A method for three-dimensional imaging of point targets based on a multi-layer ring array of vortex electromagnetic waves

Abstract

This invention relates to a three-dimensional imaging method for point targets based on a multi-layer ring array of vortex electromagnetic waves, comprising: transmitting electromagnetic vortex wave transmission signals to form multi-mode target electromagnetic vortex echo signals; performing range migration correction on the target electromagnetic vortex echo signals to obtain corrected signals; performing azimuth compression processing on the corrected signals, followed by inverse fast Fourier transform in the azimuth direction to obtain an azimuth-focused image; obtaining the optimal focused image based on the pixel amplitude of the azimuth-focused image; performing constant false alarm rate target detection on the optimal focused image to obtain slow and fast time index values; performing azimuth super-resolution processing based on the total signal of the target electromagnetic vortex echoes to obtain the target's azimuth information; and determining the target's three-dimensional spatial coordinates based on the slow and fast time index values ​​and the azimuth information. This invention improves target imaging resolution.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing technology, and specifically to a three-dimensional imaging method for point targets based on a multi-layer ring array of vortex electromagnetic waves. Background Technology

[0002] Vortex electromagnetic waves are electromagnetic waves carrying orbital angular momentum. Their annular radiation field intensity distribution and helical phase wavefront give them the ability to modulate phase information in the azimuth direction. Therefore, vortex electromagnetic waves have received increasing attention in radar imaging, rotating target detection, and other fields in recent years. The introduction of the concept of Orbital Angular Momentum (OAM) has injected new vitality into the field of sensing. Unlike spin angular momentum, i.e., polarization effect, OAM essentially describes the macroscopic physical characteristics of electromagnetic waves, characterizing the degree of rotation around an axis during electromagnetic wave propagation. Thus, electromagnetic vortex waves are defined. Theoretically, the range of OAM mode values ​​can be infinitely large, becoming a completely new dimension outside the time, frequency, and polarization domains.

[0003] Unlike traditional plane waves that carry only linear momentum, vortex electromagnetic waves have a spiral wavefront and a unique "phase singularity" and "hollow" intensity distribution. This revolutionary characteristic brings a disruptive advantage to radar detection. Traditional solid aperture radar suffers from limited resolution, limited Doppler information, and a lack of target 3D reconstruction capabilities. By utilizing the unique advantages of multimodal electromagnetic vortex waves in super-resolution imaging, target 3D reconstruction, and rotating Doppler extraction, long-term, high-resolution monitoring based on hovering or slow-moving platforms can be achieved, acquiring new observables of the target vortex dimension and improving target discrimination capabilities.

[0004] While generating vortex electromagnetic waves using a single-layer uniform ring array is relatively simple in structure, it has significant limitations in practical high-resolution multidimensional imaging applications. When a single-layer ring array simultaneously generates multiple orbital angular momentum modes, the vortex beams of different modes naturally have different divergence angles. Higher-order modes have larger hollow regions and more severe divergence, which means that when illuminating a target, the energy of each mode cannot be effectively converged in the same observation area in space, seriously affecting the signal-to-noise ratio of the echo signal and the subsequent fine calculation of azimuth information.

[0005] Meanwhile, single-layer ring arrays belong to far-field synthesis methods. Due to the physical size of a single ring and the spacing of array elements, they are prone to sparse array arrangement when exciting multiple modes. This will directly affect the phase characteristics of the vortex field, causing distortion of the antenna pattern, which in turn leads to severe inter-mode coupling, decreased purity of single-mode radiation field, and deterioration of the continuity of phase distribution in the azimuth dimension.

[0006] The generation of vortex electromagnetic waves using a single-layer ring array has significant drawbacks, which greatly limits the imaging resolution and multi-dimensional parameter extraction capabilities of electromagnetic vortex radar in complex scenarios. Therefore, it is urgent to study vortex electromagnetic wave imaging methods based on multi-layer ring arrays to fully explore the potential of vortex electromagnetic waves in multi-dimensional imaging applications. Summary of the Invention

[0007] To address the aforementioned problems in the existing technology, this invention provides a three-dimensional imaging method for point targets based on a multi-layer ring array of vortex electromagnetic waves. The technical problem to be solved by this invention is achieved through the following technical solution: This invention provides a method for three-dimensional imaging of point targets based on a multi-layer ring array of vortex electromagnetic waves, comprising: A radar imaging model is established to transmit electromagnetic vortex wave transmission signals with multiple orbital angular momentum modes in a multi-transmit and multi-receive mode and form multi-mode target electromagnetic vortex echo signals. The radar antenna adopts a multi-layer concentric ring antenna array. The target electromagnetic vortex echo signal is subjected to range migration correction that varies with the range frequency and azimuth frequency to obtain the corrected signal; The corrected signal is subjected to azimuth compression processing, and then azimuth-focused image is obtained by azimuth-focused inverse fast Fourier transform. The minimum entropy mode is determined based on the pixel amplitude of the image after focusing in the azimuth direction for each orbital angular momentum mode in order to obtain the best focused image; Perform constant false alarm rate target detection on the optimally focused image to obtain the slow time index value and fast time index value of the target; The total electromagnetic vortex echo signal of the target is obtained from all the target electromagnetic vortex echo signals, and azimuth dimension super-resolution processing is performed based on the total electromagnetic vortex echo signal of the target to obtain the azimuth dimension information of the target. The three-dimensional spatial coordinates of the target are determined based on the target's slow time index value, fast time index value, and orientation dimension information.

[0008] In one embodiment of the present invention, a radar imaging model is established to transmit electromagnetic vortex wave transmission signals of multiple orbital angular momentum modes in a multi-transmitter, multi-receiver mode and form multi-mode target electromagnetic vortex echo signals, including: A radar imaging model is established to obtain the geometric parameters of the point target in the radar coordinate system when the radar platform is in motion. The geometric parameters include the instantaneous position of the radar, the coordinates of the point target, the instantaneous slant range, the instantaneous azimuth angle, and the instantaneous elevation angle. A radar antenna model of a multi-layer concentric ring antenna array is established. A multi-transmit and multi-receive communication mode is adopted to transmit electromagnetic vortex wave transmission signals with different orbital angular momentum modes through the multi-layer concentric ring antenna array and simultaneously receive the reflected echo signals from multiple scattering points on the target. The electromagnetic vortex wave emission signal and the reflected echo signal are subjected to Fourier transforms respectively. The conjugate result of the Fourier transformed electromagnetic vortex wave emission signal is multiplied with the Fourier transformed reflected echo signal in the frequency domain. The result of the multiplication is then subjected to an inverse Fourier transform to restore it to the time domain, thus obtaining the target electromagnetic vortex echo signal after range-dimensional pulse compression.

[0009] In one embodiment of the present invention, the multi-layer concentric ring antenna array is located on multiple concentric rings, each layer of the concentric ring antenna array is provided with several uniformly arranged antenna elements, and each layer of the concentric ring antenna array corresponds to a different orbital angular momentum mode.

[0010] In one embodiment of the present invention, the target electromagnetic vortex echo signal is subjected to range migration correction varying with range frequency and azimuth frequency to obtain a corrected signal, including: The target electromagnetic vortex echo signal is subjected to a fast Fourier transform to obtain a frequency domain signal; Determine the range envelope signal containing the range migration amount, the range envelope signal being represented as:

[0011] in, This is the distance envelope signal. The closest slope distance. For wavelength, For azimuth frequency, For radar platform speed; The distance migration is determined based on the distance envelope signal, and the distance migration is expressed as:

[0012] in, For distance migration, To compensate for the frequency; By using an interpolation method based on the sinc function, the frequency domain signal is resampled in the range direction using the range migration term to straighten the range migration curve and obtain a corrected signal parallel to the azimuth frequency axis.

[0013] In one embodiment of the present invention, the corrected signal is subjected to azimuth compression processing, and then an azimuth-focused image is obtained by performing an inverse fast Fourier transform, including: Construct an azimuth matched filter, which is expressed as follows:

[0014] in, For azimuth matched filters, For azimuth frequency, This is the azimuth tuning frequency.

[0015] The corrected signal is multiplied with the azimuth matched filter in the frequency domain to obtain a frequency-domain compressed signal. The frequency domain compressed signal is subjected to inverse fast Fourier transform to obtain the azimuth-focused image.

[0016] In one embodiment of the present invention, determining the minimum entropy mode based on the pixel amplitude of the azimuth-focused image for each orbital angular momentum mode to obtain the optimal focused image includes: For the first l The pixel amplitude values ​​of each pixel in the image after azimuth focusing are normalized to determine the first... l A normalized probability distribution; According to the l The normalized probability distribution determines the first... l The entropy value of the image after azimuth focusing; Compare the entropy values ​​of each azimuth-focused image, select the orbital angular momentum mode corresponding to the azimuth-focused image with the smallest entropy value as the minimum entropy mode, and take the azimuth-focused image corresponding to the minimum entropy mode as the optimal focused image.

[0017] In one embodiment of the present invention, constant false alarm rate target detection is performed on the optimally focused image to obtain the slow time index value and fast time index value of the target, including: The target detection result is obtained by using the unit average constant false alarm rate detection algorithm to perform target detection on the optimally focused image; The target's coordinate information in the optimally focused image is extracted from the target detection result. The row coordinates of the coordinate information are determined as the slow time index value of the target, and the column coordinates of the coordinate information are determined as the fast time index value of the target.

[0018] In one embodiment of the present invention, a total target electromagnetic vortex echo signal is obtained based on all the target electromagnetic vortex echo signals, and azimuth super-resolution processing is performed based on the total target electromagnetic vortex echo signal to obtain the target's azimuth information, including: The total electromagnetic vortex echo signal is obtained based on all the electromagnetic vortex echo signals, and a compressed sensing model is established based on the total electromagnetic vortex echo signal. The total electromagnetic vortex echo signal is subjected to azimuth dimension super-resolution processing using a sparse Bayesian learning algorithm to obtain an estimate of the azimuth dimension sparse signal. The azimuth information of the target is obtained from the estimated value of the azimuth sparse signal.

[0019] In one embodiment of the present invention, a sparse Bayesian learning algorithm is used to perform azimuth-dimensional super-resolution processing on the total electromagnetic vortex echo signal to obtain an estimate of the azimuth-dimensional sparse signal, including: S1. Construct the likelihood function of the total signal of the electromagnetic vortex echo; S2. Set the azimuth dimension sparse signal to follow a Gaussian prior distribution with zero mean, and construct the prior probability distribution of the azimuth dimension sparse signal; S3, in the i In the next iteration, based on the hyperparameter vector and noise accuracy of the current iteration, the posterior probability distribution is determined according to Bayesian theory, and the mean and covariance matrix of the azimuth dimension sparse signal are determined, wherein the hyperparameter vector is used to control the sparsity of the azimuth dimension sparse signal. S4. Based on the mean and covariance matrix of the posterior probability distribution, update the hyperparameter vector and noise accuracy using the second type of maximum likelihood estimation to obtain the... i +1 iterations of hyperparameter vector and noise accuracy; S5. Repeat the iterative process until the preset convergence condition is met, and use the mean value obtained from the last iteration as the estimated value of the azimuth dimension sparse signal.

[0020] In one embodiment of the present invention, determining the three-dimensional spatial coordinates of the target based on the target's slow-time index value, fast-time index value, and orientation dimension information includes: Based on the target's slow time index value, fast time index value, and orientation dimension information, the spherical coordinates of the target are determined; Using the spherical coordinates as the base coordinates, a transformation from the lower-view coordinates to the radar coordinate system is performed to obtain the intermediate coordinates; Based on the intermediate coordinates and flight altitude, the three-dimensional spatial coordinates of the target are determined.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows: By employing the weighting effect of a multi-layer concentric ring array, this invention not only effectively overcomes the defects of traditional single-layer arrays in multi-mode transmission, such as severe divergence of high-order mode beams and difficulty in energy convergence, but also adjusts the vortex beams of different modes to the same divergence angle, significantly improving the signal-to-noise ratio of the target echo signal and the purity of the single-mode radiation field. This invention reconstructs the dimensions of multimodal transmit and receive signals in three-dimensional synthetic aperture radar (SAR) imaging and implements range migration correction that varies with the range and azimuth frequencies in the two-dimensional frequency domain. This eliminates the significant impact of the arc-shaped trajectory formed by the target echo on the imaging quality when it is not corrected, greatly improves the focusing accuracy of azimuth compression, and realizes high-precision three-dimensional spatial reconstruction of complex targets. This invention achieves the best imaging effect with the most concentrated energy by traversing and calculating the entropy value of each modal focused image before target detection to determine the minimum entropy mode. Combined with the improved constant false alarm rate (CFAR) target detection algorithm, it effectively avoids occlusion effect and target missed detection, thereby ensuring extremely high accuracy and reliability of three-dimensional spatial coordinate solution.

[0022] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0023] Figure 1 This is a flowchart illustrating a three-dimensional imaging method for point targets based on a multi-layer ring array of vortex electromagnetic waves provided by the present invention. Figure 2 This is a schematic diagram of a vortex electromagnetic wave radar detection scenario provided by the present invention; Figure 3 This is a three-dimensional imaging result image provided by the present invention after distance migration correction and spatial coordinate reconstruction. Detailed Implementation

[0024] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0025] Example 1 Please see Figure 1 , Figure 1 This is a flowchart illustrating a three-dimensional imaging method for point targets based on a multi-layer ring array of vortex electromagnetic waves, provided by the present invention. The present invention provides a three-dimensional imaging method for point targets based on a multi-layer ring array of vortex electromagnetic waves, comprising: Step 1: Establish a radar imaging model, transmit electromagnetic vortex wave transmission signals of multiple orbital angular momentum modes in a multi-transmit and multi-receive mode, and form multi-mode target electromagnetic vortex echo signals.

[0026] In one specific embodiment, step 1 may include: Step 1.1: Establish a radar imaging model and obtain the geometric parameters of the point target in the radar coordinate system when the radar platform is in motion. The geometric parameters include the instantaneous position of the radar, the coordinates of the point target, the instantaneous slant range, the instantaneous azimuth angle, and the instantaneous elevation angle.

[0027] Specifically, such as Figure 2 As shown, a ground coordinate system O-XYZ is established with the center of the imaging area as the origin, where the XOY plane represents the horizontal plane, and the Z-axis is perpendicular to the XOY plane and points downwards, representing the height direction. The radar travels at a velocity v along a path parallel to the corresponding slow time... The radar moves in the positive Y-axis direction at an altitude of Flyhight. The radar moves along the y-axis at Flyhight altitude, and its velocity is denoted as v. A uniform circular array (UCA) on the xOy plane of the Cartesian coordinate system O-xyz is used to generate vortex waves to observe the area. The z-axis is perpendicular to the surface of the UCA and indicates the altitude direction. A receiving antenna located at the center of the UCA receives the echo. For simplicity, the origin O of the Cartesian coordinate system is set as the center of the radar's trajectory. In the imaging scene, the position of any object is represented as... The location of the radar is The time when the radar arrives at point O is defined as slow time. The origin. express The instantaneous azimuth angle between the receiving antenna and the target at all times.

[0028] For ease of geometric derivation, a radar coordinate system O-xyz is established at the same origin. Rotating O-xyz around the Y-axis by a downward angle β yields O-XYZ. Simultaneously, the normal to the UCA is parallel to the x-axis, and the angle between the normal and the ground surface (XOY plane) is β. The instantaneous position of the radar... (i.e., the position of the UCA phase center) can be represented in the radar coordinate system O-xyz as:

[0029] in, For radar in slow time Location coordinates, , , These represent the radar's coordinates in the x-axis, y-axis, and z-axis directions, respectively. This represents the radar's altitude.

[0030] Assuming a point target Located within the imaging region, ignoring the distances between different array elements and the target, and treating the UCA as an equivalent phase center located at the center of the array circle, the distance between the radar and the point target p can be expressed as:

[0031] in, In slow time The distance between the radar and the point target p, also known as the instantaneous slant range.

[0032] The azimuth component of any scattering point on point target p in the radar coordinate system and pitch components It is with slow time The relevant functions are:

[0033] in, This indicates the argument of a complex number.

[0034] Establish a ground coordinate system O-XYZ and a radar coordinate system O-xyz. Let the coordinates of any point in O-XYZ be (X,Y,Z) and the coordinates in O-xyz be (x,y,z). Then the transformation relationship between the two coordinate systems is as follows:

[0035] in, It is a rotation matrix for rotating about the y-axis by an angle β (counterclockwise is the positive direction).

[0036] In the ground coordinate system O-XYZ, the coordinates of target P are: radar coordinates are In the radar system O-xyz, the coordinates of point target P are... radar coordinates are Therefore:

[0037] From the geometric relationships shown in the radar system o-xyz, we can obtain:

[0038] in, In slow time The instantaneous distance between the radar and the point target p at any given time. In slow time The instantaneous azimuth angle of target p in the radar coordinate system at time point. In slow time The instantaneous elevation angle of target p in the radar coordinate system at a given moment.

[0039] Step 1.2: Establish a radar antenna model of a multi-layer concentric ring antenna array. Employ a multiple transmit and receive communication mode to transmit electromagnetic vortex wave transmission signals with different orbital angular momentum modes through the multi-layer concentric ring antenna array and simultaneously receive reflected echo signals from multiple scattering points on the target. The multi-layer concentric ring antenna array is located on multiple concentric rings. Each layer of the concentric ring antenna array is equipped with several uniformly arranged antenna elements (i.e., array elements), and each layer of the concentric ring antenna array corresponds to a different orbital angular momentum mode.

[0040] Specifically, the multi-layer concentric ring antenna array is located on multiple concentric rings, that is, the multi-layer ring antenna array is set concentrically, the first... l The layered ring antenna array is located in the first layer. l On the nth concentric ring, the th l The radius of the concentric rings is denoted as . , Indicates the first l The number of array elements on the nth concentric rings, i.e. the nth l Arranged on concentric rings The antenna element, the first l The first layer of the ring antenna array n l The azimuth angle of each array element is , Each mode corresponds to a different ring, meaning that the transmission / reception tasks for different orbital angular momentum modes are assigned to ring antenna arrays of different radii. The element positions are:

[0041] in, For the first l The first layer of the ring array n l The position coordinates of each array element.

[0042] After adjustment using the rotation matrix (rotation angle is the bottom view), for:

[0043] in, The pitch angle, , , y is the unit direction vector of the x, y, and z axes in three-dimensional space.

[0044] Based on a multi-layer concentric ring antenna array model, electromagnetic vortex waves with multi-mode transmission and reception are generated simultaneously. The electromagnetic vortex wave transmission signal (linear frequency modulated signal) emitted by the radar is represented as follows:

[0045] in, In a fast time , No. l The first layer of the ring array n l The electromagnetic vortex wave transmission signal emitted by each array element It is a rectangular pulse function. The duration of the pulse. For the first l The electromagnetic vortex wave transmission signal of the layered ring array uses a linear frequency modulated signal to achieve distance dimension resolution. For the first l Orbital angular momentum modes, L is the modal modulation bandwidth, and L is half the modal modulation bandwidth.

[0046] Therefore, the first lThe echo signal received by the layered loop antenna array after target scattering modulation is represented as:

[0047] in, Given fast time t and slow time t Under the conditions, the first l The echo signal received by the layered loop antenna array after being scattered and modulated by the target (from M (The sum of the electromagnetic vortex wave echo signals returned from each scattering point) For the first Backscattering coefficient at each scattering point For the first The instantaneous slant range of each scattering point The distance envelope of a rectangular window function. The synthetic aperture azimuth envelope is a function of shape sinc. The beam center deviation time is the first time. OAM azimuth angle of each scattering point At the speed of light, For carrier wavelength, for Bessel function of order 1, For wave number, The radius of the transmitting array.

[0048] Step 1.3: Perform Fourier transform (FFT) on the electromagnetic vortex wave transmitted signal and the reflected echo signal respectively. Multiply the conjugate result of the Fourier transformed electromagnetic vortex wave transmitted signal with the Fourier transformed reflected echo signal in the frequency domain. Then perform inverse Fourier transform (IFFT) on the multiplication result to restore it to the time domain, and obtain the target electromagnetic vortex echo signal after range-dimensional pulse compression.

[0049] Specifically, firstly regarding the first l The electromagnetic vortex wave transmission signal emitted by the concentric ring antenna array is subjected to a Fourier transform, and its conjugate is taken. This transform is then applied to the signal of the first concentric ring antenna array. l The reflected echo signal received by the concentric ring antenna array is subjected to Fourier transform, and then the... l The conjugate result and the first l The reflected echo signals from the Fourier transforms are multiplied together, and then the result of the multiplication is subjected to an inverse Fourier transform (IFFT) to recover to the time domain, thereby obtaining the target electromagnetic vortex echo signal after range-dimensional pulse compression.

[0050] Here, the signal at target p is the superposition of the linear frequency modulated signals transmitted by each loop antenna array:

[0051] in, For the total transmitted signal of the L-layer ring antenna array, For the first l In the first layer of the ring antenna array n l The time delay from each array element to the target p, For the first l The reflection coefficient of a layered ring antenna array.

[0052] After range compression processing, a range-dimensional pulse-compressed target electromagnetic vortex echo signal is generated. l The target electromagnetic vortex echo signal corresponding to the layered loop antenna array, after range-dimensional pulse compression, is represented as:

[0053] in, For the first l The target electromagnetic vortex echo signal corresponding to the layered ring antenna array after range-dimensional pulse compression. for The autocorrelation function, For the first The instantaneous distance from each scattering point to the radar.

[0054] Step 2: Perform range migration correction on the target electromagnetic vortex echo signal as the range frequency and azimuth frequency change to obtain the corrected signal.

[0055] Specifically, step 1 has already obtained the target electromagnetic vortex echo signal synthesized by multi-mode transceiver. However, during radar platform operation, due to changes in target range, the peak value of range pulse compression for the same target at different slow time points will appear at different times. Therefore, without range migration correction, the range-compressed signal will form an arc-shaped trajectory, which will inevitably have a significant impact on the imaging quality during subsequent azimuth compression. Therefore, this embodiment performs range migration correction in the range-azimuth frequency domain, adjusting for variations in range and azimuth frequencies, straightening the range migration curve to be parallel to the azimuth frequency axis, thus obtaining the corrected signal.

[0056] In one specific embodiment, step 2 may include: Step 2.1: Perform a fast Fourier transform on the target electromagnetic vortex echo signal to obtain the frequency domain signal.

[0057] Here, the frequency domain signal is represented as:

[0058] in, For frequency domain signals, This indicates the azimuth frequency of the SAR. This is the azimuth modulation frequency for SAR. , is the closest slant distance The function. Due to the addition of a downward viewpoint, the correction term changes compared to traditional vortex SAR imaging.

[0059] Step 2.2: Determine the distance envelope signal that includes distance migration.

[0060] Here, the distance envelope signal is approximately expressed as:

[0061] in, This is the distance envelope signal. This is the nearest slope distance.

[0062] Step 2.3: Determine the distance migration amount based on the distance envelope signal.

[0063] Here, distance migration is expressed as:

[0064]

[0065] in, For distance migration, To compensate for frequency, For the synthetic aperture length, From a bottom perspective, The tilt angle is the azimuth angle. For reference distance.

[0066] Step 2.4: Using the sinc function-based interpolation method, the frequency domain signal is resampled in the range direction using the range migration amount to straighten the range migration curve and obtain a corrected signal parallel to the azimuth frequency axis.

[0067] Here, the corrected signal is represented as:

[0068] in, This is the corrected signal.

[0069] Step 3: Perform azimuth compression processing on the corrected signal, and then obtain the azimuth-focused image by performing azimuth-focused inverse fast Fourier transform.

[0070] Specifically, based on the corrected signal, azimuth compression is achieved at each range gate through frequency matching. Then, the data is transformed back to the time domain through inverse fast Fourier transform (IFFT) in the azimuth direction to obtain a two-dimensional complex image after range-azimuth focusing, which is also the image after azimuth focusing.

[0071] In one specific embodiment, step 3 may include: Step 3.1: Construct an azimuth matched filter to perform SAR azimuth focusing on the data after RCMC.

[0072] Here, the azimuth matched filter is expressed as:

[0073] in, This is an azimuth matched filter.

[0074] Step 3.2: Multiply the corrected signal with the azimuth matched filter in the frequency domain to obtain the frequency-domain compressed signal.

[0075] Here, the frequency domain compressed signal is represented as:

[0076] in, It is a frequency domain compressed signal. This is the azimuth frequency shift for SAR.

[0077] Step 3.3: Perform an inverse fast Fourier transform on the frequency domain compressed signal to obtain the image after azimuth focusing.

[0078] Here, the image after azimuth focusing is represented as:

[0079] in, This is the image after focusing in the azimuth direction.

[0080] Step 4: Determine the minimum entropy mode based on the pixel amplitude of the focused image for each orbital angular momentum mode in order to obtain the best focused image.

[0081] Specifically, the image after azimuth focusing is preprocessed, the modal dimensions of the image are traversed and the entropy value of each modality is calculated, and the minimum entropy mode is determined to obtain the best focused image.

[0082] In one specific embodiment, step 4 may include: Step 4.1, according to the... l The pixel amplitude value of each pixel in the image after azimuth focusing is determined. l A normalized probability distribution.

[0083] Here, the normalized probability value is expressed as:

[0084] in, For the first lThe normalized probability value of the pixel located at coordinates (i, j) in the image after azimuth focusing. For the first l The pixel amplitude at (i, j) of the image after azimuth focusing.

[0085] Step 4.2, according to the first l The normalized probability distribution determines the first... l The entropy value of the image after azimuth focusing.

[0086] Here, the entropy value is expressed as:

[0087] in, For the first l The entropy value of the image after azimuth focusing. The smaller the entropy value, the more concentrated the image energy. After identifying the minimum entropy, the optimal mode of each focused image can be identified, thus enabling better target detection.

[0088] Step 4.3: Compare the entropy values ​​of each azimuth-focused image, select the orbital angular momentum mode corresponding to the azimuth-focused image with the smallest entropy value as the minimum entropy mode, and take the azimuth-focused image corresponding to the minimum entropy mode as the best focused image.

[0089] Step 5: Perform constant false alarm rate target detection on the best-focused image and obtain the slow time index value and fast time index value of the target.

[0090] In one specific embodiment, step 5 may include: Step 5.1: Use the Cell Average Constant False Alarm Rate (CA-CFAR) detection algorithm to perform target detection on the best-focused image and obtain the target detection results.

[0091] Specifically, a constant false alarm rate (CFAR) detection algorithm is used to detect each pixel in the best-focused image. The algorithm works by defining a reference window around the pixel to be detected and dynamically estimating the local background noise level by calculating the average intensity of all pixels within the reference window. Then, a detection threshold is calculated based on a preset false alarm probability. If the intensity value of the current pixel exceeds this threshold, it is determined to be a target pixel; otherwise, it is considered background. The output of this step is a binary mask or a list of target points, i.e., the target detection result, which marks the positions of all suspected target points in the best-focused image.

[0092] Here, detection probability The calculation method is as follows:

[0093] Threshold factor Only with the preset false alarm probability And it is related to the length of the reference window, that is:

[0094] in, For signal-to-noise ratio, Half the length of the reference window. The length of the reference window.

[0095] Step 5.2: Extract the coordinate information of the target in the best-focused image from the target detection results. Determine the row coordinates of the coordinate information as the slow time index value of the target, and determine the column coordinates of the coordinate information as the fast time index value of the target.

[0096] Specifically, from the target detection results generated in step 5.1, the coordinate information of each target point in the optimally focused image is extracted. In the context of SAR imaging, the rows of the image correspond to slow time (i.e., azimuth direction), and the columns of the image correspond to fast time (i.e., range direction). Therefore, the row coordinates of the target point are assigned to the slow time index value, and the column coordinates are assigned to the fast time index value. The slow time index value is used to subsequently calculate the target's position in the azimuth direction, and the fast time index value is used to calculate the instantaneous slant range from the target to the radar.

[0097] Step 6: Obtain the total electromagnetic vortex echo signal of the target based on all target electromagnetic vortex echo signals, and perform azimuth super-resolution processing based on the total electromagnetic vortex echo signal of the target to obtain the azimuth information of the target.

[0098] In one specific embodiment, step 6 may include: Step 6.1: Obtain the total electromagnetic vortex echo signal based on all electromagnetic vortex echo signals, and establish a compressed sensing model based on the total electromagnetic vortex echo signal.

[0099] Specifically, assuming the first l The first layer of concentric ring antenna array The coordinates of each array element are: The pitch angle is azimuth angle is , No. l The first layer of concentric ring antenna array The azimuth and elevation angles of each array element are The spatial steering vector of the source is:

[0100] in, For the first m The scattering point to the th l The first layer of concentric ring antenna array The spatial orientation vector of each array element For the first m The scattering point and the th l The first layer of concentric ring antenna array The elevation angle of each array element, For the first m The scattering point and the th l The first layer of concentric ring antenna array The azimuth angle of each array element.

[0101] Modality is At that time, the first l The first layer of concentric ring antenna array The modulation phase of each array element can be expressed as:

[0102] in, For the first l The first layer of concentric ring antenna array The modulation phase of each array element.

[0103] Assume there is a target p. When considering an ideal state at the i-th scattering point, all waveforms are completely orthogonal. After matched filtering, the i-th... l The first layer of concentric ring antenna array The echo signal of each array element can be represented as:

[0104] in, For the first l The first layer of concentric ring antenna array The echo signal of each array element For the first m The reflection coefficient at each scattering point For the first l The first layer of concentric ring antenna array Gaussian white noise for each array element.

[0105] Therefore, a sparse reconstruction model can be established based on the echo signal:

[0106] in, , To convert a two-dimensional signal matrix into a one-dimensional column vector, For the first l The first layer of concentric ring antenna array The dictionary matrix corresponding to each array element. For the first l The first layer of concentric ring antenna array The sparse signal vector to be reconstructed corresponding to each array element.

[0107] For a traditional single-layer antenna array, with a fixed number of elements, the modes satisfy... , This refers to the number of elements in a single-layer antenna array. For the modes of a single-layer antenna array, the dictionary matrix representation of the single-layer antenna array is as follows:

[0108] Assuming the target has M scattering points, and considering an ideal state where all waveforms are completely orthogonal, range pulse compression, and modal phase compensation are used to synthesize the modal signals. The echo signals of each modal signal can be expressed as:

[0109] in, This indicates the amplitude of each distance unit after pulse compression. Indicates the wave number magnitude.

[0110] The dictionary matrix of the single-layer antenna array constructed based on this can be represented as:

[0111] The dictionary matrix expression for a single-layer array is applied to a multi-layer circular array, as follows: Based on a multi-layer ring array architecture, each ring antenna array is independent of the others. The pulse-compressed echo signal (electromagnetic vortex echo signal) of any layer in the multi-layer concentric ring antenna array is as follows:

[0112] The total number of array layers is L. Therefore, the sum of L electromagnetic vortex echo signals is the total electromagnetic vortex echo signal.

[0113] Combining the amplitude and wavenumber of each distance unit after pulse compression, as well as the multilayer structure, the amplitude modulation term can be defined as:

[0114] in, For the first l Layered ring antenna array in mode m l Next to the m One target direction Amplitude modulation term, For the first l The radius of the layered ring antenna array, For wavelength, For the first m The elevation angle of each scattering point It is a first-order Bessel function of the first kind.

[0115] The angular axes of the three-dimensional imaging region are discretized and divided into... Each grid point corresponds to a set of spatial angles. ,in .

[0116] No. l Layered ring antenna array in mode m l The manifold vector for all spatial grids can be expressed as:

[0117] in, For the first l Layered ring antenna array in mode m l The manifold vector for all spatial grids.

[0118] The effective OAM mode range used by the system is: ,total One modality, For the minimum mode, It is the maximum mode. Then for the ... l Layered ring antenna array, combining all The observation dictionary matrix constructed from each modality can be represented as: in, For the first l Layered ring antenna array, combining all An observation dictionary matrix constructed from each modality.

[0119] The constructed observation dictionary matrix is ​​cross-correlation analyzed with the input signal to distinguish the signal information in the azimuth dimension of the target.

[0120] In the above analysis, a sparse recovery model for electromagnetic vortex radar was obtained. Based on this, and considering other influencing factors in practice, the compressed sensing model is extended to the following form:

[0121] In this embodiment, the compressed sensing model is abbreviated as: , This is the total signal of electromagnetic vortex echoes. To observe the dictionary matrix, For background noise, For the observation dimensions (i.e., x, y, z) This refers to the number of grid points in the scene. Based on the principle of compressed sensing, in-beam super-resolution can be achieved by increasing the number of grid points in the observed scene, but this is contingent on the observation scene matrix... It is a sparse matrix, that is Only a few of the scene points have non-zero values.

[0122] Step 6.2: Use the sparse Bayesian learning algorithm to perform azimuth dimension super-resolution processing on the total electromagnetic vortex echo signal to obtain the estimated value of the azimuth dimension sparse signal.

[0123] Step 6.21: Construct the likelihood function of the total electromagnetic vortex echo signal.

[0124] Specifically, in the compressed sensing model In the middle, assuming noise Set the number of iterations Then the likelihood function of the total electromagnetic vortex echo signal S can be expressed as:

[0125] in, In a given Under these conditions, the total signal of electromagnetic vortex echoes was observed. The probability, This is the noise accuracy, which is the reciprocal of the noise variance. It is the likelihood function constant.

[0126] Step 6.22: Assume that the azimuth-dimensional sparse signal follows a zero-mean Gaussian prior distribution to construct the prior probability distribution of the azimuth-dimensional sparse signal. The prior probability distribution is expressed as:

[0127] in, Let be the prior probability distribution of a sparse signal in the azimuth dimension given a hyperparameter vector. I This represents the total number of iterations. For the noise in the i-th iteration, Let be the hyperparameter vector of the i-th component. To control the sparse signal in the azimuth dimension The hyperparameters of sparsity, i.e. .

[0128] Step 6.23, in the... i In the next iteration, based on the hyperparameter vector and noise accuracy of the current iteration, the posterior probability distribution is determined according to Bayesian theory, and the mean and covariance matrix of the azimuth dimension sparse signal are determined. The hyperparameter vector is used to control the sparsity of the azimuth dimension sparse signal.

[0129] Specifically, according to Bayes' theorem, the posterior probability distribution is proportional to the product of the likelihood function and the prior probability distribution. The specific derivation involves multiplying the likelihood function and the prior probability distribution and then using the properties of the Gaussian distribution to perform mathematical derivation, ultimately obtaining the analytical expression for the posterior Gaussian distribution.

[0130] The posterior probability distribution of a sparse signal in the azimuth dimension conforms to the following Gaussian distribution:

[0131] Among them, in the case of known noise accuracy hyperparameter vector In addition to other auxiliary hyperparameters a, b, c, and d, the posterior probability distribution of the azimuth-dimensional sparse signal is given. The mean of the azimuth sparse signal is The covariance matrix is Gaussian distribution, , ,in, .

[0132] Step 6.24: Based on the mean and covariance matrix of the posterior probability distribution, update the hyperparameter vector and noise accuracy through the second type of maximum likelihood estimation to obtain the hyperparameter vector and noise accuracy for the (i+1)th iteration.

[0133] Specifically, the hyperparameters are updated using the second type of maximum likelihood estimation, and the cost function can be expressed as:

[0134] in, Let cost function be hyperparameter vector The prior distribution, For noise accuracy The prior distribution, .

[0135] Take the logarithm of both sides of the cost function equation, then... and Taking the partial derivative, we get:

[0136]

[0137] Thus, the hyperparameter vector and noise accuracy are updated, and the first... i The hyperparameter vector and noise accuracy of +1 iteration.

[0138] Step 6.25: Repeat the iterative process until the preset convergence condition is met, and use the mean value obtained from the last iteration as the estimated value of the azimuth dimension sparse signal.

[0139] Specifically, the convergence condition is that the difference (such as the L2 norm) between the estimated value of the azimuth dimension sparse signal obtained in the current iteration and the previous iteration is less than a preset threshold. If the difference is less than a preset threshold, the iteration stops and the mean value obtained in the last iteration is used as the estimated value of the azimuth dimension sparse signal.

[0140] Step 6.3: Obtain the azimuth information of the target based on the estimated value of the sparse azimuth signal.

[0141] Specifically, the estimated value of the azimuth dimension sparse signal is ultimately used as the azimuth dimension information of the target.

[0142] Step 7: Determine the target's three-dimensional spatial coordinates based on the target's slow time index value, fast time index value, and orientation information.

[0143] In one specific embodiment, step 7 may include: Step 7.1: Based on the target's slow-time index value, fast-time index value, and azimuth dimension information, determine the target's spherical coordinates, which are represented as:

[0144] in, The spherical coordinates of the target.

[0145] Step 7.2: Using the spherical coordinates (x0, y0, z0) as the base coordinates, perform a transformation from the lower-view coordinates to the radar coordinate system to obtain the intermediate coordinates, which are represented as follows:

[0146] in,( , () is the intermediate coordinate.

[0147] Step 7.3: Based on the intermediate coordinates and flight altitude, determine the target's three-dimensional spatial coordinates. The target's three-dimensional spatial coordinates are represented as follows:

[0148] in, This refers to the flight altitude.

[0149] The effects of this invention can be further illustrated by the following simulation results.

[0150] 1. Simulation conditions Assume that the vortex electromagnetic wave radar transmits a signal with a frequency of 10 GHz and a dwell time of 0.00001 seconds to illuminate the target; Suppose the multi-layer ring array has 7 layers, with corresponding element radii of 0.056m, 0.093m, 0.128m, 0.162m, 0.195m, 0.228m, and 0.260m, and corresponding element numbers of 6, 12, 18, 26, 32, 26, and 26. Assume the eddy current electromagnetic wave echo mode after receiving the multi-element echo is 8; Set two target points, and set the flight altitude to 200m and 300m respectively, for a total of two times.

[0151] 2. Simulation Results Based on the above simulation conditions, the method of this invention is used to achieve three-dimensional point target imaging, and the three-dimensional spatial coordinates of each point target are obtained. The results are as follows. Figure 3 As shown.

[0152] from Figure 3 As can be seen, by using multimodal vortex electromagnetic waves and azimuth-dimensional sparse Bayesian super-resolution algorithm, two small and adjacent targets can still be clearly and sharply distinguished independently in three-dimensional space; the target points in the three-dimensional scatter plot appear as independent circles with clear boundaries and no divergence. Through minimum entropy mode optimization and CFAR target detection, background clutter and sidelobe energy are greatly suppressed. No matter what detection distance the target is at, the system can stably extract high-quality scattering centers.

[0153] The simulation results above show that the present invention can effectively solve the target azimuth information and position parameters, give full play to the potential of vortex electromagnetic waves in multi-target multi-dimensional imaging applications, and can effectively improve the calculation accuracy of point target coordinate reconstruction, thus realizing high-resolution imaging of multi-point targets.

[0154] By employing the weighting effect of a multi-layer concentric ring array, this invention not only effectively overcomes the defects of traditional single-layer arrays in multi-mode transmission, such as severe divergence of high-order mode beams and difficulty in energy convergence, but also adjusts the vortex beams of different modes to the same divergence angle, significantly improving the signal-to-noise ratio of the target echo signal and the purity of the single-mode radiation field. This invention reconstructs the dimensions of multimodal transmit and receive signals in three-dimensional synthetic aperture radar (SAR) imaging and implements range migration correction that varies with the range and azimuth frequencies in the two-dimensional frequency domain. This eliminates the significant impact of the arc-shaped trajectory formed by the target echo on the imaging quality when it is not corrected, greatly improves the focusing accuracy of azimuth compression, and realizes high-precision three-dimensional spatial reconstruction of complex targets. This invention achieves the best imaging effect with the most concentrated energy by traversing and calculating the entropy value of each modal focused image before target detection to determine the minimum entropy mode. Combined with the improved constant false alarm rate (CFAR) target detection algorithm, it effectively avoids occlusion effect and target missed detection, thereby ensuring extremely high accuracy and reliability of three-dimensional spatial coordinate solution.

[0155] In the description of this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0156] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, disclosure, and appended claims in carrying out the claimed invention. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. A single processor or other unit can implement several functions listed in the claims. While different dependent claims may recite certain measures, this does not mean that these measures cannot be combined to produce good results.

[0157] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, any modifications made without departing from the inventive concept should be considered within the scope of protection of the present invention.

Claims

1. A method for three-dimensional imaging of point targets based on a multi-layer ring array of vortex electromagnetic waves, characterized in that, include: A radar imaging model is established to transmit electromagnetic vortex wave transmission signals with multiple orbital angular momentum modes in a multi-transmit and multi-receive mode and form multi-mode target electromagnetic vortex echo signals. The radar antenna adopts a multi-layer concentric ring antenna array. The target electromagnetic vortex echo signal is subjected to range migration correction that varies with the range frequency and azimuth frequency to obtain the corrected signal; The corrected signal is subjected to azimuth compression processing, and then azimuth-focused image is obtained by azimuth-focused inverse fast Fourier transform. The minimum entropy mode is determined based on the pixel amplitude of the image after focusing in the azimuth direction for each orbital angular momentum mode in order to obtain the best focused image; Perform constant false alarm rate target detection on the optimally focused image to obtain the slow time index value and fast time index value of the target; The total electromagnetic vortex echo signal of the target is obtained from all the target electromagnetic vortex echo signals, and azimuth dimension super-resolution processing is performed based on the total electromagnetic vortex echo signal of the target to obtain the azimuth dimension information of the target. The three-dimensional spatial coordinates of the target are determined based on the target's slow time index value, fast time index value, and orientation dimension information.

2. The point target three-dimensional imaging method according to claim 1, characterized in that, A radar imaging model is established to transmit electromagnetic vortex wave signals with multiple orbital angular momentum modes in a multi-transmitter, multi-receiver mode, forming multi-mode target electromagnetic vortex echo signals, including: A radar imaging model is established to obtain the geometric parameters of the point target in the radar coordinate system when the radar platform is in motion. The geometric parameters include the instantaneous position of the radar, the coordinates of the point target, the instantaneous slant range, the instantaneous azimuth angle, and the instantaneous elevation angle. A radar antenna model of a multi-layer concentric ring antenna array is established. A multi-transmit and multi-receive communication mode is adopted to transmit electromagnetic vortex wave transmission signals with different orbital angular momentum modes through the multi-layer concentric ring antenna array and simultaneously receive the reflected echo signals from multiple scattering points on the target. The electromagnetic vortex wave emission signal and the reflected echo signal are subjected to Fourier transforms respectively. The conjugate result of the Fourier transformed electromagnetic vortex wave emission signal is multiplied with the Fourier transformed reflected echo signal in the frequency domain. The result of the multiplication is then subjected to an inverse Fourier transform to restore it to the time domain, thus obtaining the target electromagnetic vortex echo signal after range-dimensional pulse compression.

3. The point target three-dimensional imaging method according to claim 1, characterized in that, The multi-layer concentric ring antenna array is located on multiple concentric rings. Each layer of the concentric ring antenna array is provided with several uniformly arranged antenna elements, and each layer of the concentric ring antenna array corresponds to a different orbital angular momentum mode.

4. The point target three-dimensional imaging method according to claim 1, characterized in that, The target electromagnetic vortex echo signal is subjected to range migration correction varying with both range and azimuth frequencies to obtain a corrected signal, including: The target electromagnetic vortex echo signal is subjected to a fast Fourier transform to obtain a frequency domain signal; Determine the range envelope signal containing the range migration amount, the range envelope signal being represented as: in, This is the distance envelope signal. The closest slope distance. For wavelength, For azimuth frequency, For radar platform speed; The distance migration is determined based on the distance envelope signal, and the distance migration is expressed as: in, For distance migration, To compensate for the frequency; By using an interpolation method based on the sinc function, the frequency domain signal is resampled in the range direction using the range migration term to straighten the range migration curve and obtain a corrected signal parallel to the azimuth frequency axis.

5. The point target three-dimensional imaging method according to claim 1, characterized in that, The corrected signal is subjected to azimuth compression processing, followed by azimuth-focused inverse fast Fourier transform to obtain the azimuth-focused image, including: Construct an azimuth matched filter, which is expressed as follows: in, For azimuth matched filters, For azimuth frequency, For azimuth frequency tuning; The corrected signal is multiplied with the azimuth matched filter in the frequency domain to obtain a frequency-domain compressed signal. The frequency domain compressed signal is subjected to inverse fast Fourier transform to obtain the azimuth-focused image.

6. The point target three-dimensional imaging method according to claim 1, characterized in that, The minimum entropy mode is determined based on the pixel amplitude of the azimuth-focused image for each orbital angular momentum mode to obtain the optimal focused image, including: For the first l The pixel amplitude values ​​of each pixel in the image after azimuth focusing are normalized to determine the first... l A normalized probability distribution; According to the l The normalized probability distribution determines the first... l The entropy value of the image after azimuth focusing; Compare the entropy values ​​of each azimuth-focused image, select the orbital angular momentum mode corresponding to the azimuth-focused image with the smallest entropy value as the minimum entropy mode, and take the azimuth-focused image corresponding to the minimum entropy mode as the optimal focused image.

7. The point target three-dimensional imaging method according to claim 1, characterized in that, Perform constant false alarm rate target detection on the optimally focused image to obtain the target's slow time index value and fast time index value, including: The target detection result is obtained by using the unit average constant false alarm rate detection algorithm to perform target detection on the optimally focused image; The target's coordinate information in the optimally focused image is extracted from the target detection result. The row coordinates of the coordinate information are determined as the slow time index value of the target, and the column coordinates of the coordinate information are determined as the fast time index value of the target.

8. The point target three-dimensional imaging method according to claim 1, characterized in that, The total electromagnetic vortex echo signal of the target is obtained based on all the target electromagnetic vortex echo signals, and azimuth super-resolution processing is performed on the total target electromagnetic vortex echo signal to obtain the azimuth information of the target, including: The total electromagnetic vortex echo signal is obtained based on all the electromagnetic vortex echo signals, and a compressed sensing model is established based on the total electromagnetic vortex echo signal. The total electromagnetic vortex echo signal is subjected to azimuth dimension super-resolution processing using a sparse Bayesian learning algorithm to obtain an estimate of the azimuth dimension sparse signal. The azimuth information of the target is obtained from the estimated value of the azimuth sparse signal.

9. The point target three-dimensional imaging method according to claim 8, characterized in that, The electromagnetic vortex echo total signal is subjected to azimuth-dimensional super-resolution processing using a sparse Bayesian learning algorithm to obtain an estimate of the azimuth-dimensional sparse signal, including: S1. Construct the likelihood function of the total signal of the electromagnetic vortex echo; S2. Set the azimuth dimension sparse signal to follow a Gaussian prior distribution with zero mean, and construct the prior probability distribution of the azimuth dimension sparse signal; S3, in the i In the next iteration, based on the hyperparameter vector and noise accuracy of the current iteration, the posterior probability distribution is determined according to Bayesian theory, and the mean and covariance matrix of the azimuth dimension sparse signal are determined, wherein the hyperparameter vector is used to control the sparsity of the azimuth dimension sparse signal. S4. Based on the mean and covariance matrix of the posterior probability distribution, update the hyperparameter vector and noise accuracy using the second type of maximum likelihood estimation to obtain the... i +1 iterations of hyperparameter vector and noise accuracy; S5. Repeat the iterative process until the preset convergence condition is met, and use the mean value obtained from the last iteration as the estimated value of the azimuth dimension sparse signal.

10. The point target three-dimensional imaging method according to claim 1, characterized in that, The three-dimensional spatial coordinates of the target are determined based on its slow-time index value, fast-time index value, and orientation dimension information, including: Based on the target's slow time index value, fast time index value, and orientation dimension information, the spherical coordinates of the target are determined; Using the spherical coordinates as the base coordinates, a transformation from the lower-view coordinates to the radar coordinate system is performed to obtain the intermediate coordinates; Based on the intermediate coordinates and flight altitude, the three-dimensional spatial coordinates of the target are determined.

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