Frequency agility radar target detection method and system based on dimension reduction model

Abstract

The invention discloses a frequency agility radar target detection method and system based on a dimension reduction model, and relates to the related field of radar signal processing, and the method comprises the steps: executing the down-conversion processing of an echo signal, carrying out the pulse compression processing of a down-conversion signal, carrying out the constant false alarm rate processing, and extracting a target range gate phase sequence; constructing a diagonal matrix, a distance-dimensional basis matrix, a speed-dimensional basis matrix and a unit diagonal matrix, and configuring a dimension reduction matrix; a semi-secondary splitting method is adopted to convert the dimension reduction matrix into an unconstrained form, then an auxiliary variable matrix is introduced, a distance-speed joint estimation result matrix and the auxiliary variable matrix are initialized, iterative updating is executed until convergence is achieved, and the distance-speed joint estimation result matrix is output; and establishing a radar detection signal, and generating a target detection result. The technical problems that response delay exists in existing frequency agility radar target detection, and the efficiency and practicability of a radar system are affected are solved, and the technical effects of improving the response speed and improving the radar detection efficiency and practicability are achieved.

Description

Technical Field

[0001] This application relates to the field of radar signal processing, and in particular to a method and system for target detection using frequency-agile radar based on a dimensionality reduction model. Background Art

[0002] Radar detection technology plays a crucial role in air traffic management, weather monitoring, and other fields. Accurately estimating the range and velocity of targets is one of the core challenges in radar detection. Currently, the main approach to address this problem is to use frequency-agile radar combined with compressed sensing (CS) technology for joint range-velocity estimation. However, existing methods suffer from high computational complexity due to the need to process complex dictionary matrices containing multi-dimensional parameters such as range, velocity, and carrier frequency, making it difficult to meet real-time processing requirements. This leads to technical issues related to radar response delay, impacting the efficiency and practicality of radar systems.

[0003] Currently, frequency-agile radar target detection suffers from response delays, which affects the efficiency and practicality of the radar system. Summary of the Invention

[0004] This application provides a frequency-agile radar target detection method and system based on a dimensionality reduction model. The method employs techniques such as receiving echo signals, performing down-conversion, pulse compression, and constant false alarm rate processing sequentially to extract the target range-gate phase sequence. Based on radar specifications, it constructs a diagonal matrix, range dimensionality matrix, velocity dimensionality matrix, and unit diagonal matrix of the target range-gate phase sequence. A dimensionality reduction matrix is ​​configured, and a semi-quadratic splitting method is used to transform the dimensionality reduction matrix into an unconstrained form. An auxiliary variable matrix is ​​introduced, and the range-velocity joint estimation result matrix and auxiliary variable matrix are initialized. Through iterative updates until convergence, the final output range-velocity joint estimation result matrix is ​​generated. These techniques address the technical problem of response delay in existing frequency-agile radar target detection systems, which affects the efficiency and practicality of the radar system. The method achieves the technical effect of improving response speed and enhancing the efficiency and practicality of radar detection.

[0005] This application provides a frequency-agile radar target detection method based on a dimensionality reduction model, including: after receiving the echo signal, performing down-conversion processing on the echo signal; after pulse compression processing on the down-converted signal, performing constant false alarm rate processing to extract the target range-gate phase sequence; constructing the diagonal matrix, range dimensionality matrix, velocity dimensionality matrix, and unit diagonal matrix of the target range-gate phase sequence using radar indicators, and configuring the dimensionality reduction matrix to perform optimization solution, the dimensionality reduction matrix is ​​as follows: Y=Θ⊙(AGB); where, The diagonal matrix of the target range gate phase sequence. Represented as a unit diagonal matrix, Let be the distance dimensional matrix. This represents the matrix representing the joint distance-velocity estimation results. The velocity dimensionality matrix is ​​represented by N, where N is the number of pulse cycles, P is the number of range-dimensional super-resolution units, Q is the number of velocity-dimensional super-resolution units, and ⊙ represents the dot product operation. The optimization solution includes using a semi-quadratic splitting method to transform the dimensionality-reduced matrix into an unconstrained form, then introducing an auxiliary variable matrix, initializing the range-velocity joint estimation result matrix and the auxiliary variable matrix, performing iterative updates until convergence, and outputting the range-velocity joint estimation result matrix. Based on the range-velocity joint estimation result matrix, a radar detection signal is established, and target detection results are generated.

[0006] In a possible implementation, after transforming the dimensionality-reduced matrix into an unconstrained form using a semi-quadratic splitting method, an auxiliary variable matrix is ​​introduced, and the following processing is performed: based on the Frobenius norm and L... p The norm is used for dimensionality reduction and matrix reconstruction optimization as follows: Among them, ||·|| F Characterizing the Frobenius norm, ||·|| p Characterizing L p Norm, Let be the coefficient of the first penalty term; after transforming the reconstructed and optimized dimensionality-reduced matrix into an unconstrained form using a semi-quadratic splitting method, an auxiliary variable matrix is ​​introduced, resulting in the following transformation: Where Z is the auxiliary variable matrix and λ is the coefficient of the second penalty term.

[0007] In a possible implementation, the initialization of the joint distance-velocity estimation matrix and the auxiliary variable matrix, followed by iterative updates until convergence, involves the following process: solving for the joint distance-velocity estimation matrix and the auxiliary variable matrix using the formula, as follows: Where l is the iteration number, l s Characterizing the iteration step size, G * The conjugate matrix representing the distance-velocity joint estimation result matrix G. The characterization function f with respect to G * The partial derivative of .

[0008] In a possible implementation, the solution for the joint distance-velocity estimation matrix and the auxiliary variable matrix is ​​obtained by performing the following steps: Iterative solution is performed using the formula; when the termination constraint is met, the solution converges, and the joint distance-velocity estimation matrix is ​​output. The termination constraint is as follows: Here, tol represents the tolerance threshold.

[0009] In a possible implementation, the iterative solution using the formula involves performing the following processing: calculation as follows: Will Substitute to G was calculated l+1 , will G l+1 Substitute to Z was calculated l+1 ,in,[·] -1 Characterize the reciprocal of each element of the matrix, A H B represents the conjugate transpose of the distance vidiquity matrix A. H The conjugate transpose of the velocity vidimetric matrix B.

[0010] In a possible implementation, the down-conversion processing of the echo signal is performed by the following steps: The processed down-converted signal is as follows: Where t represents the time axis of the LFM signal, τ is the time delay of the radar received echo, rect(·) represents the window function, and T p Let be the pulse width of the LFM signal, j be the imaginary unit in the complex number, and μ represent the modulation frequency of the LFM signal, μ = B' / T p B' represents the bandwidth of the LFM signal.

[0011] In a possible implementation, the following processing is performed: In the pulse compression processing of the down-converted signal, the matched filter is as follows: The pulse compression processing results are as follows: s MY (t-τ)=T p sinc(πB'(t-τ))exp(-j2πf n τ); where f n This represents the carrier frequency magnitude of the nth pulse of the frequency-agile radar's transmitted signal.

[0012] In a possible implementation, the following processing is performed: the distance dimensional matrix takes the following form: Among them, a ig f represents the element in the i-th row and g-th column of the distance vidi matrix A. i-1 Indicates the magnitude of the pulse carrier frequency in row i-1. The distance value characterizing the g-1 column pulse.

[0013] In a possible implementation, the following processing is performed: the velocity wiki matrix takes the following form: Among them, b ig The element in the i-th row and g-th column of the velocity vidi matrix B, f g-1 The magnitude of the pulse carrier frequency in column g-1. The velocity value of the i-1th row pulse is represented.

[0014] This application also provides a frequency-agile radar target detection system based on a dimensionality reduction model, including: an echo signal processing module, used to perform down-conversion processing on the received echo signal, perform pulse compression processing on the down-converted signal, perform constant false alarm rate processing, and extract the target range gate phase sequence; and a dimensionality reduction matrix construction module, used to construct the diagonal matrix, range dimensionality matrix, velocity dimensionality matrix, and unit diagonal matrix of the target range gate phase sequence using radar indicators, and configure the dimensionality reduction matrix to perform optimization solution, the dimensionality reduction matrix is ​​as follows: Y=Θ⊙(AGB); where, The diagonal matrix of the target range gate phase sequence. Represented as a unit diagonal matrix, Let be the distance dimensional matrix. This represents the matrix representing the joint distance-velocity estimation results. The system comprises: a velocity dimensionality matrix, where N is the number of pulse cycles, P is the number of range-dimensional super-resolution units, Q is the number of velocity-dimensional super-resolution units, and ⊙ represents dot product; a matrix solving module, which uses a semi-quadratic splitting method to transform the dimensionality-reduced matrix into an unconstrained form, introduces an auxiliary variable matrix, initializes the range-velocity joint estimation result matrix and the auxiliary variable matrix, performs iterative updates until convergence, and outputs the range-velocity joint estimation result matrix; and a target detection result generation module, which establishes a radar detection signal based on the range-velocity joint estimation result matrix and generates target detection results.

[0015] The proposed method and system for frequency-agile radar target detection based on a dimensionality reduction model, as described in this application, firstly performs down-conversion processing on the received echo signal, then performs pulse compression processing on the down-converted signal, followed by constant false alarm rate (CFAR) processing to extract the target range-gate phase sequence. Next, using radar indicators, it constructs the diagonal matrix, range dimensionality matrix, velocity dimensionality matrix, and unit diagonal matrix of the target range-gate phase sequence, and configures the dimensionality reduction matrix for optimization. The dimensionality reduction matrix is ​​as follows: Y = Θ⊙(AGB); where, The diagonal matrix of the target range gate phase sequence. Represented as a unit diagonal matrix, Let be the distance dimensional matrix. This represents the matrix representing the joint distance-velocity estimation results. The velocity dimensionality matrix is ​​represented by N, where N is the number of pulse cycles, P is the number of range-dimensional super-resolution units, Q is the number of velocity-dimensional super-resolution units, and ⊙ represents dot product. The optimization solution involves using a semi-quadratic splitting method to transform the dimensionality-reduced matrix into an unconstrained form, introducing an auxiliary variable matrix, initializing the range-velocity joint estimation result matrix and the auxiliary variable matrix, performing iterative updates until convergence, outputting the range-velocity joint estimation result matrix, and finally establishing a radar detection signal based on the range-velocity joint estimation result matrix to generate target detection results. This achieves the technical effect of improving response speed, enhancing radar detection efficiency, and improving practicality. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments of the present invention will be briefly described below. Flowcharts are used in this application to illustrate the operations performed by the method according to the embodiments of the present application. It should be understood that the preceding or following operations are not necessarily performed precisely in sequence. Instead, various steps can be processed in reverse order or simultaneously as needed. Furthermore, other operations can be added to these processes, or one or more steps can be removed from these processes.

[0017] Figure 1 This is a flowchart illustrating the frequency-agile radar target detection method based on a dimensionality reduction model provided in this application embodiment.

[0018] Figure 2 The range dimension resolution slice with a super-resolution magnification of 1 is provided in the frequency agile radar target detection method based on a dimensionality reduction model in the embodiments of this application.

[0019] Figure 3 The range dimension resolution slice with a super-resolution magnification of 2 is provided in the frequency agile radar target detection method based on a dimensionality reduction model in the embodiments of this application.

[0020] Figure 4 The range dimension resolution slice with a super-resolution magnification of 4 is provided in the frequency agile radar target detection method based on a dimensionality reduction model in the embodiments of this application.

[0021] Figure 5 The velocity dimension resolution slice with a super-resolution magnification of 1x is shown in the frequency agile radar target detection method based on a dimensionality reduction model provided in the embodiments of this application.

[0022] Figure 6 The velocity dimension resolution slice with a super-resolution magnification of 2x is shown in the frequency agile radar target detection method based on a dimensionality reduction model provided in the embodiments of this application.

[0023] Figure 7The velocity dimension resolution slice with a super-resolution magnification of 4x is shown in the frequency agile radar target detection method based on a dimensionality reduction model provided in the embodiments of this application.

[0024] Figure 8 This is a schematic diagram of the structure of a frequency-agile radar target detection system based on a dimensionality reduction model, provided in an embodiment of this application.

[0025] Figure labeling: Echo signal processing module 10, dimensionality reduction matrix construction module 20, matrix solving module 30, target detection result generation module 40. Detailed Implementation

[0026] The above description is merely an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, specific embodiments of this application are given below.

[0027] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description of this application will be provided in conjunction with the accompanying drawings. The described embodiments should not be considered as limitations on this application. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0028] In the following description, references to "some embodiments" describe a subset of all possible embodiments. However, it is understood that "some embodiments" can be the same or different subsets of all possible embodiments and can be combined with each other without conflict. The terms "first" and "second" are used merely to distinguish similar objects and do not represent a specific ordering of objects. The terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or server that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or modules not explicitly listed or inherent to these processes, methods, products, or devices. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only.

[0029] This application provides a method for target detection using frequency-agile radar based on a dimensionality reduction model, such as... Figure 1 As shown, the method includes:

[0030] Step S100: After receiving the echo signal, perform down-conversion processing on the echo signal, perform pulse compression processing on the down-converted signal, perform constant false alarm rate processing, and extract the target range gate phase sequence.

[0031] Specifically, after the echo signal enters the radar receiver, the received radar echo signal first undergoes down-conversion processing, converting the high-frequency signal into a lower-frequency intermediate-frequency signal for subsequent processing. For example, if the radar receives a signal at a frequency of 5 GHz, down-conversion will convert it to 500 MHz. The down-converted signal then undergoes pulse compression, a signal processing technique used to improve the radar's range resolution. For example, pulse compression is achieved using a matched filter, converting wide pulses into narrow pulses. The pulse-compressed signal then undergoes constant false alarm rate (CFAR) processing to detect target signals and suppress noise and interference. For example, the cell-averaged CFAR algorithm is used to identify targets. The target's range-gated phase sequence is extracted from the processed signal, providing a preliminary representation of the target's range and velocity information. For example, the target's range is determined by analyzing the phase changes of the signal.

[0032] In one possible implementation, the down-conversion processing of the echo signal, step S100 further includes step S110, and the processed down-converted signal is as follows:

[0033]

[0034] Where t represents the time axis of the LFM signal, τ is the time delay of the radar received echo, rect(·) represents the window function, and T p Let be the pulse width of the LFM signal, j be the imaginary unit in the complex number, and μ represent the modulation frequency of the LFM signal, μ = B' / T p B' represents the bandwidth of the LFM signal.

[0035] Specifically, window functions are used to limit the time range of a signal and reduce sidelobe effects. Time delay refers to the signal propagation delay caused by target distance and is used to estimate the target's range. Frequency modulation (FM) refers to the rate at which the frequency in an LFM signal changes linearly with time and is used to estimate the target's velocity. Pulse width refers to the duration of a single pulse in a radar signal.

[0036] Frequency-agile radar is a special type of radar system that transmits signals by rapidly changing the carrier frequency within a certain bandwidth. These signals are linear frequency modulated (LFM) signals, whose frequency changes linearly with time. The mathematical model for the transmitted signal of frequency-agile radar is as follows:

[0037]

[0038] Where s(t) represents the signal transmitted by the radar at time t. It is a window function, this function is in arrive The value is 1 between times and 0 at other times, f nThe carrier frequency of the nth pulse of the frequency-agile radar transmitted signal is represented by f. n =f0+d n Δf, f0 represents the starting frequency of the frequency-agile radar's transmitted signal, d n The frequency modulation code of the nth pulse is an integer ranging from 0 to M-1, where M is the number of carrier frequency points of the frequency agile radar, Δf represents the sub-bandwidth of the frequency agile radar, and t is a time variable.

[0039] Radar echo reception delay Where R0 is the initial distance between the radar and the target, v is the velocity of the target relative to the radar, and T is the initial distance between the radar and the target. r Here, is the pulse repetition interval (PRI), and c is the propagation speed of electromagnetic waves in free space. As time progresses, the target moves radially, and the echo delay changes with the PRI. For the nth pulse, the received echo delay τ is: Therefore, the mathematical model for the frequency-agile radar echo signal is:

[0040]

[0041] In one possible implementation, step S100 further includes step S120, wherein the matched filter in the pulse compression processing of the down-converted signal is as follows: The pulse compression processing results are as follows:

[0042] s MY (t-τ)=T p sinc(πB'(t-τ))exp(-j2πf n τ);

[0043] Among them, f n This represents the carrier frequency magnitude of the nth pulse of the frequency-agile radar's transmitted signal.

[0044] Specifically, a preliminary signal form is obtained through down-conversion processing, and these signals are further processed using pulse compression technology to improve the range resolution of the radar system. This is achieved using a matched filter. It is a rectangular window function used to limit the pulse width of a signal to T. p ,exp(-jπμt 2 ) is a frequency modulation term used to match the frequency modulation characteristics of the LFM signal. In the pulse compression processing result, sinc(πB'(t-τ)) is the sinc function used to implement pulse compression, exp(-j2πf n τ) is a phase term used to adjust the time delay τ caused by the target distance.

[0045] The pulse compression results are processed using constant false alarm rate (CFAR) to extract the target range gate phase, and its amplitude is normalized. The final target range gate phase sequence is represented as follows:

[0046]

[0047] For multiple targets, the target range-gate phase sequence is in summative form, as follows:

[0048]

[0049] Where K is the target quantity, τ k R is the radar echo delay of the k-th target. k v is the initial distance to the k-th target. k It is the radial velocity of the k-th target.

[0050] Step S200: Construct the diagonal matrix, range dimensionality matrix, velocity dimensionality matrix, and unit diagonal matrix of the target range-gated phase sequence using radar indicators, and configure the dimensionality reduction matrix to perform optimization. The dimensionality reduction matrix is ​​as follows:

[0051] Y = Θ⊙(AGB);

[0052] in, The diagonal matrix of the target range gate phase sequence. Represented as a unit diagonal matrix, Let be the distance dimensional matrix. This represents the matrix representing the joint distance-velocity estimation results. The velocity dimensional matrix is ​​represented by N, where N is the number of pulse cycles, P is the number of super-resolution units in the range dimension, Q is the number of super-resolution units in the velocity dimension, and ⊙ represents the dot product operation.

[0053] Specifically, It is the diagonal matrix form of the target range-gated phase sequence s(n). The diagonal matrix is ​​a square matrix where all elements outside the main diagonal are zero, and each diagonal element corresponds to the phase information of a target. Constructing the unit diagonal matrix. Used for sampling effective information, a unit diagonal matrix is ​​a diagonal matrix where all diagonal elements are 1 and all other elements are 0. A range wiki matrix is ​​constructed based on the radar's transmitted signal and the target's range information. For example, if the radar transmits a linear frequency modulated signal, then This will include the responses of these signals at different distances. Based on the target's velocity information, a velocity wiki matrix will be constructed. For example, if the target moves at a constant speed, then This will include the Doppler frequency shift information corresponding to these velocities. A joint range-velocity estimation matrix will be constructed. Used to store the final estimation results, for the joint range-velocity estimation matrix. In this context, the two dimensions of the matrix correspond to range and velocity, respectively, and the range-velocity grid containing non-zero units represents the target's range-velocity parameters. Substituting this matrix into the dimensionality-reduction matrix Y = Θ⊙(SGB), and performing optimization, we can solve for the target's range and velocity. Here, the dimensionality matrix refers to the matrix used in radar signal processing to represent target range and velocity information. ⊙ represents the Hadamard product, which is the element-wise multiplication of two matrices. Where P ≥ N, Q ≥ N.

[0054] Among them, matrix With matrix The representation is as follows:

[0055]

[0056] The distance dimensional matrix is ​​in the following form:

[0057]

[0058] Among them, a ig f represents the element in the i-th row and g-th column of the distance vidi matrix A. i-1 Indicates the magnitude of the pulse carrier frequency in row i-1. The distance value characterizing the g-1 column pulse.

[0059] matrix The representation is as follows:

[0060]

[0061] The velocity wiki matrix takes the following form:

[0062]

[0063] Among them, b ig The element in the i-th row and g-th column of the velocity vidi matrix B, f g-1 The magnitude of the pulse carrier frequency in column g-1. The velocity value of the i-1th row pulse is represented.

[0064] matrix The representation is as follows:

[0065]

[0066] Step S300, optimization solution includes using a semi-quadratic splitting method to transform the dimension reduction matrix into an unconstrained form, then introducing an auxiliary variable matrix, initializing the distance-velocity joint estimation result matrix and the auxiliary variable matrix, performing iterative updates until convergence, and outputting the distance-velocity joint estimation result matrix.

[0067] Specifically, the semi-quadratic splitting (HQS) method is used to transform the dimensionality-reduced matrix into an unconstrained form and introduces an auxiliary variable matrix. For example, the original problem is transformed into a more easily solvable form, while the introduction of auxiliary variables simplifies computation. The distance-velocity joint estimation matrix G and the auxiliary variable matrix are initialized. For example, these matrices can be initialized as zero matrices or identity matrices. Iterative updates are performed until convergence, and the distance-velocity joint estimation matrix is ​​output. For example, gradient descent is used for iterative updates until the change in matrix G is less than a certain threshold.

[0068] In one possible implementation, after the semi-quadratic splitting method is used to transform the dimensionality-reduced matrix into an unconstrained form and an auxiliary variable matrix is ​​introduced, step S300 further includes step S310, based on the Frobenius norm and L... p The norm is used for dimensionality reduction and matrix reconstruction optimization as follows:

[0069]

[0070] Among them, ||·|| F Characterizing the Frobenius norm, ||·|| p Characterizing L p Norm, This is the coefficient for the first penalty term.

[0071] Specifically, using the Frobenius norm and L p The Frobenius norm is used to construct the optimization model, and an auxiliary variable matrix is ​​introduced to simplify the solution process. The Frobenius norm of a matrix is ​​the square root of the sum of the squares of all its elements, used to measure the "size" of the matrix. p The norm is the sum of the p-th powers of the absolute values ​​of all its elements, raised to the power of 1 / p. It measures the "sparseness" of the elements in a matrix. The coefficient of the first penalty term is used to balance the Frobenius norm and the L-norm. p The influence of norms.

[0072] Step S320: After transforming the reconstructed and optimized dimensionality-reduced matrix into an unconstrained form using a semi-quadratic splitting method, an auxiliary variable matrix is ​​introduced, and the transformation is as follows:

[0073]

[0074] Where Z is the auxiliary variable matrix and λ is the coefficient of the second penalty term.

[0075] Specifically, an auxiliary variable matrix Z is introduced to further simplify the solution process. The auxiliary variable matrix is ​​used to assist in the solution, and the coefficient of the second penalty term is used to control the difference between G and Z.

[0076] In one possible implementation, the initialization of the joint distance-velocity estimation result matrix and the auxiliary variable matrix, followed by iterative updates until convergence, further includes step S330, which involves solving for the joint distance-velocity estimation result matrix and the auxiliary variable matrix using the following formula:

[0077]

[0078] Where l is the iteration number, l s Characterizing the iteration step size, G * The conjugate matrix representing the distance-velocity joint estimation result matrix G. The characterization function f with respect to G * The partial derivative of .

[0079] Specifically, This is transformed into a problem of minimizing a function, that is, solving for the function f(G,G) * Regarding the minimization problem of G, where, Right now, This represents the difference between observed data and model predictions, i.e., the data fidelity term. The sparsity of the auxiliary variable matrix Z is represented by the sparsity regularization term. The difference between the distance-velocity joint estimation matrix G and the auxiliary variable matrix Z is represented by the smoothness regularization term.

[0080] First, initialize the G and Z matrices. In each iteration, update the G and Z matrices according to the above formula, and check whether the updated matrices meet the convergence condition, such as the change being less than a preset threshold. When the iteration converges, output the final G matrix as the joint distance-velocity estimation result. Iteration step size l s Used to control the step size of each iteration update. Is the function f with respect to G * The conjugate gradient (i.e., the conjugate of the complex gradient).

[0081] In one possible implementation, the step S300, which involves solving the joint distance-velocity estimation result matrix and the auxiliary variable matrix using a formula, further includes step S340: iteratively solving the formula. When the termination constraint is met, it indicates that the solution has converged, and the joint distance-velocity estimation result matrix is ​​output. The termination constraint is as follows:

[0082] Here, tol represents the tolerance threshold.

[0083] Specifically, the distance-velocity joint estimation matrix G and the auxiliary variable matrix Z are iteratively updated using a formula until the convergence condition is met. When the termination constraint is met, it indicates that the solution has converged, and the distance-velocity joint estimation matrix is ​​output. The tolerance threshold in the termination constraint represents the allowed error range, used to check whether the difference between the current iteration's estimation result and the observed data is within an acceptable range. Finally, when the termination condition is met, G... l+1 This is the result of the joint estimation of target range and velocity.

[0084] In one possible implementation, the iterative solution using the formula further includes step S341, calculating... as follows:

[0085]

[0086] Will Substitute to G was calculated l+1 , will G l+1 Substitute to Z was calculated l+1 ,in,[·] -1 Characterize the reciprocal of each element of the matrix, A H B represents the conjugate transpose of the distance vidiquity matrix A. H The conjugate transpose of the velocity vidimetric matrix B.

[0087] Specifically, first, the gradient of f with respect to G is calculated. Among them, G * It is the conjugate transpose of G, and the gradient represents the rate of change of the function at G, used to guide how to update G to minimize the function f. Where G... l and Z l These are the G and Z matrices for the current iteration, respectively. The calculated gradient is used to update the G matrix, i.e. Finally, update the Z matrix to minimize it.

[0088] Step S400: Establish radar detection signals based on the range-velocity joint estimation result matrix and generate target detection results.

[0089] Specifically, after completing the aforementioned iterative optimization process, a range-velocity joint estimation result matrix G is obtained. This matrix contains the range and velocity information of each target detected by the radar. Based on the range-velocity joint estimation result matrix G, a radar detection signal can be established. That is, the information in matrix G is converted into a signal format that the radar system can recognize and process, including adjustments to parameters such as signal amplitude, frequency, and phase, to ensure that the radar system can effectively detect and track targets. Once the radar detection signal is established, the radar system can use these signals for target detection and early warning identification, including analyzing signal characteristics such as signal strength, duration, and change patterns to identify potential threats or important targets. The radar system will classify and evaluate the detected targets according to preset rules or algorithms to determine whether an early warning signal needs to be issued. When the radar system identifies a possible threat or important event, it issues an early warning signal. These signals can be visual (such as warnings on a screen), audible (such as alarm sounds), or other forms of notification so that operators can respond promptly.

[0090] The following is a specific example. Suppose a radar system is being used to monitor a specific airspace to detect and track potential aerial targets, such as aircraft or drones. The radar system starts up and begins transmitting frequency-agile radar signals. The radar receives echo signals from aerial targets, performs down-conversion, pulse compression, and constant false alarm rate processing on the echo signals, and extracts the target's range-gate phase sequence. An optimization algorithm (as described in the iterative update process above) is used to calculate the range-velocity joint estimation result matrix G. Based on the information in G, a radar detection signal is established, identifying salient features indicating the presence of targets. For example, if the value of an element exceeds a preset threshold, a target is considered to be present. Using a rule-based method, targets are classified according to their range and velocity information. For example, a high-speed moving target might be an aircraft, while a low-speed moving target might be a drone. The threat posed by the target to airspace safety is assessed; for example, if a target approaches a sensitive area at high speed, a higher level of alert is triggered. Based on the threat assessment results, corresponding warning signals are generated. If a target is considered a threat, the system will issue an alarm, such as displaying a warning message on the console and emitting an audible alarm through the speaker. The system reports detected target information and early warning signals to operators, who then perform further analysis and decision-making based on the received information, such as dispatching interceptors or activating defense systems. In this way, the radar system can effectively monitor the airspace and promptly detect and respond to potential threats.

[0091] The following is a computational complexity analysis of the method described: In the dimensionality reduction model Y = L⊙(AGB), the dimensions of each matrix are as follows: Let N represent the dimension of the matrix space, P represent the number of hyper-resolution units in the range dimension, and Q represent the number of hyper-resolution units in the velocity dimension. ⊙ represents the dot product, i.e., the Hadmar product. Where P ≥ N and Q ≥ N.

[0092] Let the maximum number of iterations be L. The iterative process of the method is mainly divided into four stages. In each iteration, It mainly involves 4 matrix multiplications, 1 matrix dot product, 1 scalar-matrix multiplication, and 2 matrix subtractions, with a computational complexity of O(2^(NPQ(P+Q)+N)). 2 +PQ)). It mainly involves one scalar-matrix multiplication and one matrix subtraction, with a computational complexity of O(2PQ). It mainly includes two matrix element operations, two scalar-matrix multiplications, one matrix dot product, and one matrix addition, with a computational complexity of O(6PQ). The computational complexity mainly includes two matrix multiplications, one matrix dot product, one matrix subtraction, and one Frobenius norm calculation, with a computational complexity of O(NPQ(P+Q)+3N). 2 In summary, when iterating L times, the time complexity of the method can be O(L(3NPQ(P+Q)+5N)). 2 +10PQ)) represents the complexity. O(3LNPQ(P+Q)) is the dominant term for computational complexity. The computational complexity of the existing OMP method is O(LNP) 2 Q 2 +L 2 PQ+L 3 ), O(LNP 2 Q 2) The computational complexity is the dominant term. Comparing the dominant terms of computational complexity of the two methods, the complexity of the proposed method is order 5, while that of the OMP algorithm is order 6. Therefore, the complexity of the proposed method is significantly lower than that of the existing OMP method.

[0093] The simulation results of the method are shown below. The radar simulation parameters used in the simulation are shown in Table 1. The frequency-agile radar uses Costas coding, and N = M. The comparison methods include L1 norm, Iterative Shrinkage-Thresholding Algorithm (ISTA), and Greedy Iterative OMP.

[0094] Table 1: List of Simulation Parameters for Frequency Agile Radar

[0095] Parameter type Parameter size <![CDATA[Starting carrier frequency f0]]> 10GHz <![CDATA[PRIT r ]]> 200μs <![CDATA[Pulse emission duration T p > 10μs Number of transmitted pulses N 64 Frequency agility points M 64 Carrier frequency switching bandwidth Δf 10MHz LFM signal bandwidth B' 10MHz signal sampling frequency 20MHz Frequency hopping range 640MHz

[0096] The computer equipment used in the experiment was as follows: CPU AMD Ryzen 7 8845H 3.8GHz, solid-state drive size 512G, memory size 32GB, operating system Windows 11, software MATLAB 20 23b. The experimental data were obtained from 500 Monte Carlo experiments, and the experimental results are shown in Tables 2-7.

[0097] Table 2: Comparison of time consumption for different methods under different noise levels at a super-resolution magnification of 1.

[0098]

[0099]

[0100] Table 3: Comparison of time consumption for different methods under different noise levels at a super-resolution magnification of 2.

[0101] Method\SNR 10dB 5dB 0dB -5dB -10dB -15dB <![CDATA[L1 norm]]> 13.7221s 13.3280s 13.7944s 12.4244s 13.5215s 12.6489s ISTA 4.0188s 4.0718s 4.1315s 3.8574s 3.6833s 3.6768s OMP 0.3383s 0.3404s 0.3403s 0.3433s 0.3344s 0.3344s This method 0.0972s 0.1003s 0.1029s 0.0953s 0.0885s 0.0881s

[0102] Table 4: Comparison of time consumption for different methods under different noise levels at a super-resolution magnification of 4.

[0103] Method\SNR 10dB 5dB 0dB -5dB -10dB -15dB <![CDATA[L1 norm]]> 73.0445s 70.4746s 73.6857s 70.7936s 66.2772s 66.5881s ISTA 10.1118s 9.9907s 8.3865s 7.4661s 7.9094s 7.8729s OMP 1.3713s 1.3932s 1.0893s 0.9594s 0.9577s 0.9681s This method 0.1635s 0.1651s 0.1218s 0.1027s 0.1078s 0.1071s

[0104] Table 5: Comparison of RSME under different methods and different noise levels at a super-resolution magnification of 1.

[0105] Method\SNR 10dB 5dB 0dB -5dB -10dB -15dB <![CDATA[L1 norm]]> 0.0006 0.0011 0.0018 0.0031 0.0081 0.0104 ISTA 0.0101 0.0098 0.0097 0.0128 0.0127 0.0223 OMP 0.0009 0.0015 0.0025 0.0044 0.0079 0.0171 This method 0.0022 0.0023 0.0029 0.0022 0.0031 0.0029

[0106] Table 6: Comparison of RSME under different methods and different noise levels at a super-resolution magnification of 2.

[0107] Method\SNR 10dB 5dB 0dB -5dB -10dB -15dB <![CDATA[L1 norm]]> 0.0004 0.0005 0.0006 0.0015 0.0031 0.0049 ISTA 0.0173 0.0174 0.0177 0.0178 0.0197 0.0239 OMP 0.0004 0.0008 0.0013 0.0025 0.0047 0.0071 This method 0.0061 0.0067 0.0109 0.0113 0.0114 0.0119

[0108] Table 7: Comparison of RSME under different methods and different noise levels at a super-resolution magnification of 4.

[0109] Method\SNR 10dB 5dB 0dB -5dB -10dB -15dB <![CDATA[L1 norm]]> 0.0003 0.0003 0.0004 0.0008 0.0015 0.0029 ISTA 0.0202 0.0203 0.0199 0.0208 0.0218 0.0259 OMP 0.0003 0.0004 0.0007 0.0012 0.0061 0.0041 This method 0.0011 0.0051 0.0053 0.0059 0.0079 0.0079

[0110] Figures 2-7 This is the result of resolution analysis performed by this method from different dimensions: super-resolution magnification, signal-to-noise ratio, distance, and velocity. Among these, Figure 2 , Figure 3 , Figure 4 This is the result of range resolution analysis on targets with the same speed but different distances. Figure 5 , Figure 6 , Figure 7 The results of velocity resolution analysis for targets at the same distance but different velocities.

[0111] The simulation results show that the proposed method achieves comparable accuracy to existing technologies in target parameter estimation, accurately reconstructing target range and velocity information. Furthermore, in resolution tests, the proposed method demonstrates similar resolution capabilities to existing technologies, effectively distinguishing adjacent targets. However, the proposed method achieves a significant improvement in computational efficiency. By employing the Kronecker product, gradient descent, and semi-quadratic splitting algorithms, the proposed method drastically reduces computational complexity, thereby accelerating the iterative solution process. This allows radar systems to process data and output results more quickly.

[0112] This embodiment of the application employs the following techniques: after receiving the echo signal, it sequentially performs down-conversion, pulse compression, and constant false alarm rate processing to extract the target range-gate phase sequence. Based on radar indicators, it constructs the diagonal matrix, range wiki matrix, velocity wiki matrix, and unit diagonal matrix of the target range-gate phase sequence. It configures the dimensionality reduction matrix, uses a semi-quadratic splitting method to transform the dimensionality reduction matrix into an unconstrained form, introduces an auxiliary variable matrix, initializes the range-velocity joint estimation result matrix and the auxiliary variable matrix, and iteratively updates them until convergence, finally outputting the range-velocity joint estimation result matrix. These techniques solve the technical problem of response delay in target detection in existing frequency-agile radars, which affects the efficiency and practicality of the radar system. This achieves the technical effect of improving response speed and enhancing the efficiency and practicality of radar detection.

[0113] In the above text, refer to Figures 1-7 This paper describes in detail a frequency-agile radar target detection method based on a dimensionality-reduced model according to embodiments of the present invention. Next, reference will be made to... Figure 8 A frequency-agile radar target detection system based on a dimensionality reduction model is described according to an embodiment of the present invention.

[0114] The frequency-agile radar target detection system based on a dimensionality reduction model according to embodiments of the present invention addresses the technical problem of response delay in existing frequency-agile radar target detection systems, which affects the efficiency and practicality of the radar system. It achieves the technical effect of improving response speed and enhancing the efficiency and practicality of radar detection. The frequency-agile radar target detection system based on a dimensionality reduction model includes: an echo signal processing module 10, a dimensionality reduction matrix construction module 20, a matrix solving module 30, and a target detection result generation module 40.

[0115] The echo signal processing module 10 is used to perform down-conversion processing on the received echo signal, perform pulse compression processing on the down-converted signal, perform constant false alarm rate processing, and extract the target range gate phase sequence. The dimensionality reduction matrix construction module 20 is used to construct the diagonal matrix, range dimensionality matrix, velocity dimensionality matrix, and unit diagonal matrix of the target range gate phase sequence using radar indicators, and configure the dimensionality reduction matrix to perform optimization solving. The dimensionality reduction matrix is ​​as follows: Y = L⊙(AGB); where, The diagonal matrix of the target range gate phase sequence. Represented as a unit diagonal matrix, Let be the distance dimensional matrix. This represents the matrix representing the joint distance-velocity estimation results. The velocity dimensionality matrix is ​​represented by N, where N is the number of pulse cycles, P is the number of range-dimensional super-resolution units, Q is the number of velocity-dimensional super-resolution units, and ⊙ represents the dot product operation. The matrix solving module 30 is used to convert the dimension-reduced matrix into an unconstrained form using a semi-quadratic splitting method, introduce an auxiliary variable matrix, initialize the range-velocity joint estimation result matrix and the auxiliary variable matrix, perform iterative updates until convergence, and output the range-velocity joint estimation result matrix. The target detection result generation module 40 is used to establish a radar detection signal based on the range-velocity joint estimation result matrix and generate target detection results.

[0116] The specific configuration of the matrix solving module 30 will be described in detail below. As mentioned above, after the dimensionality-reduced matrix is ​​transformed into an unconstrained form using a semi-quadratic splitting method, an auxiliary variable matrix is ​​introduced. The matrix solving module 30 may further include: a matrix reconstruction optimization unit for optimization based on the Frobenius norm and L... p The norm is used for dimensionality reduction and matrix reconstruction optimization as follows: Among them, ||·|| F Characterizing the Frobenius norm, ||·|| p Characterizing L p Norm, Here is the coefficient of the first penalty term; the transformation unit is used to transform the dimension reduction matrix of the reconstruction optimization into an unconstrained form using a semi-quadratic splitting method, and then introduces an auxiliary variable matrix, as follows: Where Z is the auxiliary variable matrix and λ is the coefficient of the second penalty term.

[0117] The initialization of the joint distance-velocity estimation result matrix and the auxiliary variable matrix, followed by iterative updates until convergence, may be further categorized into several matrix solving modules. The matrix solving module 30 may include a matrix solving unit used to solve for the joint distance-velocity estimation result matrix and the auxiliary variable matrix using formulas, as follows: Where l is the iteration number, l s Characterizing the iteration step size, G * The conjugate matrix representing the distance-velocity joint estimation result matrix G. The characterization function f with respect to G * The partial derivative of .

[0118] The method of solving the joint distance-velocity estimation matrix and the auxiliary variable matrix using formulas may further include a constraint setting subunit for iterative solution using formulas. When the termination constraint condition is met, it indicates convergence of the solution, and the joint distance-velocity estimation matrix is ​​output. The termination constraint condition is as follows: Here, tol represents the tolerance threshold.

[0119] The iterative solution using formulas, and the constraint setting sub-unit, may further include: calculation. as follows: Will Substitute to G was calculated l+1 , will G l+1 Substitute to Z was calculated l+1 ,in,[·] -1 Characterize the reciprocal of each element of the matrix, A H B represents the conjugate transpose of the distance vidiquity matrix A. H The conjugate transpose of the velocity vidimetric matrix B.

[0120] The specific configuration of the echo signal processing module 10 will be described in detail below. As mentioned above, to perform down-conversion processing of the echo signal, the echo signal processing module 10 may further include: the processed down-converted signal as follows: Where t represents the time axis of the LFM signal, τ is the time delay of the radar received echo, rect(·) represents the window function, and T p Let be the pulse width of the LFM signal, j be the imaginary unit in the complex number, and μ represent the modulation frequency of the LFM signal, μ = B' / T p B' represents the bandwidth of the LFM signal.

[0121] The echo signal processing module 10 may further include: in the pulse compression processing of the down-converted signal, the matched filter is as follows: The pulse compression processing results are as follows: s MY (t-τ)=T p sinc(πB'(t-τ))exp(-j2πf n τ); where f n This represents the carrier frequency magnitude of the nth pulse of the frequency-agile radar's transmitted signal.

[0122] The specific configuration of the dimensionality reduction matrix construction module 20 will be described in detail below. As mentioned above, the dimensionality reduction matrix construction module 20 may further include: the distance dimensionality matrix in the following form: Among them, a igf represents the element in the i-th row and g-th column of the distance vidi matrix A. i-1 Indicates the magnitude of the pulse carrier frequency in row i-1. The distance value characterizing the g-1 column pulse.

[0123] The dimension reduction matrix construction module 20 may further include: the velocity dimensionality matrix in the following form: Among them, b ig The element in the i-th row and g-th column of the velocity vidi matrix B, f g-1 The magnitude of the pulse carrier frequency in column g-1. The velocity value of the i-1th row pulse is represented.

[0124] The frequency-agile radar target detection system based on a dimensionality reduction model provided in this embodiment of the invention can execute the frequency-agile radar target detection method based on a dimensionality reduction model provided in any embodiment of the invention, and has the corresponding functional modules and beneficial effects of the method.

[0125] Although this application makes various references to certain modules in the system according to the embodiments of this application, any number of different modules can be used and run on user terminals and / or servers. The various units and modules included are only divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of each functional unit are only for easy distinction between each other and are not used to limit the scope of protection of this invention.

[0126] The specific embodiments described above do not constitute a limitation on the scope of protection of this application. Those skilled in the art should understand that various modifications, combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application. In some cases, the actions or steps described in this application can be performed in a different order than that shown in the embodiments and still achieve the desired results. Furthermore, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

Claims

1. A frequency-agile radar target detection method based on a dimensionality reduction model, characterized in that, The method includes: After receiving the echo signal, the echo signal is down-converted, the down-converted signal is pulse-compressed, and then constant false alarm rate processing is performed to extract the target range gate phase sequence. Using radar indicators, we construct the diagonal matrix, range wiki matrix, velocity wiki matrix, and unit diagonal matrix of the target range-gated phase sequence, and then configure a dimensionality reduction matrix to perform optimization. The dimensionality reduction matrix is ​​as follows: Y = Θ⊙(AGB); in, The diagonal matrix of the target range gate phase sequence. Represented as a unit diagonal matrix, Let be the distance dimensional matrix. This represents the matrix representing the joint distance-velocity estimation results. The velocity dimensional matrix is ​​represented by N, where N is the number of pulse cycles, P is the number of super-resolution units in the range dimension, Q is the number of super-resolution units in the velocity dimension, and ⊙ represents the dot product operation. The optimization solution involves using a semi-quadratic splitting method to transform the dimension-reduced matrix into an unconstrained form, then introducing an auxiliary variable matrix, initializing the joint distance-velocity estimation result matrix and the auxiliary variable matrix, performing iterative updates until convergence, and outputting the joint distance-velocity estimation result matrix. The radar detection signal is established based on the range-velocity joint estimation result matrix, and the target detection result is generated.

2. The frequency-agile radar target detection method based on a dimensionality reduction model as described in claim 1, characterized in that, The method of using semi-quadratic splitting to transform the dimension-reduced matrix into an unconstrained form and then introducing an auxiliary variable matrix includes: Based on Frobenius norm and L p The norm is used for dimensionality reduction and matrix reconstruction optimization as follows: Among them, ||·|| F Characterizing the Frobenius norm, ||·|| p Characterizing L p Norm, The coefficient of the first penalty term; After transforming the reconstructed and optimized dimensionality-reduced matrix into an unconstrained form using a semi-quadratic splitting method, an auxiliary variable matrix is ​​introduced, resulting in the following transformation: Where Z is the auxiliary variable matrix and λ is the coefficient of the second penalty term.

3. The frequency-agile radar target detection method based on a dimensionality reduction model as described in claim 2, characterized in that, The initialization of the joint distance-velocity estimation matrix and auxiliary variable matrix, followed by iterative updates until convergence, includes: The distance-velocity joint estimation matrix and auxiliary variable matrix are solved using the formula, as follows: Where l is the iteration number, l s Characterizing the iteration step size, G * The conjugate matrix representing the distance-velocity joint estimation result matrix G. The characterization function f with respect to G * The partial derivative of .

4. The frequency-agile radar target detection method based on a dimensionality reduction model as described in claim 3, characterized in that, The process of solving the joint distance-velocity estimation matrix and auxiliary variable matrix using formulas includes: The solution is solved iteratively using the formula. The solution converges when the termination constraint is met. The joint distance-velocity estimation matrix is ​​then output. The termination constraint is as follows: Here, tol represents the tolerance threshold.

5. The frequency-agile radar target detection method based on a dimensionality reduction model as described in claim 4, characterized in that, The iterative solution using formulas includes: calculate as follows: Will Substitute to G was calculated l+1 , will G l+1 Substitute to Z was calculated l+1 ,in,[·] -1 Characterize the reciprocal of each element of the matrix, A H B represents the conjugate transpose of the distance vidiform matrix A. H The conjugate transpose of the velocity vidimetric matrix B.

6. The frequency-agile radar target detection method based on a dimensionality reduction model as described in claim 1, characterized in that, The down-conversion processing of the echo signal includes: The processed downconversion signal is as follows: Where t represents the time axis of the LFM signal, τ is the time delay of the radar received echo, rect(·) represents the window function, and T p Let be the pulse width of the LFM signal, j be the imaginary unit in the complex number, and μ represent the modulation frequency of the LFM signal, μ = B' / T p B' represents the bandwidth of the LFM signal.

7. The frequency-agile radar target detection method based on a dimensionality reduction model as described in claim 1, characterized in that, In the pulse compression processing of the down-converted signal, the matched filter is as follows: The pulse compression processing results are as follows: s MY (t-τ)=T p sinc(πB'(t-τ))exp(-j2πf n (t); Among them, f n This represents the carrier frequency magnitude of the nth pulse of the frequency-agile radar's transmitted signal.

8. The frequency-agile radar target detection method based on a dimensionality reduction model as described in claim 1, characterized in that, The distance wiki matrix is ​​in the following form: Among them, a ig f represents the element in the i-th row and g-th column of the distance vidi matrix A. i-1 Indicates the magnitude of the pulse carrier frequency in row i-1. The distance value characterizing the g-1 pulse.

9. The frequency-agile radar target detection method based on a dimensionality reduction model as described in claim 1, characterized in that, The velocity wiki matrix takes the following form: Among them, b ig The element in the i-th row and g-th column of the velocity vidi matrix B, f g-1 The magnitude of the pulse carrier frequency in column g-1. The velocity value of the i-1 line pulse is represented.

10. A frequency-agile radar target detection system based on a dimensionality reduction model, characterized in that, The system is used to implement the frequency-agile radar target detection method based on a dimensionality reduction model as described in any one of claims 1-9, and the system comprises: The echo signal processing module is used to perform down-conversion processing on the received echo signal, perform pulse compression processing on the down-converted signal, perform constant false alarm rate processing, and extract the target range gate phase sequence. The dimensionality reduction matrix construction module is used to construct the diagonal matrix, range dimensionality matrix, velocity dimensionality matrix, and unit diagonal matrix of the target range-gated phase sequence using radar indicators, and to configure the dimensionality reduction matrix to perform optimization solutions. The dimensionality reduction matrix is ​​as follows: Y = Θ⊙(AGB); where, The diagonal matrix of the target range gate phase sequence. Represented as a unit diagonal matrix, Let be the distance dimensional matrix. This represents the matrix representing the joint distance-velocity estimation results. The velocity dimensional matrix is ​​represented by N, where N is the number of pulse cycles, P is the number of super-resolution units in the range dimension, Q is the number of super-resolution units in the velocity dimension, and ⊙ represents the dot product operation. The matrix solving module is used to transform the dimension-reduced matrix into an unconstrained form using a semi-quadratic splitting method, then introduce an auxiliary variable matrix, initialize the joint distance-velocity estimation result matrix and the auxiliary variable matrix, perform iterative updates until convergence, and output the joint distance-velocity estimation result matrix. The target detection result generation module is used to establish a radar detection signal based on the range-velocity joint estimation result matrix and generate target detection results.

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