Radiation source positioning method for reconstructing electromagnetic spectrum map based on Gaussian process regression

Abstract

The invention belongs to the field of electromagnetic spectrum monitoring, and relates to a radiation source positioning method for reconstructing an electromagnetic spectrum map based on Gaussian process regression, which comprises the following steps of: S1, deploying a sensing node in a target area to acquire RSSI (Received Signal Strength Indicator) data and normalizing the RSSI data; s2, constructing an electromagnetic spectrum map based on Gaussian process regression, modeling spatial correlation by adopting an RBF (Radial Basis Function) kernel function, and predicting RSSI (Received Signal Strength Indicator) for all grid points by maximizing edge likelihood optimization parameters; s3, expanding the coverage area according to the spectrum map and calculating the coordinates of the center of mass to obtain the potential position of the radiation source; and S4, in combination with the logarithmic distance path loss model, fitting the relationship between the distance logarithm and the RSSI by adopting a least square method, and selecting the position with the minimum fitting error as a final result. Compared with Kriging interpolation, the method has better spatial integrity and precision, can overcome the defect of incomplete boundary interpolation, remarkably improves the positioning precision, only needs RSSI data, does not need priori information, and is low in cost, flexible in deployment and high in adaptability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of electromagnetic spectrum monitoring and radiation source positioning, and relates to a radiation source positioning method based on Gaussian process regression reconstruction of an electromagnetic spectrum map. BACKGROUND

[0002] With the rapid development of electronic and communication technologies and the continuous increase in the number of radio devices, people are facing an increasingly complex electromagnetic environment, and the demand for monitoring of electromagnetic spectrum and electromagnetic radiation sources is also increasing. In order to realize efficient electromagnetic space control, the position information of each radiation source in the region must be mastered through radiation source positioning.

[0003] In the positioning algorithm based on a distributed sensing network, commonly used positioning parameters include angle of arrival (AOA), time difference of arrival (TDOA), frequency difference of arrival (FDOA), received signal strength indicator (RSSI), etc. Although there have been a large number of related researches at present, most of the positioning algorithms have certain limitations in application: the positioning algorithms based on AOA, TDOA and FDOA have high hardware costs, and the positioning accuracy depends on whether the positioning parameters can be accurately obtained; the positioning algorithm based on RSSI does not require additional detection equipment, and has low hardware cost, but usually requires known environmental prior information.

[0004] In recent years, the concept of electromagnetic spectrum map has been proposed and widely studied. The electromagnetic spectrum map combines the actual geographical environment to describe the electromagnetic environment of the target region from the dimensions of time domain, frequency domain, electromagnetic signal strength, etc. Among them, the distribution of electromagnetic signal strength can reflect the number and position of radiation sources.

[0005] The construction method of the electromagnetic spectrum map is divided into indirect construction method and direct construction method. The indirect construction method needs to know the position, power and other parameters of the radiation source as prior information, so it cannot position unknown radiation sources. The direct construction method, also known as the spatial interpolation method, directly uses the data collected by the sensing nodes for interpolation.

[0006] However, in practical applications, on the one hand, due to the limited number of sensing nodes, the RSSI data collected is very scarce, and the estimated data obtained after spatial interpolation will deviate from the true data; on the other hand, some sensing nodes far away from the radiation source are severely disturbed by noise, and the data collected itself has a large error, thereby further reducing the accuracy of the interpolation estimation. In the case of low accuracy of the electromagnetic spectrum map, the point with the strongest electromagnetic signal strength cannot be accurately matched with the real position of the radiation source, and high-precision positioning cannot be achieved by using the electromagnetic spectrum map alone.

[0007] The above method has the following defects:

[0008] 1. The electromagnetic spectrum map constructed based on the traditional interpolation method has low accuracy, especially in the boundary region and the sparse region of sensing nodes;

[0009] 2. The method of positioning based on the maximum signal strength point of the electromagnetic spectrum map alone has a large error;

[0010] 3. There is no effective positioning accuracy optimization mechanism, and the optimal estimate cannot be selected from multiple candidate positions. SUMMARY

[0011] In order to solve the above technical problems in the background art, the present application provides a radiation source positioning method based on Gaussian process regression reconstruction of an electromagnetic spectrum map.

[0012] In order to achieve the above purpose, the present application adopts the following technical solutions:

[0013] A radiation source positioning method based on Gaussian process regression reconstruction of an electromagnetic spectrum map, the radiation source positioning method based on Gaussian process regression reconstruction of an electromagnetic spectrum map comprising the following steps:

[0014] 1) Data acquisition and preprocessing: randomly deploying sensing nodes in the target region, collecting the RSSI data of each node, and normalizing the data;

[0015] 2) Electromagnetic spectrum map construction: performing grid processing on the target region, and using Gaussian process regression or Kriging interpolation algorithm to estimate the RSSI value of the grid points without deploying sensing nodes, to construct a complete electromagnetic spectrum map;

[0016] 3) Radiation source position estimation: according to the RSSI value of each grid point in the electromagnetic spectrum map, the potential position set of the radiation source is obtained by gradually expanding the coverage area and calculating the centroid;

[0017] 4) Radiation source position determination: based on the distance relationship between the sensing nodes and the candidate positions, combining the log-distance path loss model of the electromagnetic signal, using the least squares method to fit, and selecting the position with the smallest fitting error as the final positioning result.

[0018] The specific implementation of the Gaussian process regression algorithm in step 2) is as follows:

[0019] Assume that the RSSI observation y(x) at any location x in space follows a Gaussian process prior:

[0020]

[0021] in It is a mean function. Covariance function, commonly used Kernel function:

[0022]

[0023] in For signal variance, This is the kernel width parameter.

[0024] For test points The mean and variance of its posterior distribution are as follows:

[0025]

[0026]

[0027] in for The kernel matrix of the training data, The kernel vectors for the test and training points. The kernel value of the test point. To observe the noise variance.

[0028] The specific steps for estimating the location of the radiation source in step 3) are as follows:

[0029] a) Based on the electromagnetic spectrum map, the area composed of grid points with signal strength higher than -90dBm is divided into key areas, and the total number of grid points in the key areas is N;

[0030] b) Set the initial value of parameter K, let K=1;

[0031] c) Sort the grid points in the key area in descending order of RSSI value, and select the first K grid points with larger RSSI values;

[0032] d) Determine if the loop termination condition K≥ is met. If the condition is met, the loop stops; otherwise, it continues.

[0033] e) Calculate the centroid coordinates of the region composed of K grid points, and record the centroid coordinates;

[0034] f) Update the K value, let , where ΔK is a preset step size parameter, return to step c).

[0035] The specific method for determining the location of the radiation source in step 4) is as follows:

[0036] Based on the logarithmic distance path loss model:

[0037]

[0038] in For received power, For transmission power, (d) represents the path loss at distance d. This is the path loss index. For reference distance.

[0039] For each candidate location and each sensing node, calculate the logarithm of the distance. The linear relationship with the RSSI value was fitted using the least squares method:

[0040]

[0041] Calculate the fitting error for each candidate position, and select the position with the smallest fitting error as the final localization result.

[0042] Preferably, the specific implementation of the Kriging interpolation algorithm in step 2) of this invention is as follows:

[0043] Let the estimated value of the interpolation point be... The data collected by m sensing nodes within its neighborhood are Where i = 1, 2, ..., m, then:

[0044]

[0045] in The weights are calculated using the mutability function:

[0046]

[0047] Weight Solve using the following system of equations:

[0048]

[0049]

[0050] in For Lagrange multipliers, The values ​​represent the mutation function values ​​between nodes.

[0051] Preferably, the kernel function parameters in the Gaussian process regression used in this invention are optimized by maximizing the marginal likelihood:

[0052]

[0053] in The parameters are the kernel function parameters, and the optimal parameters are obtained by solving the gradient optimization algorithm.

[0054] The advantages of this invention are:

[0055] 1. This invention uses the Gaussian process regression method to construct an electromagnetic spectrum map, which has better spatial integrity and interpolation accuracy compared with the traditional Kriging interpolation method, and can effectively solve the problem of incomplete interpolation in boundary regions.

[0056] 2. This invention proposes a radiation source location estimation algorithm based on the centroid iteration of the coverage area, which can effectively extract multiple candidate locations from the electromagnetic spectrum map and avoid the limitations of single-point positioning.

[0057] 3. This invention combines a logarithmic distance path loss model for location determination and utilizes the physical characteristics of signal propagation to optimize the positioning results, thus significantly improving positioning accuracy.

[0058] 4. The method of the present invention only requires RSSI data and does not require any prior information, and has the characteristics of low hardware cost, high deployment flexibility and strong environmental adaptability. Attached Figure Description

[0059] Figure 1 This is a flowchart of the method of the present invention;

[0060] Figure 2 It is a real electromagnetic spectrum map of the simulated target area;

[0061] Figure 3 The results are from a radiation source localization method based on the Kriging interpolation method to reconstruct the electromagnetic spectrum map.

[0062] Figure 4 The results are from a radiation source localization method based on Gaussian process regression to reconstruct the electromagnetic spectrum map;

[0063] Figure 5 This is a box plot comparing the errors in radiation source localization based on Gaussian process regression and electromagnetic spectrum map reconstruction based on Kriging interpolation. Detailed Implementation

[0064] This invention provides a radiation source localization method based on Gaussian process regression to reconstruct an electromagnetic spectrum map. The overall process is as follows: Figure 1 As shown, the specific implementation steps include the following:

[0065] 1) Data Acquisition and Preprocessing:

[0066] Several sensing nodes are deployed within the target area. Each node collects received radio signal strength (RSSI) data based on its own location, forming the raw observation dataset. To eliminate the dimensional differences in RSSI observations between different nodes, all observation data are normalized.

[0067]

[0068] The spatial location of each node is combined with the normalized RSSI observations to construct the training sample set for the Gaussian process regression model.

[0069] 2) Reconstructing the electromagnetic spectrum map based on Gaussian process regression:

[0070] Assuming any position in space RSSI observations at [location] It is an unknown function The output shows Gaussian noise.

[0071]

[0072] in, Let i be the position of the i-th node. To observe the noise variance.

[0073] Assumption Prior to a Gaussian process:

[0074]

[0075] in, It is the mean function (usually set to 0). It is the covariance function (kernel function), commonly using the RBF kernel:

[0076]

[0077] in, For signal variance, This is the kernel width parameter.

[0078] For the training set and test points It has a joint Gaussian distribution:

[0079]

[0080] in:

[0081]

[0082] yes The kernel matrix,

[0083]

[0084]

[0085] According to the conditional distribution property of the Gaussian distribution, the posterior distribution of the test point is as follows:

[0086]

[0087] The kernel function parameters in GPR (such as ) can be automatically optimized by maximizing the marginal likelihood (log-likelihood):

[0088]

[0089] For all grid points make predictions to obtain the mean field of the spatial RSSI distribution , which is the reconstructed spectrum map. <00​​​​​​​​​​​​​​​​​​​​​​​​​​​​​ΔK is a parameter that needs to be set in the algorithm to control the area of ​​radiation coverage expansion in each loop. Return to step c).

[0099] 4) Determining the location of the radiation source:

[0100] Based on the estimated locations in the potential location set of radiation sources and the relative relationship between the distance to sensing nodes and RSSI values, locations in the set are screened and determined. The theoretical model of electromagnetic signal propagation path loss shows that in radio channels, the average received signal strength gradually decreases with increasing distance. The most common empirical path loss model is the logarithmic distance model, and ideally, its path loss formula is:

[0101]

[0102] in This represents path loss (dB). The radiation source's emission power (dB). The received power (dB) at the sensing node. This is the path loss index. The distance (m) between the radiation source and the sensing node. Reference distance (m) The path loss (dB) is at the reference distance.

[0103] For ease of derivation, let the reference distance be 1m. Transforming the above equation, we get:

[0104]

[0105] It is a constant related to the power of the radiation source.

[0106]

[0107] Logarithm of the distance between the sensing node and the radiation source With the RSSI data collected There exists a linear function relationship. Using this relationship, the estimated location with the smallest positioning error can be selected. Based on the data collected by the sensing nodes and the estimated locations in the set, [the following is done]... and A linear function is fitted using the least squares method, and the fitting error corresponding to each estimated position is calculated. The estimated position that minimizes the fitting error has the smallest positioning error.

[0108] Repeating steps 1) to 4) allows us to estimate the location of any radiation source within the region, thereby obtaining the distribution of all radiation sources throughout the region and completing the radiation source localization based on the electromagnetic spectrum map.

[0109] Example:

[0110] Consider a 10km × 10km area with three stationary radiation sources operating at different frequencies: 1.0GHz, 1.1GHz, and 1.2GHz. The target area is gridded along both the x-axis and y-axis at 50m intervals. Sensing nodes are then randomly deployed within the area. The actual electromagnetic spectrum map is shown below. Figure 2 As shown.

[0111] The radiation source localization method based on Gaussian process regression to reconstruct the electromagnetic spectrum map is employed in this invention. Experimental results show that the radiation source localization method based on Gaussian process regression to reconstruct the electromagnetic spectrum map outperforms traditional Kriging interpolation in terms of spatial integrity, interpolation accuracy, and robustness. The radiation source localization method based on Kriging interpolation to reconstruct the electromagnetic spectrum map is as follows: Figure 3 As shown, the results of the radiation source localization method based on Gaussian process regression to reconstruct the electromagnetic spectrum map are as follows: Figure 4 As shown in the box plot, the errors in radiation source localization are compared between Gaussian process regression and Kriging interpolation-based electromagnetic spectrum map reconstruction. Figure 5 As shown, GPR can effectively overcome the shortcomings of Kriging interpolation in boundary and sparse regions, ensuring the spatial integrity and continuity of the spectrum map throughout the simulation area, and providing more reliable technical support for radiation source localization.

[0112] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for locating radiation sources based on Gaussian process regression to reconstruct an electromagnetic spectrum map, characterized in that, Includes the following steps: S1. Deploy sensing nodes within the target area to collect RSSI data and perform normalization preprocessing; S2. Construct an electromagnetic spectrum map based on the Gaussian process regression algorithm, use the RBF kernel function to model spatial correlation, optimize the kernel function parameters by maximizing the marginal likelihood, and perform RSSI prediction for all grid points. S3. Based on the electromagnetic spectrum map, gradually expand the coverage area and calculate the centroid coordinates to obtain the set of potential radiation source locations; S4. Combining the logarithmic distance path loss model, the least squares method is used to fit the linear relationship between the logarithm of the distance and RSSI, and the position with the smallest fitting error is selected as the final positioning result.

2. The radiation source localization method based on Gaussian process regression to reconstruct an electromagnetic spectrum map according to claim 1, characterized in that: The specific method of normalization preprocessing in step S1 is to process the raw RSSI data collected by each sensing node according to the formula: Normalization is performed to eliminate the dimensional differences between observations at different nodes, and the spatial location of each node is combined with the normalized RSSI observations to construct the training sample set for the Gaussian process regression model.

3. The radiation source localization method based on Gaussian process regression to reconstruct an electromagnetic spectrum map according to claim 1, characterized in that: In step S2, the Gaussian process regression algorithm assumes RSSI observations at any position x in the assumption space. Obeying Gaussian process prior ,in It is a mean function. Let be the covariance function, and the expression for the RBF kernel function is: ,in For signal variance, This is the kernel width parameter.

4. The radiation source localization method based on Gaussian process regression to reconstruct an electromagnetic spectrum map according to claim 1, characterized in that: The specific method for estimating the location of the radiation source in step S3 is to divide the area composed of grid points with signal strength higher than -90dBm in the electromagnetic spectrum map into key areas, set the initial value of parameter K to 1, sort the grid points in the key areas in descending order of RSSI value, select the first K grid points with larger RSSI values, calculate the centroid coordinates of the area composed of these K grid points, record the centroid coordinates and update the K value, repeat the above process until all grid points have been traversed to obtain the potential location set of the radiation source.

5. The radiation source localization method based on Gaussian process regression to reconstruct an electromagnetic spectrum map according to claim 1, characterized in that: The expression for the logarithmic distance path loss model in step S4 is as follows: After deformation, the result is Where C is a constant related to the power of the radiation source, calculated using the logarithm of the distance between the sensing node and the radiation source. With RSSI data Given a linear function relationship, the least squares method is used to fit each estimated position in the candidate position set, and the estimated position with the smallest fitting error is selected as the final positioning result.

6. The radiation source localization method based on Gaussian process regression to reconstruct an electromagnetic spectrum map according to claim 3, characterized in that: In the Gaussian process regression, the mean and variance of the posterior distribution of the test point x are respectively... and ,in The kernel matrix of the training data, The kernel vectors for the test and training points. The kernel value of the test point. To observe the noise variance.

7. The radiation source localization method based on Gaussian process regression to reconstruct an electromagnetic spectrum map according to claim 3, characterized in that: The specific method for optimizing the kernel function parameters by maximizing the edge likelihood is through optimizing the log-likelihood function. To automatically determine the signal variance in the RBF kernel function and kernel width parameter .

8. The radiation source localization method based on Gaussian process regression to reconstruct an electromagnetic spectrum map according to claim 4, characterized in that: The update method for parameter K in step S3 is as follows: ΔK is a preset step size parameter used to control the area of ​​radiation coverage expansion in each cycle, and the centroid calculation formula is the arithmetic mean of the coordinates of the selected grid points.

9. The radiation source localization method based on Gaussian process regression to reconstruct an electromagnetic spectrum map according to claim 5, characterized in that: The specific implementation of the least squares fitting method involves calculating the distance d between each candidate position and each sensing node, and establishing... Linear relationship with RSSI The fitting error is calculated, and the candidate location with the smallest fitting error is selected as the final location result of the radiation source.

10. The radiation source localization method based on Gaussian process regression to reconstruct an electromagnetic spectrum map according to claim 1, characterized in that: The target area is gridded according to a preset interval, and sensing nodes are randomly deployed in the target area. The number of nodes is determined according to the size of the area and the positioning accuracy requirements. Repeating steps S1 to S4 can achieve simultaneous positioning of multiple radiation sources in the area.

Images