g, the received signal strength RSS estimation value of the grid point is:

[0120]

[0121] Where R * (F g ) represents the received signal strength RSS estimate value at the grid point g; F g represents the kernel function of the grid point g; q is the unknown coefficient; F q represents the kernel function of the qth grid point.

[0122] In this embodiment, the optimized TPS function is used to perform interpolation calculations on all grids respectively to obtain a new data vector mapping and generate an estimated RSS value for each grid point. In formula (12), a grid point is regarded as a data point.

[0123] Step 4.6: Generate a spectrum diagram of the regional model based on the spectrum situation generation algorithm using the received signal strength RSS estimates of all grid points.

[0124] In this embodiment, the RSS estimation value obtained by interpolation is used to generate a three-dimensional spectrum situation diagram, the spectrum situation is depicted by the spectrum diagram, the function coefficient value is obtained by simulation analysis and visualization of the signal distribution of the target area, and the estimation value of the position point is calculated.

[0125] This implementation method has greatly improved the accuracy and error of the spectrum map after construction, while also having the excellent performance of the traditional algorithm. The TPS algorithm can speed up the speed of the traditional compressed sensing single algorithm while ensuring that the error points generated by it are connected to improve accuracy. The compressed sensing algorithm can make up for the problem that the TPS algorithm cannot be constructed around the radiation source.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A spectrum situation generation method based on compressed sensing and thin plate splines, characterized in that: The method comprises the following steps: Step 1: Construct a regional model based on the spectrum situation generation algorithm, including: L radiation sources, H sensors and several data processing centers, and collect the received signal strength RSS value of each sensor location; Step 2: Construct the TPS function based on the received signal strength RSS value at each sensor location; Step 3: Divide the regional model based on the spectrum situation generation algorithm into T grids, establish the restriction conditions of the TPS function, and use the restriction conditions to optimize the TPS function to obtain the optimized TPS function; Step 4: Use the optimized TPS function to calculate the received signal strength RSS estimate of each grid point in the regional model based on the spectrum situation generation algorithm, and use the received signal strength RSS estimate of all grid points to generate a spectrum diagram of the regional model based on the spectrum situation generation algorithm.

2. The spectrum situation generation method based on compressed sensing and thin plate splines according to claim 1, characterized in that: The step 1 further comprises: Step 1.1: Establish a three-dimensional target area (X, Y, Z); where X represents the horizontal axis; Y represents the vertical axis; and Z represents the vertical axis; Step 1.2: Randomly set L radiation sources, H sensors and several data processing centers in the three-dimensional target area (X, Y, Z) to construct a spatial area scene graph; Step 1.3: Get the positions of all sensors in the spatial region scene graph and construct a sensor position set Get the positions of all radiation sources in the spatial region scene graph and construct a radiation source position set in represents the position of the hth sensor; represents the position of the lth radiation source; Step 1.4: Use the equidistant segmentation method to divide the spatial region scene graph into I grids, and ensure that no two or more radiation sources are located in the same grid, and obtain the regional model based on the spectrum situation generation algorithm; Step 1.5: Calculate the received signal strength RSS value of each sensor location in the regional model based on the spectrum situation generation algorithm, and construct the RSS value set {W1, W2, ..., W H }, where W1 represents the RSS value collected by the first sensor; W2 represents the RSS value collected by the second sensor; W H Indicates the RSS value collected by the Hth sensor.

3. The spectrum situation generation method based on compressed sensing and thin plate splines according to claim 2 is characterized in that: The calculation method of the received signal strength RSS value at the location of each sensor in step 1.5 is as follows: construct a simplified path loss model of the sensor when collecting the RSS value, and for any sensor, calculate the path loss of the sensor when receiving the signal from each radiation source, calculate the received signal strength received by the sensor from all radiation sources in each grid, and sum them up to obtain the received signal strength RSS value at the location of the sensor; The received signal strength RSS value is expressed as: Where W h represents the RSS value collected by the hth sensor; P h represents the measurement error of the hth sensor; a represents the ath grid; δ τ represents the radiation power of the τth radiation source; Represents the sum of the signal strengths from all grids received by the sensor; represents the simplified path loss model of the sensor when collecting RSS values, T0 represents the reference distance between the radiation source and the sensor without considering the path loss, represents the distance between the sensor and the radiation source, represents the location of the sensor, represents the location of the radiation source, and when hour, when hour, Where μ represents the path loss factor.

4. The spectrum situation generation method based on compressed sensing and thin plate splines according to claim 3 is characterized in that: The method for constructing the TPS function in step 2 is: for any sensor location (α, β, ε) in the regional model based on the spectrum situation generation algorithm, where α represents the horizontal axis coordinate of the data point; β represents the vertical axis coordinate of the data point; ε represents the vertical axis coordinate of the data point; construct the TPS function G (α, β, ε), expressed as: Where n represents the number of received signal strength RSS values; λ represents the received signal strength RSS value collected by the λth sensor; χ λ are unknown coefficients, and λ=1,...,n; ω1, ω2, ω3, ω4 are unknown coefficients; p λ represents the weight of the received signal strength RSS value collected by the λth sensor; α λ Indicates the horizontal axis coordinate of the position of the λth sensor; β λ Indicates the vertical coordinate of the position of the λth sensor; ε λ represents the vertical axis coordinate of the position of the λth sensor; p represents the weight of the received signal strength RSS value; U(·) is the radial basis function, and its complete form is: r ijk =|P i (a i ,b i ,he i )-P j (a j ,b j ,he j )-P k (a k ,b k ,he k ) Where U(r ijk ) represents the radial basis function; r ijk represents the Euclidean distance between the location of the i-th sensor, the location of the j-th sensor, and the location of the k-th sensor; P i Represents the weight of the received signal strength RSS value collected by the i-th sensor; α i Indicates the horizontal axis coordinate of the location of the i-th sensor; β i Indicates the vertical coordinate of the location of the i-th sensor; ε i represents the vertical axis coordinate of the position of the i-th sensor; P j Represents the weight of the received signal strength RSS value collected by the jth sensor; α j Indicates the horizontal axis coordinate of the jth sensor location; β j Indicates the vertical coordinate of the jth sensor location; ε j represents the vertical axis coordinate of the jth sensor location; P k Represents the weight of the received signal strength RSS value collected by the kth sensor; α k Indicates the horizontal axis coordinate of the kth sensor location; β k Indicates the vertical coordinate of the kth sensor location; ε k Indicates the vertical coordinate of the location of the kth sensor.

5. The spectrum situation generation method based on compressed sensing and thin plate splines according to claim 4 is characterized in that: The step 3 further comprises: Step 3.1: Use the average equidistant method to re-divide the regional model based on the spectrum situation generation algorithm into T grids, and ensure that no two or more radiation sources are located in the same grid, and then re-obtain the position of each sensor in the regional model based on the spectrum situation generation algorithm; Step 3.2: Construct the constraints of the TPS function based on the thin plate spline interpolation method, including: The displacement of the TPS function under boundary conditions is zero; The normal displacement of the TPS function on the boundary is zero; The curvature of the TPS function at the boundary is zero; The torque exerted by the TPS function on the boundary is zero; Step 3.3: For any sensor in the regional model based on the spectrum situation generation algorithm after the grid is re-divided, the received signal strength RSS value of the sensor location is re-collected, and the received signal strength RSS value is transmitted to the data processing center closest to the sensor; Step 3.4: After the received signal strength RSS values ​​of all sensors are transmitted to the data processing center, the data retrieved from each data processing center are calculated respectively; Step 3.5: Optimize the TPS function using the constraints of the TPS function and the data retrieved from all data processing centers to obtain the optimized TPS function, which is used to calculate the RSS estimate value at each sensor location.

6. The spectrum situation generation method based on compressed sensing and thin plate splines according to claim 5, characterized in that: The optimized TPS function is expressed as: Where R * (x i ,y i ,z i ) indicates that the i-th sensor is at position (x i ,y i ,z i ) is the estimated RSS value at .

7. The spectrum situation generation method based on compressed sensing and thin plate splines according to claim 6, characterized in that: The step 4 further comprises: Step 4.1: For the regional model based on the spectrum situation generation algorithm divided into T grids, the received signal strength RSS values ​​of all sensor locations in the regional model are interpolated to obtain the kernel matrix P; Step 4.2: Obtain the distance between every two grid points in the regional model based on the spectrum situation generation algorithm, and use the distance between the grid points to calculate the matrix D and the kernel function matrix K; Step 4.3: Transmit the received signal strength RSS values ​​of all sensor locations to the data processing center closest to the sensor, calculate the data received by each data processing center, and construct a data vector r = [R1, R2, ..., R M ] T ; R1 represents the data retrieved by the first data center; R2 represents the data retrieved by the second data center; R M Indicates the data retrieved by the Mth data center; Step 4.4: Use the kernel function of each grid point in the kernel function matrix K to replace the data vector r = [R1, R2, ..., R M ] T The data collected by each data processing center is used to obtain a new data vector r′=[F1,F2,...,F Q ] T ; Where F1 represents the kernel function of the first grid point; F2 represents the kernel function of the second grid point; F Q represents the kernel function of the Qth grid point; Step 4.5: Substitute the new data vector r′=[F1,F2,...,F Q ] T Substitute the optimized TPS function and obtain the received signal strength RSS estimation value of each grid point by solving the unknown function value in the optimized TPS function; Step 4.6: Generate a spectrum diagram of the regional model based on the spectrum situation generation algorithm using the received signal strength RSS estimates of all grid points.

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