Self-adaptive spectrum completion method for non-uniform sampling scene based on unmanned aerial vehicle platform

Abstract

The invention discloses a non-uniform sampling scene self-adaptive frequency spectrum completion method based on an unmanned aerial vehicle platform. The method comprises the following steps: identifying an area shielded by a building; simulating the relationship between the signal intensity and the distance change; training a multi-head graph attention network embedded by building constraint to obtain a frequency spectrum completion intelligent model; in an initial sampling stage, a safety area is generated, candidate waypoints are created, and waypoints around each building are connected to form an unmanned aerial vehicle flight path; adopting an inverse distance weighting algorithm or a Kriging algorithm to finish initial completion so as to estimate the approximate position of the radiation source; and simulating deployment of the unmanned aerial vehicle for secondary sampling, carrying out dense sampling around the identified radiation source, then adaptively perfecting a sampling result by using a spectrum completion intelligent model, completing space completion of spectrum data, and constructing a radio frequency spectrogram. According to the method, the spectrum reconstruction performance is remarkably improved, and the collaborative optimization problem of high-precision requirement and low-cost implementation in urban complex scenes is effectively solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of electromagnetic spectrum perception and reconstruction, and specifically relates to an adaptive spectrum completion method based on a non-uniform sampling scenario of an unmanned aerial vehicle platform. Background Art

[0002] The spectrum map generated using spectrum mapping technology, also known as the radio environment map (REM), is a digital representation of the radio frequency environment. By integrating multidimensional spatial spectrum data, it can intuitively reflect the spatial distribution characteristics of signal strength, which is of great value for improving spectrum situational awareness and dynamic resource scheduling efficiency. Existing spectrum mapping research focuses on how to reconstruct a complete spectrum situation map from a small amount of spectrum situation data, namely, spectrum completion methods. As a key component of electromagnetic spatial situation reconstruction, existing spectrum mapping technology urgently needs further research. Spectrum completion methods are the core technical support for reconstructing a complete spectrum map from sparsely sampled data. Therefore, research on spectrum completion methods is crucial. Spectrum completion methods are widely used in both military and civilian fields. In military applications, spectrum completion methods reconstruct the spatial characteristics of the battlefield electromagnetic environment, providing fundamental data support for improving signal source localization accuracy in electronic reconnaissance and mitigating multipath interference in countermeasure scenarios. In the civilian sector, spectrum completion methods also have great research prospects and application potential in emerging wireless communication fields such as intelligent transportation systems, unmanned aerial vehicles (UAVs), the Internet of Things, and 5G.

[0003] To improve spectrum reconstruction performance in non-uniform sampling scenarios while reducing sampling costs, further research is needed on methods for completing non-uniformly sampled spectrum data in complex urban scenarios. Fixed trajectory planning models in complex urban scenarios struggle to adapt to the spatially heterogeneous distribution of radiation sources, leading to sampling blind spots in core areas. Traditional spatial correlation modeling methods are unable to accurately characterize complex electromagnetic coupling effects such as non-line-of-sight propagation, resulting in residual multipath interference distortion. Therefore, it is necessary to design an adaptive sampling spectrum completion method for non-uniform sampling scenarios assisted by simulated drones, effectively integrating a multi-head graph attention network to capture complex environmental features and achieve spectrum data completion at a low monitoring cost.

[0004] Existing spectrum data completion methods can be divided into two categories: model-based and data-based. Model-based spectrum completion methods typically assume prior information, such as the signal propagation model and signal source parameters. This method is often suitable for specific scenarios where the source parameters are known or the channel environment is relatively stable. Forward modeling can distinguish between situations where the emitter parameters are fully, partially, or undetermined. In the first case, known emitter parameters are directly used to calculate the spectrum signal coverage using a propagation model to construct a spectrum situation map. In the second case, if other emitter parameters such as transmit power and antenna characteristics are known, the transmitter location must be estimated before applying the spectrum situation construction method in the first case. However, if only the transmitter location is known, other parameters must be estimated before using the selected propagation model. In the last case, all emitter parameters must be estimated before constructing a spectrum situation map. Model-based spectrum completion methods rely on parameters such as transmitter location and signal strength differentials. Accurately obtaining transmitter parameters in complex environments is difficult, significantly impacting spectrum map accuracy.

[0005] Among data-based spectrum completion methods, deep learning-based spectrum completion methods have attracted much attention due to their powerful learning capabilities. Existing research uses deep neural networks (DNNs) to generate radio maps. However, deploying dense sensor networks in complex and changing real-world environments is costly. In contrast, drone-based sampling offers a scalable, flexible, and cost-effective alternative that combines high maneuverability with the ability to collect detailed three-dimensional spatial data, with significant advantages in the presence of obstacles or dynamically changing terrain. Some have proposed exploring drone-assisted REM construction through simulation.

[0006] The aforementioned spectrum sensing methods based on deep neural networks (DNNs) rely on densely deployed sensor arrays for data collection. These methods face the dual constraints of significantly increased deployment costs and insufficient dynamic networking adaptability and accuracy in complex physical environments, significantly limiting system scalability and practical engineering effectiveness. To address these issues, the present invention achieves high spectrum map reconstruction accuracy within limited computing resources by synergizing dynamic trajectory optimization based on building topology constraints and electromagnetic correlation learning using a multi-head graph attention network. Summary of the Invention

[0007] Purpose of the invention: The present invention proposes an adaptive spectrum completion method for non-uniform sampling scenarios based on UAV platforms. This method overcomes the limitations of UAV sampling trajectory planning, significantly improves spectrum reconstruction performance, and keeps sampling costs at a low level for a long time, effectively solving the problem of collaborative optimization between "high-precision requirements" and "low-cost implementation" in complex urban scenarios.

[0008] Technical solution: The present invention provides an adaptive spectrum completion method for non-uniform sampling scenarios based on UAV platforms, comprising the following steps:

[0009] (1) Select an urban environment as the target area, discretize the target area into a uniform three-dimensional grid, and identify the area blocked by buildings;

[0010] (2) Based on transmission power, path loss, and antenna gain, a mathematical model of the sensor receiving signal is established to simulate the relationship between signal strength and distance changes;

[0011] (3) In the initial sampling stage, a dynamic path planning algorithm is used to simulate sparse sampling along the building contour based on UAVs. The contour extraction technology is used to construct a mask matrix based on the grid resolution to identify and extract the building boundary point set, and a safe area is generated along the normal direction;

[0012] (4) Create candidate waypoints in the safe area and connect the waypoints around each building to form the UAV flight path; a three-level spiral sampling strategy is used to create candidate waypoints in the building area; a double sine waveform orthogonal superposition sampling strategy is used to create candidate waypoints in the non-building area;

[0013] (5) In the initial sampling stage, the inverse distance weighted algorithm or Kriging algorithm is used to complete the initial completion to estimate the approximate location of the radiation source;

[0014] (6) After estimating the approximate location of the radiation source, simulate the deployment of drones for secondary sampling; perform dense sampling around the identified radiation source, and then use the multi-head graph attention network to adaptively improve the sampling results, complete the spatial completion of the spectrum data, and construct a radio spectrum map;

[0015] (7) Dynamically adjust antenna parameters to generate N simulated sample data, which are divided into training set, validation set, and test set;

[0016] (8) The training set and validation set are input into the multi-head graph attention network embedded with architectural constraints. The changes in validation loss are dynamically monitored according to the early stopping strategy to determine whether the model has converged and terminate the training. After the training is completed, the spectrum completion intelligent model is obtained. The test set data is input into the spectrum completion intelligent model and the spectrum completion result is output.

[0017] Furthermore, the three-dimensional grid in step (1) is:

[0018] Mesh data M with three-dimensional spatial structure i ∈R W×H×3 , where R represents a set of real numbers, W represents the number of grids in the x-direction, and H represents the number of grids in the y-direction; define and generate the building mask matrix: B i,j ∈{0, 1}W×H , with B i,j =1 identifies grid points that are blocked by buildings.

[0019] Furthermore, the mathematical model of the sensor receiving the signal in step (2) is:

[0020] P R =P T -P L (d)+G T +G R

[0021] Among them, P T Represents the transmission power, P L (d) represents the path loss caused by distance d, G T and G R Represent the gains of the transmitting antenna and the receiving antenna respectively.

[0022] Furthermore, the process of creating candidate waypoints in the building area using the three-level spiral sampling strategy in step (4) is as follows:

[0023] In the building area, a three-level spiral sampling strategy is adopted, with the building as the center and a spiral path generated according to the preset spiral parameters:

[0024] x i =x c +r (l) ·cos(θ i ),y i =y c +r (l) ·sin(θ i )

[0025] p i (l) =(x i ,y i )

[0026] r (l) =r0+Δr·l,l=0,1,...,L-1

[0027]

[0028] Among them, (x c ,y c ) is the center coordinate of the building, L represents the number of spiral turns, r (l) is the radius of the first circle, r0 is the base radius, Δr is the radius step, N θ is the total number of sampling points per circle, θ i is the spiral angle value of the i-th sampling point, ε i For θ iThe random perturbation angle, ε max is the upper limit of the angular perturbation, Indicates that from the interval [-ε max ,ε max ] uniform random sampling, the probability of each value is equal, p i (l) is the spiral path coordinate;

[0029] The spiral path is discretized into continuous path points through the Bresenham algorithm, and sampling points that meet the conditions are searched near the path points:

[0030] For each pair of adjacent points p i (l) ,p i+1 (l) , perform integer grid discrete path i (l) =Bresenham(p i (l) ,p i+1 (l) ), for each discrete path point (p x ,p y )∈path i (l) , search for candidate points C in the non-building nodes in the graph that meet the following conditions:

[0031] C(p x ,p y )={x i ,y i ||x i -p x |<δ p ,|y i -p y |<δ p}

[0032] Among them, δ p is the grid search threshold; select the one closest to the path point from the candidate * =argmin i ||(x i ,y i )-(p x ,p y )||2, and mark node i* as sampled.

[0033] Furthermore, the process of creating candidate waypoints in the non-building area using the double-sine waveform orthogonal superposition sampling strategy in step (4) is as follows:

[0034] A dual-sine waveform orthogonal superposition sampling strategy is used in non-building areas. Waveform path points are generated based on preset waveform parameters. The waveform path is discretized using the Bresenham algorithm, and sampling points that meet the requirements are searched near the path points. A wavy sampling path is generated by evenly arranging several equidistant sampling columns on the waveform path and calculating the waveform sampling coordinates at each column. Sampling points are determined near the path points by searching for points that meet the requirements and updating the mask matrix.

[0035] Set the vertical coordinate range of all non-building nodes in the current layer:

[0036] y min =min{y i},y max =max{y i}

[0037] Then the center height and span are:

[0038] Assume that the horizontal coordinate range of all non-building nodes in the current layer is:

[0039] x min =min{x i},x max =max{x i}

[0040] For the horizontal coordinate interval [x min ,x max ] is divided into N sampling columns:

[0041]

[0042] The parameters of the kth waveform are: {A (k) ,f (k) ,φ (k) ,y o (k)}, k=1,...,K, where A (k) represents the amplitude of the kth waveform, f (k) represents the frequency of the kth waveform, φ (k) Indicates the phase of the kth waveform, y o (k) Indicates the y-axis offset of the k-th waveform, where K represents the number of preset waveforms;

[0043] For the kth waveform path, the following sine function is used to calculate the path ordinate:

[0044] p i =(x i ,y i )

[0045] Among them, p i is the waveform path coordinate; for any continuous path point pair p i ,p i+1 , using the Bresenham algorithm to generate its discrete path: The path is composed of a series of integer grid points to ensure the path coherence in the graph space;

[0046] For each waypoint From the set of non-building and unsampled nodes in the current layer, select the candidate sampling point set C that meets the following conditions:

[0047] C(p x ,p y )={x i ,y i ||x i -p x |<δ p ,|y i -p y |<δ p}

[0048] Among them, δ p is the grid search threshold; select the one closest to the path point from the candidate: i * =argmin i ||(x i ,y i )-(p x ,p y )||2, and mark node i* as sampled.

[0049] Furthermore, the process of using the inverse distance weighted algorithm to complete the initial estimation of the approximate location of the radiation source in step (5) is as follows:

[0050] In the IDW algorithm, for an unsampled point p, the received signal strength formula Z is calculated as follows:

[0051]

[0052] Among them, Z(x i ) represents the signal strength received at the i-th sampling point, d(x i ,p) represents the distance between the i-th sampling point and the interpolation point, p is the weight index, and n is the number of adjacent sampling points involved in the interpolation.

[0053] Furthermore, the process of using the Kriging algorithm in step (5) to complete the initial estimation of the approximate location of the radiation source is as follows:

[0054] Setting the Gaussian variation model and geographic distance measurement method, in the Kriging algorithm, the received signal strength Z of the interpolation point is expressed as:

[0055]

[0056] Among them, λ i Represents the i-th sample point x i The weights are determined by solving the Kriging equation.

[0057] Furthermore, the implementation process of step (6) is as follows:

[0058] Determine the location of the radiation source for secondary sampling: Calculate the sampling probability based on the distance (d1, d2) between any sampling point and the primary and secondary radiation sources, as shown below:

[0059]

[0060] Among them, λ represents the distance attenuation coefficient, α0 and α1 represent the sampling probability of high-density areas near the radiation source of different values, p0 represents the sampling probability of medium-density areas close to the radiation source, and p min represents the sampling probability of the sparse area far away from the radiation source, r1 represents the sampling radius of the high-density area near the radiation source, and r2 represents the sampling radius of the medium-density area close to the radiation source;

[0061] Bernoulli sampling is performed on all candidate points according to the above probabilities, and the primary and secondary sources are forcibly included. Sampling results that exceed the target number are screened according to probability weighting, and if insufficient, they are randomly supplemented to maintain a stable overall sampling rate.

[0062] In the multi-head graph attention network, each node calculates its output by aggregating the representations of its neighboring nodes; the attention mechanism α normalized by the softmax function is introduced, and the attention coefficient α i,j and update node representation h i ′ is calculated as follows:

[0063]

[0064] Among them, x i ,x j Represents the input feature vector of node i, j respectively; a T represents the learnable attention vector; ε represents the set of edges; [x i ‖x j ‖e i,j ] represents vector concatenation operation, {h j |j∈V} and {h i′|i∈V} represents the node set of the input layer and the output layer respectively, W represents the weight, a represents a single-layer feedforward neural network, e i,j represents edge features, LeakyReLU is an activation function, σ(.) represents a nonlinear function, and K represents the number of heads.

[0065] Furthermore, the implementation process of step (7) is as follows:

[0066] 20% of non-building units are randomly selected from each simulated data set, and each set of samples can be expressed as: where r k Indicates the sampling position, y k Indicates the spectrum intensity value at the corresponding position, M i It is grid data with a three-dimensional spatial structure.

[0067] Furthermore, the multi-head graph attention network embedded with the building constraint in step (8) includes three independent attention heads, and the weight matrix dimension of each head is 128; an edge feature fusion attention mechanism is designed, and the building spacing and signal attenuation rate are used as edge attributes, and the attention coefficient is calculated through the activation function LeakyReLU; for each node, the features of the 150 nearest nodes in the neighborhood are dynamically aggregated, layer normalization is used to suppress noise, and multi-head attention aggregation is performed; the building topology constraint is embedded, the building node features are forced to be zero, and the signal strength of non-building nodes is updated through gated residual connections.

[0068] Beneficial effects: Compared with the existing technology, the beneficial effects of the present invention are: 1. The adaptive sampling spectrum completion framework proposed in the present invention replaces traditional fixed-point monitoring with a drone secondary sampling scheme, eliminating the high deployment and maintenance costs of fixed monitoring nodes, and using the drone lightweight platform to achieve rapid deployment and dynamic density adjustment, greatly reducing hardware costs, and breaking through the bottlenecks of redundant hardware dependence and poor regional adaptability of fixed schemes; 2. The adaptive sampling spectrum completion framework proposed in the present invention embeds building topology constraints into sampling path planning, and combines the graph neural network to dynamically correct the spatial correlation model, while ensuring flight safety, making the non-uniform sampling completion accuracy close to the theoretical optimal value, and significantly suppressing building edge artifacts and multipath interference distortion. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is a flow chart of the present invention;

[0070] Figure 2 This is a visual comparison of the spectrum completion and reconstruction effects of the method of the present invention and the IDW and Kriging methods;

[0071] Figure 3 This is a visual comparison diagram of the spectrum completion and reconstruction effects using the sampling of the present invention and ideal discrete sampling; DETAILED DESCRIPTION

[0072] The present invention will be further described in detail below with reference to the accompanying drawings.

[0073] like Figure 1 As shown, the present invention proposes an adaptive spectrum completion method based on a non-uniform sampling scenario of an unmanned aerial vehicle platform, which specifically includes the following steps:

[0074] Step 1: Environment modeling and meshing: An urban environment is selected as the target area, and the target area is discretized into a uniform three-dimensional grid: M i ∈R W×H×3 , where R represents a set of real numbers, W represents the number of grids in the x-direction, and H represents the number of grids in the y-direction. Define and generate the building mask matrix: B i,j ∈{0, 1} W×H , with B i,j =1 identifies grid points that are blocked by buildings.

[0075] Step 2: Sensor measurement modeling: Based on the transmission power, path loss, and antenna gain, a mathematical model of the sensor receiving signal is established, which can be expressed as: P R =P T -P L (d)+G T +G R , where P T Represents the transmission power, P L (d) represents the path loss caused by distance d, G T and G R Denote the gains of the transmitting antenna and the receiving antenna respectively. The modeling initialization parameters are shown in Table 1.

[0076] Table 1 Initialization input parameters for modeling

[0077] category parameter Numerical Study Area size 325m×270m Grid resolution 5m (W=65m, H=54m) Height Slice <![CDATA[z1=5m,z2=20m,z3=35m]]> Transmitter parameters Operating frequency 1.8GHz bandwidth 10MHz Transmit power 13dBm Antenna gain 0dB

[0078] Step 3: UAV sampling path planning: In the initial sampling stage, a dynamic path planning algorithm is used to simulate UAV-based sparse sampling along the building contours. The contour extraction technology is used to construct a building mask matrix based on the grid resolution to extract the building boundary point set; to avoid collisions, a safe area is generated along the normal direction.

[0079] Step 4: Create candidate waypoints in the safe area and connect the waypoints around each building to form the drone flight path.

[0080] In the building area, a three-level spiral sampling strategy is adopted, with the building as the center and a spiral path generated according to the preset spiral parameters:

[0081] xi =x c +r (l) ·cos(θ i ),y i =y c +r (l) ·sin(θ i )

[0082] p i (l) =(x i ,y i )

[0083] r (l) =r0+Δr·l,l=0,1,...,L-1

[0084]

[0085] Among them, (x c ,y c ) is the center coordinate of the building, L represents the number of spiral turns, r (l) is the radius of the first circle, r0 is the base radius, Δr is the radius step, N θ is the total number of sampling points per circle, θ i is the spiral angle value of the i-th sampling point, ε i For θ i The random perturbation angle, ε max is the upper limit of the angular perturbation, Indicates that from the interval [-ε max ,ε max ] uniform random sampling, the probability of each value is equal, p i (l) are the spiral path coordinates.

[0086] The spiral path is discretized into continuous path points using the Bresenham algorithm, and sampling points that meet the conditions are searched near the path points.

[0087] For each pair of adjacent points p i (l) ,p i+1 (l) , perform integer grid discrete path i (l) =Bresenham(p i (l) ,p i+1 (l) ), for each discrete path point (p x ,p y )∈path i (l), search for candidate points C in the non-building nodes in the graph that meet the following conditions:

[0088] C(p x ,p y )={x i ,y i ||x i -p x |<δ p ,|y i -p y |<δ p}

[0089] Among them, δ p is the grid search threshold, which is 0.7. Select the one closest to the path point from the candidate: i * =argmin i ||(x i ,y i )-(p x ,p y )||2, and mark node i* as sampled.

[0090] A double-sine waveform orthogonal superposition sampling strategy is adopted in non-building areas. Waveform path points are generated based on preset waveform parameters. The waveform path is discretized using the Bresenham algorithm, and sampling points that meet the conditions are searched near the path points. A wavy sampling path is generated by evenly arranging several equidistant sampling columns on the waveform path and calculating the waveform sampling coordinates at each column. Near the path points, the sampling points are determined by searching for points that meet the conditions and updating the mask matrix.

[0091] Set the vertical coordinate range of all non-building nodes in the current layer:

[0092] y min =min{y i},y max =max{y i}

[0093] Then the center height and span are:

[0094] Assume that the horizontal coordinate range of all non-building nodes in the current layer is:

[0095] x min =min{x i},x max =max{x i}

[0096] For the horizontal coordinate interval [x min ,x max ] is divided into N sampling columns:

[0097]

[0098] The parameters of the kth waveform are: {A (k) ,f (k) ,φ (k) ,y o (k)}, k=1,...,K, where A (k) represents the amplitude of the kth waveform, f (k) represents the frequency of the kth waveform, φ (k) Indicates the phase of the kth waveform, y o (k) Indicates the y-axis offset of the k-th waveform, where K represents the number of preset waveforms.

[0099] For the kth waveform path, the following sine function is used to calculate the path ordinate:

[0100] p i =(x i ,y i )

[0101] Among them, p i is the waveform path coordinate. For any continuous path point pair p i ,p i+1 , using the Bresenham algorithm to generate its discrete path: The path consists of a series of integer grid points to ensure the path coherence in the graph space.

[0102] For each waypoint From the set of non-building and unsampled nodes in the current layer, select the candidate sampling point set C that meets the following conditions:

[0103] C(p x ,p y )={x i ,y i ||x i -p x |<δ p ,|y i -p y |<δ p}

[0104] Among them, δ p is the grid search threshold, which is 0.6. Select the one closest to the path point from the candidate: i * =argmin i ||(x i ,y i )-(p x ,p y)||2, and mark node i* as sampled.

[0105] Step 5: In the initial sampling stage, relatively simple traditional algorithms such as inverse distance weighted (IDW) algorithm and Kriging algorithm are used to complete the initial completion to estimate the approximate location of the radiation source;

[0106] Perform inverse distance weighted (IDW) interpolation on unsampled points: With the target node as the center, search for up to 150 nearest sampled neighbor nodes, calculate the distance weights between them and the target node based on the Euclidean distance, and use a weighted average calculation with a weight exponent of 6; when no valid sampling points are available in the neighborhood, use the mean signal strength of all sampling points in the current layer to fill in.

[0107] In the IDW algorithm, for an unsampled point p, the received signal strength formula Z is calculated as follows:

[0108]

[0109] Among them, Z(x i ) represents the signal strength received at the i-th sampling point, d(x i ,p) represents the distance between the i-th sampling point and the interpolation point, p is the weight index, and n is the number of adjacent sampling points involved in the interpolation.

[0110] Perform Kriging interpolation optimization: Based on the Gaussian variogram model, the covariance relationship between spatial locations is constructed; at the same time, the coordinate type is set to geographic mode to utilize the spatial distribution characteristics of the nodes to improve the accuracy of the interpolation estimation. In the Kriging algorithm, the received signal strength Z of the interpolation point is expressed as:

[0111]

[0112] Among them, λ i Represents the i-th sample point x i The weights are determined by solving the Kriging equation.

[0113] Step 6: After estimating the approximate location of the emitter, simulate the deployment of drones for secondary sampling. Dense sampling is performed around the identified emitter, and a multi-head graph attention network (GATv2) is used to adaptively refine the sampling results, completing the spatial completion of the spectrum data and ultimately constructing a radio spectrum map.

[0114] Determine the location of the radiation source for secondary sampling: Calculate the sampling probability based on the distance (d1, d2) between any sampling point and the primary and secondary radiation sources, as shown below:

[0115]

[0116] Among them, λ represents the distance attenuation coefficient, α0 and α1 represent the sampling probability of high-density areas near the radiation source of different values, p0 represents the sampling probability of medium-density areas close to the radiation source, and p min represents the sampling probability of the sparse area far away from the radiation source, r1 represents the sampling radius of the high-density area near the radiation source, and r2 represents the sampling radius of the medium-density area close to the radiation source. The λ value is 15, the α0 value is 0.8, the α1 value is 0.7, the p0 value is 0.4, and the p min The value is 0.1, the r1 value is 30, and the r2 value is 60.

[0117] Bernoulli sampling is performed on all candidate points according to the above probability, and the primary and secondary sources are forcibly included; the sampling results that exceed the target number are screened according to probability weighting, and if they are insufficient, they are randomly supplemented to maintain the overall sampling rate stable.

[0118] In GATv2, which has stronger generalization ability, each node calculates its output by aggregating the representations of its neighboring nodes. In order to better handle noise and improve representation ability, an attention mechanism α normalized by the softmax function is introduced. Attention coefficient α i,j and update node representation h i ′ is calculated as follows:

[0119]

[0120] Among them, x i ,x j Represents the input feature vector of node i, j respectively; a T represents the learnable attention vector; ε represents the set of edges; [x i ‖x j ‖e i,j ] represents vector concatenation operation, {h j |j∈V} and {h i ′|i∈V} represents the node set of the input layer and the output layer respectively, W represents the weight, a represents a single-layer feedforward neural network, e i,j represents edge features, LeakyReLU is an activation function, σ(.) represents a nonlinear function, K represents the number of heads, and T represents a transposition operation.

[0121] Step 7: The antenna parameters are dynamically adjusted to generate N simulated sample data, which are divided into a training set, a validation set, and a test set.

[0122] 20% of non-building units are randomly selected from each simulated data set, and each set of samples can be expressed as: where r k Indicates the sampling position, y kIndicates the spectrum intensity value at the corresponding position, M i is the 3D mesh from step 1.

[0123] Step 8: Input the training set and validation set into the multi-head graph attention network embedded with building constraints. Dynamically monitor the changes in validation loss based on the early stopping strategy to determine whether the model has converged and terminate training. After training is completed, the spectrum completion intelligent model is obtained. Input the test set data into the spectrum completion intelligent model and output the spectrum completion results.

[0124] A multi-head graph attention network embedded with building constraints was constructed, configured with three independent attention heads, each with a weight matrix dimension of 128. An edge feature fusion attention mechanism was designed, incorporating building spacing and signal attenuation as edge attributes, and the attention coefficient was calculated using the LeakyReLU activation function. For each node, the features of the 150 nearest nodes in the neighborhood were dynamically aggregated, layer normalization was used to suppress noise, and multi-head attention aggregation was performed. Building topology constraints were embedded, forcing the features of building nodes to be zero, and non-building nodes were updated with signal strength via gated residual connections.

[0125] The proposed framework was trained for 1000 epochs using the Adam optimizer, with a learning rate of 0.0001 and a batch size of 32. Mean squared error loss was used as the loss function. In the following experiments, the dataset was split into training, validation, and test sets with an 8:1:1 ratio. Training was terminated if the validation loss did not decrease within 10 epochs. Experiments were conducted on a computer powered by a GeForce GTX 2080Ti GPU.

[0126] Figure 2 This is a visual comparison of the spectrum completion and reconstruction effects of GATv2, IDW, and Kriging methods of the present invention. Figure 2 It can be seen that compared with the case where both initial sampling and secondary sampling use traditional interpolation methods (IDW, Kriging), the method of the present invention shows lower reconstruction error and higher overall reconstruction accuracy in spectrum reconstruction, and the difference is obvious in the visualization results, showing a better mapping effect.

[0127] Figure 3 This is a visual comparison of the spectrum completion and reconstruction effects of the present invention (GATv2+AS-SC) and ideal discrete sampling (GATv2+Discrete Sampling). Figure 3 It can be seen that combining the GATv2 structure with the traditional algorithm can also make the reconstruction accuracy close to the accuracy under ideal random sampling conditions, highlighting that the method proposed in this invention has strong adaptability and engineering practicality.

[0128] This invention improves the dynamic optimization algorithm of the trajectory of building topology constraints, designs a creative solution that uses traditional interpolation methods for initial sampling and secondary sampling combined with graph neural network completion methods, and significantly improves the spectrum reconstruction accuracy in complex urban scenes by dynamically optimizing the drone sampling path and graph neural network modeling of building constraint spatial characteristics, significantly suppressing building edge artifacts and multipath interference distortion, and greatly reducing hardware costs.

[0129] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. An adaptive spectrum completion method for non-uniform sampling scenarios based on UAV platforms, characterized by: The following steps are involved: (1) Select an urban environment as the target area, discretize the target area into a uniform three-dimensional grid, and identify the area blocked by buildings; (2) Based on transmission power, path loss, and antenna gain, a mathematical model of the sensor receiving signal is established to simulate the relationship between signal strength and distance changes; (3) In the initial sampling stage, a dynamic path planning algorithm is used to simulate sparse sampling along the building contour based on UAVs. The contour extraction technology is used to construct a mask matrix based on the grid resolution to identify and extract the building boundary point set, and a safe area is generated along the normal direction; (4) Create candidate waypoints in the safe area and connect the waypoints around each building to form the UAV flight path; a three-level spiral sampling strategy is used to create candidate waypoints in the building area; a double sine waveform orthogonal superposition sampling strategy is used to create candidate waypoints in the non-building area; (5) In the initial sampling stage, the inverse distance weighted algorithm or Kriging algorithm is used to complete the initial completion to estimate the approximate location of the radiation source; (6) After estimating the approximate location of the radiation source, simulate the deployment of drones for secondary sampling; perform dense sampling around the identified radiation source, and then use the multi-head graph attention network to adaptively improve the sampling results, complete the spatial completion of the spectrum data, and construct a radio spectrum map; (7) Dynamically adjust antenna parameters to generate N simulated sample data, which are divided into training set, validation set, and test set; (8) The training set and validation set are input into the multi-head graph attention network embedded with architectural constraints. The changes in validation loss are dynamically monitored according to the early stopping strategy to determine whether the model has converged and terminate the training. After the training is completed, the spectrum completion intelligent model is obtained. The test set data is input into the spectrum completion intelligent model and the spectrum completion result is output.

2. The adaptive spectrum completion method for non-uniform sampling scenarios based on UAV platforms according to claim 1 is characterized in that: The three-dimensional grid in step (1) is: Mesh data M with three-dimensional spatial structure i ∈R W×H×3 , where R represents a set of real numbers, W represents the number of grids in the x-direction, and H represents the number of grids in the y-direction; define and generate the building mask matrix: B i,j ∈{0, 1} W×H , with B i,j =1 identifies grid points that are blocked by buildings.

3. The adaptive spectrum completion method for non-uniform sampling scenarios based on UAV platforms according to claim 1 is characterized in that: The mathematical model of the sensor receiving the signal in step (2) is: P R =P T -P L (d)+G T +G R Among them, P T Indicates the transmission power, P L (d) represents the path loss caused by distance d, G T and G R Represent the gains of the transmitting antenna and the receiving antenna respectively.

4. The adaptive spectrum completion method for non-uniform sampling scenarios based on UAV platforms according to claim 1 is characterized in that: The implementation process of creating candidate waypoints in the building area using the three-level spiral sampling strategy in step (4) is as follows: In the building area, a three-level spiral sampling strategy is adopted, with the building as the center and a spiral path generated according to the preset spiral parameters: x i =x c +r (l) ·cos(θ i ),y i =y c +r (l) ·sin(θ i ) p i (l) =(x i ,y i ) r (l) =r0+Δr·l,l=0,1,...,L-1 e i ~U(-e max ,he max ),i=0,1,...,N θ -1 Among them, (x c ,y c ) is the center coordinate of the building, L represents the number of spiral turns, r (l) is the radius of the first circle, r0 is the base radius, Δr is the radius step, N θ is the total number of sampling points per circle, θ i is the spiral angle value of the i-th sampling point, ε i For θ i The random perturbation angle, ε max is the upper limit of the angular perturbation, Indicates that from the interval [-ε max ,ε max ] uniform random sampling, the probability of each value is equal, p i (l) is the spiral path coordinate; The spiral path is discretized into continuous path points through the Bresenham algorithm, and sampling points that meet the conditions are searched near the path points: For each pair of adjacent points p i (l) ,p i+1 (l) , perform integer grid discrete path i (l) =Bresenham(p i (l) ,p i+1 (l) ), for each discrete path point (p x ,p y )∈path i (l) , search for candidate points C in the non-building nodes in the graph that meet the following conditions: C(p x ,p y )={x i ,y i ||x i -p x |<δ p ,|y i -p y |<δ p } Among them, δ p is the grid search threshold; select the one closest to the path point from the candidate * =argmin i ||(x i ,y i )-(p x ,p y )||2, and mark node i* as sampled.

5. The adaptive spectrum completion method for non-uniform sampling scenarios based on UAV platforms according to claim 1 is characterized in that: The process of creating candidate waypoints in the non-building area using the double sine waveform orthogonal superposition sampling strategy in step (4) is as follows: A dual-sine waveform orthogonal superposition sampling strategy is used in non-building areas. Waveform path points are generated based on preset waveform parameters. The waveform path is discretized using the Bresenham algorithm, and sampling points that meet the requirements are searched near the path points. A wavy sampling path is generated by evenly arranging several equidistant sampling columns on the waveform path and calculating the waveform sampling coordinates at each column. Sampling points are determined near the path points by searching for points that meet the requirements and updating the mask matrix. Set the vertical coordinate range of all non-building nodes in the current layer: and min =min{and i },and max =max{and i } Then the center height and span are: Assume that the horizontal coordinate range of all non-building nodes in the current layer is: x min =min{x i },x max =max{x i } For the horizontal coordinate interval [x min ,x max ] is divided into N sampling columns: The parameters of the kth waveform are: {A (k) ,f (k) ,φ (k) ,y o (k) }, k=1,...,K, where A (k) represents the amplitude of the kth waveform, f (k) represents the frequency of the kth waveform, φ (k) Indicates the phase of the kth waveform, y o (k) Indicates the y-axis offset of the k-th waveform, where K represents the number of preset waveforms; For the kth waveform path, the following sine function is used to calculate the path ordinate: p i =(x i ,y i ) Among them, p i is the waveform path coordinate; for any continuous path point pair p i ,p i+1 , using the Bresenham algorithm to generate its discrete path: The path is composed of a series of integer grid points to ensure the path coherence in the graph space; For each waypoint From the set of non-building and unsampled nodes in the current layer, select the candidate sampling point set C that meets the following conditions: Among them, δ p is the grid search threshold; select the one closest to the path point from the candidate: i * =argmin i ||(x i ,y i )-(p x ,p y )||2, and mark node i* as sampled.

6. The adaptive spectrum completion method for non-uniform sampling scenarios based on UAV platforms according to claim 1 is characterized in that: The process of using the inverse distance weighted algorithm to complete the initial estimation of the approximate location of the radiation source in step (5) is as follows: In the IDW algorithm, for an unsampled point p, the received signal strength formula Z is calculated as follows: Among them, Z(x i ) represents the signal strength received at the i-th sampling point, d(x i ,p) represents the distance between the i-th sampling point and the interpolation point, p is the weight index, and n is the number of adjacent sampling points involved in the interpolation.

7. The adaptive spectrum completion method for non-uniform sampling scenarios based on UAV platforms according to claim 1 is characterized in that: The process of using the Kriging algorithm to complete the initial estimation of the approximate location of the radiation source in step (5) is as follows: Setting the Gaussian variation model and geographic distance measurement method, in the Kriging algorithm, the received signal strength Z of the interpolation point is expressed as: Among them, λ i Represents the i-th sample point x i The weights are determined by solving the Kriging equation.

8. The adaptive spectrum completion method for non-uniform sampling scenarios based on UAV platforms according to claim 1 is characterized in that: The implementation process of step (6) is as follows: Determine the location of the radiation source and perform secondary sampling: Calculate the sampling probability p(p) based on the distance (d1, d2) between any sampling point and the primary and secondary radiation sources, respectively, as follows: Among them, λ represents the distance attenuation coefficient, α0 and α1 represent the sampling probability of high-density areas near the radiation source of different values, p0 represents the sampling probability of medium-density areas close to the radiation source, and p min represents the sampling probability of the sparse area far away from the radiation source, r1 represents the sampling radius of the high-density area near the radiation source, and r2 represents the sampling radius of the medium-density area close to the radiation source; Bernoulli sampling is performed on all candidate points according to the above probabilities, and the primary and secondary sources are forcibly included. Sampling results that exceed the target number are screened according to probability weighting, and if insufficient, they are randomly supplemented to maintain a stable overall sampling rate. In the multi-head graph attention network, each node calculates its output by aggregating the representations of its neighboring nodes; the attention mechanism α normalized by the softmax function is introduced, and the attention coefficient α i,j and update node representation h i ′ is calculated as follows: Among them, x i ,x j Represents the input feature vector of node i, j respectively; a T represents the learnable attention vector; ε represents the set of edges; [x i ‖x j ‖e i,j ] represents vector concatenation operation, {h j |j∈V} and {h i ′|i∈V} represents the node set of the input layer and the output layer respectively, W represents the weight, a represents a single-layer feedforward neural network, e i,j represents edge features, LeakyReLU is an activation function, σ(.) represents a nonlinear function, K represents the number of heads, and T represents a transposition operation.

9. The adaptive spectrum completion method for non-uniform sampling scenarios based on UAV platforms according to claim 1, characterized in that: The implementation process of step (7) is as follows: 20% of non-building units are randomly selected from each simulated data set, and each set of samples can be expressed as: where r k Indicates the sampling position, y k Indicates the spectrum intensity value at the corresponding position, M i It is grid data with a three-dimensional spatial structure.

10. The adaptive spectrum completion method for non-uniform sampling scenarios based on UAV platforms according to claim 1, characterized in that: The multi-head graph attention network embedded with building constraints in step (8) includes three independent attention heads, and the weight matrix dimension of each head is 128; an edge feature fusion attention mechanism is designed, and the building spacing and signal attenuation rate are used as edge attributes, and the attention coefficient is calculated by the activation function LeakyReLU; For each node, dynamically aggregate the features of the 150 nearest nodes in the neighborhood, use layer normalization to suppress noise, and perform multi-head attention aggregation; Building topology constraints are embedded to force the features of building nodes to be zero, and non-building nodes update their signal strengths through gated residual connections.

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