Building structure three-dimensional reconstruction method based on unmanned aerial vehicle-mounted through-wall radar

Abstract

The invention belongs to the technical field of building three-dimensional reconstruction, and particularly relates to a building three-dimensional reconstruction method based on an unmanned aerial vehicle-mounted through-the-wall radar, and the method specifically comprises the steps: setting a reflection power coefficient function according to the non-vertical echo influence, and building a multi-layer wall radar echo model based on the reflection power coefficient function; calculating an azimuth-distance two-dimensional matrix under the condition of considering non-vertical echoes by using the echo model, and obtaining a BP imaging model based on angle weighting according to the two-dimensional matrix; generating an echo model in a set three-dimensional building layout scene, performing imaging by using the BP imaging model, and taking a real wall structure in the scene as a label to obtain a training data set; performing neural network training by using the training data set; echo signals collected by the unmanned aerial vehicle through-the-wall radar are input into the trained neural network, and three-dimensional reconstruction of the building structure is achieved.

Description

Technical Field

[0001] This invention belongs to the field of building 3D reconstruction technology, and particularly relates to a building 3D reconstruction method based on UAV-borne through-wall radar. Background Technology

[0002] With economic and technological development, cities are seeing an increasing number of high-rise buildings. Understanding their three-dimensional layout is a crucial component of smart buildings and the Internet of Things (IoT), providing services for various applications such as disaster relief and possessing significant practical and research value. Therefore, building layout reconstruction technology has received increasing attention and research in recent years.

[0003] Building layout reconstruction technology can be divided into two-dimensional reconstruction and three-dimensional reconstruction according to the reconstruction form. Two-dimensional reconstruction refers to restoring the building's floor plan layout, which is relatively traditional and has been widely studied. Three-dimensional reconstruction can more intuitively reflect the building structure, which is relatively novel and has been studied less. Since building layout reconstruction mainly relies on the penetrating properties of low-frequency electromagnetic waves, it can also be divided into reflection type and transmission type according to the principle. The reflection type refers to the electromagnetic wave transmitting and receiving antennas being located on the same side of the building, obtaining its layout by the reflected waves from the wall; the transmission type refers to the transmitting and receiving antennas being located on both sides of the building, obtaining its layout by the electromagnetic waves that penetrate the wall.

[0004] In terms of 2D reconstruction, Song et al. from the National University of Defense Technology used a single-sided fixed MIMO radar in reflection mode to reconstruct building layouts and perceive human targets. However, the reconstructed layout suffered from excessive clutter, making it impossible to confirm wall positions without prior internal information. Li et al. from the University of Electronic Science and Technology of China used a MIMO radar mounted on a dual-sided mobile vehicle, employing CT technology in transmission mode to achieve 2D reconstruction based on path delay. However, this method suffered from low resolution. Furthermore, the experimental scenario in this study was relatively simple, making it impossible to determine its applicability in complex scenarios. Zhang et al. from Beijing Institute of Technology used a UAV-borne radar in reflection mode to fly around a building, superimposing SAR imaging results from two perspectives to achieve 2D reconstruction. However, this method suffered from poor reconstruction fidelity and wall skew.

[0005] Research on 3D reconstruction of buildings is relatively lacking. The Netherlands Academy of Sciences, led by Smits et al., used a reflection-mode MIMO-SAR radar system, achieving some success on strong scattering bodies. However, the limited array length resulted in low height resolution, failing to clearly reflect the 3D structure of buildings. Guo et al. from the University of Electronic Science and Technology of China used transmission-mode CT technology, synchronously moving the transmitting and receiving antennas on both sides of the wall via a guide rail, and solving the problem using the receiving delay and 3D-TV algorithm. However, due to antenna installation limitations, the height imaging range of this method is very limited, making it unsuitable for high-rise buildings. Karanam et al. used a transmission-mode Wi-Fi method, employing two small UAVs to synchronously fly around the building, acquiring detection data via Wi-Fi signals. Although the UAV-borne Wi-Fi mode avoids the limitation of height imaging range, the method suffers from low imaging fidelity due to the motion and positioning errors of the two UAVs and the inherent limitations of the Wi-Fi signal itself.

[0006] In terms of improving the image fidelity of architectural layout reconstruction, some image enhancement studies have been conducted, but they are all limited to two-dimensional layout reconstruction, and the improvement in image quality is limited. Aftanas et al. proposed using edge detection and Hough transform to extract wall structures, but there is a problem of not being able to accurately determine the starting position of the walls. In 2013, Jia et al. from Chengdu University of Technology proposed using an MNK detector to fuse multi-view imaging results, but the architectural layout is relatively coarse. In 2019, Jia et al. used generative adversarial networks to achieve multipath and raster lobe ghosting suppression in architectural layout, but the processing performance for complex building structures and actual radar imaging data still needs further verification.

[0007] Existing two-dimensional or three-dimensional building reconstruction methods struggle to balance image range, resolution, and fidelity, failing to demonstrate their practicality in complex scenes. Furthermore, existing building layout enhancement methods are limited to two-dimensional layout reconstruction, with very limited enhancement effects, failing to meet the needs of three-dimensional reconstruction of complex building scenes. Summary of the Invention

[0008] In view of this, the present invention proposes a method for three-dimensional reconstruction of building structures based on UAV-borne through-wall radar. This method can achieve high-precision three-dimensional reconstruction of complex building scenes, is applicable to the field of building three-dimensional reconstruction, and belongs to a robust and robust three-dimensional reconstruction method.

[0009] The technical solution for implementing the present invention is as follows:

[0010] A method for 3D reconstruction of buildings based on UAV-borne through-wall radar, the specific process of which is as follows:

[0011] Step 1, establish a multi-layer wall radar echo model: set the reflection power coefficient function according to the influence of non-vertical echo, and establish a multi-layer wall radar echo model based on the reflection power coefficient function;

[0012] Step 2, Angle-weighted BP imaging model: Calculate the azimuth-range two-dimensional matrix considering non-vertical echoes using the echo model, and obtain the angle-weighted BP imaging model based on the two-dimensional matrix.

[0013] Step 3, construct the training dataset: Generate an echo model in the set 3D building layout scene, and use the BP imaging model to perform imaging, and use the real wall structure in the scene as the label to obtain the training dataset;

[0014] Step 4, Network Training and 3D Reconstruction: The neural network is trained using the training dataset; the echo signal collected by the UAV through-wall radar is input into the trained neural network to realize the 3D reconstruction of the building structure.

[0015] Optionally, the present invention considers the total radar echo as a weighted superposition of all wall echoes within a circular region with a radius of 1 / k, and the echo model is as follows:

[0016]

[0017] Where G(θ) represents the reflection power coefficient function, s i,j This represents the echo from the front or back wall of the i-th wall, where j=1 represents the front wall and j=2 represents the back wall. ρ m The value represents the maximum radius of the circular region, and w(ρ,φ) indicates whether there is a wall at that location; if it exists, the value is 1, and if it does not exist, the value is 0. ρ and Let W represent the radius and argument of the two-dimensional circular polar coordinate integral, respectively. i It is the result of integrating the right-hand side of the first equation, and it is a variable that is only related to the wall.

[0018] Optionally, the reflection power coefficient function G(θ) of the present invention is:

[0019]

[0020] Where θ represents the line connecting the radar and the network point. The included angle, Let k be the unit normal vector of the wall. -1 This indicates the maximum angular range; the first zero of the sinc function is located at θ = k. -1 The location.

[0021] Optionally, the angle-weighted BP imaging model described in this invention is as follows:

[0022]

[0023] Among them, S * (t a ,t k () indicates that non-vertical echoes are considered. The following is a two-dimensional orientation-distance matrix, W i (t a ) represents variables related to the wall; f0 is the center frequency of the radar transmitted wave, and t p For the two-way time delay of the electromagnetic wave from the radar to the grid point, t a Indicates the time.

[0024] Optionally, the training set of the present invention includes three-dimensional backpropagation (BP) images from N perspectives, and the neural network has N channels, with the three-dimensional BP images from N perspectives serving as the N channel dimensions of the input data.

[0025] Optionally, the training dataset of the present invention includes four parts: an ideal data subset without noise and UAV position error, a data subset containing only noise, a data subset containing only UAV position error, and a data subset containing both noise and position error.

[0026] Optionally, the present invention further describes the method of uniformly dividing noisy data into five parts based on signal-to-noise ratios of 0dB, 5dB, 10dB, 15dB, and 20dB.

[0027] Optionally, the neural network described in this invention is an improved U-Net. The improvement includes two aspects: first, adding a CBAM attention layer after the upsampling and downsampling layers; and second, using residual connections to replace the direct skip connections of U-Net.

[0028] Optionally, the improvement described in this invention further includes adding a downsampling and upsampling unit based on residual connections after the CBAM module of the codec.

[0029] The beneficial effects of this invention are as follows:

[0030] This invention proposes a method for 3D reconstruction of building structures based on UAV-borne through-wall radar. The invention derives a radar echo model for multi-layered wall scenes, proposes an angle-weighted BP imaging algorithm based on traditional BP imaging, and constructs an improved U-Net neural network architecture suitable for building reconstruction. This achieves high-precision 3D reconstruction of complex building scenes, making it applicable to the field of 3D building reconstruction and representing a robust and effective 3D reconstruction method.

[0031] This invention is widely applicable to urban building detection scenarios and offers a significant improvement in accuracy compared to traditional methods. Attached Figure Description

[0032] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments 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.

[0033] Figure 1 This is a partial dataset display. (a)-(c) represent data for one wall, (d)-(f) represent data for two walls, and (g)-(i) represent data for three walls.

[0034] Figure 2 This is the proposed improved U-Net structure;

[0035] Figure 3 These are the actual test scenarios and flight trajectories: (a) UAV, (b) test flight scenario, and (c) actual test flight trajectory.

[0036] Figure 4 These are comparison images of BP imaging results: (a) true value of the wall, (b) traditional imaging results, and (c) imaging results of the method proposed in this invention.

[0037] Figure 5 These are the measured results: (a) height projection of the true building layout, (b) height projection of the original building image, (c) height projection of the network output, (d) true three-dimensional building layout, (e) original three-dimensional building image, and (f) three-dimensional network output.

[0038] Specific implementation process

[0039] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0040] It should be noted that, in the absence of conflict, the following embodiments and features can be combined with each other; and, based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0041] It should be noted that various aspects of embodiments within the scope of the appended claims are described below. It will be apparent that the aspects described herein can be embodied in a wide variety of forms, and any particular structure and / or function described herein is merely illustrative. Based on this disclosure, those skilled in the art will understand that one aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects set forth herein can be used to implement the device and / or practice the method. Additionally, this device and / or method can be implemented using structures and / or functionalities other than one or more of the aspects set forth herein.

[0042] This application provides a method for three-dimensional reconstruction of building structures based on UAV-borne through-wall radar, which is achieved through the following steps:

[0043] Step 1: Establish a radar echo model of a multi-layered wall;

[0044] For the common scenario where the radar beam is pointed perpendicular to the wall, the reflected wave is mainly the reflection of the perpendicularly incident electromagnetic wave; therefore, the perpendicular incidence case is considered first. The power transmission coefficient R for perpendicularly incident electromagnetic waves... p With power reflection coefficient T p As shown in the following formula. Power transmission coefficient R p That is, the ratio of transmitted power to incident power, the power reflection coefficient T. p This represents the ratio of reflected power to incident power, where η1 and η2 are the characteristic wave impedances of the two media, respectively.

[0045]

[0046] Assume medium 1 is free space and medium 2 is a wall, and let the wall have a relative permittivity of ε. r Let ε0 be the permittivity of free space and μ0 be the permeability of a homogeneous medium with a relative permeability of 1. Then we have: Therefore, the above equation can be simplified to the following equation:

[0047]

[0048] For the i-th wall in the radar radial direction, the echo from the front wall undergoes 4i-4 transmissions and 1 reflection, while the echo from the rear wall undergoes 4i-2 transmissions and 1 reflection. Therefore, the relative energy of the wall echo can be expressed as follows: Where A... i,1 and A i,2 These represent the relative echo energy of the front and rear walls of the i-th wall, respectively (subscript i starts from 1).

[0049]

[0050] As can be seen from the above formula, for every additional layer of wall an electromagnetic wave passes through, the echo signal will undergo 4 more transmissions, and the echo energy of deep walls will be very weak.

[0051] Assume the radar transmit waveform is a linear frequency modulated continuous wave with a center frequency of f0, a bandwidth of B, and a duration of T. p Let the fast time be t. k If the time delay of the object echo is τ, then the original radar echo can be expressed as:

[0052]

[0053] Where K = B / T p Let d be the frequency modulation slope, and rect(·) be the rectangular function. Since electromagnetic waves propagate slower in a wall than in free space, the extra time an electromagnetic wave takes to pass through a wall is shown in the following formula, where d is the wall thickness and c is the speed of light in free space:

[0054]

[0055] Therefore, for scenarios with multiple walls, combining the previous equations, we can obtain the expression for the total radar echo, as shown in the following equation. In the equation, j=1 represents all front wall echoes, j=2 represents all rear wall echoes, and n represents the total number of walls in the radar radial direction.

[0056]

[0057] In the formula, s i,1 and s i,2 Let τ represent the echoes from the front wall (j=1) and the back wall (j=2) of the i-th wall, respectively. i,1 and τ i,2 Let represent the two-way time delay of the front and rear walls of the i-th wall, respectively, as shown in the following formula:

[0058]

[0059] In the formula, τ i D represents the two-way time delay from the center of the i-th wall to the radar. i d represents the radial distance from the center of the i-th wall to the radar. i This represents the thickness of the i-th wall.

[0060] The above derivation only considers vertical echoes; in reality, non-vertical echoes can also affect the echo. Let the unit normal vector of the wall be... So, the connection between the radar and the network points and The included angle θ can be expressed as follows:

[0061]

[0062] For a larger θ, the reflection coefficient is smaller; conversely, for a smaller θ, the reflection coefficient is larger. Based on the reflection properties of electromagnetic waves on a wall, the reflection power coefficient function is set as shown in the following equation. Here, k is a hyperparameter that determines the angular range.

[0063]

[0064] The total radar echo can be considered as a weighted superposition of all wall echoes within a circular region of radius 1 / k, then s i,j It can be modified into a two-dimensional circular integral on the wall.

[0065]

[0066] Where ρ and Let represent the radius and argument of the two-dimensional circular polar coordinate integral, respectively. The value ρ is either 1 or 0, indicating whether there is a wall at that location. m Represents the maximum radius of the circular region, satisfying ρ m = dtan(1 / k). Since the distance change is small, the effect of ρ on s is ignored. i,j The impact will be s i,j Moving outside the integral, we obtain the following equation. The integral equation depends only on the wall structure and radar position, with variable W... i express

[0067]

[0068] Therefore, the corrected total echo expression is:

[0069]

[0070] Step 2: Propose an angle-weighted BP imaging algorithm;

[0071] According to the traditional BP algorithm, for each azimuth time t a After removing the carrier and compressing the pulse from the received signal, the following approximate equation can be obtained: S * (t a ,t k ) represents the azimuth-range two-dimensional matrix considering the non-vertical echo case.

[0072]

[0073] Where F(·) represents the carrier removal and pulse compression operations. Let the radar's three-dimensional position vector be p. r The three-dimensional position vector of a certain imaging grid point is p n Then the imaging result I at the grid point * (pn ) can be expressed as the following formula, where t p For electromagnetic waves from radar p r to grid point p n Two-way delay.

[0074]

[0075] The above formula is the derivation of the traditional BP algorithm imaging formula. However, S * (t a ,t p It is not a single scattering point, but rather the radar at t a All energy is coupled at the distance corresponding to the given time. To avoid the impact of this coupling on imaging, S should be... * (t a ,t p Replace ) with S(t) a ,t p ,p n That is, replacing the energy of the coupling with p. n The energy corresponding to each point individually should satisfy the following equation.

[0076]

[0077] W i (t a ) represents W i .

[0078] Therefore, the proposed angle-weighted BP imaging algorithm formula is obtained:

[0079]

[0080] In traditional backpropagation (BP) algorithms, given a fixed wall structure and radar trajectory, the integrand depends only on the distance between the radar and the grid points; that is, the integrand value is the same on circles with the same distance. In other words, traditional BP imaging algorithms assume the target object could originate from any direction at the same distance, with equal probability in each direction. This is based on the prior assumption of equal probability without any prior information, a generalized approach. However, this assumption does not hold true in wall imaging; the probability distribution on circles with the same distance should be proportional to the relative energy of the echo. The proposed angle-weighted BP algorithm, compared to traditional BP algorithms, effectively improves the imaging quality of wall targets, especially when sampling points are sparse. It significantly suppresses energy in non-target areas, which is crucial for subsequent sample set construction.

[0081] Step 3: Construct the dataset required for network training;

[0082] In the dataset generation process, the azimuth and range imaging ranges of the scene are set to 0–12.8m, and the height imaging range is 0–3m. Windows with doors and windows are randomly generated within the scene range at different positions, heights, thicknesses, and dielectric constants to form a 3D architectural layout, which serves as the labels for the dataset.

[0083] Subsequently, echo signals are generated based on the 3D building layout and the aforementioned wall echo and energy model, and 3D BP imaging is performed (noise can be added to the echo signals). Next, 3D BP images in four directions are generated based on the echo signals (the positional error of the UAV can be considered). Finally, the 3D BP images in the four directions are used as the four channel dimensions of the input data.

[0084] This method considers two error sources: noise and UAV position error. The dataset is divided into four parts: an ideal subset without noise or UAV position error, a subset containing only noise, a subset containing only UAV position error, and a subset containing both noise and position error. The total dataset contains 1900 data sets, with the training and validation sets randomly partitioned in a 6:4 ratio. For noisy data, it is evenly divided into five parts based on signal-to-noise ratios (0dB, 5dB, 10dB, 15dB, and 20dB), as follows: Figure 1 As shown.

[0085] Step 4: Propose an improved U-Net and train the network;

[0086] To obtain the mapping relationship between radar 3D BP imaging results and the actual wall structure from multiple perspectives, this step employs a neural network approach. The network used in this step is an optimization and improvement based on U-Net. Traditional U-Net networks are suitable for 2D image segmentation; to make it applicable to 3D wall reconstruction, this step makes targeted improvements to the network structure. The improvements to U-Net in this step are mainly twofold: adding a CBAM attention layer after upsampling and downsampling, and replacing the direct skip connections of U-Net with residual connections.

[0087] CBAM, composed of cascaded channel attention layers and spatial attention layers, effectively captures the weight relationships between different spatial locations and channels in the input. In the scenario addressed in this step, the input is dense 3D BP imaging results, while the labels are sparse real wall structures, requiring the network to extract spatial information. Furthermore, different input channels correspond to different observation perspectives, necessitating the network's ability to extract channel features for fusion. Therefore, the CBAM layer is well-suited for this scenario, effectively enhancing the network's ability to recognize walls. Additionally, traditional U-Net, during upsampling, directly merges previous information using skip connections. The merged information may exhibit significant spatial and channel differences; therefore, the addition of the CBAM layer ensures smoother stitching after skip connections.

[0088] In the traditional U-Net network, skip connections are used between the encoder and decoder of corresponding layers. The encoder's feature map is copied after each downsampling step and directly connected to the corresponding upsampling step of the decoder. The network can combine shallow and deep features, thus taking into account both local and global information. This method adds res connections to the traditional direct skip connections, and adds downsampling and upsampling units based on residual connections after the CBAM module of the encoder and decoder. By introducing the residual module, the nonlinear expressive power of U-Net is enhanced, giving the decoder a more flexible feature selection space when reconstructing images. This allows the network to better adapt to the subtle boundary information changes in complex 3D images, making it more suitable for applications such as architectural layout reconstruction.

[0089] This invention introduces the Cbam attention mechanism module based on U-Net and uses residual modules to replace skip connections, which can effectively extract and fuse wall structure features from multiple perspectives. By inputting the 3D imaging results from different perspectives into the improved U-Net network, the 3D structure of the building can be obtained. Simulation and experimental data show that the comparison of images before and after the network is finalized, as well as quantitative index analysis, demonstrate that the layout reconstruction effect of the proposed method is significantly improved compared to the original SAR image, verifying the robustness and generalization of the method, proving that it is a novel and effective 3D building layout method.

[0090] The overall results of the proposed improved U-Net are as follows: Figure 2 As shown, the input is data with 4 channels and a shape of 128*128*32, representing the 3D BP imaging results from 4 viewpoints; the output is single-channel data of the same shape, representing the actual structure of the wall. The CBAM block is located at the beginning of each layer of the encoder and decoder, and the output of each encoder layer is concatenated with the corresponding output of the decoder via a residual block.

[0091] This completes a method for three-dimensional reconstruction of building structures using UAV-borne through-wall radar.

[0092] To overcome the limitations of imaging range and achieve layout reconstruction of high-rise buildings, this invention employs an unmanned aerial vehicle (UAV) platform and uses reflective through-wall radar to ensure theoretical accuracy of the reconstruction. To achieve 3D reconstruction, this invention adopts a detection mode where the UAV flies around the building from multiple perspectives at different altitudes, using a height-oriented synthetic aperture to ensure height-oriented resolution. To avoid poor image quality in the reconstructed images, this invention optimizes the direct overlay of multiple perspectives into a multi-view fusion network based on an improved U-Net, using deep neural networks to fuse and extract wall features. Example

[0093] To further verify the generalization performance of the algorithm, we conducted a field test on the second floor of a building. After setting the DJI flight control program, the drone automatically flew around the building in a square trajectory, rotating its body during viewpoint changes to keep the through-wall radar facing the wall. The altitude interval of the flight trajectory was set to 0.25 meters, with a total of 12 laps, corresponding to an altitude detection range of approximately 3 meters, roughly consistent with the height of the first floor of the building. Figure 3 As shown.

[0094] Before comparing the images before and after inputting them into the network, we first take measured data from one direction to verify the aforementioned angle-weighted BP imaging algorithm. Figure 4 A comparison of the height projection of traditional BP results and the height projection of the proposed angle-weighted BP clearly shows that the proposed algorithm has better image quality and can clearly display the position of the wall.

[0095] Figure 5 The experimental results show that the proposed network correctly reconstructed most of the building structure; however, some wall structures were missing. (Comparison) Figure 5 As can be seen from (b) and 5(c), the network output has fully extracted the input information.

[0096] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for three-dimensional reconstruction of a building based on unmanned airborne through-the-wall radar, characterized by, The specific process is: establishing a multi-layer wall radar echo model: setting a reflection power coefficient function according to the influence of non-vertical echoes, and establishing a multi-layer wall radar echo model based on the reflection power coefficient function; the BP imaging model based on angle weighting: using the echo model to calculate the azimuth-range two-dimensional matrix considering non-vertical echoes, and obtaining the BP imaging model based on angle weighting according to the two-dimensional matrix; constructing a training data set: generating an echo model under a set three-dimensional building layout scene, imaging using the BP imaging model, and taking the real wall structure in the scene as a label to obtain a training data set; network training and three-dimensional reconstruction: using the training data set for neural network training; the echo signal collected by the UAV through-wall radar is input into the trained neural network to realize three-dimensional reconstruction of the building structure.

2. The method of claim 1, wherein, The total radar echo can be regarded as the weighted superposition of all wall echoes in a circular area with a radius of 1 / k, and the echo model is: where G(θ) is the reflection power coefficient function, s i,j represents the echo of the front wall or the back wall of the ith wall, j = 1 represents the front wall, and j = 2 represents the back wall, ρ m represents the maximum radius of the circular region, w(ρ, φ) represents whether there is a wall at this position, and takes the value 1 if there is a wall and 0 if there is no wall, and ρ and φ represent the radius and the argument of the two-dimensional circular polar coordinate integration, respectively.

3. The method of claim 1, wherein the method further comprises: The reflection power coefficient function G(θ) is: where θ is the angle between the line connecting the radar and the network point and the wall surface unit normal vector, k is a hyperparameter that determines the angular range, k -1 denotes the maximum angular range.

4. The method of claim 2, wherein the method further comprises: The BP imaging model based on angle weighting is obtained according to the two-dimensional matrix: where S * (t a ,t k ) represents a two-dimensional matrix of azimuth-range considering non- vertical echoes under the wall, W i (t a ) is a variable related to the wall; f0is the center frequency of the radar transmitted wave, t p is the two-way time delay of the electromagnetic wave from the radar to the grid point, t a represents the time.

5. The method of claim 1, wherein, The training set includes N three-dimensional BP images under different viewing angles, and the number of channels of the neural network is N, and the three-dimensional BP images under N viewing angles are used as N channel dimensions of input data.

6. The method of claim 5, wherein the method further comprises: The number of viewing angles is 4.

7. The method of claim 5, wherein the method further comprises: The training data set includes four parts, which are ideal data subsets without noise and UAV position error, data subsets containing only noise, data subsets containing only UAV position error, and data subsets containing both noise and position error.

8. The method of claim 6, wherein the method further comprises: For the noise-containing data, it is divided into 5 parts according to the signal-to-noise ratio of 0dB, 5dB, 10dB, 15dB and 20dB.

9. The method of claim 1, wherein, The neural network is an improved U-Net, and the improvement includes two aspects: one is to add a CBAM attention layer after the up-sampling and down-sampling layers, and the other is to use residual connection instead of direct skip connection of U-Net.

10. The method of claim 9, wherein, The improvement also includes: adding residual connection-based down-sampling and up-sampling units after the CBAM module of the codec.

Images