Spectrum map construction method combining spectrum surveying and mapping and data completion

Abstract

The invention discloses a spectrum map construction method combining spectrum surveying and mapping and data completion, which is characterized in that a Gaussian process is introduced to carry out combined modeling on a spectrum space field, the problem of splitting of the whole surveying and mapping process and the whole data completion process in the prior art is solved, and collaborative optimization of the surveying and mapping process and the data completion process is realized; then, a sampling value evaluation index is constructed by taking Gaussian process prediction uncertainty as a core, and monitoring equipment is guided to carry out adaptive sampling oriented to a non-cooperative signal source coverage area, so that data redundancy caused by blind sampling is avoided, and the data utilization rate is improved; and finally, on the basis of an online model updating mechanism of an expanded data set, enabling the complemented model to continuously reflect the latest environment cognition and reversely guide the subsequent sampling decision, and finally, remarkably improving the precision, stability and convergence efficiency of spectrum map construction under the condition of relatively low sampling cost.

Description

Technical Field

[0001] This invention relates to the field of spectrum map construction technology, and specifically to a spectrum map construction method that combines spectrum mapping and data completion. Background Technology

[0002] In recent years, with the rapid development of 5G communication technology, the Internet of Things, smart cities and "Internet+" and other emerging technologies, the demand for spectrum resources has exploded, involving multiple areas of the national economy and social life. At the same time, the existing extensive spectrum allocation mechanism can no longer meet the ever-increasing demand for spectrum, leading to increasingly prominent spectrum resource contradictions. It is urgent to achieve the rational allocation and efficient utilization of spectrum resources through refined management methods.

[0003] Electromagnetic spectrum mapping, as an important technical means for multidimensional characterization of the electromagnetic environment, can quantitatively describe and visualize the spatial distribution of electromagnetic energy and spectrum resources from multiple dimensions such as frequency, spatial location, and field strength, combined with geographic information systems. By constructing high-precision spectrum maps, we can not only comprehensively grasp the distribution status of spectrum resources and provide data support for spectrum monitoring, interference analysis, and resource scheduling, but also play an important role in alleviating spectrum resource shortages and improving spectrum utilization efficiency.

[0004] The existing technology is as follows: CN202410446883 discloses a method for spectrum mapping in complex urban environments. This method starts with 3D electromagnetic propagation modeling, discretizing the monitoring area into a voxel grid and constructing a propagation dictionary. It determines the number and spatial distribution of sampling points that meet reconstruction requirements through compressed sensing and eigenvalue threshold analysis, and further employs a nearest neighbor strategy to plan UAV sampling trajectories for data acquisition. Based on this, sparse electromagnetic target signals are first recovered, and then Gaussian processes are used to model and correct shadow fading, thereby constructing a 3D spectrum map. This scheme, by combining compressed sensing theory and propagation mechanism modeling, improves mapping accuracy in complex environments to some extent. However, the sampling location and quantity are mainly determined once based on offline thresholds and dictionary analysis. The sampling process is difficult to dynamically adjust according to the model's cognitive state, and the completion process is mainly used as a post-processing correction method, failing to guide sampling decisions in reverse. This results in a relatively disconnect between the mapping and completion stages, making it difficult to simultaneously achieve data utilization efficiency and spectrum map reconstruction accuracy within limited sampling costs.

[0005] CN202411922547 discloses a method for constructing a spectrum coverage map based on a preset acquisition path and gridded modeling. This method delineates the acquisition range according to base station parameters, pre-plans the acquisition path, guides the monitoring equipment to traverse and collect spectrum data along a predetermined trajectory, and fills in unmeasured areas through gridded processing and a distance-weighted / propagation model, thereby constructing a spectrum coverage map. This scheme has a clear process and is simple to implement, enabling large-scale spectrum mapping with relatively low system complexity, and has certain advantages in engineering implementation and computational overhead. However, from the perspective of sampling strategy, the sampling location of this method mainly relies on traversal acquisition along a preset path. The sampling process focuses on geometric coverage rather than information value assessment, making it difficult to differentiate and dynamically adjust based on the contribution of different regions to spectrum map reconstruction. In practical applications, redundant sampling is easily generated in areas with low information gain, while insufficient attention is paid to high-value areas, resulting in limited overall data utilization and low sampling efficiency. Under the constraint of limited sampling costs, it is difficult to further improve the performance of spectrum map construction.

[0006] The disadvantages of existing technology are as follows: 1. The surveying and mapping and data completion processes are disconnected, lacking joint modeling and collaborative optimization mechanisms, making it difficult to simultaneously balance surveying efficiency and spectrum map reconstruction accuracy under the constraint of limited sampling costs; 2. In the spectrum mapping process, the existing sampling strategies mainly focus on spatial geometric coverage and lack information value-oriented design, which easily leads to redundant sampling, resulting in low data utilization and low sampling efficiency. 3. Existing data completion methods still lack adaptability and feedback capabilities, making it difficult to support collaborative mapping needs. Summary of the Invention

[0007] The purpose of this invention is to address the aforementioned problems by providing a method for constructing a spectrum map that combines spectrum mapping and data completion. This method overcomes the disconnect between mapping and completion processes in existing technologies by introducing a Gaussian process to jointly model the spectrum space field, achieving synergistic optimization between the two. Furthermore, it constructs a sampling value evaluation index based on the uncertainty of Gaussian process prediction, guiding monitoring equipment to conduct adaptive sampling in areas covered by non-cooperative signal sources, thus avoiding data redundancy caused by blind sampling and improving data utilization. Simultaneously, through an online model update mechanism based on an expanded dataset, the completion model can continuously reflect the latest environmental understanding and guide subsequent sampling decisions, ultimately significantly improving the accuracy, stability, and convergence efficiency of spectrum map construction under relatively low sampling costs.

[0008] The technical solution adopted in this invention is as follows: A method for constructing a spectrum map by combining spectrum mapping and data completion, the method comprising: Acquire the initial sampling dataset in the spectral space field; The Gaussian process is used to model the spectral space field to obtain the predicted mean and predicted variance of the signal strength at the current sampling point; Based on the obtained predicted mean and predicted variance, a sampling value evaluation index function is constructed to obtain the sampling position of the next target point; Plan the sampling path from the current location to the next target location, and collect spectrum data sequentially along the planned path until the target location is reached, and obtain the new sampling data sample set; The newly acquired sample data set is incorporated into the initial sample dataset to update the spectral space model modeled by the Gaussian process; The process of repeatedly modeling and updating the model is iterated to output a spectrum map.

[0009] Furthermore, the acquisition of the initial sampling dataset specifically includes: Let the continuous region of the three-dimensional spectrum space be At several sampling locations The signal strength measured at is The real electromagnetic radiation field is denoted as Collect N samples to form the initial dataset As shown in the following formula: (1) In the formula, To measure noise, .

[0010] Furthermore, the modeling specifically involves: unknown electromagnetic radiation field Modeled as a Gaussian process, as follows: (2) In the formula, It is the prior mean function. The covariance kernel function; The covariance kernel function includes a composite kernel function of a shadow fading correlation term and a local smoothing term, let... The composite covariance kernel function is specifically expressed as follows: (3) Based on the initial dataset By maximizing the log-marginal likelihood for the hyperparameters of the corresponding covariance kernel function and the noise variance Estimation is performed to complete the initialization of the Gaussian process regression model. Then, it is assumed that the existing expanded dataset from round t is collected. ,in Then, after the t-th round of data collection, for any position to be predicted... The predicted mean is as follows: (4) The prediction variance is as follows: (5).

[0011] Furthermore, the evaluation index includes a confidence upper bound term. Spatial distance coverage terms associated with the set of sampled points The evaluation function is as follows: (6) In the formula, Weighting for space exploration; Among them, the upper bound of confidence level As shown in the following formula: (7) In the formula, The normalized expected value of the forecast. The normalized standard deviation of the forecast. Confidence coefficient; Space exploration weight As shown in the following formula: (8) In the formula, This represents the volume of the region with high uncertainty at the initial stage of the model. The volume of the region with high uncertainty at the t-th iteration of the model is given by the following formula: (9) (10) In the formula, To predict the standard deviation The value of the p-quantile in the middle.

[0012] Furthermore, obtaining the sampling location of the next target point specifically includes adopting a neighborhood consistency sampling point selection strategy, that is, selecting the point with the highest average neighborhood score as the high-value target for the next sampling. : Define the neighborhood set of position z , As shown in the following formula: (11) In the formula, The neighborhood radius; Calculate the neighborhood average score of each point within the region, and select the point with the highest neighborhood average score as the target point for the next data collection. As shown in the following formula: (12).

[0013] Furthermore, the path planning specifically includes: Define the monitoring device as a discrete network: Set the movement step size of the monitoring device to The reachable discrete network point set is , Let X be the sequence of points for the sampling path to be planned, as shown in the following formula: (13) Each edge on the sampling path is recorded as an undirected line segment. The set of edges that history has traversed is as follows: (14) The cost function is defined as follows: (15) In the formula, For the information benefits of the path, This is the path loss term. For corner smoothing, Starting direction penalty items, among which... As shown in the following formula: (16) Path loss term As shown in the following formula: (17) Corner smoothing term As shown in the following formula: (18) Starting direction penalty As shown in the following formula: (19) In the formula, The direction at the end of the previous segment; In summary, the path planning process can be modeled as an optimization problem as shown in the following equation: (20) In the formula, For safety distance constraints, The maximum scaling factor allowed for path length relative to the straight-line distance between the start and end points. This is for determining the case where the projection intervals are collinear and overlap. Solve the optimization problem to obtain the sampling path from the current position to the next target position.

[0014] Furthermore, the update process is as follows: After the path exploration in round t is completed, the newly added sample data set is obtained. The newly added sample data set Incorporate historical datasets Forming an expanded dataset ; Use augmented datasets Update the hyperparameters of the composite covariance kernel function The solution is obtained by maximizing the log-marginal likelihood (MLE), as shown in the following equation: (twenty one) In the formula: (twenty two) Solve These parameters constitute the updated Gaussian process model parameters and are used as the model parameters for calculating the prediction mean and prediction variance in the (t+1)th round.

[0015] Furthermore, the iterative process specifically includes: When the global average uncertainty corresponding to the prediction variance Below the preset threshold When sampling resources are used up to the preset budget, the sampling process is terminated and the final spectrum map is output.

[0016] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: The method of this invention realizes joint modeling and closed-loop collaborative optimization of the spectrum mapping and data completion processes, significantly improving the overall construction efficiency and effect. Existing technologies mostly adopt a serial processing mode of sampling first and then completion. The completion process is mainly used as a post-processing correction means, which is difficult to guide the sampling decision in reverse, resulting in the separation of the mapping and completion stages. This invention introduces a Gaussian process to uniformly model the spectrum space field and updates the model online based on the expanded dataset after each round of sampling. This makes the sampling decision always dependent on the current model's perception of the environment, forming a closed-loop iterative process of modeling-sampling-updating-re-sampling. Thus, under limited sampling conditions, it continuously approximates the real electromagnetic environment and realizes the collaborative optimization of mapping and completion.

[0017] The method of this invention uses adaptive sampling driven by uncertainty to effectively improve the sampling targeting and data utilization. It uses Gaussian process prediction variance to characterize the uncertainty level of different regions and uses this as the core to evaluate the information value of each candidate sampling location. This guides the monitoring equipment to prioritize sampling of key areas that contribute more to the reconstruction, avoiding redundant measurements in areas with low information value. Thus, while ensuring the reconstruction accuracy, it improves the utilization rate of sampling data and reduces the overall measurement cost.

[0018] Compared to random sampling and coverage sampling strategies that emphasize spatial geometric coverage, the method of this invention exhibits superior reconstruction accuracy and convergence performance under low sampling rate conditions. Experimental results show that, within a sampling rate range of 7.25% to 49.75%, compared to existing coverage sampling or random sampling methods, the method of this invention reaches a lower error level earlier in terms of the root mean square error (RMSE) and mean absolute error (MAE) of the spectrum map construction results, demonstrating superior convergence performance. Among these, the relative advantage of the method of this invention is particularly significant under low sampling rate conditions, with the maximum relative reduction in RMSE and MAE reaching 63.02% and 66.38%, respectively. Attached Figure Description

[0019] Figure 1 This is a flowchart of a spectrum map construction method combining spectrum mapping and data completion according to the present invention; Figure 2 This is a flowchart of the process of constructing a scoring function and selecting target points in the method of the present invention; Figure 3 This is a graph showing the trend of root mean square error (RMSE) as a function of the number of sampling points under different sampling rates during the implementation of the method of the present invention. Figure 4 This is a graph showing the trend of the mean absolute error (MAE) with the number of sampling points under different sampling rates during the implementation of the method of the present invention. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings.

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0022] Example This embodiment provides a method for constructing a spectrum map by combining spectrum mapping and data completion, such as... Figure 1 As shown, please follow these steps: Obtaining the initial sampling dataset: Assume a continuous region in three-dimensional space There are radiation sources of unknown number and location, and monitoring equipment is used at several sampling locations. The signal strength measured at is The real electromagnetic radiation field is denoted as Collect N samples to form the initial dataset As shown in the following formula: (1) In the formula, To measure noise, Because signal strength distribution varies at different altitudes, in practical applications, monitoring terminal equipment is usually installed at a fixed altitude. Sampling is performed to simplify the problem to two-dimensional field modeling. .

[0023] Modeling the spectral space field using Gaussian processes: unknown electromagnetic radiation field Modeled as a Gaussian process: (2) In the formula, It is the prior mean function. This is the covariance kernel function, used to characterize spatial correlation; Among them, the covariance kernel function is defined, and let The composite covariance kernel function is expressed as follows: (3) The first term in the formula is the Gudmundson shadow kernel, which is used to characterize the large-scale shadow fading effect caused by factors such as terrain and building obstruction during electromagnetic propagation, reflecting the spatial correlation characteristics of signal strength; the second term is the Matérn (v=5 / 2) kernel, which is used to describe the smooth variation characteristics of signal strength at small and medium scales, thereby enhancing the model's ability to express local changes; the above kernel functions are superimposed to comprehensively characterize the correlation structure of signal strength at different spatial scales.

[0024] Based on the initial dataset By maximizing the log-marginal likelihood, the kernel function hyperparameters and noise variance are affected. Estimate and complete the initialization of the Gaussian process regression model.

[0025] In the initial stage, due to insufficient prior knowledge of the monitoring area, the model's predicted mean has not yet formed obvious spatial structure characteristics, and the corresponding predicted variance is generally high across the entire domain. If a path planning strategy with a limited field of view is adopted based solely on local information gain, it is easy for the monitoring equipment to repeatedly sample in local high uncertainty areas, thereby weakening the effective acquisition of global information and affecting the model's overall exploration capability and convergence efficiency.

[0026] To balance global exploration capabilities with the computational feasibility of path planning, this embodiment models the sampling process as a two-stage optimization problem: in the first stage, a high-value target point is selected globally; in the second stage, the path planning process leading to the target point is modeled as an information perception optimization problem, maximizing the accumulated information gains along the way while satisfying motion constraints. By decoupling the target selection and path generation processes, the efficiency of path planning and the feasibility of the algorithm are improved while ensuring the globality of exploration.

[0027] Calculate the expected value and prediction variance of the signal strength. Using an initialized or updated Gaussian process regression model, predict the expected value and variance of signal strength at each location in the region; assume that an expanded dataset is available in round t. ,in Then, after the t-th round of exploration, for any position to be predicted The predicted mean is as follows: (4) The prediction variance is as follows: (5) In the formula, It can be used to measure the model's response to the expected value. The degree of uncertainty.

[0028] Selection of the next target point: The key to selecting target points in the first stage lies in establishing a scoring index that can quantify the sampling value of each location in space, used to determine the target points for the next movement of the monitoring equipment. To balance spatial coverage and model-driven information gain during the sampling process, this embodiment constructs a composite scoring function to evaluate the comprehensive value of candidate sampling points; such as... Figure 2 As shown, it specifically includes: Establish evaluation indicators In Bayesian models, commonly used evaluation metrics include Probability of Improvement (PI), Expectation Improvement (EI), Entropy, and Upper Confidence Bound (UCB). In this embodiment, it is necessary to actively explore regions with high uncertainty; therefore, the upper confidence bound is chosen as a sub-item of the scoring metric. The upper confidence bound (UCB) effectively balances the relationship between "utilizing" (going to areas with strong known signals) and "exploring" (going to areas with high uncertainty), as shown in the following equation: (7) In the formula, The normalized expected value of the forecast. The normalized standard deviation of the forecast. The confidence coefficient is used to balance the relative weights of the predicted mean and the uncertainty term; a larger one... This will strengthen the exploration of regions with high uncertainty, while smaller ones The focus is on utilizing regions with high predicted values; in this embodiment, It is set to an adaptive parameter that gradually decreases as the global uncertainty of the model decreases, so as to achieve a gradual transition of the sampling strategy from exploration to exploitation.

[0029] To improve overall spatial coverage efficiency and avoid over-concentration of sampling in local areas, and considering that Gaussian processes are used far from the current dataset... The location of the dataset typically has higher prediction uncertainty; when the upper bound of the confidence level (UCB) is the same, the distance from the current dataset should be assigned. Further locations have higher exploration priority; therefore, this embodiment introduces an evaluation item based on frontal distance coverage. Used to characterize candidate positions Relative to the current sample set The spatial coverage value is as follows: (twenty three) In the formula, The set of coordinates of each location in space from the sampled points The minimum Euclidean distance; A larger value indicates that the location is spatially farther away from the sampled area, has higher geometric novelty, and helps guide monitoring equipment to expand into uncovered areas.

[0030] To achieve an adaptive transition of the sampling strategy from "spatial coverage expansion exploration" to "model-driven fine sampling", spatial exploration weights are introduced. Used to dynamically weigh the frontier distance coverage term against the UCB term; the value range is... As shown in the following formula: (8) In the formula, This represents the volume of the region with high uncertainty at the initial stage of the model. This represents the volume of the region with high uncertainty at the t-th iteration of the model; it can be represented by... The maturity level of the model is measured as follows: (9) (10) In the formula, To predict the standard deviation The value of the p-quantile in the middle. The smaller the value, the better the model's understanding of the overall region, in which case the spatial exploration effort can be reduced; conversely, spatial exploration should be emphasized during the sampling process.

[0031] Combining the above two types of sub-scoring items, the final scoring function is constructed as follows: (6) In the formula, For the normalized frontier distance term, the scoring function adopts a convex combination form, adaptively balancing spatial frontier exploration and model-driven sampling; when the model is not yet mature, A larger value indicates that the scoring function is more biased towards the leading edge distance term, encouraging monitoring equipment to prioritize expanding the sampling coverage and reducing sampling redundancy in local areas; as the model matures, As the value decreases, the scoring function gradually shifts towards... To guide monitoring equipment to perform fine sampling in high-value or high-uncertainty areas, dynamic adaptive weights are introduced. The exploration and utilization of balanced space has clear physical significance and engineering necessity.

[0032] Target point selection: After establishing the scoring function, a greedy selection method is used when choosing sampling points. The largest point, but due to the single point Since the values ​​are easily affected by noise and calculation errors, this embodiment adopts a neighborhood consistency sampling point selection strategy, that is, selecting the point with the highest average neighborhood score as the high-value target for the next sampling. The details are as follows: Define the neighborhood set of position z , : (11) In the formula, The neighborhood radius defines the range of the neighborhood of position z.

[0033] Calculate the neighborhood average score of each point within the region, and select the point with the highest neighborhood average score as the target point for the next data collection. : (12) Path planning: At the established target point Then, from the current location of the monitoring equipment arrive Finding the optimal flyable path is a problem that can be modeled as an optimization problem, specifically including: Define a discrete network reachable by the monitoring device: Set the movement step size of the monitoring device to 1. The reachable discrete network point set is , It is the entire observation area A subset of, i.e. Let X be the sequence of points for the sampling path to be planned. (13) Each edge on the sampling path is recorded as an undirected line segment. The set of edges that history has traversed is as follows: (14) Define the cost function: The overall goal of optimization is to minimize the cost function, as shown below: (15) In the formula, For the information benefits of the path, This is the path loss term. For corner smoothing, Starting direction penalty item, As shown in the following formula: (16) In spatial location Compare Higher elevations are more valuable and worth the resources to collect, even if it means taking detours or detours. In low-value areas, the model automatically considers that the location to be of little value and not worth taking a detour to collect data; this approach can maximize information gains while saving resources.

[0034] Path loss term As shown in the following formula: (17) Corner smoothing term As shown in the following formula: (18) Starting direction penalty As shown in the following formula: (19) In the formula, This is the direction of the end of the previous segment (unit vector).

[0035] Modeling the optimization problem: The path planning process is modeled as the following optimization problem: (20) In the formula, This indicates a safe distance constraint, used to restrict monitoring equipment from avoiding no-fly zones and obstacles during path exploration; This represents the maximum scaling factor that allows the path length to be scaled relative to the straight-line distance between the start and end points. This indicates the determination of the "collinear and overlapping projection intervals" situation, which is used to constrain the sampling device from repeatedly traversing the already visited path segment.

[0036] By solving the above optimization problem, the optimal path from the current starting point to the target point can be obtained. Spectral data is then collected sequentially along this planned path until the target location is reached. This yields a new data sample set. .

[0037] Update the Gaussian regression model: Incremental sampling and dataset expansion: After t rounds of path exploration, a new sample set is obtained. Incorporate it into the historical dataset Forming an expanded dataset , As shown in the following formula: (twenty four) In the formula, Let be the number of newly sampled samples in round t of exploration. Then the updated expanded dataset is: (25) This expanded dataset ,in ; used to reflect the latest observational information of the current electromagnetic environment; let , indicating up to the The total number of cumulative samples in each round.

[0038] Update the hyperparameters of the covariance kernel function: Let nuclear matrix Then the observed covariance is: (26) With new dataset Update hyperparameters Solve using Maximum Log Marginal Likelihood (MLE): (twenty one) in: (twenty two) Solve These parameters constitute the updated Gaussian process model parameters and are used as the model parameters for calculating the prediction mean and prediction variance in the (t+1)th round.

[0039] Closed-loop iteration and frequency domain map output: Repeat the modeling to model update process to establish a closed-loop iterative process of modeling-sampling-update, until any of the following termination conditions are met: (1) Global average uncertainty Less than the threshold .

[0040] (2) The sampling resources have reached the preset budget.

[0041] Verification process: like Figure 3 and Figure 4As shown, within a sampling rate range of 7.25% to 49.75%, compared to existing coverage sampling or random sampling methods, the method of this invention can reach a smaller error level earlier in terms of the root mean square error (RMSE) and mean absolute error (MAE) of the spectrum map construction results, demonstrating superior convergence performance. In particular, under low sampling rate conditions, the relative advantage of the method of this invention is especially significant, with the maximum relative reduction in RMSE and MAE reaching 63.02% and 66.38%, respectively.

[0042] This article uses specific embodiments to illustrate the principles and implementation methods of the present invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of the present invention. It should be noted that those skilled in the art can make several improvements and modifications to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A method for constructing a spectrum map by combining spectrum mapping and data completion, characterized in that, The method includes: Acquire the initial sampling dataset in the spectral space field; The Gaussian process is used to model the spectral space field to obtain the predicted mean and predicted variance of the signal strength at the current sampling point; Based on the obtained predicted mean and predicted variance, a sampling value evaluation index function is constructed to obtain the sampling position of the next target point; Plan the sampling path from the current location to the next target location, and collect spectrum data sequentially along the planned path until the target location is reached, and obtain the new sampling data sample set; The newly acquired sample data set is incorporated into the initial sample dataset to update the spectral space model modeled by the Gaussian process; The process of repeatedly modeling and updating the model is iterated to output a spectrum map.

2. The method for constructing a spectrum map by combining spectrum mapping and data completion according to claim 1, characterized in that, The acquisition of the initial sampling dataset specifically includes: Let the continuous region of the three-dimensional spectrum space be At several sampling locations The signal strength measured at is The real electromagnetic radiation field is denoted as Collect N samples to form the initial dataset As shown in the following formula: （1） In the formula, To measure noise, .

3. The method for constructing a spectrum map by combining spectrum mapping and data completion according to claim 2, characterized in that, The modeling specifically refers to: unknown electromagnetic radiation field Modeled as a Gaussian process, as follows: （2） In the formula, It is the prior mean function. The covariance kernel function; The covariance kernel function includes a composite kernel function of a shadow fading correlation term and a local smoothing term, let... The composite covariance kernel function is specifically expressed as follows: （3） Based on the initial dataset By maximizing the log-marginal likelihood for the hyperparameters of the corresponding covariance kernel function and the noise variance Estimation is performed to complete the initialization of the Gaussian process regression model. Then, it is assumed that the existing expanded dataset from round t is collected. ,in Then, after the t-th round of data collection, for any position to be predicted... The predicted mean is as follows: （4） The prediction variance is as follows: （5）。 4. The method for constructing a spectrum map by combining spectrum mapping and data completion according to claim 3, characterized in that, The evaluation indicators include the upper bound of the confidence level. Spatial distance coverage terms associated with the set of sampled points The evaluation function is as follows: （6） In the formula, Weighting for space exploration; Among them, the upper bound of confidence level As shown in the following formula: （7） In the formula, The normalized expected value of the forecast. The normalized standard deviation of the forecast. Confidence coefficient; Space exploration weight As shown in the following formula: （8） In the formula, This represents the volume of the region with high uncertainty at the initial stage of the model. The volume of the region with high uncertainty at the t-th iteration of the model is given by the following formula: （9） （10） In the formula, To predict the standard deviation The value of the p-quantile in the middle.

5. The method for constructing a spectrum map by combining spectrum mapping and data completion according to claim 4, characterized in that, The acquisition of the sampling location of the next target point specifically includes adopting a neighborhood consistency sampling point selection strategy, that is, selecting the point with the highest average neighborhood score as the high-value target for the next sampling. : Define the neighborhood set of position z , As shown in the following formula: （11） In the formula, The neighborhood radius; Calculate the neighborhood average score of each point within the region, and select the point with the highest neighborhood average score as the target point for the next data collection. As shown in the following formula: （12）。 6. The method for constructing a spectrum map by combining spectrum mapping and data completion according to claim 5, characterized in that, The path planning specifically includes: Define the monitoring device as a discrete network: Set the movement step size of the monitoring device to The reachable discrete network point set is , Let X be the sequence of points for the sampling path to be planned, as shown in the following formula: （13） Each edge on the sampling path is recorded as an undirected line segment. Then the set of edges that history has traversed is as follows: （14） The cost function is defined as follows: （15） In the formula, For the information benefits of the path, This is the path loss term. For corner smoothing, Starting direction penalty items, among which... As shown in the following formula: （16） Path loss term As shown in the following formula: （17） Corner smoothing term As shown in the following formula: （18） Starting direction penalty As shown in the following formula: （19） In the formula, This refers to the direction at the end of the previous segment; In summary, the path planning process can be modeled as an optimization problem as shown in the following equation: （20） In the formula, For safety distance constraints, The maximum scaling factor allowed for path length relative to the straight-line distance between the start and end points. This is for determining the case where the projection intervals are collinear and overlap. Solve the optimization problem to obtain the sampling path from the current position to the next target position.

7. The method for constructing a spectrum map by combining spectrum mapping and data completion according to claim 6, characterized in that, The update process is as follows: After the path exploration in round t is completed, the newly added sample data set is obtained. The newly added sample data set Incorporate historical datasets Forming an expanded dataset ; Use augmented datasets Update the hyperparameters of the composite covariance kernel function The solution is obtained by maximizing the log-marginal likelihood (MLE), as shown in the following equation: （21） In the formula: （22） Solve These parameters constitute the updated Gaussian process model parameters and are used as the model parameters for calculating the prediction mean and prediction variance in the (t+1)th round.

8. A method for constructing a spectrum map by combining spectrum mapping and data completion according to any one of claims 1 to 7, characterized in that, The iterative process is specifically as follows: When the global average uncertainty corresponding to the prediction variance Below the preset threshold When sampling resources are used up to the preset budget, the sampling process is terminated and the final spectrum map is output.

Images