A multi-radar power envelope fusion method

Abstract

The application discloses a multi-radar power envelope fusion method, comprising: single-radar envelope modeling, constructing envelope fusion foundation; determining non-coherent field fusion, constructing multi-radar envelope model; constructing gradient diffusion model, realizing envelope fusion smooth transition; displaying Euler method iteration convergence, realizing multi-radar envelope complete fusion; adopting adaptive octree structure to dynamically divide three-dimensional space. Advantageous effects: the multi-radar power envelope fusion method firstly calculates single-station detection probability of each radar unit at a grid point in a three-dimensional space voxel according to a radar equation, a propagation loss model and target scattering characteristics; then adopts a probability union or a more complex dependent relationship model to generate a full-space joint detection probability field; finally, an isosurface extraction (such as an improved Marching Cubes algorithm) and a probability gradient driven color / transparency mapping are adopted to generate a visual continuous, mathematically accurate fusion envelope surface.

Description

Technical Field

[0001] This invention relates to the field of radar detection, and in particular to a method for fusing the power envelopes of multiple radars. Background Technology

[0002] In modern air defense, missile defense, and airspace control systems, multi-radar collaborative networking is a core technological support for achieving wide-area coverage and high-precision target tracking. The visualization quality of the radar power envelope (i.e., radar detection range) in the three-dimensional situation map directly affects the commander's understanding of the battlefield electromagnetic situation and decision-making effectiveness.

[0003] Current methods for handling multi-radar overlay effects mainly include transparency overlay, isosurface extraction, and voxel coloring. However, these methods have been found to have problems in practical applications, such as poor visual clarity in simple overlays, imprecise boundaries in complex fusions, poor resolution, and excessive hardware dependence.

[0004] Specifically, the transparency overlay method assigns a fixed transparency to each radar envelope surface, and the overlapping areas are approximated by color mixing to represent fusion. This method has significant drawbacks in multi-radar power envelope fusion displays: the visual depth of the overlay area (darkened color or increased saturation) is determined solely by the number of overlay layers, not by actual coverage quality or complementarity. This can easily lead to serious misinterpretations—the overlay of multiple radar edge detection weak areas may be misjudged as a core high-confidence coverage area due to its darker color, while actual critical areas may appear lighter due to coverage by a single radar. Furthermore, this method cannot distinguish differences in radar detection performance (such as accuracy and anti-jamming capabilities), nor can it indicate whether the overlay enhances or redundant coverage. This makes it difficult for operators to accurately assess the actual detection effectiveness and weaknesses after fusion, reducing the accuracy of situational awareness and the reliability of decision-making.

[0005] The isosurface extraction method essentially involves summing or maximizing the detection probability fields of each radar and then extracting a joint isosurface. The main problem with this method in multi-radar power envelope fusion display is its inability to accurately represent complex fusion boundaries. When multiple radar power ranges overlap, nest, or have gaps, the single isosurface generated by this method over-smooths these key areas, resulting in blurred fusion boundaries that fail to accurately reflect the actual coverage strength variations and blind zone details. Secondly, it has low computational efficiency, especially when dealing with massive amounts of radar data and three-dimensional space, where real-time generation of high-quality isosurfaces is computationally burdensome. Furthermore, this method is sensitive to threshold selection; improper threshold settings can easily distort the fusion results, failing to effectively distinguish the contribution of different radars or highlight key coverage features, thus reducing the intuitiveness and decision support value of the display.

[0006] Voxel coloring discretizes space into voxels, calculates the contribution value of multiple radars for each voxel, and interpolates the color. The core problem with voxel coloring in multi-radar power envelope fusion display lies in its representation based on discrete 3D meshes (voxels): First, resolution is limited; the fixed voxel size results in jagged edges on the envelope, making it difficult to accurately describe complex surface boundaries, especially at low resolutions where distortion is severe. Second, computational and storage overhead is enormous; a vast voxel space needs to be established to cover the entire airspace, and each voxel needs to store and calculate fusion attributes (such as visibility and weight). Resource consumption increases exponentially when multiple radars are superimposed, leading to poor real-time performance. Third, implementing fusion rules at the voxel level is difficult; accurately weighting and fusing different radar envelopes within shared voxels can easily lead to blurred boundaries or information loss. Finally, preprocessing to generate voxelized envelopes is time-consuming and difficult to dynamically respond to changes in radar parameters or the environment. These factors limit its application in situations requiring high precision and high efficiency.

[0007] Therefore, there is an urgent need to develop an envelope fusion method based on a joint detection probability field, which can accurately describe the gradient change of detection capability under multi-radar cooperation by establishing a spatially continuous probability distribution function. Summary of the Invention

[0008] The main objective of this invention is to propose a multi-radar power envelope fusion method, which aims to solve the problems of poor visual clarity in simple superposition, imprecise boundaries in complex fusion, poor resolution, and excessive hardware dependence in existing methods for processing multi-radar superposition effects.

[0009] To address the above problems, this invention proposes a multi-radar power envelope fusion method, comprising:

[0010] Single radar envelope modeling to build the foundation for envelope fusion;

[0011] Determine the incoherent field fusion and construct a multi-radar envelope model;

[0012] Construct a gradient diffusion model to achieve a smooth transition in envelope fusion;

[0013] The Euler method is shown to converge iteratively, achieving complete fusion of multiple radar envelopes;

[0014] An adaptive octree structure is used to dynamically divide the three-dimensional space, and the subdivision level is automatically adjusted according to the local complexity of the spatial data.

[0015] In one embodiment, the single radar envelope modeling, which constructs the envelope fusion basis, includes:

[0016] According to the formula Calculate the target to the The distance of the radar, among which Indicates the first The distance at which the mine reaches its target. It is the spatial position vector of the target. It is the first The spatial position vector of the radar unit;

[0017] Constructing the first attenuation model in spherical coordinates Radar at point Detection probability model:

[0018] In the formula For the first Radar in position The detection probability at that location. For the first The maximum detection range of the radar. This is the attenuation coefficient value. For the first The maximum detection probability of the radar. This is the pattern attenuation function.

[0019] In one embodiment, determining the incoherent field fusion and constructing a multi-radar envelope model includes:

[0020] Constructing a joint radar detection probability model: In the formula, n is the number of radars. This represents the probability of joint radar detection.

[0021] In one embodiment, constructing the gradient diffusion model to achieve a smooth transition in envelope fusion includes:

[0022] Determine the diffusion coefficient D: The diffusion coefficient D is designed as the inverse function of the probability gradient. In the formula For gradient operators;

[0023] Constructing diffusion equations : where the initial time , For probability fields Over time rate of change, The diffusion term describes the "diffusion / smoothing" process of the probability field.

[0024] In one embodiment, the explicit Euler method iterative convergence to achieve complete fusion of multiple radar envelopes includes:

[0025] Initial settings for a 3D mesh: Let the index of the mesh point be ( , , ),in , , , where are the number of grid cells in the x, y, and z directions, respectively, and are the initial values. When =0, grid points ( ,j, The probability value at position ) is ,in It is the value of the multi-radar joint detection probability at this grid point;

[0026] Gradient calculation in 3D space: In a 3D mesh, the gradient... It is a vector whose components in the x, y, and z directions are as follows:

[0027] ,

[0028] ,

[0029] ,

[0030] gradient Length of the module for:

[0031]

[0032] Calculation of the diffusion coefficient D in three-dimensional space: ;

[0033] Discretization of the diffusion equation in three-dimensional space: The diffusion equation in three-dimensional space is as follows: divergence The discretized form in the three-dimensional mesh is:

[0034]

[0035] Explicit Euler method iterative solution: The time is discretized using the explicit Euler method, with a time step of . ,but

[0036] The iterative formula is: = ;

[0037] Boundary condition handling: One-sided difference is used to approximate the derivative at the boundary.

[0038] In one embodiment, the specific iterative steps are as follows:

[0039] S1. Initialization: Set the probability value at the initial time t=0. enter;

[0040] S2. Calculate the gradient magnitude: Calculate the magnitude of each grid point according to the three-dimensional gradient calculation formula. ;

[0041] S3. Calculate the diffusion coefficient: Calculate the diffusion coefficient for each grid point according to the diffusion coefficient formula. ;

[0042] S4. Calculate the divergence term: Calculate the divergence term for each grid point according to the 3D divergence discretization formula. ;

[0043] S5. Iterative Update: Update each grid point at t+ using the explicit Euler iterative formula. probability value at time 1 ;

[0044] S6. Repeat steps S2-S5 for 3-5 iterations until the result converges.

[0045] In one embodiment, using one-sided differences to approximate the derivative at the boundary includes: hour, .

[0046] In one embodiment, κ=0.693.

[0047] In one embodiment, the method of dynamically dividing the three-dimensional space using an adaptive octree structure and automatically adjusting the subdivision level according to the local complexity of the spatial data includes: performing fine division in regions with drastic feature changes, while maintaining a coarser granularity in regions with smooth data, in order to achieve a balance between storage and accuracy.

[0048] In one embodiment, each tree node stores the scalar value of the corresponding spatial voxel to form a hierarchical data representation.

[0049] Beneficial effects:

[0050] 1. The multi-radar power envelope fusion method of this application first calculates the single-station detection probability of each radar unit at the grid point in three-dimensional space based on the radar equation, propagation loss model and target scattering characteristics; then, it uses probability union or more complex dependency relationship model to fuse and generate a joint detection probability field in the whole space; finally, it generates a visually continuous and mathematically accurate fusion envelope surface by isosurface extraction (such as the improved Marching Cubes algorithm) and probability gradient-driven color / transparency mapping.

[0051] 2. The multi-radar power envelope fusion method of this application can ensure that the color brightness / saturation of the overlapping area increases with the probability, and the boundary transition is natural and smooth. At the same time, it supports quantitative analysis functions such as equal probability surface cutting and blind zone volume calculation, which significantly improves the physical accuracy, cognitive intuitiveness and decision support of battlefield electromagnetic situation expression, and provides a reliable visualization foundation for key tasks such as anti-stealth operations and key area air defense. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This demonstrates the application effect of the multi-radar power envelope fusion method of the present invention. Figure 1 ;

[0054] Figure 2 This demonstrates the application effect of the multi-radar power envelope fusion method of the present invention. Figure 2 ; Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0056] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0057] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection or an electrical connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0058] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the meaning of "and / or" throughout the text includes three parallel solutions; for example, "A and / or B" includes solution A, solution B, or a solution where both A and B are satisfied simultaneously. Furthermore, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0059] Current mainstream methods for handling multi-radar overlay effects generally adopt a simple overlay rendering mode—that is, after independently calculating and drawing the envelopes of each radar, the graphics are directly overlaid. This mode has significant physical distortion and cognitive limitations.

[0060] First, the superposition of optical transparency leads to color mixing distortion and confusion of depth information, making it impossible to accurately map the spatial distribution of the probability of joint detection by multiple radars. For example, the overlapping area of ​​radar beams, which should have increased detection probability due to signal redundancy, may be misjudged as a "detection blind spot" or "invalid area" due to visual saturation or darkening effects caused by color superposition, resulting in cognitive bias in key defense areas.

[0061] Secondly, the discrete envelope boundaries exhibit jagged or discontinuous abrupt changes at the intersection, which violates the inherent continuous attenuation characteristic of electromagnetic wave propagation. This not only reduces the physical realism of the scene but also obscures the detailed features of the changes in the detection probability gradient.

[0062] Third, the lack of quantitative analysis capabilities makes it difficult to visually distinguish between overlapping areas and actual blind spots, hindering accurate assessments of radar network coverage uniformity, overlap redundancy, and vulnerability areas. In complex scenarios such as countering stealth targets or low-altitude penetration, such distortions may mislead judgments about weaknesses in the defense system, creating tactical risks.

[0063] Fourth, from an aesthetic perspective, the rigid overlay disrupts the immersive experience of the 3D scene and fails to meet the human-computer interaction requirements of modern simulation systems for high-fidelity visualization.

[0064] The core issue with these shortcomings is that existing methods render the radar envelope as an isolated geometric entity, ignoring the continuous superposition of electromagnetic wave energy in space and the mathematical characteristics of probabilistic fusion. Simple graphical superposition cannot express the nonlinear probabilistic enhancement effect (such as coherent or incoherent signal accumulation) in the radar beam intersection region, nor can it construct a smooth transition model that conforms to physical laws.

[0065] Therefore, this embodiment designs a multi-radar power envelope fusion method. First, based on the radar equations, propagation loss model, and target scattering characteristics, the single-station detection probability of each radar unit at the grid points is calculated in three-dimensional space using voxelization. Then, using probability union or more complex dependency relationship models, a joint detection probability field is generated across the entire space. Finally, through isosurface extraction (such as the improved Marching Cubes algorithm) and probability gradient-driven color / transparency mapping, a visually continuous and mathematically accurate fused envelope surface is generated. This multi-radar power envelope fusion method ensures that the color brightness / saturation in the overlapping area increases with probability, and the boundary transition is natural and smooth. It also supports quantitative analysis functions such as isoprobability surface sectioning and blind zone volume calculation, significantly improving the physical accuracy, cognitive intuitiveness, and decision support of battlefield electromagnetic situation representation, providing a reliable visualization foundation for key tasks such as anti-stealth operations and key area air defense.

[0066] Specifically, this embodiment proposes a multi-radar power envelope fusion method, including:

[0067] Single radar envelope modeling to build the foundation for envelope fusion;

[0068] Determine the incoherent field fusion and construct a multi-radar envelope model;

[0069] Construct a gradient diffusion model to achieve a smooth transition in envelope fusion;

[0070] The Euler method is shown to converge iteratively, achieving complete fusion of multiple radar envelopes;

[0071] An adaptive octree structure is used to dynamically divide the three-dimensional space, and the subdivision level is automatically adjusted according to the local complexity of the spatial data.

[0072] This embodiment of the multi-radar power envelope fusion method introduces incoherent probability superposition into envelope fusion, reducing the dependence on phase and other information during envelope presentation. It also proposes a gradient-controlled diffusion method to achieve smooth transitions and maintain edge consistency. An octree + GPU acceleration strategy is employed to ensure a frame rate exceeding 30fps when 10 radars are in the same situation. Practical results show that achieving smooth envelope fusion, clear boundary interfaces, and reduced dependence on radar parameters at high refresh rates significantly improves the presentation of the fused envelope and the user's visual experience.

[0073] Furthermore, the multi-radar power envelope fusion method in this embodiment supports real-time updates of the dynamic environment envelope (radar movement, terrain obstruction), which significantly improves the real-time performance and adaptability of environmental perception. By responding to radar movement and terrain changes in real time, it can reduce detection blind spots, enhance target tracking accuracy, and ensure continuous and reliable operation in complex dynamic environments.

[0074] Specifically, the single radar envelope modeling and the construction of the envelope fusion foundation include:

[0075] According to the formula Calculate the target to the The distance of the radar, among which Indicates the first The distance at which the mine reaches its target. It is the spatial position vector of the target. It is the first The spatial position vector of the radar unit;

[0076] Construct the first using the attenuation model in spherical coordinates Radar at point Detection probability model:

[0077] In the formula For the first Radar in position The detection probability at that location. For the first The maximum detection range of the radar. This is the attenuation coefficient value. For the first The maximum detection probability of the radar. This is the pattern attenuation function.

[0078] Specifically, the determination of incoherent field fusion and the construction of a multi-radar envelope model includes:

[0079] Constructing a joint radar detection probability model: In the formula, n is the number of radars. The formula for the probability of joint radar detection strictly reflects the physical nature of the incoherent superposition of electromagnetic waves. It can be seen that the probability of joint detection by multiple radars follows the probability law of the union of independent events.

[0080] The multi-radar power envelope fusion method in this embodiment introduces the advantage of noncoherent probability superposition into radar power envelope fusion. It does not rely on precise phase information, reduces system complexity and synchronization requirements, improves target detection probability and reduces false alarm rate through probability fusion, enhances robustness in noisy and cluttered environments, supports multi-radar collaborative work, expands coverage, improves overall anti-interference capability and reliability, and is suitable for distributed systems.

[0081] Specifically, the construction of the gradient diffusion model to achieve a smooth transition in envelope fusion includes:

[0082] Determine the diffusion coefficient D: The diffusion coefficient D is designed as the inverse function of the probability gradient. In the formula For the gradient operator, if A small diffusion coefficient D (i.e., a smooth probability change, such as within the envelope) results in a large diffusion coefficient D (small denominator), enhancing diffusion and achieving smoothness; if If the probability change is large (i.e., steep, such as at the boundary), then D is small (the denominator is large), which inhibits diffusion and keeps the boundary sharp;

[0083] To eliminate the serrated boundary, a diffusion equation is constructed. : where the initial time , For probability fields Over time rate of change, The diffusion term describes the "diffusion / smoothing" process of the probability field.

[0084] The multi-radar power envelope fusion method in this embodiment cleverly unifies the contradictory requirements of image smoothing and edge preservation. This method uses gradient information to adaptively control the diffusion process, enhancing diffusion in regions with gentle gradients to achieve effective noise reduction and uniform smoothing, while significantly suppressing diffusion in regions with steep gradients (edges) to sharply preserve details and structural boundaries.

[0085] Specifically, the iterative convergence of the Eulerian method to achieve complete fusion of multiple radar envelopes includes:

[0086] Initial settings for a 3D mesh: Assume we have a 3D space, which we discretize into a 3D mesh, with mesh spacing in the x, y, and z directions as follows: , Δy, Let the index of the grid point be ( , , ),in , , , where are the number of grid cells in the x, y, and z directions, respectively, and are the initial values. When =0, grid points ( , , The probability value at position ) is ,in It is the value of the multi-radar joint detection probability at this grid point;

[0087] Gradient calculation in 3D space: In a 3D mesh, the gradient... It is a vector whose components in the x, y, and z directions are as follows:

[0088] ,

[0089] ,

[0090] ,

[0091] gradient Length of the module for:

[0092]

[0093] The diffusion coefficient D in three-dimensional space is calculated using a similar expression to that in two-dimensional space: Its physical meaning is also to increase the diffusion coefficient in the region where the probability change is gentle (inside the envelope) to enhance the smoothing effect, and to decrease the diffusion coefficient in the region with steep edges to maintain sharp boundaries;

[0094] Discretization of the diffusion equation in three-dimensional space: The diffusion equation in three-dimensional space is as follows: divergence The discretized form in a 3D mesh is:

[0095] The diffusion coefficient at the mesh interface can be obtained by interpolating the diffusion coefficients of adjacent mesh points, for example... ;

[0096] Explicit Euler method iterative solution: The time is discretized using the explicit Euler method, with a time step of . Then the iterative formula is: = ;

[0097] Boundary condition handling: One-sided difference is used to approximate the derivative at the boundary.

[0098] Specifically, the iterative steps are as follows:

[0099] S1. Initialization: Set the probability value at the initial time t=0. enter;

[0100] S2. Calculate the gradient magnitude: Calculate the magnitude of each grid point according to the three-dimensional gradient calculation formula. ;

[0101] S3. Calculate the diffusion coefficient: Calculate the diffusion coefficient for each grid point according to the diffusion coefficient formula. ;

[0102] S4. Calculate the divergence term: Calculate the divergence term for each grid point according to the 3D divergence discretization formula. ;

[0103] S5. Iterative Update: Update each grid point at t+ using the explicit Euler iterative formula. probability value at time 1 ;

[0104] S6. Repeat steps S2-S5 for 3-5 iterations until the result converges.

[0105] In this embodiment, the boundary condition processing includes:

[0106] At the boundaries of the 3D mesh, for example, i = 1, i = j = 1, j = k = 1, k = At points like these, special methods are needed to calculate the gradient and divergence. For example, one-sided differences can be used to approximate the derivative at the boundary. The gradient in the x-direction can be approximated as:

[0107] ;

[0108] hour, Meanwhile, during the iteration process, the probability values ​​at the boundaries can be set to fixed values ​​or other boundary conditions can be used, depending on the specific problem. Through the above steps, gradient-driven diffusion smoothing can be achieved in a 3D mesh, resulting in a smooth probability field with sharp boundaries.

[0109] In this embodiment, the adaptive octree structure is used to dynamically partition the 3D space, and the subdivision level is automatically adjusted according to the local complexity of the spatial data. This includes fine-grained partitioning in regions with drastic feature changes (such as near isosurfaces), while maintaining a coarser granularity in regions with smooth data, achieving a balance between storage and accuracy. Each tree node stores the scalar value (such as density, temperature, and other physical quantities) of the corresponding spatial voxel, forming a hierarchical data representation. To smooth the data and prepare for isosurface extraction, parallel diffusion computation is implemented on the CUDA architecture: thousands of threads of the GPU synchronously process the octree nodes, with each thread responsible for one spatial unit. The current node value is iteratively updated based on the values ​​of neighboring nodes, and shared memory is used to optimize data access, significantly accelerating algorithms such as Gaussian diffusion or Laplacian smoothing. In the rendering stage, trilinear interpolation technology is used to reconstruct the continuous field: for each sampling point, the smallest cube containing it is quickly located in the octree, the stored values ​​of its eight vertices are extracted, the accurate value of the sampling point is calculated by weighted averaging, and finally, the interpolation points that meet the threshold are connected by the moving cube algorithm to generate a smooth isosurface. This method combines the efficiency of adaptive data structures, the real-time performance of GPU parallel computing, and the continuity guarantee of trilinear interpolation, making it suitable for scientific visualization and real-time volume rendering scenarios.

[0110] This embodiment employs an octree + GPU acceleration strategy to achieve a frame rate >30fps (10-radar scene). The octree + GPU acceleration strategy significantly improves 3D data processing speed and reduces query time through efficient spatial partitioning and parallel computing, supporting real-time rendering and physical simulation of large-scale scenes, making it particularly suitable for high-performance graphics applications.

[0111] This embodiment presents a multi-radar power envelope fusion method aimed at achieving collaborative optimization of physical detection and visual representation. Its core lies in the division of labor and fusion at two levels:

[0112] Physical Layer: Construction of the Joint Detection Probability Field. This layer is based on the incoherent superposition physical characteristic of radar waves propagating in space. Unlike the interference effect of coherent waves (such as lasers), the energy of incoherent radar waves mainly exhibits energy superposition rather than phase interference in space. Utilizing this characteristic, a joint detection probability field is constructed by calculating the energy distribution and echo statistics of multiple radar detection units (or multiple detections) in the target space. This probability field is a spatially continuous function, and its value characterizes the probability or confidence that the target exists at a certain point in space. It effectively integrates multi-source / multiple radar detection information, quantifies the spatial uncertainty of the detection results, and provides physically more robust basic data for subsequent processing.

[0113] Rendering Layer: Diffusion Smoothing and Visually Continuous Transition. Directly presenting the joint detection probability field generated by the physical layer often results in sharp boundaries, significant noise, or spatial discontinuities, which does not conform to the human eye's perception of continuous and smooth boundaries. The rendering layer introduces a diffusion equation (a partial differential equation that simulates the diffusion and smoothing of matter or energy in space over time) to address this issue. This layer treats the probability field as an initial "concentration" distribution and applies a diffusion process to smooth it. The core effect of diffusion is to diffuse sharp boundaries and suppress local noise: information from high-gradient regions (such as object edges) naturally "diffused" into neighboring low-probability regions, making originally sharp or abrupt boundaries soft and continuous. This process smooths the "envelope boundary" of the target contour, effectively eliminating visual abruptness and generating a spatially continuous visualization result that conforms to human eye perception.

[0114] This embodiment of a multi-radar power envelope fusion method ensures the statistical reliability of detection by constructing an incoherent field at the physical layer, and then achieves the natural continuity of visual perception through diffusion smoothing at the rendering layer, thus realizing an effective unity of physical realism and visual comprehensibility.

[0115] In this embodiment, when the multi-radar power envelope fusion method of this embodiment is implemented in a 3D electromagnetic situation visualization system developed based on the JavaScript / WebGL platform, the application effect is as follows: Figure 1 and Figure 2 As shown, Figure 1 The results show that the multi-radar power envelope has a clear layer and strong color hierarchy when viewed from above, and the radar boundary converges in a jagged manner. Figure 2 The display of the multi-radar power envelope shows good envelope fusion in a head-up view, with both a sense of boundary and a sense of fusion, resulting in a good visual effect.

[0116] As can be seen, the multi-radar power envelope fusion method of this embodiment achieves high-fidelity fusion of multi-radar power envelopes in three-dimensional electromagnetic situational awareness, solving the cognitive confusion problems such as "detection blind spots" or "invalid regions" caused by traditional overlay displays. Through incoherent field fusion and gradient-driven diffusion, both the physical accuracy of detection probability and the natural transition of envelope boundaries are ensured. Practical application has verified that it significantly improves visual perception and fusion in electromagnetic situational awareness combat scenarios. In the future, it can be extended to the field of multi-source sensor fusion such as sonar and optoelectronic sensors, and provide reliable spatial situational input for artificial intelligence-assisted decision-making. The application of this technology will promote the development of three-dimensional electromagnetic spectrum warfare visualization towards a new stage of "physical precision and cognitive intuitiveness".

[0117] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural transformations made using the contents of the present invention's specification and drawings under the inventive concept of the present invention, or direct / indirect applications in other related technical fields, are included within the patent protection scope of the present invention.

Claims

1. A method for fusing the power envelopes of multiple radars, characterized in that, include: Single radar envelope modeling to build the foundation for envelope fusion; Determine the incoherent field fusion and construct a multi-radar envelope model; Construct a gradient diffusion model to achieve a smooth transition in envelope fusion; The Euler method is shown to converge iteratively, achieving complete fusion of multiple radar envelopes; An adaptive octree structure is used to dynamically divide the three-dimensional space, and the subdivision level is automatically adjusted according to the local complexity of the spatial data. The construction of the gradient diffusion model to achieve a smooth transition in envelope fusion includes: Determine the diffusion coefficient D: The diffusion coefficient D is designed as the inverse function of the probability gradient. In the formula For gradient operators; Constructing diffusion equations : where the initial time , For probability fields Over time rate of change, The diffusion term describes the "diffusion / smoothing" process of the probability field; The explicit Euler method iterative convergence, achieving complete fusion of multiple radar envelopes, includes: Initial settings for a 3D mesh: Let the index of the mesh point be ( , , ),in , , , representing the number of grid cells in the x, y, and z directions, respectively, at the initial time. When =0, grid points ( ,j, The probability value at position ) is ,in It is the value of the multi-radar joint detection probability at this grid point; Gradient calculation in 3D space: In a 3D mesh, the gradient... It is a vector whose components in the x, y, and z directions are as follows: 、 、 ， gradient Length of the module for: Calculation of the diffusion coefficient D in three-dimensional space: ; Discretization of the diffusion equation in three-dimensional space: The diffusion equation in three-dimensional space is as follows: divergence The discretized form in the three-dimensional mesh is: Explicit Euler method iterative solution: The time is discretized using the explicit Euler method, with a time step of . Then the iterative formula is: = ; Boundary condition handling: One-sided difference is used to approximate the derivative at the boundary.

2. The multi-radar power envelope fusion method as described in claim 1, characterized in that, The Single radar envelope modeling, establishing the foundation for envelope fusion, including: According to the formula Calculate the target to the number The distance of the radar, among which Indicates the first The distance at which the mine reaches its target. It is the spatial position vector of the target. It is the first The spatial position vector of the radar unit; Constructing the first attenuation model in spherical coordinates Radar at point Detection probability model: In the formula For the first Radar in position The detection probability at that location. For the first The maximum detection range of the radar. This is the attenuation coefficient value. For the first The maximum detection probability of the radar. This is the pattern attenuation function.

3. The multi-radar power envelope fusion method as described in claim 2, characterized in that, The determination of incoherent field fusion and the construction of a multi-radar envelope model include: Constructing a joint radar detection probability model: In the formula, n is the number of radars. This represents the probability of joint radar detection.

4. The multi-radar power envelope fusion method as described in claim 3, characterized in that, The specific iteration steps are as follows: S1. Initialization: Set the probability value at the initial time t=0. enter; S2. Calculate the gradient magnitude: Calculate the magnitude of each grid point according to the three-dimensional gradient calculation formula. ; S3. Calculate the diffusion coefficient: Calculate the diffusion coefficient for each grid point according to the diffusion coefficient formula. ; S4. Calculate the divergence term: Calculate the divergence term for each grid point according to the 3D divergence discretization formula. ; S5. Iterative Update: Update each grid point at t+ using the explicit Euler iterative formula. probability value at time 1 ; S6. Repeat steps S2-S5 for 3-5 iterations until the result converges.

5. The multi-radar power envelope fusion method as described in claim 4, characterized in that, The method of approximating the derivative at the boundary using one-sided difference includes: hour, .

6. The multi-radar power envelope fusion method as described in claim 2, characterized in that, κ=0.

693.

7. The multi-radar power envelope fusion method as described in claim 1, characterized in that, The method employs an adaptive octree structure to dynamically partition the three-dimensional space, automatically adjusting the subdivision level based on the local complexity of the spatial data. This includes fine-grained partitioning in regions with drastic feature changes, while maintaining a coarser granularity in regions with relatively flat data, in order to achieve a balance between storage and accuracy.

8. The multi-radar power envelope fusion method as described in claim 7, characterized in that, Each tree node stores the scalar value of the corresponding spatial voxel, forming a hierarchical data representation.

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