A radar super-resolution method for low, small and slow cluster targets

Abstract

The present invention discloses a radar super-resolution method for low, small and slow cluster targets. Aiming at the problem of limited range resolution in traditional radar air detection technology, a sparse super-resolution method based on the range-Doppler plane is introduced. First, a convolution echo signal model of the cluster target range-Doppler plane is constructed, and then a sparse regularization method is used to complete target estimation, including an initialization step, a range-dimensional pulse compression step, a cluster target echo model construction step, a sparse super-resolution target function establishment step and a super-resolution imaging result output step. This method can break through the inherent range resolution limitation of the radar system under conventional signal-to-noise ratio conditions, and has broad application prospects in cluster target super-resolution scenarios.

Description

Technical Field

[0001] The present invention belongs to the field of radar technology, and mainly relates to cluster UAV super-resolution technology. Background Art

[0002] In recent years, the rapid development of drone technology is not only reflected in the significant growth of functional diversity and quantity, but also gave rise to the emerging concept of "drone swarm", and its application scope is becoming increasingly wide. However, along with this trend, the use of swarm drones to carry out attacks or snooping is also common, posing a severe challenge to public safety and privacy protection. Various types of "low, slow and small" aircraft have become regulated. "Low, slow and small" aircraft refer to flying targets with a flight altitude of less than 500 meters, a speed of less than 200 kilometers per hour, and a radar reflection area of ​​less than 2 square meters. Consumer and small drones flying at low altitudes are typical "low, slow and small" targets. In order to effectively deal with the complex threats brought by cluster drone targets, the drone detection radar system must have the ability to accurately estimate the size of the drone swarm (i.e. the number of individuals) and accurately depict the outline of the group, so as to achieve comprehensive monitoring and evaluation of cluster targets. However, due to the similar motion characteristics of drone swarms, the detection radar is limited by many factors, which will cause multiple adjacent targets to overlap and affect the detection effect. Therefore, it is required to improve the resolution of cluster targets during signal processing.

[0003] At present, most of the research focuses on improving the performance of single UAV detection and target type recognition. There are also methods for improving the resolution of group targets, such as the literature "Array radar single pulse group target resolution method [J]" (Wang Luoshengbin, Zeng Hui, Xu Zhenhai, Modern Radar, 2021, 43(09): 6-13.) Starting from the radar resolution mechanism, based on parameterized models and maximum likelihood estimation, combined with the flexible airspace processing capabilities of array radar, two methods, adaptive single pulse and four-channel single pulse, are given to achieve group target resolution. However, the premise of the array radar single pulse group target resolution method is to predict the prior information of the number of targets, but some group target scenarios are difficult to obtain, and it is necessary to study the target number estimation method. The paper "A beam-domain azimuth estimation algorithm for super-resolution of swarm UAVs[J]" (Zhou Qingchen, Li Xiaomeng, Shen Xianzhao, et al. Radar Science and Technology, 2024, 22(03):300-305) proposes a beam-domain azimuth super-resolution estimation algorithm. This method not only avoids the high computational complexity and the need to select hyperparameters of traditional sparse representation angle measurement methods, but also has good resolution capabilities under non-ideal conditions such as a single snapshot number and a small spatial angle interval of the incident signal. However, this method is for super-resolution in azimuth and elevation airspace, and does not break through the inherent range resolution limit of the radar system. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a method for effectively realizing radar super-resolution detection of cluster targets in view of the problem that the distance dimension is easily aliased when the current radar detects low, small and slow cluster targets.

[0005] The technical solution adopted by the present invention to solve the above technical problems is a radar super-resolution method for low, small and slow cluster targets, comprising the steps of:

[0006] Initialization steps: Set the radar transmit signal bandwidth B, radar transmit signal pulse width T and frequency modulation slope ; Sampling the distance dimension echo to obtain a two-dimensional echo signal of the azimuth dimension and the distance dimension;

[0007] The steps of range-dimensional pulse compression are as follows: Fourier transform the echo along the range dimension to obtain a two-dimensional echo matrix; construct a range-dimensional pulse compression reference function using the frequency modulation slope and the pulse width of the radar transmission signal, and then perform Fourier transform to obtain the reference function spectrum; multiply the two-dimensional echo matrix with the reference function spectrum, and then perform inverse Fourier transform on the multiplication result to obtain the time domain result after range-dimensional pulse compression;

[0008] The steps of constructing the cluster target echo model are as follows: the azimuth dimension of the time domain result after the range dimension pulse compression is fast Fourier transformed to obtain the range-Doppler domain echo data matrix; the cluster target echo model is constructed by performing the two-dimensional convolution of the scattering coefficient of the cluster target in the range-Doppler space of the radar system and the range-Doppler domain echo data matrix, and then adding the random noise in the range-Doppler space;

[0009] The objective function establishment steps of sparse super-resolution are as follows: the range dimension signal amplitude is extracted from the cluster target echo model, and the signal convolution matrix is ​​constructed using the range dimension convolution kernel function. Discretize the range dimension signal amplitude to obtain the range dimension super-resolution model ;Use sparse regularization method to improve the distance dimension super-resolution model Describe and obtain the objective function of sparse super-resolution;

[0010] Super-resolution imaging result output steps:

[0011] Iteratively solve and calculate the gradient of the objective function and output the distance-dimensional scattering coefficient vector of the cluster target The super-resolution imaging result.

[0012] Specifically, the specific expression of iterative solution to calculate the gradient of the objective function is:

[0013]

[0014] in, is the distance-dimensional scattering coefficient vector of the cluster target No. The result of the iteration, is a vector No. The result of the iteration, represents transpose, is the regularization parameter, is a diagonal matrix, For vector The i-th element of for The i-th element of is a constant introduced to solve the L1 norm non-differentiable problem.

[0015] Aiming at the problem of limited range resolution in traditional radar air detection technology, the present invention introduces a super-resolution method based on the range-Doppler plane, namely: firstly, a super-resolution convolution echo signal model of cluster target range-Doppler plane is constructed, and then a sparse regularization method is used to estimate the position of cluster targets.

[0016] The beneficial effect of the present invention is that it can break through the inherent distance resolution limitation of the radar system under conventional signal-to-noise ratio conditions and has broad application prospects in cluster target super-resolution scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flowchart of the method provided by the present invention.

[0018] Figure 2 It is a schematic diagram of the simulation target distribution used in the specific implementation manner of the present invention.

[0019] Figure 3 It is the original echo data in the specific implementation manner of the present invention.

[0020] Figure 4 It is the result of distance-dimensional pulse compression in a specific implementation manner of the present invention.

[0021] Figure 5 yes Figure 4 The result is a range-dimensional profile of the echo of a certain pulse.

[0022] Figure 6 It is the range-Doppler result obtained by azimuth-dimensional Fourier transform in a specific implementation manner of the present invention.

[0023] Figure 7 yes Figure 6 The range dimension profile of the Doppler unit where the target is located in the result.

[0024] Figure 8 These are the four target results estimated by the sparse regularized super-resolution method in the specific implementation manner of the present invention.

[0025] Fig. 9 Yes Figure 8 The range dimension profile result of the Doppler frequency gate where the target is located. DETAILED DESCRIPTION

[0026] The method of the present invention comprises:

[0027] Step 1: First, establish the radar baseband echo signal model.

[0028] Assume that the pulse width of the radar transmission signal is T, the signal bandwidth is B, and the center frequency of the radar transmission signal is and FM slope The radar transmits multiple pulse signals at a fixed beam position. After receiving and processing by the radar, a two-dimensional echo baseband signal of a point target with normalized amplitude and time variables of distance dimension and azimuth dimension can be obtained. for:

[0029] (1)

[0030] in, is a rectangular envelope function, is an exponential function, is the distance dimension time variable, also called fast time, is the azimuthal time variable, also called slow time, is the distance from the radar to the target, is the time it takes for the beam center to sweep across the target, is the azimuth rectangular window function, is the speed of light, is the radial velocity of the target. Usually, in order to obtain a higher target signal-to-noise ratio, the radar system will match the waveform parameters according to the target speed in system design to ensure that the target will not cross the distance resolution unit within a multi-pulse accumulation time. , Indicates the distance of the target from the radar.

[0031] Step 2: Range-dimensional pulse compression.

[0032] 2-1 Perform distance-dimensional Fourier transform:

[0033] (2)

[0034] is the two-dimensional echo signal after the range-dimensional Fourier transform, The size is , represents the fast time frequency domain variable, that is, the distance dimension frequency domain variable, Is an imaginary unit.

[0035] Substituting formula (1) into the integral sign in formula (2), the phase in the integral sign is for:

[0036] (3)

[0037] Applying the stationary phase principle (POSP) to integrate formula (2), the result is:

[0038] (4)

[0039] 2-2 Perform distance-dimensional pulse compression.

[0040] In the distance dimension, the echo after Fourier transform in the above distance dimension is pulse compressed in the frequency domain, and the pulse compression reference function for:

[0041] (5)

[0042] After Fourier transforming formula (5), we can get the reference function spectrum: for:

[0043] (6)

[0044] Multiplying formula (4) and formula (6) and performing pulse compression operation on the linear frequency modulated pulse signal in the frequency domain, we obtain:

[0045] (7)

[0046] Perform inverse Fourier transform on the multiplication result to obtain the time domain result after distance-dimensional pulse compression. :

[0047] (8)

[0048] It indicates that the inverse Fourier transform is performed in the distance dimension. It can be seen that the pulse compression output spectrum of the linear frequency modulation pulse signal is rectangular, and the corresponding time domain waveform is a sinc function.

[0049] Step 3: Obtain the range-Doppler two-dimensional echo model of the cluster target.

[0050] Fourier transform in the slow time dimension can complete the coherent accumulation of targets with a certain radial velocity to improve the signal-to-noise ratio. Therefore, the detection of drones is usually carried out in the range-Doppler plane. Therefore, the method proposed in the present invention needs to transform the echo to the range-Doppler plane for processing. The specific operation is: Fourier transform formula (8) in the azimuth slow time dimension to convert the range-azimuth data to the range-Doppler domain:

[0051] (9)

[0052] in, represents the slow-time frequency domain variable, It means to perform a fast Fourier transform on the slow time dimension, that is, to perform a fast Fourier transform on the azimuth dimension. for Formula (9) is the range-Doppler impulse response of a unit amplitude point target.

[0053] The cluster target echo model is the two-dimensional convolution of the scattering coefficient of multiple point targets and the impulse response.

[0054] (10)

[0055] in, represents the convolution operation, is the scattering coefficient of cluster targets in the range-Doppler space of the radar system, is the random noise in the range-Doppler space.

[0056] Step 4: Establish the objective function of sparse super-resolution.

[0057] 4-1 Construct the signal convolution matrix H.

[0058] Since this paper mainly performs super-resolution on the range dimension amplitude, the range dimension signal amplitude is converted from the cluster target echo model Extracted from:

[0059] (11)

[0060] in, represents the signal amplitude in the distance dimension, is the distance dimension convolution kernel function, is the distance dimension scattering coefficient of the cluster target, is the random noise of the radar system receiver.

[0061] For the convenience of calculation, this Discretization into distance dimension super-resolution model :

[0062] (12)

[0063] in, , and for dimensional column vector, is the distance dimension convolution kernel function Determine the convolution matrix. Convolution kernel function for distance dimension Discretization obtains the discretized convolution kernel function vector , l is The sinc function with the center as the center is taken to the left and right to the length where the first side lobe begins.

[0064] (13)

[0065] Therefore, the distance dimension super-resolution problem can be transformed into the target scattering coefficient estimation problem.

[0066] 4-2 Construct sparse regularized super-resolution objective function.

[0067] In order to alleviate the sensitivity of super-resolution methods to noise and effectively utilize the sparse characteristics of cluster targets, a sparse regularization method is used to solve the convolution model of the distance dimension for super-resolution. The regularization method is a least squares method with a regularization penalty term, which is used to alleviate the ill-conditioned problem of deconvolution. The objective function of sparse super-resolution is described as follows:

[0068] (14)

[0069] in, is the L2 norm, is the L1 norm, is the data fidelity term, is the regularization term, It is a regularization parameter, which is used to adjust the weight ratio between the regularization term and the fidelity term, and is usually determined by the L-curve method.

[0070] Step 5: Output of super-resolution imaging results.

[0071] 5-1 Calculate the gradient of the objective function:

[0072] In order to solve the objective function, we first need to calculate the gradient of the objective function.

[0073] (15)

[0074] in Representative Matrix The transpose of is a small constant introduced to solve the L1 norm non-differentiable problem. is a diagonal matrix, For vector The i-th element of .

[0075] Then setting the equation equal to zero, we get:

[0076] (16)

[0077] 5-2 Iterative solution:

[0078] Multiply both sides of the above equation by , It is Iteration results. and Approximately equal, so according to Picard multiplication iteration method, the following iterative solution formula can be obtained:

[0079] (17)

[0080] in For vector The ith element of .

[0081] After the iterative solution is completed, the distance-dimensional scattering coefficient of the cluster target is output = The scattering coefficient of a target refers to the radar reflectivity of a target per unit cross-sectional area in the incident direction. The more accurately the radar estimates the distribution of the cluster target reflection coefficient in the distance dimension, the higher the image resolution. Therefore, the distance-dimensional scattering coefficient of the cluster target is obtained. The super-resolution imaging result can be formed.

[0082] The embodiment is verified by simulation experiment, and all steps and conclusions are verified correct on Matlab2020. The embodiment is described in detail below. Figure 1 shown.

[0083] Step 1: Parameter initialization.

[0084] Set the simulation target scene parameters. The target scene is as follows: Figure 2 As shown in the figure, four small UAV point targets in cluster formation are set at the positions of 2985m, 3000m, 3015m and 3030m away from the radar respectively. The system scattering coefficient of each target is consistent and normalized to 1. The radar system noise is set according to the signal-to-noise ratio of 20dB. Since it is a cluster formation target, the radial velocity of each target is consistent and set to 6m / s. Set the radar system parameters, radar center frequency The linear frequency modulation signal is 10GHz, the transmission signal bandwidth B is 5MHz, the transmission signal pulse width T is 20us, and the frequency modulation slope is , the number of transmitted pulses The pulse repetition frequency is 128 In order to perform super-resolution processing in the distance dimension, a higher sampling rate is used Sample the distance dimension echo to obtain a two-dimensional echo signal The matrix form of , the matrix size is ,like Figure 3 shown.

[0085] Step 2: Perform range-dimensional pulse compression.

[0086] Constructing distance-dimensional pulse compression reference function based on system parameters ,in , The echo is Fourier transformed along the distance dimension and compared with the spectrum of the pulse compression reference function Multiply, and then perform inverse Fourier transform on the result to the time domain to complete the echo The time domain result is obtained by pulse compression in the distance dimension , is the matrix expression of formula (8), the scale remains unchanged, such as Figure 4 As shown, Figure 4 The echo distance profile of a pulse in Figure 5 shown.

[0087] Step 3: Get the range-Doppler two-dimensional echo of the cluster target.

[0088] Echo data matrix after pulse compression , perform a fast Fourier transform on its azimuth slow time dimension to obtain the transformed range-Doppler domain echo data matrix , whose scale remains unchanged, such as Figure 6 As shown, Figure 6 The range profile of the Doppler unit where the target is located is as follows: Figure 7 Reuse , the scattering coefficient of cluster targets in the radar system range-Doppler space and the random noise in the range-Doppler space to generate cluster target echo model .

[0089] Step 4: Construct the distance dimension convolution matrix.

[0090] According to the system parameters, the distance dimension convolution kernel function Discretization, where m, get the discretized convolution kernel function vector , since the target original echo mainly depends on the response between the first side lobes of the convolution kernel function, in order to reduce the matrix size and reduce the amount of calculation, its length For The sinc function centered at m is taken to the left and right to the length of the beginning of the first side lobe, here is . Thus, the system convolution matrix is ​​obtained :

[0091] (18)

[0092] Step 5: Perform super-resolution estimation along the distance dimension.

[0093] The matrix of the range-Doppler domain echo data No. ( The initial value of is 1) The amplitude of the row data is the original echo to be processed The objective function of super-resolution estimation is constructed according to formula (14).

[0094] Step 6: Use the iterative formula to estimate the optimal solution.

[0095] The objective function gradient is obtained according to expression (15). , the regularization parameter The L curve method is used to determine. Then, the optimal solution of the target is iteratively estimated using formula (17), and the initial value of the iteration is set for . Determine whether the iteration termination condition is met:

[0096] (19)

[0097] in is the threshold set according to the noise variance. and If formula (19) is not satisfied, update Continue iterating until the iteration termination condition is met .

[0098] Step 7: Determine the echo Whether the 128 rows of data have been processed, that is, whether , if it meets the requirement, the range-dimensional scattering coefficient of the cluster target in the range-Doppler space of the radar system is output. The super-resolution imaging result is formed; otherwise , repeat steps 5 and 6, and finally obtain the cluster target super-resolution method result of the present invention, such as Figure 8 As shown, Figure 8 The range dimension profile of the Doppler gate where the target is located is as follows Fig. 9 shown.

[0099] The target echo is compressed by pulse in the range dimension and transformed by Fourier transform in the azimuth dimension as shown below: Figure 6 As shown, the four point targets are spaced 15 meters apart, which is less than the distance resolution after radar pulse compression processing. , and the radial velocities of the targets are consistent, so the four targets cannot be distinguished in the range-Doppler plane. Figure 7This is the range dimension profile of the Doppler unit where the four point targets are located. It can be seen that the echoes of the four point targets are overlapped and cannot be separated from each other. Figure 8 This is the result of the cluster target super-resolution method of the present invention. It can be seen that the four target points are clearly separated in the distance dimension; Fig. 9 This is the distance profile of the Doppler gate where the target is located. From the result, it can be seen more clearly that the four target points are clearly resolved. Therefore, the target distance resolution after processing by the present invention is better than the original distance resolution of the radar, and the distance super-resolution of cluster targets is achieved.

Claims

1. A radar super-resolution method for low, small and slow cluster targets, characterized in that: Includes steps: Initialization steps: Set the transmit signal bandwidth B, radar transmit signal pulse width T and frequency modulation slope K r ; Sampling the distance dimension echo to obtain a two-dimensional echo signal of the azimuth dimension and the distance dimension; Range-dimensional pulse compression steps: Perform Fourier transform on the echo along the distance dimension to obtain a two-dimensional echo matrix; construct a distance-dimensional pulse compression reference function using the frequency modulation slope and the pulse width of the radar transmission signal, and then perform Fourier transform to obtain the reference function spectrum; multiply the two-dimensional echo matrix with the reference function spectrum, and then perform inverse Fourier transform on the multiplication result to obtain the time domain result after distance-dimensional pulse compression; Cluster target echo model construction steps: Perform fast Fourier transform on the azimuth dimension of the time domain result after range-dimension pulse compression to obtain the range-Doppler domain echo data matrix; perform two-dimensional convolution of the scattering coefficient of cluster targets in the range-Doppler space of the radar system and the range-Doppler domain echo data matrix, and add random noise in the range-Doppler space to form a cluster target echo model; Steps to establish the objective function of sparse super-resolution: The range dimension signal amplitude is extracted from the cluster target echo model, and the signal convolution matrix H is constructed using the range dimension convolution kernel function to discretize the range dimension signal amplitude to obtain the range dimension super-resolution model s; The sparse regularization method is used to describe the distance dimension super-resolution model s to obtain the objective function of sparse super-resolution; Super-resolution imaging result output step: iteratively solve and calculate the gradient of the objective function, and output the super-resolution imaging result formed by the distance-dimensional scattering coefficient vector x of the cluster target; Cluster target echo model S ddf (f η ,τ) is specifically: in, represents the convolution operation, f η is the frequency domain variable in the azimuth dimension, τ is the time domain variable in the distance dimension, x(f η ,τ) is the scattering coefficient of cluster targets in the range-Doppler space of the radar system, S 2df (f η ,τ) is the range-Doppler domain echo data matrix, n(f η ,τ) is the random noise in the range-Doppler space; Range-Doppler domain echo data matrix S 2df (f η ,τ) is specifically: Among them, η is the azimuth time variable, FFT η Indicates the fast Fourier transform of the orientation dimension, s rc (η,τ) is the time domain result after range-dimensional pulse compression, c is the speed of light, v is the radial velocity of the target, exp is the exponential function, R0 represents the distance of the target from the radar, W a is the spectrum form of the azimuth rectangular window function, f0 is the center frequency of the radar transmission signal, η c is the time it takes for the center of the beam to scan the target, and j is an imaginary unit.

2. The method according to claim 1, characterized in that: The specific expression of iterative solution to calculate the gradient of the objective function is: Among them, x k is the k-th iteration result of the distance-dimensional scattering coefficient vector x of the cluster target, x k-1 is the k-1th iteration result of vector x, T represents the transpose, λ is the regularization parameter, diag{·} is the diagonal matrix, x i is the i-th element of vector x, (x i ) k-1 For x k-1 The i-th element of , ε is a constant introduced to solve the L1 norm non-differentiable problem.

3. The method according to claim 1, characterized in that: Distance dimension convolution kernel function h imp (τ) is specifically: Among them, R0 represents the distance between the target and the radar, and τ is the distance dimension time variable.

4. The method according to claim 1, characterized in that: The distance-dimensional pulse compression reference function refer(τ) is specifically: Among them, rect is the rectangular envelope function, exp is the exponential function, and τ is the distance dimension time variable.

5. The method according to claim 4, characterized in that: Reference function spectrum H(f τ ) specifically: Among them, f τ Represents a distance-dimensional frequency-domain variable.

6. The method according to claim 1, characterized in that: Time domain results after range-dimensional pulse compression rc (η,τ) is specifically: Among them, IFFT τ represents the inverse Fourier transform in the distance dimension, S out (η,f τ ) is the result of multiplying the two-dimensional echo matrix and the reference function spectrum, w a is the azimuth rectangular window function.

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