Method and system for constructing high-precision electromagnetic spectrum map in terrain environment

Abstract

This invention relates to the field of radio technology, specifically disclosing a method and system for constructing a high-precision electromagnetic spectrum map of a terrain-undulating environment. The method includes: acquiring spectrum data within a region to be constructed, the spectrum data including signal strength and geographical location; combining the terrain undulation elevation information of the region to be constructed with the signal strength and matching it with observation points according to resolution to obtain the terrain undulation elevation information of the observation points; establishing a model for the terrain undulation elevation information of the observation points based on a Gaussian regression process, and optimizing the model using hyperparameters of a kernel function; and constructing a spectrum map of the region to be constructed using the monitored values ​​of the spectrum data within the region to be constructed as input, according to the posterior probability estimation formula of the Gaussian regression process.

Description

Technical Field

[0001] This invention relates to the field of radio technology, specifically to a method and system for constructing high-precision electromagnetic spectrum maps of terrain-undulating environments. Background Technology

[0002] With the booming development of emerging information technologies such as 5G, the Internet of Things, and "Internet Plus," an increasing number of frequency-consuming devices are being put into use, leading to unprecedented growth in spectrum resource demand across multiple sectors, including the national economy, social life, and national defense. Spectrum maps can depict spectrum data from multiple dimensions, including geographical location, frequency, time, and energy, integrating and presenting multi-dimensional electromagnetic spectrum spatial data. Furthermore, spectrum maps provide insights into the distribution of electromagnetic spectrum resources, laying the foundation for refined management and ultimately improving their utilization rate.

[0003] In real-world applications, topographical undulations cause radio wave propagation attenuation, resulting in spatial heterogeneity in electromagnetic spectrum maps. When the location of the radiation source is unknown, traditional construction methods include spatial interpolation, matrix completion, and compressed sensing. However, these methods typically ignore the influence of actual terrain, leading to low accuracy in spectrum map construction.

[0004] Deep learning methods can incorporate topographic maps during application, but they typically require a large pre-generated dataset, and datasets covering all electromagnetic propagation scenarios are prohibitively large. Furthermore, discrepancies between the theoretical propagation models used in the datasets and actual radio wave propagation can lead to generalization problems.

[0005] In summary, existing traditional methods cannot address the impact of terrain undulations on the accuracy of electromagnetic spectrum map construction. While deep learning can consider terrain effects, its practicality is limited, suffering from two major problems: the need for pre-built datasets and limitations in generalization. Therefore, there is a need to develop new methods for constructing high-precision electromagnetic spectrum maps for terrain-undulating environments. Summary of the Invention

[0006] To achieve the objectives of this invention, this application provides a method for constructing a high-precision electromagnetic spectrum map of a terrain-undulating environment, comprising:

[0007] Step S1: Obtain spectrum data within the area to be constructed, the spectrum data including: signal strength and geographical location;

[0008] Step S2: Combine the terrain undulation elevation information of the area to be constructed with the signal strength and match it with the observation point according to the resolution to obtain the terrain undulation elevation information of the observation point;

[0009] Step S3: Establish a model based on the terrain undulation and elevation information of the observation point using the Gaussian regression process, and optimize the model parameters using the hyperparameters of the kernel function;

[0010] Step S4: Based on the posterior probability estimation formula of the Gaussian regression process, use the monitoring values ​​of the spectral data in the region to be constructed as input to construct a spectral map of the region to be constructed.

[0011] In some specific embodiments, step S1 further includes: using a data center to aggregate the spectrum data, clean the data, and align the time of the sensors.

[0012] In some specific embodiments, based on the spectrum data at the current moment, it is determined whether the current electromagnetic environment has changed. If the electromagnetic environment has changed, the electromagnetic spectrum map is reconstructed.

[0013] In some specific embodiments, in step S3, the kernel function k T (x,x′) is determined according to the following formula:

[0014]

[0015] in, and These represent spatial correlation and topographic correlation, respectively; s and s' represent their two-dimensional spatial coordinates; H and H' represent their spatial digital elevation coordinates; σ f σ represents the overall kernel function magnitude. n Indicates the noise level, δ pq Denotes the Kronecker-delta function, k RQ (x, x′) is the kernel function of the rational quadratic kernel, α represents the smoothness parameter of the rational quadratic kernel, and σ RQ Let D represent the magnitude of the rational quadratic kernel, and let l represent the dimension of the input variable. d This represents the length scale of each variable to adjust the influence of each dimension, adapting to changes in data across different dimensions. d and x d' and represent the coordinates of data points x and x' in the d-th dimension, respectively.

[0016] In some specific embodiments, step S4 includes:

[0017] Step S41: Predict the power value of the point to be predicted within the region to be constructed based on the multivariate Gaussian distribution equation;

[0018] Step S42: Based on the conditional probability distribution of the power values, predict the mean power value of the point to be predicted using the posterior probability estimation formula, thereby constructing a spectrum map.

[0019] To achieve the same inventive objective, this application also provides a high-precision electromagnetic spectrum map construction system for terrain undulation environments, comprising:

[0020] Data acquisition module: used to acquire spectrum data within the area to be constructed, the spectrum data including signal strength and geographical location;

[0021] Information matching module: used to combine the terrain undulation elevation information of the area to be constructed with the signal strength and match it with the observation point according to the resolution to obtain the terrain undulation elevation information of the observation point;

[0022] Model building module: used to build a model based on the terrain undulation and elevation information of the observation points using the Gaussian regression process, and to optimize the model parameters using the hyperparameters of the kernel function;

[0023] Map building module: Used to build a spectral map of the region to be built by using the monitoring values ​​of the spectral data in the region to be built as input, based on the posterior probability estimation formula of the Gaussian regression process.

[0024] In some specific embodiments, the data acquisition module is also used to: aggregate the spectrum data, clean the data, and align the time of the sensors using a data center.

[0025] In some specific embodiments, based on the spectrum data at the current moment, it is determined whether the current electromagnetic environment has changed. If the electromagnetic environment has changed, the electromagnetic spectrum map is reconstructed.

[0026] In some specific embodiments, in the model building module, the kernel function k T (x,x′) is determined according to the following formula:

[0027]

[0028] in, and These represent spatial correlation and topographic correlation, respectively; s and s' represent their two-dimensional spatial coordinates; H and H' represent their spatial digital elevation coordinates; σ f σ represents the overall kernel function magnitude. n Indicates the noise level, δ pq Denotes the Kronecker-delta function, k RQ (x, x′) is the kernel function of the rational quadratic kernel, α represents the smoothness parameter of the rational quadratic kernel, and σ RQ Let D represent the magnitude of the rational quadratic kernel, and let l represent the dimension of the input variable. d This represents the length scale of each variable to adjust the influence of each dimension, adapting to changes in data across different dimensions. d and xd' and represent the coordinates of data points x and x' in the d-th dimension, respectively.

[0029] In some specific embodiments, the map building module is used to perform the following steps:

[0030] Step S41: Predict the power value of the point to be predicted within the region to be constructed based on the multivariate Gaussian distribution equation;

[0031] Step S42: Based on the conditional probability distribution of the power values, predict the mean power value of the point to be predicted using the posterior probability estimation formula, thereby constructing a spectrum map.

[0032] The beneficial effects of the above technical solution are as follows:

[0033] This invention, based on the Gaussian regression process and tailored to the characteristics of terrain-undulating environments, provides a method and system for constructing high-precision spectrum maps that incorporate terrain features. The invention designs a kernel function that incorporates digital elevation data into correlation calculations. This method effectively improves the accuracy of spectrum map construction under sparse sampling conditions, providing a new technical approach for electromagnetic spectrum management in terrain-undulating environments. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 A flowchart illustrating a method for constructing a high-precision electromagnetic spectrum map of a terrain-undulating environment, as provided in an embodiment of the present invention;

[0036] Figure 2 An architecture diagram of a method for constructing a high-precision electromagnetic spectrum map of a terrain undulation environment, provided as an embodiment of the present invention;

[0037] Figure 3 A comparison chart of the visualization effects of a method for constructing a high-precision electromagnetic spectrum map of a terrain undulation environment and other methods, provided as an embodiment of the present invention;

[0038] Figure 4 A performance comparison chart of a method for constructing a high-precision electromagnetic spectrum map of a terrain-undulating environment and other methods under different sampling rates and different numbers of radiation sources, provided as an embodiment of the present invention;

[0039] Figure 5This is a schematic diagram of a high-precision electromagnetic spectrum map construction system for terrain undulation environments, provided as an embodiment of the present invention. Detailed Implementation

[0040] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0041] Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar symbols denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0042] Example 1

[0043] One embodiment of the present invention provides a method for constructing a high-precision electromagnetic spectrum map of a terrain-undulating environment, referring to... Figure 1 As shown, it includes:

[0044] Step S1: Obtain spectrum data within the area to be constructed. The spectrum data includes signal strength and geographical location. The set of geographical location and signal strength is denoted as... In the formula x i ∈R 2 R represents two-dimensional spatial coordinates. i Represents position x i The power value at that location.

[0045] Specifically, the location x is obtained through interpolation using a regional fixed-resolution elevation map (DEM). i The corresponding elevation H i Then x i ={s,H} i , where s represents the two-dimensional geographic location coordinates and H represents the digital elevation coordinates of that location.

[0046] In a specific embodiment of the present invention, step S1 further includes: using a data center to perform data aggregation, data cleaning, and sensor time alignment on the spectrum data.

[0047] In one specific embodiment of the present invention, based on the spectrum data at the current moment, it is determined whether the current electromagnetic environment has changed. If the electromagnetic environment has changed, the electromagnetic spectrum map is reconstructed.

[0048] Step S2: Combine the terrain undulation elevation information of the area to be constructed with the signal strength and match it with the observation point according to the resolution to obtain the terrain undulation elevation information of the observation point.

[0049] Step S3: Establish a model based on the terrain undulation and elevation information of the observation point using the Gaussian regression process, and optimize the model parameters using the hyperparameters of the kernel function.

[0050] In one specific embodiment of the present invention, the relationship between the received power value R(x) at any position x is modeled as an implicit function f(x) superimposed with noise. The implicit function assumption conforms to the Gaussian process prior:

[0051] R(x) = f(x) + ε,

[0052] f(x)~GP(m(x),k(x,x′)),

[0053] Where m(x) represents the mean function of the expected power value at location x, and k(x,x′) represents the covariance function. The observed locations and power values ​​are represented as {X,R}, where X = [x1,x2,...,x′]. n ] T R = [R1, R2, ..., R n ] T The set of locations of points to be predicted in the construction of the spectrum map is represented as The set of power values ​​to be predicted is represented as Then the observed value R and the value to be predicted R * The joint distribution is denoted as:

[0054]

[0055] Where m(X) and m(X) * Let K(X,X)∈R represent the mean vector of the observed values ​​and the values ​​to be predicted. n×n K(X,X) represents the covariance matrix of the observed values. * )∈R n×m K(X) represents the covariance matrix between observed and predicted values. * ,X * )∈R m×m Let I represent the covariance matrix of the predicted values, and let I represent the identity matrix.

[0056] In this invention, a kernel function k is designed specifically for the spectral map construction problem and is adaptable to terrain undulation scenarios. T (x,x′):

[0057]

[0058] in, and σ represents spatial correlation and topographic correlation, respectively. s and s' represent their two-dimensional spatial coordinates, and H and H' represent their spatial digital elevation coordinates. f σ represents the overall kernel function magnitude. n Indicates the noise level, δ pq This represents the Kronecker-delta function. k RQ (x, x′) is and The specific computational form of the kernel function is the Rational Quadratic Kernel (RQ) kernel function. α represents the RQ kernel smoothness parameter, and σ... RQ This represents the kernel function magnitude of the RQ kernel. It is part of calculating the similarity between data points, where D represents the dimension of the input variable, l d This indicates the length scale of each variable. This item can adjust the influence of each dimension to adapt to changes in the data across different dimensions. d and x d' and represent the coordinates of data points x and x' in the d-th dimension, respectively.

[0059] To optimize this problem, K y Recorded as Based on the properties of Gaussian processes, the logarithmic marginal probability density is expressed as:

[0060]

[0061] This problem can be transformed into a nonnegativity function minimization problem:

[0062]

[0063] Its derivative is:

[0064]

[0065] This parameter optimization problem can be optimized using gradient descent-type optimization methods, including but not limited to gradient descent, LBFGS, and Adam methods. The hyperparameter θ includes {σ...} n ,σ f ,(σ RQ ,α,l d ) S ,(σ RQ ,α,l d ) DEM}

[0066] Step S4: Based on the posterior probability estimation formula of the Gaussian regression process, use the monitoring values ​​of the spectral data in the region to be constructed as input to construct a spectral map of the region to be constructed.

[0067] In a specific embodiment of the present invention, step S4 includes:

[0068] Step S41: Predict the power value of the point to be predicted within the region to be constructed based on the multivariate Gaussian distribution equation;

[0069] Step S42: Based on the conditional probability distribution of the power values, predict the mean power value of the point to be predicted using the posterior probability estimation formula, thereby constructing a spectrum map.

[0070] Based on the posterior probability estimation formula of the Gaussian regression process, the power value of the point to be predicted is predicted.

[0071]

[0072] Figure 2 This invention demonstrates the workflow of a high-precision electromagnetic spectrum map construction system for terrain-undulating environments. In the system design provided by this invention, ubiquitous non-dedicated user devices first collect and sense spectrum data, which is then aggregated in a data center. The data center then aggregates, cleans, and aligns the sensor data to the time of the sensors. Based on the current sensor data, it determines whether the current electromagnetic environment has changed, such as an increase or decrease in the number of radiation sources. If the electromagnetic environment has changed, it needs to be processed according to… Figure 1 The described S1-S4 algorithm flow constructs an electromagnetic spectrum map. Finally, the central control center issues corresponding control commands to users to support applications such as user spatial navigation and positioning, network resource optimization, and dynamic spectrum access.

[0073] The effects of the present invention will be further explained below with reference to simulation experiments.

[0074] The simulation experiments of this invention were conducted on a CPU i9-10850K and a GPU 3080Ti graphics card. During parameter optimization, the network was trained for 500 epochs, and the Adam optimization algorithm was selected as the optimizer with a learning rate of 0.05. A typical mountain scene of 1.2km x 1.2km was selected for simulation verification using the Longley-Rice model in Winprop simulation software at a resolution of 16m.

[0075] Figure 3This diagram presents a comparison of the visualization effects of the spectrum maps constructed using the method of this invention and other methods. The method of this invention is named GPRT. Other visualization comparisons include True Radio Map, Radial Basis Function Interpolation (RBF), Kernel Ridge Regression (KRR), Multikernel Learning, and Gaussian Process with Combined Kernel Functions (GPR-C). The three axes represent spatial two-dimensionality and topographic relief, respectively. The left-hand color bar represents the power distribution, and the right-hand color bar represents the error distribution of the base map. As can be seen in the diagram, the spatial error distribution of the GPRT method is smaller on the topographic relief side.

[0076] Figure 4 The graph shows a performance comparison between the method of this invention and other methods under different sampling rates and different numbers of radiation sources. Figure 4 The horizontal axis represents the sampling ratio, and the vertical axis represents the root mean square error of the reconstruction. Compared to several other methods, the method in this embodiment of the invention has the smallest root mean square error, indicating that the method of this invention has higher accuracy than existing methods. Therefore, the method proposed in this invention, based on sparse observations, can achieve high-precision construction of a spectrum map.

[0077] This invention, based on the Gaussian regression process and tailored to the characteristics of terrain-undulating environments, provides a method and system for constructing high-precision spectrum maps that incorporate terrain features. The invention designs a kernel function that incorporates digital elevation data into correlation calculations. This method effectively improves the accuracy of spectrum map construction under sparse sampling conditions, providing a new technical approach for electromagnetic spectrum management in terrain-undulating environments.

[0078] Example 2

[0079] One embodiment of the present invention provides a high-precision electromagnetic spectrum map construction system for terrain undulation environments, referring to... Figure 5 As shown, it includes:

[0080] Data acquisition module 10: used to acquire spectrum data within the area to be constructed, the spectrum data including signal strength and geographical location;

[0081] Information matching module 20: used to combine the terrain undulation elevation information of the area to be constructed with the signal strength and match it with the observation point according to the resolution to obtain the terrain undulation elevation information of the observation point;

[0082] Model building module 30: used to build a model based on the terrain undulation and elevation information of the observation point based on the Gaussian regression process, and to optimize the model parameters using the hyperparameters of the kernel function;

[0083] Map building module 40: Used to build a spectral map of the region to be built by using the monitoring values ​​of the spectral data in the region to be built as input, based on the posterior probability estimation formula of the Gaussian regression process.

[0084] In one specific embodiment of the present invention, the data acquisition module is further configured to: use a data center to perform data aggregation, data cleaning, and sensor time alignment on the spectrum data.

[0085] In one specific embodiment of the present invention, based on the spectrum data at the current moment, it is determined whether the current electromagnetic environment has changed. If the electromagnetic environment has changed, the electromagnetic spectrum map is reconstructed.

[0086] In a specific embodiment of the present invention, in the model building module, the kernel function k T (x,x′) is determined according to the following formula:

[0087]

[0088] in, and σ represents spatial correlation and topographic correlation, respectively. s and s' represent their two-dimensional spatial coordinates, and H and H' represent their spatial digital elevation coordinates. f σ represents the overall kernel function magnitude. n Indicates the noise level, δ pq This represents the Kronecker-delta function. k RQ (x, x′) is and The specific computational form of the kernel function is the Rational Quadratic Kernel (RQ) kernel function. α represents the RQ kernel smoothness parameter, and σ... RQ This represents the kernel function magnitude of the RQ kernel. It is part of calculating the similarity between data points, where D represents the dimension of the input variable, l d This indicates the length scale of each variable. This item can adjust the influence of each dimension to adapt to changes in the data across different dimensions. d and x d' and represent the coordinates of data points x and x' in the d-th dimension, respectively.

[0089] In one specific embodiment of the present invention, the map building module is used to perform the following steps:

[0090] Step S41: Predict the power value of the point to be predicted within the region to be constructed based on the multivariate Gaussian distribution equation;

[0091] Step S42: Based on the conditional probability distribution of the power values, predict the mean power value of the point to be predicted using the posterior probability estimation formula, thereby constructing a spectrum map.

[0092] The system proposed in this application can be implemented using hardware including a memory and a processor, wherein the processor stores computer instructions for implementing the spectrum map construction method of mountain environment combined with terrain proposed in this invention, and when the computer instructions are executed by the processor, the above method can be implemented.

[0093] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

[0094] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The embodiments of the present invention are described with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing terminal equipment to cause a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1The steps of the functions specified in one or more boxes. Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the invention. Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0095] The methods and apparatus provided by the present invention have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

[0096] In the description of this specification, references to terms such as "an embodiment," "some embodiments," "example," "specific example," or "a specific embodiment" or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for constructing a high-precision electromagnetic spectrum map of a terrain-undulating environment, characterized in that, include: Step S1: Obtain spectrum data within the area to be constructed, the spectrum data including: signal strength and geographical location; Step S2: Combine the terrain undulation elevation information of the area to be constructed with the signal strength and match it with the observation point according to the resolution to obtain the terrain undulation elevation information of the observation point; Step S3: Establish a model based on the terrain undulation and elevation information of the observation point using the Gaussian regression process, and optimize the model parameters using the hyperparameters of the kernel function; Step S4: Based on the posterior probability estimation formula of the Gaussian regression process, use the monitoring values ​​of the spectral data in the region to be constructed as input to construct a spectral map of the region to be constructed. In step S3, the kernel function Determined according to the following formula: in, and These represent spatial correlation and topographic correlation, respectively. s and s’ Represents the two-dimensional spatial coordinates of both. H and H’ This represents the spatial digital elevation coordinates of both. This represents the overall kernel function magnitude. Indicates the noise level. This represents the Kronecker-delta function. The kernel function is a rational quadratic kernel. This represents the rational quadratic kernel smoothness parameter. This represents the magnitude of the kernel function of a rational quadratic kernel. D Indicates the dimension of the input variable. This indicates the length scale of each variable, allowing adjustment of the influence of each dimension to accommodate changes in data across different dimensions. and These represent data points x and x' at the th, respectively. d Dimensional coordinates.

2. The method for constructing a high-precision electromagnetic spectrum map of a terrain-undulating environment according to claim 1, characterized in that, Step S1 also includes: using a data center to aggregate the spectrum data, clean the data, and align the sensor time.

3. The method for constructing a high-precision electromagnetic spectrum map of a terrain-undulating environment according to claim 2, characterized in that, Based on the current spectrum data, determine whether the current electromagnetic environment has changed. If the electromagnetic environment has changed, reconstruct the electromagnetic spectrum map.

4. The method for constructing a high-precision electromagnetic spectrum map of a terrain-undulating environment according to claim 1, characterized in that, Step S4 includes: Step S41: Predict the power value of the point to be predicted within the region to be constructed based on the multivariate Gaussian distribution equation; Step S42: Based on the conditional probability distribution of the power values, predict the mean power value of the point to be predicted using the posterior probability estimation formula, thereby constructing a spectrum map.

5. A high-precision electromagnetic spectrum map construction system for terrain undulation environments, characterized in that, include: Data acquisition module: used to acquire spectrum data within the area to be constructed, the spectrum data including signal strength and geographical location; Information matching module: used to combine the terrain undulation elevation information of the area to be constructed with the signal strength and match it with the observation point according to the resolution to obtain the terrain undulation elevation information of the observation point; Model building module: used to build a model based on the terrain undulation and elevation information of the observation points using the Gaussian regression process, and to optimize the model parameters using the hyperparameters of the kernel function; Map building module: Used to build a spectral map of the region to be built by using the monitoring values ​​of the spectral data in the region to be built as input, based on the posterior probability estimation formula of the Gaussian regression process. In the model building module, the kernel function Determined according to the following formula: in, and These represent spatial correlation and topographic correlation, respectively. s and s’ Represents the two-dimensional spatial coordinates of both. H and H’ This represents the spatial digital elevation coordinates of both. This represents the overall kernel function magnitude. Indicates the noise level. This represents the Kronecker-delta function. The kernel function is a rational quadratic kernel. This represents the rational quadratic kernel smoothness parameter. This represents the magnitude of the kernel function of a rational quadratic kernel. D Indicates the dimension of the input variable. This indicates the length scale of each variable, allowing adjustment of the influence of each dimension to accommodate changes in data across different dimensions. and These represent data points x and x' at the th, respectively. d Dimensional coordinates.

6. The high-precision electromagnetic spectrum map construction system for terrain undulation environments according to claim 5, characterized in that, The data acquisition module is also used to: aggregate the spectrum data, clean the data, and align the sensor time using the data center.

7. The high-precision electromagnetic spectrum map construction system for terrain undulation environments according to claim 6, characterized in that, Based on the current spectrum data, determine whether the current electromagnetic environment has changed. If the electromagnetic environment has changed, reconstruct the electromagnetic spectrum map.

8. The high-precision electromagnetic spectrum map construction system for terrain undulation environments according to claim 5, characterized in that, The map building module is used to perform the following steps: Step S41: Predict the power value of the point to be predicted within the region to be constructed based on the multivariate Gaussian distribution equation; Step S42: Based on the conditional probability distribution of the power values, predict the mean power value of the point to be predicted using the posterior probability estimation formula, thereby constructing a spectrum map.

Images