Distributed radar coherent method based on multi-task compressed sensing

Abstract

The invention provides a distributed radar coherent method based on multi-task compressed sensing, which belongs to the field of radar signal processing and information fusion, and is solved by the following technical scheme: (1) firstly, establishing a distributed radar single-input multi-output system model, and performing down-conversion and pulse compression processing on a received signal; (2) designing a compressed sensing dictionary, establishing a linear relation between a received signal and a target sparse scattering coefficient, and reducing data transmission quantity by using a compressed sensing theory; (3) adopting a Bayesian multi-task compressed sensing algorithm, and realizing efficient iterative reconstruction through sequential updating of hyper-parameters, matrix decomposition and approximate solution; and (4) finally, introducing a phase consistency constraint, solving a compensation phase based on information entropy optimization, and realizing cross-substation signal phase alignment. According to the method, efficient reconstruction and cross-station signal coherence of the sparse scattering target information of the distributed radar system are realized.

Description

Technical Field

[0001] This invention relates to the field of radar signal processing and information fusion, specifically to a distributed radar coherent method based on multi-task compressed sensing. Background Technology

[0002] With the rapid development of distributed radar technology, multi-station cooperative detection has shown significant advantages in target detection, parameter estimation, and low-observable target identification. Compared with monostatic radar, distributed radar, by spatially distributing multiple receiving substations, can effectively improve spatial coverage and target observability, and enhance anti-jamming and anti-stealth performance.

[0003] In traditional distributed radar systems, each receiving substation typically needs to transmit complete echo data to a central processing unit for centralized processing. However, with the increase in the number of receiving substations and the expansion of observation bandwidth, the number of echo sampling points per station grows exponentially. Directly transmitting raw data would overburden the communication link, making it difficult to meet the application requirements under real-time processing and bandwidth-constrained conditions.

[0004] On the other hand, multi-station collaboration requires coherent accumulation of echoes from each substation to enhance the signal-to-noise ratio and improve target detection performance. However, the radar cross section (RCS) of a target varies significantly at different observation angles. This variation introduces random phase perturbations, leading to phase inconsistencies between the echoes from different substations. Unlike traditional local oscillator drift, clock skew, or channel mismatch, these phase errors are more random and difficult to compensate for using conventional hardware calibration or time synchronization methods. This significantly affects the coherent accumulation performance of multi-station echoes, thereby reducing detection performance and parameter estimation accuracy. Summary of the Invention

[0005] This invention proposes a distributed radar coherent method based on multi-task compressed sensing. Addressing the phase errors in RCS observations from each substation and the communication overhead caused by large-scale echo data transmission across multiple stations, it achieves efficient reconstruction of sparse scattering point information and cross-station signal coherence, thereby improving the target detection and parameter estimation performance of distributed radar. The technical solution provided by this invention is as follows:

[0006] A distributed radar coherent method based on multi-task compressed sensing includes the following steps:

[0007] Step 1: Establish a distributed radar single-transmitter multiple-receiver system model, and perform down-conversion and pulse compression processing on the received signals;

[0008] Step 2: Divide the three-dimensional detection space into a discrete spatial grid, construct a compressed sensing dictionary, and establish a linear relationship between the received signal and the sparse scattering coefficient of the target on the discrete spatial grid.

[0009] Step 3: Use the Bayesian multi-task compressed sensing algorithm to perform iterative solution;

[0010] Step 4: Introduce phase consistency constraints, optimize the compensation phase based on information entropy, and achieve cross-substation signal phase alignment.

[0011] Preferably, the single-transmitter multiple-receiver system model in step 1 is as follows: the coordinates of one transmitting station are... The coordinates of the M receiving stations are Signals emitted by the system's transmitting station for

[0012]

[0013] in, For time, This is the radar transmission waveform. For carrier frequency, This represents an exponential function with the natural logarithm e as its base. The imaginary unit; radar transmission waveform Take a linear frequency modulated signal:

[0014]

[0015] in For bandwidth, For frequency modulation duration;

[0016] No. Signal received by each receiving station

[0017]

[0018] in The number of targets detected. The complex reflection coefficient of the target. For receiving station noise, For the first The first receiving station detected the Two-way delay generated by each target:

[0019]

[0020] in For the first The coordinates of the target At the speed of light, The Euclidean distance is given by coordinates .

[0021] Preferred, the first Signal received by each receiving station Perform downconversion and pulse compression processing to obtain :

[0022]

[0023]

[0024] in for The conjugate of complex numbers, The first pulse pressure after Noise at each receiving station The radar waveform after pulse compression: .

[0025] Preferably, step 2 specifically involves: dividing the three-dimensional detection space into L discrete grid points, for the first... Each receiving station is used to construct its observation dictionary. N is the number of discrete sampling points for each echo response. For the set of complex numbers:

[0026]

[0027] in ; ; , The sampling interval is... For the first The first receiving station The time delay generated by the target location corresponding to each grid point;

[0028] A linear relationship is established between the received signal and the sparse scattering coefficients of the target on a discrete spatial grid:

[0029]

[0030]

[0031] in In order to receive signals, The original signal, This is a noise signal.

[0032] Preferably, step 3 employs a fast algorithm for multi-task compressed sensing in the complex domain, which sequentially updates individual hyperparameters and combines matrix factorization and approximate solutions for efficient iteration.

[0033] Treating the M receiving stations as M tasks, a hierarchical Laplace prior model is used to obtain the mean. Covariance Matrix :

[0034]

[0035] in For hyperparameters A diagonal matrix consisting of diagonal elements. This is for taking the conjugate transpose of a matrix; for hyperparameters The update defines the matrix in the measurement model. :

[0036]

[0037]

[0038] in Given the identity matrix, approximate the solution for hyperparameters. :

[0039]

[0040]

[0041]

[0042] in, For hyperparameters Hyperparameters that depend on a specific Gamma distribution; and To control the hyperparameters of the Gamma distribution; These are intermediate variables that depend on the observed signal and the current basis function;

[0043] In each sequential iteration, based on the current... The estimation results are used to update the hyperparameters synchronously. :

[0044]

[0045] For hyperparameters Prior parameters satisfying the Gamma distribution; repeated iterations Until hyperparameters If the change is less than a preset threshold, or the basis function set is no longer updated, the final output will be the reconstructed signal for each substation. .

[0046] Preferably, step 4 specifically includes:

[0047] The reconstructed signals of each receiving station are denoted as . ,in Indicates the first The first receiving station The mean value recovered from each target is obtained by introducing a compensated phase. Obtain the joint signal :

[0048]

[0049] Define the information entropy function: Solve using optimization methods The extreme points are thus used to obtain the compensated phase. Each receiving station The corresponding compensation phase is , for The conjugate of complex numbers.

[0050] Preferred solution The process of finding the extreme point is as follows:

[0051]

[0052]

[0053] in To obtain the real part of a complex number, To obtain the imaginary part of a complex number, For any integer, This indicates a corner-taking operation. for The conjugate of complex numbers, for The conjugate of complex numbers, for The conjugate of complex numbers.

[0054] Compared with the prior art, the beneficial effects achieved by the present invention are: the present invention solves the communication overhead problem of large-scale echo data transmission from multiple sites in distributed radar systems and the random phase error caused by RCS observation of each substation, realizes efficient reconstruction of sparse scattering target information and cross-site signal coherence, thereby improving the target detection and parameter estimation performance of distributed radar. Attached Figure Description

[0055] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0056] Figure 1 This is a flowchart of the present invention;

[0057] Figure 2 This is a schematic diagram of a distributed radar coherent system model;

[0058] Figure 3 The results of a distributed coherent radar system detecting multiple scattering targets;

[0059] Figure 4 Comparison of phase error before and after applying phase alignment constraints;

[0060] Figure 5 The performance comparison results of phase alignment constraint before and after applying matched filtering and under different pulse pressure signal-to-noise ratios are presented. Detailed Implementation

[0061] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0062] To make the above-mentioned objectives, features and effects of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0063] Example 1: As Figure 1 As shown, this invention provides a distributed radar coherent method based on multi-task compressed sensing, comprising the following steps:

[0064] Step 1: Establish a distributed radar single-transmitter multiple-receiver system model, and perform down-conversion and pulse compression processing on the received signals.

[0065] Assuming the distributed radar is a single-transmitter, multiple-receiver system with one transmitting station and M receiving stations, such as... Figure 2 As shown. The coordinates of the launch site are... The coordinates of the receiving station are .

[0066] Signals emitted by the system's transmitting station

[0067]

[0068] in, For time, This is the waveform transmitted by the radar. For carrier frequency, This represents an exponential function with the natural logarithm e as its base. The unit is the imaginary number; the radar transmit waveform is taken as a linear frequency modulated (LFM) signal, that is:

[0069]

[0070] in For bandwidth, This refers to the frequency modulation bandwidth.

[0071] No. Signal received by each receiving station

[0072]

[0073] in The number of targets detected. The complex reflection coefficient of the target. For receiving station noise, For the first The first receiving station detected the The two-way delay generated by each target ;No. The first receiving station detected the Two-way delay caused by each target for:

[0074]

[0075] in For the first The coordinates of the target At the speed of light, The Euclidean distance is given by coordinates;

[0076] For the The signal received by the receiving station Perform down-conversion to obtain the signal

[0077]

[0078] The first The signal after downconversion at each receiving station Pulse compression processing is performed to obtain the pulse-compressed signal.

[0079]

[0080]

[0081] in for The conjugate of complex numbers, The first pulse pressure after Noise from individual receiving stations;

[0082] Will Substitution In the middle, the radar waveform after pulse compression is obtained. :

[0083]

[0084] Furthermore, the first The pulsed signal from each receiving station Transform into:

[0085]

[0086] Step 2: Design a compressed sensing dictionary to establish a linear relationship between the received signal and the target sparse scattering coefficient, and use compressed sensing theory to reduce the amount of data transmission.

[0087] According to the The pulsed signal from each receiving station The expression shows that the observable signal exhibits significant sparsity in the target's time delay parameter domain, meaning that only a small number of non-zero scattering points correspond to the target echo. Therefore, this invention introduces compressed sensing theory, which, while ensuring sparse reconstruction performance, allows for effective signal recovery through a small number of observations without transmitting the complete original echo data, thus significantly reducing the data transmission volume from the substation to the master station.

[0088] Within the compressed sensing framework, dictionary design is a core step. This invention first divides the three-dimensional detection space into L discrete grid points, with each grid point corresponding to a potential target scattering location.

[0089] Regarding the first Each receiving station is used to construct its observation dictionary. Each column of this dictionary corresponds to the echo response of a grid point, and N is the number of discrete sampling points for each echo response. For the set of complex numbers:

[0090]

[0091] in ; ; , The sampling interval is... For the first The first receiving station The time delay generated by the target location corresponding to each grid point;

[0092] Observation dictionary Expand:

[0093]

[0094] Specifically, each column vector consists of discrete sampled values ​​obtained after processing the transmitted signal with a corresponding time delay. This dictionary allows the received signal to be... Establish a linear relationship with the sparse scattering coefficients of the target on a discrete spatial grid:

[0095]

[0096]

[0097] in In order to receive signals, The original signal, Assuming the signal is noise, and that the target scattering points are sparsely distributed over distance, with the number of targets much smaller than the number of grid cells, i.e. The following sparse equations can be constructed:

[0098]

[0099] Where K is sparsity (the number of targets detected). It is the square of the 2-norm. It is a zero norm.

[0100] Step 3: The Bayesian multi-task compressed sensing algorithm is adopted to achieve efficient iterative reconstruction through sequential hyperparameter updates, matrix factorization and approximate solutions.

[0101] Traditional compressed sensing methods typically reconstruct each observation signal independently, failing to fully utilize the correlation between different measurements. Multi-task compressed sensing achieves information sharing by combining the correlation signals from multiple substations in a distributed radar system, thereby improving reconstruction accuracy while reducing the amount of observation data. Each receiving substation is considered a task, resulting in M ​​tasks. In formula (12)... We establish independent additive Gaussian white noise, and let the variance of the Gaussian white noise be... ,set up Then the observed signal The conditional probability distribution is:

[0102]

[0103] in It follows a complex Gaussian distribution;

[0104] To improve signal sparsity, give Introducing the Gamma distribution:

[0105]

[0106] in It follows a Gamma distribution. and To control the hyperparameters of the Gamma distribution, satisfying ; A function of the Gamma distribution that satisfies ;

[0107] For the original signal To further enhance sparsity modeling capabilities, a hierarchical Laplace model is adopted to replace the traditional Laplace prior. Its hierarchical structure is described as follows:

[0108] First layer, assumption It satisfies a zero-mean complex Gaussian distribution, depending on the precision parameter. :

[0109]

[0110] in For precision parameters;

[0111] Second layer, parameters It follows a special Gamma distribution and depends on the hyperparameters. :

[0112]

[0113] in For hyperparameters;

[0114] The third layer, hyperparameters It follows a Gamma distribution, and the prior parameter is: :

[0115]

[0116] in satisfy ;

[0117] Hierarchical Laplace prior models are more suitable for modeling sparse signals than traditional Laplace priors due to their narrower main lobe and higher tail characteristics.

[0118] The conditional distribution can be derived from the above formula. mean Covariance Matrix :

[0119]

[0120]

[0121] in For hyperparameters A diagonal matrix consisting of diagonal elements. This is the operation of taking the conjugate transpose of a matrix;

[0122] In addition, hyperparameters can be eliminated through edge integration. Impact:

[0123]

[0124] This invention employs a fast algorithm for multi-task compressed sensing in the complex domain. By sequentially updating individual hyperparameters and combining matrix decomposition and approximate solutions, it achieves efficient iteration.

[0125] To update hyperparameters separately Define the matrix in the measurement model :

[0126]

[0127] in It is the identity matrix;

[0128] Through Woodbury decomposition, it can be found that... Decomposed into:

[0129]

[0130] in For without The matrix (containing only the basis functions corresponding to other hyperparameters). For measurement matrix The List;

[0131] By maximizing the logarithmic marginal likelihood function Hyperparameters can be solved approximately. :

[0132]

[0133] in For intermediate variables that depend on the observed signal and the current basis function, the following condition must be met:

[0134]

[0135] Furthermore, through calculation, the hyperparameters can be approximately derived. Analytical solution:

[0136]

[0137]

[0138] Each iteration chooses the option that maximizes the logarithmic marginal likelihood function. The candidate basis functions are then used to update the basis function set until all relevant basis functions are included in the model.

[0139] Using Woodbury's inverse matrix identity, the covariance matrix can be updated quickly. Signal Mean and intermediate variables To avoid full matrix operations, in each sequential iteration, based on the current... The estimation results are used to update the hyperparameters synchronously. :

[0140]

[0141] Repeated iterations Until hyperparameters If the change is less than a preset threshold, or the basis function set is no longer updated, the final output will be the reconstructed signal for each substation. .

[0142] Step 4: Introduce phase consistency constraints, optimize the compensation phase based on information entropy, and achieve cross-substation signal phase alignment.

[0143] While reconstructing signals from each substation using Bayesian multi-task compressed sensing leverages shared information among the substations, it lacks coherent processing between them. Therefore, this invention addresses the coherence problem in distributed radar systems by applying phase consistency constraints during the multi-task compressed sensing iteration process, thereby ensuring that the reconstructed signal from each substation is coherent.

[0144] Because each substation uses the average value Reconstruction signal Therefore, this invention adds a phase consistency constraint to each iteration. In this invention, the information entropy function is used to... The phase term differences between them are compensated.

[0145] For different receiving stations, the reconstructed signal is denoted as... ,in Indicates the first The first receiving station The average value recovered from each target is obtained. Simultaneously, the phase of the recovered signals from different receiving stations is adjusted to eliminate phase differences, and then accumulated to obtain the average value. :

[0146]

[0147] in It is the unknown compensation phase that needs to be solved;

[0148] Information entropy is defined as :

[0149]

[0150] in It is a constant, satisfying ;

[0151] Formula (31) can be rewritten as:

[0152]

[0153] After ignoring the constant term, we get :

[0154]

[0155] Therefore, phase compensation for multiple receiving nodes can be transformed into applying a target function. Finding the extreme points:

[0156]

[0157] Will Substituting into (34), we get:

[0158]

[0159] in To obtain the real part of a complex number, for The conjugate of complex numbers;

[0160] Further results were obtained:

[0161]

[0162]

[0163] in To obtain the real part of a complex number, To obtain the imaginary part of a complex number, For any integer, This indicates a corner-taking operation. for The conjugate of complex numbers, for The conjugate of complex numbers;

[0164] Therefore, by solving the compensation phase Each station The corresponding compensation phase is ,in for The conjugate complex number. In each iteration of multi-task compressed sensing, the result is... By applying phase consistency constraints, the recovered coherent scattering coefficients can be obtained, thereby reconstructing the signals of each substation and realizing distributed radar system detection and coherence.

[0165] Example 2: Simulation experiments were conducted using MATLAB to verify the method proposed in this invention. The experimental results show the effectiveness of the proposed method. The simulation results are described below:

[0166] Simulation parameters: carrier frequency ,bandwidth Pulse duration The number of sampling points N=8000, the sampling rate is 160MHz, and the coordinates of the transmitting station are... .

[0167] This invention transmits a linear frequency modulated signal from a transmitting station; receives echo signals containing reflections from multiple scattering targets, performs down-conversion and pulse compression processing; and defines the radar's region of interest as a three-dimensional cubic space, along... The direction is 14000 to 15000m. The cubic region is uniformly divided into 6 grid points in each dimension, for a total of 216 three-dimensional grid points. A dictionary atom for compressed sensing is constructed based on the position of each grid point. In the fourth step, a multi-task compressed sensing algorithm with added phase consistency constraints is applied to the observed data to recover the coherent scattering signal and detect the position of the target point. Figure 3 The comparison between the positions of multiple detected target points in the grid and the actual target points shows that the positions of the actual targets and the detected targets are consistent, indicating a good detection effect. Figure 4 To set the signal-to-noise ratio after pulse compression to 40dB, the phase error results were obtained by comparing the scattering coefficients recovered by multi-task compressed sensing before and after applying phase consistency constraints through 100 repeated experiments and taking the average value. It can be seen that the phase error is greatly improved after adding phase consistency constraints. Figure 5 A performance comparison was made between ordinary multi-task compressed sensing, multi-task compressed sensing with phase alignment constraints, and matched filtering under different pulse compression signal-to-noise ratios. The results show that the performance of multi-task compressed sensing with phase alignment constraints is closer to that of matched filtering, indicating that the coherent performance of the multi-task compressed sensing algorithm with phase alignment constraints is closer to the ideal performance.

[0168] Example 3: The computer-readable storage medium of this example stores a computer program that, when executed by a processor, implements the steps in the distributed radar coherent method based on multi-task compressed sensing in Example 1.

[0169] The computer-readable storage medium in this embodiment can be an internal storage unit of the terminal, such as the terminal's hard disk or memory; the computer-readable storage medium in this embodiment can also be an external storage device of the terminal, such as a plug-in hard disk, smart memory card, secure digital card, flash memory card, etc. equipped on the terminal; furthermore, the computer-readable storage medium can include both the terminal's internal storage unit and external storage devices.

[0170] The computer-readable storage medium of this embodiment is used to store computer programs and other programs and data required by the terminal. The computer-readable storage medium can also be used to temporarily store data that has been output or will be output.

[0171] Example 4: The computer device of this example includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the distributed radar coherent method based on multi-task compressed sensing in Example 1.

[0172] In this embodiment, the processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc. The memory can include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory can also include non-volatile random access memory. For example, the memory can also store device type information.

[0173] Those skilled in the art will clearly understand that each implementation can be achieved using software plus the necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0174] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A distributed radar coherent method based on multi-task compressed sensing, characterized in that, Includes the following steps: Step 1: Establish a distributed radar single-transmitter multiple-receiver system model, and perform down-conversion and pulse compression processing on the received signals; Step 2: Divide the three-dimensional detection space into a discrete spatial grid, construct a compressed sensing dictionary, and establish a linear relationship between the received signal and the sparse scattering coefficient of the target on the discrete spatial grid. Step 3: Use the Bayesian multi-task compressed sensing algorithm to perform iterative solution; Step 4: Introduce phase consistency constraints, optimize the compensation phase based on information entropy, and achieve cross-substation signal phase alignment.

2. The distributed radar coherent method based on multi-task compressed sensing according to claim 1, characterized in that, The single-transmitter multiple-receiver system model in step 1 is as follows: the coordinates of one transmitting station are... The coordinates of the M receiving stations are Signals emitted by the system's transmitting station for ； in, For time, This is the radar transmission waveform. For carrier frequency, This represents an exponential function with the natural logarithm e as its base. The imaginary unit; radar transmission waveform Take a linear frequency modulated signal: ； in For bandwidth, For frequency modulation duration; No. Signal received by each receiving station ; ； in The number of targets detected. The complex reflection coefficient of the target. For receiving station noise, For the first The first receiving station detected the Two-way delay generated by each target: ； in For the first The coordinates of the target At the speed of light, The Euclidean distance is given by coordinates .

3. The distributed radar coherent method based on multi-task compressed sensing according to claim 2, characterized in that, No. Signal received by each receiving station Perform downconversion and pulse compression processing to obtain : ； ； in for The conjugate of complex numbers, The first pulse pressure after Noise at each receiving station The radar waveform after pulse compression: .

4. The distributed radar coherent method based on multi-task compressed sensing according to claim 3, characterized in that, Step 2 specifically involves dividing the three-dimensional detection space into L discrete grid points, and for the first... Each receiving station is used to construct its observation dictionary. N is the number of discrete sampling points for each echo response. For the set of complex numbers: ； in ; ; , The sampling interval is... For the first The first receiving station The time delay generated by each grid point corresponding to the target location; A linear relationship is established between the received signal and the sparse scattering coefficients of the target on a discrete spatial grid: ； ； in In order to receive signals, The original signal, This is a noise signal.

5. A distributed radar coherent method based on multi-task compressed sensing according to claim 4, characterized in that, Step 3 employs a fast algorithm for multi-task compressed sensing in the complex domain, which sequentially updates individual hyperparameters and combines matrix factorization and approximate solutions for efficient iteration: Treating the M receiving stations as M tasks, a hierarchical Laplace prior model is used to obtain the mean. Covariance Matrix : ； in For hyperparameters A diagonal matrix consisting of diagonal elements. This is for taking the conjugate transpose of a matrix; for hyperparameters The update defines the matrix in the measurement model. : ； ； in Given the identity matrix, approximate the solution for hyperparameters. : ； ； ； in, For hyperparameters Hyperparameters that depend on a specific Gamma distribution; and To control the hyperparameters of the Gamma distribution; These are intermediate variables that depend on the observed signal and the current basis function; In each sequential iteration, based on the current... The estimation results are used to update the hyperparameters synchronously. : ； For hyperparameters Prior parameters satisfying the Gamma distribution; repeated iterations Until hyperparameters If the change is less than a preset threshold, or the basis function set is no longer updated, the final output will be the reconstructed signal for each substation. .

6. The distributed radar coherent method based on multi-task compressed sensing according to claim 4, characterized in that, Step 4 is as follows: The reconstructed signals of each receiving station are denoted as... ,in Indicates the first The first receiving station The mean value recovered from each target is obtained by introducing a compensated phase. Obtain the joint signal : ； Define the information entropy function: Solve using optimization methods The extreme points are thus used to obtain the compensated phase. Each receiving station The corresponding compensation phase is , for The conjugate of complex numbers.

7. A distributed radar coherent method based on multi-task compressed sensing according to claim 6, characterized in that, Solve The process of finding the extreme point is as follows: ； ； in To obtain the real part of a complex number, To obtain the imaginary part of a complex number, For any integer, This indicates a corner-taking operation. for The conjugate of complex numbers, for The conjugate of complex numbers, for The conjugate of complex numbers.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the distributed radar coherent method based on multi-task compressed sensing as described in any one of claims 1-7.

9. A computer device comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the distributed radar coherent method based on multi-task compressed sensing as described in any one of claims 1-7.

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