Multi-radar power envelope fusion method

Abstract

The invention discloses a multi-radar power envelope fusion method, which comprises the steps of performing single-radar envelope modeling, and constructing an envelope fusion foundation; incoherent field fusion is determined, and a multi-radar envelope model is constructed; constructing a gradient diffusion model to realize envelope fusion smooth transition; euler method iterative convergence is displayed, and multi-radar envelope complete fusion is realized; and dynamically dividing a three-dimensional space by adopting a self-adaptive octree structure. The multi-radar power envelope fusion method has the beneficial effects that firstly, according to a radar equation, a propagation loss model and target scattering characteristics, the single-station detection probability of each radar unit at a grid point is calculated in a three-dimensional space voxelization mode; a probability union set or a more complex dependency relationship model is adopted, and a total-space joint detection probability field is generated through fusion; finally, through contour surface extraction (such as an improved March i ng Cubes algorithm) and color / transparency mapping driven by probability gradient, a fusion envelope curved surface with continuous vision and accurate mathematics is generated.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of radar detection, in particular to a multi-radar power envelope fusion method. BACKGROUND

[0002] In the modern air defense and anti-missile and airspace control system, multi-radar cooperative networking is the core technical support to realize wide-area coverage and high-precision target tracking. The visualization quality of radar power envelope (i.e. radar detection range) in the three-dimensional situation map directly affects the commander's cognition and decision-making effectiveness of the battlefield electromagnetic situation.

[0003] The current methods for processing multi-radar superposition effects mainly include transparency superposition method, isosurface extraction method, voxel coloring method, etc. These methods have been found to have problems such as poor visual degree of simple superposition, imprecise complex fusion boundary, poor resolution, and excessive dependence on hardware, etc. in practical application.

[0004] Specifically, the transparency superposition method gives each radar envelope surface a fixed transparency, and the overlapping area is approximated by color mixing to represent fusion. The transparency superposition method has obvious defects in multi-radar power envelope fusion display: the visual depth (color deepening or saturation increase) of the superposition area is determined by the number of superposition layers, rather than the actual coverage quality or complementarity. This can easily cause serious misjudgment - the superposition of multiple radar edge detection weak areas may be misjudged as a core high-confidence coverage area due to deep color, while the actual key area may show a lighter color due to single radar coverage. At the same time, this method cannot distinguish the differences in detection performance of different radars (such as accuracy, anti-interference ability), nor can it reflect whether the superposition is an enhanced coverage or a redundant coverage, making it difficult for operators to accurately assess the actual detection effectiveness and weak links after fusion, reducing the accuracy of situation awareness and the reliability of decision-making.

[0005] The isosurface extraction method is essentially to sum or take the maximum value of each radar detection probability field, and then extract the joint isosurface. The main problem of the isosurface extraction method in multi-radar power envelope fusion display is that it is difficult to accurately express the complex fusion boundary: when multiple radar power ranges overlap, nest or have gaps, the single isosurface generated by this method will excessively smooth these key areas, resulting in a blurred fusion boundary that cannot accurately reflect the actual coverage strength changes and blind area details. Secondly, the calculation efficiency is low, especially when facing massive radar data and three-dimensional space, real-time generation of high-quality isosurface has a large calculation burden. In addition, this method is sensitive to threshold selection, and improper threshold setting can easily cause distortion of the fusion result, making it difficult to effectively distinguish the contribution of different radars or highlight key coverage features, reducing the intuitiveness of the display and the value of decision support.

[0006] The voxel coloring method discretizes space into voxels, calculates multi-radar contribution values for each voxel, and interpolates coloring. The core problem of the voxel coloring method in multi-radar power envelope fusion display is that the expression method is based on a discrete three-dimensional grid (voxel): first, the resolution is limited, and the fixed size of the voxel causes the envelope edge to present a jagged shape, which is difficult to accurately describe the complex curved boundary, especially with serious distortion at low resolution. Secondly, the calculation and storage overhead is huge, and a huge voxel space needs to be established to cover the entire airspace, and each voxel needs to store and calculate the fusion attribute (such as visibility, weight), and the resource consumption increases exponentially when multiple radars are superimposed, which is poor in real-time. Thirdly, it is difficult to implement the fusion rule at the voxel level, and how to accurately weight and fuse different radar envelopes in the shared voxel easily leads to boundary blurring or information loss. Finally, the pre-processing of generating voxelized envelope itself is time-consuming and difficult to dynamically respond to changes in radar parameters or environment. These factors limit its application in high-precision and high-performance occasions.

[0007] Therefore, it is urgent to develop an envelope fusion method based on a joint detection probability field, which accurately describes the detection capability gradient change under the cooperation of multiple radars by establishing a spatial continuous probability distribution function. SUMMARY

[0008] The main purpose of the present application is to propose a multi-radar power envelope fusion method, which aims to solve the problems of the existing methods for processing the superposition effect of multiple radars, such as poor visual degree of simple superposition, non-precise complex fusion boundary, poor resolution, and excessive dependence on hardware.

[0009] To solve the above problems, the present application proposes a multi-radar power envelope fusion method, comprising:

[0010] Single radar envelope modeling, constructing envelope fusion basis;

[0011] Determining non-coherent field fusion, constructing multi-radar envelope model;

[0012] Constructing a gradient diffusion model to realize smooth transition of envelope fusion;

[0013] Displaying Euler method iteration convergence to realize complete fusion of multi-radar envelope;

[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 an embodiment, the single radar envelope modeling, constructing envelope fusion basis comprises:

[0016] According to the formula The distance from the target to the i-th radar is calculated, where R i represents the distance from the i-th radar to the target, is the spatial position vector of the target, is the spatial position vector of the i-th radar;

[0017] The detection probability model of the i-th radar at point is constructed by using the attenuation model in the spherical coordinate system:

[0018] wherein is the detection probability of the i-th radar at position , R max,i is the maximum detection distance of the i-th radar, κ is the attenuation coefficient value, P max,i is the maximum detection probability of the i-th radar, Atten(θ i ,φ i ) is the directional pattern attenuation function.

[0019] In an embodiment, the determining the incoherent field fusion and constructing the multi-radar envelope model comprises:

[0020] constructing a radar joint detection probability model: wherein n is the number of radars, is the joint detection probability.

[0021] In an embodiment, the constructing the gradient diffusion model and realizing the envelope fusion smooth transition comprises:

[0022] determining a diffusion coefficient D: the diffusion coefficient D is designed as the inverse function of the probability gradient: wherein is the gradient operator;

[0023] constructing a diffusion equation wherein the initial time is the change rate of the probability field u with time t, is the diffusion term, describing the "diffusion / smoothing" process of the probability field.

[0024] In an embodiment, the displaying the Euler method iteration convergence and realizing the complete fusion of the multi-radar envelope comprises:

[0025] initial setting under the three-dimensional grid: the index of the grid point is set as (i,j,k), wherein i=1,2,...,N x , j=1,2,...,N y , k=1,2,...,N z are the grid numbers in the x, y and z directions respectively, the probability value of the grid point (i,j,k) at the initial time t=0 is u(i,j,k,0)=P fuse (i,j,k), wherein P fuse (i,j,k) is the value of the multi-radar joint detection probability at the grid point.

[0026] Gradient calculation in three-dimensional space: In a three-dimensional grid, the gradient is a vector whose components in the x, y, z directions are respectively:

[0027] The modulus of the gradient is

[0028] Calculation of diffusion coefficient D in three-dimensional space:

[0029] Discretization of the diffusion equation in three-dimensional space: The diffusion equation in three-dimensional space is: where the divergence in discrete form in a three-dimensional grid is:

[0030]

[0031] Explicit Euler method iteration solution: Discretize time using the explicit Euler method, with time step Δt, then the iteration formula is:

[0032] Boundary condition processing: Use one-sided difference to approximate the derivative at the boundary.

[0033] In an embodiment, the specific iteration steps are as follows:

[0034] S1, initialization: input the probability value u(i, j, k, 0) = P fuse (i, j, k) at the initial time t = 0;

[0035] S2, calculate the gradient modulus: calculate the modulus of each grid point according to the three-dimensional gradient calculation formula

[0036] S3, calculate the diffusion coefficient: calculate the diffusion coefficient D(i+1, j, k) of each grid point according to the diffusion coefficient formula;

[0037] S4, calculate the divergence term: calculate the divergence term of each grid point according to the three-dimensional divergence discretization formula

[0038] S5, iteration update: update the probability value u(i, j, k, t+Δt) of each grid point at time t+Δt using the explicit Euler iteration formula;

[0039] S6, repeat steps S2-S5 for 3-5 iterations until the result converges.

[0040] ​In an embodiment, the employing single-sided difference to approximate the derivative at the boundary comprises: i = N x ,

[0041] In an embodiment, κ = 0.693.

[0042] In an embodiment, the employing adaptive octree structure to dynamically divide the three-dimensional space, automatically adjusting the subdivision level according to the local complexity of the spatial data comprises: performing fine division in areas with sharp feature changes, and maintaining a relatively coarse granularity in data flat areas, to achieve a balance between storage and accuracy.

[0043] In an embodiment, each tree node stores the scalar value of the corresponding spatial voxel to form a hierarchical data representation.

[0044] Advantages:

[0045] 1. The multi-radar power envelope fusion method of the present application first calculates the single-station detection probability of each radar unit at the grid point in the three-dimensional voxel according to the radar equation, the propagation loss model and the target scattering characteristics; then adopts probability union or more complex dependency models to generate a full-space joint detection probability field; finally, through isosurface extraction (such as the improved Marching Cubes algorithm) and probability gradient driven color / transparency mapping, a visually continuous and mathematically accurate fusion envelope surface is generated.

[0046] 2. The multi-radar power envelope fusion method of the present application can ensure that the color brightness / saturation in the overlapping area is enhanced with the increase of probability, and the boundary transition is naturally smooth, while supporting quantitative analysis functions such as isoprobability surface sectioning and blind area volume calculation, significantly improving the physical accuracy, cognitive intuitiveness and decision support of battlefield electromagnetic situation expression, and providing a reliable visualization cornerstone for key tasks such as anti-stealth combat and key point air defense. BRIEF DESCRIPTION OF DRAWINGS

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0048] Figure 1 is the application effect of the multi-radar power envelope fusion method of the present application Figure One ;

[0049] Figure 2 is the application effect of the multi-radar power envelope fusion method of the present application Figure Two ; DETAILED DESCRIPTION

[0050] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort fall within the protection scope of the present application.

[0051] It should be noted that if the embodiments of the present application involve directional indications (such as up, down, left, right, front, back, etc.), the directional indications are only used to explain the relative positional relationship, movement condition, etc. between components in a certain posture (as shown in the drawings), and if the certain posture changes, the directional indications also change accordingly.

[0052] In the present application, unless otherwise explicitly specified and limited, the terms “connection”, “fixation” and the like should be understood in a broad sense, for example, “fixation” can be fixed connection, or detachable connection, or integral; can be mechanical connection, or electrical connection; can be direct connection, or indirect connection through an intermediate medium; can be internal connection of two elements or interaction relationship between two elements, unless otherwise explicitly limited. For a person of ordinary skill in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0053] In addition, if the embodiments of the present application involve “first”, “second” and the like, the “first”, “second” and the like are only for description purposes, and cannot be understood as indicating or implying the relative importance of the indicated technical features or implicitly indicating the number of the indicated technical features. Therefore, the features with “first” and “second” can explicitly or implicitly include at least one of the features. In addition, the meaning of “and / or” appearing throughout the text includes three parallel solutions. Taking “A and / or B” as an example, it includes A solution, or B solution, or A and B solutions. In addition, the technical solutions of each embodiment can be combined with each other, but it must be based on the fact that a person of ordinary skill in the art can realize it, and when the combination of technical solutions contradicts each other or cannot be realized, it should be considered that the combination of technical solutions does not exist, and is not within the protection scope of the present application.

[0054] The current mainstream method for processing the superposition effect of multiple radars generally adopts a simple superposition rendering mode, that is, each radar envelope is calculated and drawn independently, and then the graphics are directly overlapped. This mode has significant physical distortion and cognitive limitations.

[0055] Firstly, the superimposed optical transparency leads to color mixing distortion and depth information confusion, which cannot accurately map the spatial distribution of multi-radar joint detection probability. For example, the radar beam overlap area enhances the detection probability due to signal redundancy, but visually it may be saturated or darkened due to color superposition, which is misjudged as a "detection blind area" or "invalid area", causing cognitive bias of key defense areas.

[0056] Secondly, the discrete envelope boundary presents a jagged or discontinuous mutation at the intersection, which violates the inherent continuous attenuation characteristics of electromagnetic wave propagation, not only reducing the physical realism of the scene, but also obscuring the details of the detection probability gradient change.

[0057] Thirdly, the quantitative analysis capability is poor, and the superimposed area and the real blind area are difficult to distinguish visually, which hinders the accurate evaluation of radar network coverage uniformity, overlap redundancy and vulnerability area. In complex scenes such as anti-stealth targets or low-altitude penetration, such distortion may mislead the judgment of weak links in the defense system, forming tactical risks.

[0058] Fourthly, in terms of aesthetics, the rigid superposition destroys the immersion of the three-dimensional scene, and it is difficult to meet the demand of modern simulation system for high-fidelity visualization of human-computer interaction.

[0059] The core of these defects is that the existing method renders the radar envelope as an isolated geometric entity, ignoring the continuous superposition nature of electromagnetic wave energy in space and the mathematical properties of probability fusion. Simple graphic superposition cannot express the nonlinear probability enhancement effect of radar beam intersection area (such as signal coherent or incoherent accumulation), nor can it build a smooth transition model consistent with physical laws.

[0060] Therefore, the embodiment designs a multi-radar power envelope fusion method. First, according to the radar equation, the propagation loss model and the target scattering characteristics, the single station detection probability of each radar unit at the grid point in the three-dimensional space is calculated; then the probability union or more complex dependent relationship model is used to generate a full-space joint detection probability field; finally, through the isosurface extraction (such as the improved Marching Cubes algorithm) and the probability gradient driven color / transparency mapping, a visually continuous and mathematically accurate fusion envelope surface is generated. The multi-radar power envelope fusion method of the embodiment can ensure that the color brightness / saturation of the overlapping area is enhanced with the increase of the probability, and the boundary transition is naturally smooth, while supporting quantitative analysis functions such as isoprobability surface sectioning and blind area volume calculation, significantly improving the physical accuracy, cognitive intuitiveness and decision support of battlefield electromagnetic situation expression, and providing a reliable visualization cornerstone for key tasks such as anti-stealth combat and air defense.

[0061] Specifically, the embodiment proposes a multi-radar power envelope fusion method, which comprises:

[0062] Single radar envelope modeling, building envelope fusion foundation;

[0063] Determine the incoherent field fusion, build a multi-radar envelope model;

[0064] Build a gradient diffusion model to achieve smooth transition of envelope fusion;

[0065] Show Euler method iteration convergence, realize the complete fusion of multi-radar envelope;

[0066] 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.

[0067] The multi-radar power envelope fusion method of the embodiment introduces non-coherent probability superposition into envelope fusion, reduces the dependence on phase information when the envelope is presented; and proposes a gradient control diffusion method to realize smooth transition and edge preservation; adopts octree+GPU acceleration strategy to ensure that the frame rate of 10 radars in the same situation is increased to more than 30fps. Practice shows that under high refresh rate, the envelope fusion is smooth, the boundary interface is clear, and the dependence on radar parameters is reduced, which greatly improves the fusion envelope presentation and user's visual sense;

[0068] In addition, the multi-radar power envelope fusion method of the embodiment supports real-time update of dynamic environment envelope (radar motion, terrain occlusion), and has the advantages of significantly improving the real-time performance and adaptability of environment perception. By responding to radar movement and terrain changes in real time, the detection blind area can be reduced, the target tracking accuracy can be improved, and the continuous and reliable operation in complex dynamic environment can be ensured.

[0069] Specifically, the single radar envelope modeling, building envelope fusion foundation includes:

[0070] According to the formula The distance from the target to the ith radar is calculated, where R i represents the distance from the ith radar to the target, is the spatial position vector of the target, is the spatial position vector of the ith radar;

[0071] The attenuation model under the spherical coordinate system is used to build the detection probability model of the ith radar at point

[0072] In the formula, is the detection probability of the ith radar at position R max,i is the maximum detection distance of the ith radar, κ is the attenuation coefficient value, preferably κ=0.693, P max,i is the maximum detection probability of the ith radar, Atten(θ i ,φ​i ) is a directivity attenuation function.

[0073] Specifically, the determining the incoherent field fusion and constructing the multi-radar power envelope model comprises:

[0074] Constructing a radar joint detection probability model: In the formula, n is the number of radars, is the radar joint detection probability, and the formula strictly reflects the physical nature of electromagnetic wave incoherent superposition.

[0075] The multi-radar power envelope fusion method of the embodiment has the advantages of introducing incoherent probability superposition into radar power envelope fusion, without relying on accurate phase information, reducing system complexity and synchronization requirements, improving target detection probability and reducing false alarm rate through probability fusion, enhancing robustness in noise and clutter environment, supporting multi-radar cooperative work, expanding coverage, improving overall anti-interference capability and reliability, and being suitable for distributed systems.

[0076] Specifically, the constructing the gradient diffusion model and realizing envelope fusion smooth transition comprises:

[0077] Determining a diffusion coefficient D: the diffusion coefficient D is designed as an inverse function of the probability gradient: In the formula, is a gradient operator, and if is small (i.e., the probability changes gently, such as inside the envelope), the diffusion coefficient D is large (the denominator is small), the diffusion is enhanced, and the smoothing is realized; if is large (i.e., the probability changes steeply, such as the boundary), D is small (the denominator is large), the diffusion is inhibited, and the boundary is kept sharp;

[0078] To eliminate the boundary sawtooth, a diffusion equation is constructed Where the initial time is is the rate of change of the probability field u with time t, is a diffusion term, which describes the "diffusion / smoothing" process of the probability field.

[0079] The multi-radar power envelope fusion method of the embodiment ingeniously unifies the contradictory requirements of image smoothing and edge preservation. The method uses gradient information to adaptively control the diffusion process, enhances diffusion in the gradient gentle area to realize effective noise reduction and uniform smoothing, and significantly inhibits diffusion in the gradient steep (edge) area to sharply preserve details and structural boundaries.

[0080] Specifically, the displaying Euler method iteration convergence and realizing complete fusion of the multi-radar envelope comprises:

[0081] Initial setting under three-dimensional grid: assuming we have a three-dimensional space, which is discretized into a three-dimensional grid, the spacing of the grid in x, y, z direction is Δx, Δy, Δz respectively, and the index of the grid point is (i, j, k), where i = 1, 2, …, N x , j = 1, 2, …, N y , k = 1, 2, …, N z are the number of grids in x, y, z direction respectively, at the initial time t = 0, the probability value of the grid point (i, j, k) is u(i, j, k, 0) = P fuse (i, j, k), where P fuse (i, j, k) is the value of the multi-radar joint detection probability at the grid point;

[0082] Gradient calculation in three-dimensional space: in the three-dimensional grid, the gradient is a vector, and its components in x, y, z direction are respectively:

[0083] The modulus of the gradient is

[0084] The calculation of the diffusion coefficient D in three-dimensional space, the expression of the diffusion coefficient D in the three-dimensional grid is similar to two-dimensional, which is: Its physical meaning is also to increase the diffusion coefficient in the probability variation flat area (envelope inside) to enhance the smoothing effect, and to reduce the diffusion coefficient in the steep edge area to maintain the sharp boundary;

[0085] Discretization of diffusion equation in three-dimensional space: the diffusion equation in three-dimensional space is: Where the divergence in the three-dimensional grid is discretized as:

[0086]

[0087] Here D(i+0.5, j, k) etc. represent the diffusion coefficient on the grid interface, which can be obtained by interpolation of the diffusion coefficients of adjacent grid points, for example

[0088] Explicit Euler method iteration solution: the explicit Euler method is used to discretize time, and the time step is Δt, then the iteration formula is:

[0089] Boundary condition processing: single-sided difference is used to approximate the derivative at the boundary.

[0090] Specifically, the specific iteration steps are as follows: ​

[0091] S1, initialization: set the initial probability value u(i, j, k, 0) = P at time t = 0 fuse (i, j, k) input;

[0092] S2, calculate the gradient modulus: calculate the modulus of each grid point according to the three-dimensional gradient calculation formula

[0093] S3, calculate the diffusion coefficient: calculate the diffusion coefficient D(i+1, j, k) of each grid point according to the diffusion coefficient formula

[0094] S4, calculate the divergence term: calculate the divergence of each grid point according to the three-dimensional divergence discretization formula

[0095] S5, iterative update: update the probability value u(i, j, k, t+Δt) of each grid point at time t+Δt using the explicit Euler iteration formula

[0096] S6, repeat steps S2-S5 for 3-5 iterations until the result converges.

[0097] In this embodiment, the boundary condition processing includes:

[0098] At the boundary of the three-dimensional grid, for example, i = 1, i = N x , j = 1, j = N r , k = 1, k = N z and other positions, special processing methods need to be used to calculate the gradient and divergence, such as using one-sided difference to approximate the derivative at the boundary, for example, the gradient in the x direction can be approximated as:

[0099] i = 1,

[0100] i = N x , At the same time, during the iteration process, the probability value at the boundary can be set to a fixed value or other boundary conditions according to the specific problem. Through the above steps, the gradient-driven diffusion smoothing can be realized under the three-dimensional grid, and the smooth and sharp boundary probability field result is obtained.

[0101] In this embodiment, the adaptive octree structure is used to dynamically divide the three-dimensional space, and the local complexity of the spatial data is automatically adjusted according to the subdivision level, including: in the area with dramatic changes in characteristics (such as the vicinity of the isosurface), fine division is performed, while in the data flat area, a relatively coarse granularity is maintained, and the balance between storage and precision is achieved. 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, a parallel diffusion calculation is implemented on the CUDA architecture: thousands of threads of the GPU are synchronized to process the octree nodes, each thread is responsible for a spatial unit, the current node value is iteratively updated according to the adjacent node values, and the shared memory is used to optimize data access, which significantly speeds up algorithms such as Gaussian diffusion or Laplace smoothing. In the rendering stage, the trilinear interpolation technique 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 average, and finally the interpolation points that meet the threshold are connected to generate smooth isosurfaces through marching cubes algorithm. This method combines the efficiency of adaptive data structure, the real-time performance of GPU parallel computing, and the continuity guarantee of trilinear interpolation, and is suitable for scientific visualization and real-time volume rendering scenarios.

[0102] The octree+GPU acceleration strategy of the multi-radar power envelope fusion method of this embodiment greatly improves the three-dimensional data processing speed, reduces the query time, supports real-time rendering and physical simulation of large-scale scenes, and is particularly suitable for high-performance graphics applications.

[0103] The multi-radar power envelope fusion method of this embodiment aims to realize the collaborative optimization of physical detection and visual presentation. Its core lies in the division and fusion of two levels:

[0104] Physical layer: joint detection probability field construction. This level is based on the non-coherent superposition physical characteristics of radar waves in space. Unlike the interference effect of coherent waves (such as laser), the energy of non-coherent radar waves mainly presents energy superposition rather than phase interference in space. By using this characteristic, the energy distribution and echo statistical characteristics of multiple radar detection units (or multiple detections) in the target space are calculated to construct a joint detection probability field. This probability field is a spatial continuous function, whose value represents the possibility or confidence of the target existing at a certain point in space. It effectively fuses multi-source / multi-time radar detection information and quantifies the spatial uncertainty of the detection result, providing more robust physical basis data for subsequent processing;

[0105] Rendering layer: diffusion smoothing and visual continuous transition. Directly presenting the joint detection probability field generated by the physical layer often has problems such as sharp boundary, obvious noise and spatial discontinuity, which does not conform to the human eye's perception habit of continuous and smooth boundary. The rendering layer introduces the diffusion equation (a partial differential equation that simulates the diffusion and smoothing of matter or energy in space over time) to solve this problem. This layer regards 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: the information in the high gradient area (such as the edge of the object) will naturally "diffuse" to the adjacent low probability area, making the originally sharp or abrupt boundary soft and continuous. This process smooths the "envelope boundary" of the target contour, effectively eliminating the visual abruptness and generating a visual result that is consistent with human eye perception and spatial continuous transition.

[0106] The multi-radar power envelope fusion method of the embodiment ensures the statistical reliability of detection through the non-coherent field construction of the physical layer, and realizes the natural continuity of visual perception through the diffusion smoothing of the rendering layer, effectively unifying physical reality and visual understandability.

[0107] In the embodiment, when the multi-radar power envelope fusion method of the embodiment is implemented based on the three-dimensional electromagnetic situation visualization system developed on the JavaScript / WebGL platform, the application effect is as shown in Figure 1 and Figure 2 Figure 1 It shows that the multi-radar power envelope is clear in layer and has strong color hierarchy, and the radar boundary converges in a jagged manner in the overhead state. Figure 2 It shows that the multi-radar power envelope is well fused in the horizon state, both boundary and fusion are embodied, and the visual effect is good.

[0108] It can be seen that the multi-radar power envelope fusion method of the embodiment realizes high-fidelity fusion of multi-radar power envelope in three-dimensional electromagnetic situation, and solves the cognitive confusion problem of "detection blind area" or "invalid area" caused by traditional superimposed display. Through non-coherent field fusion and gradient-driven diffusion, both the physical accuracy of detection probability and the natural transition of envelope boundary are realized. Through practical application verification, it significantly improves the visual sense and fusion degree in the scene of electromagnetic situation reaction combat. In the future, it can be extended to the field of multi-source sensor fusion such as sonar and photoelectricity, and provide reliable spatial situation input for artificial intelligence assisted decision-making. The application of this technology will promote the visualization of three-dimensional electromagnetic spectrum war to a new stage of "physical precision and cognitive intuition".

[0109] ​The above merely describes the preferred embodiments of the present application, and is not intended to limit the patent scope of the present application. Any equivalent structural changes made according to the content of the present application specification and drawings, or direct / indirect application in other related technical fields, are included in the patent protection scope of the present application.

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.

2. The multi-radar power envelope fusion method as described in claim 1, characterized in that, The single radar envelope modeling, which establishes the foundation for envelope fusion, includes: According to the formula Calculate the distance from the target to the i-th radar, where R i This represents the distance at which the i-th radar reaches the target. It is the spatial position vector of the target. It is the spatial position vector of the i-th radar; The attenuation model of the i-th radar at point is constructed using a spherical coordinate system. Detection probability model: In the formula For the i-th radar at position The detection probability at location R max，i Let P be the maximum detection range of the i-th radar, κ be the attenuation coefficient, and P be the maximum detection range of the i-th radar. max，i Let Atten(θ) be the maximum detection probability of the i-th radar. i , φ i ) 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. To allow for the detection probability of two tigers.

4. The multi-radar power envelope fusion method as described in claim 3, characterized in that, 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 The initial time Let u be the rate of change of the probability field with time t. The diffusion term describes the "diffusion / smoothing" process of the probability field.

5. The multi-radar power envelope fusion method as described in claim 4, characterized in that, The explicit Euler method iterative convergence, achieving complete fusion of multiple radar envelopes, includes: Initial settings for a 3D mesh: Let the indices of the mesh points be (i,j,k), where i = 1,2,...,N x j = 1, 2, ..., N y k = 1, 2, ..., N z Let be the number of grid cells in the x, y, and z directions, respectively. At the initial time t = 0, the probability value at grid point (i, j, k) is u(i, j, k, 0) = P. fuse (i, j, k), where P fuse (i, j, k) 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: Using the explicit Euler method to discretize time with a time step of Δt, the iterative formula is as follows: Boundary condition handling: One-sided difference is used to approximate the derivative at the boundary.

6. The multi-radar power envelope fusion method as described in claim 5, characterized in that, The specific iteration steps are as follows: S1. Initialization: Set the probability value u(i,j,k,0) = P at the initial time t=0. fuse Input (i, j, k); 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 D(i+1, j, k) 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 the probability value u(i, j, k, t+Δt) of each grid point at time t+Δt using the explicit Euler iterative formula; S6. Repeat steps S2-S5 for 3-5 iterations until the result converges.

7. The multi-radar power envelope fusion method as described in claim 5, characterized in that, The method of approximating the derivative at the boundary using one-sided difference includes: i = N x hour, 8. The multi-radar power envelope fusion method as described in claim 2, characterized in that, κ = 0.

693.

9. The multi-radar power envelope fusion method as described in claim 1, characterized in that, The method of using an adaptive octree structure to dynamically divide the three-dimensional space and automatically adjust the subdivision level according to the local complexity of the spatial data includes: performing fine division in areas with drastic feature changes, while maintaining a coarser granularity in areas with smooth data, in order to achieve a balance between storage and accuracy.

10. The multi-radar power envelope fusion method as described in claim 1, characterized in that, Each tree node stores the scalar value of the corresponding spatial voxel, forming a hierarchical data representation.

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