Ship complex HRRP sparse estimation method and system matched with K distribution clutter characteristics

Abstract

The invention discloses a ship complex HRRP sparse estimation method and system matched with K distribution clutter characteristics. According to the method, K distribution is adopted to constrain the probability characteristics of sea clutters, single-parameter random distribution is adopted to constrain the sparse characteristics of ship complex HRRP, A-D test is adopted to determine the sparse parameter q of ship complex HRRP, the problem that clutter models are mismatched when an existing sparse optimization method is applied to ship complex HRRP estimation under the non-Gaussian sea clutter background is solved, and the robustness of ship complex HRRP estimation is improved. And the performance loss of ship multi-HRRP estimation caused by clutter model mismatch is obviously reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to a ship complex HRRP sparse estimation method and system that matches K-distribution clutter characteristics. Background Art

[0002] High Resolution Range Profile (HRRP) is the sum of all complex echo vectors of target scatterers within a single range unit, corresponding to the projection of the complex echo of the target scattering center on the radar line of sight. In the application of high-resolution sea radar, because the complex HRRP contains rich information about the target, many target classification and recognition technologies have been developed based on the complex HRRP.

[0003] For most of the complex HRRP of ships, some strong scattering units mainly come from the masts, superstructures, cranes and weapons of the ship. Sparsity is also an inherent characteristic of the complex HRRP of ships. However, in the application of sea radar, since sea clutter exhibits strong non-Gaussian characteristics, it poses a serious challenge to the estimation of the complex HRRP of ships. Therefore, the problem of ship complex HRRP estimation can be attributed to estimating the sparse ship complex HRRP from the radar complex echo containing non-Gaussian sea clutter.

[0004] So far, many sparse optimization methods have been developed to recover target signals in noise. The current methods take the existence of noise into account, but most of them assume that the background noise is Gaussian noise. In the sparse estimation of high-resolution sea radar, sea clutter exhibits a long-tailed non-Gaussian characteristic. Therefore, directly applying these sparse optimization methods to ship complex HRRP estimation will cause serious performance loss. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a method and system for sparse estimation of complex HRRP of a ship matching the clutter characteristics of K distribution.

[0006] In a first aspect, the present invention provides a method for sparsely estimating complex HRRP of a ship matching K distribution characteristics, comprising:

[0007] Get raw radar echo data;

[0008] A threshold detection method is used to obtain the distance interval where the ship's complex HRRP is located on the original radar echo data;

[0009] The radar echo signal within the distance interval is represented as a vector matrix model;

[0010] A sparse optimization method matching the K distribution characteristics is applied to the vector matrix model of the radar echo signal to achieve the estimation of the ship's complex HRRP.

[0011] In a second aspect, the present invention provides a ship complex HRRP sparse estimation system matching K distribution characteristics, comprising:

[0012] A data acquisition module, used to acquire raw radar echo data;

[0013] The threshold detection module is used to perform threshold detection on the original radar echo data to determine the distance interval where the ship's complex HRRP is located;

[0014] A model building module, used for representing the radar echo signal within the distance interval as a vector matrix model;

[0015] The estimation module is used to estimate the complex HRRP of the ship by applying a sparse optimization method that matches the K distribution characteristics.

[0016] In a third aspect, the present invention provides a computer-readable storage medium having program instructions stored thereon, wherein the program instructions implement the above method when executed.

[0017] In a fourth aspect, the present invention provides a computer program product, comprising a computer program / instruction, which implements the above method when executed by a processor.

[0018] Beneficial effects of the present invention: The present invention adopts K distribution to constrain the probabilistic characteristics of sea clutter, adopts a single-parameter random distribution to constrain the sparse characteristics of the ship's complex HRRP, and adopts AD test to determine the sparse parameter q of the ship's complex HRRP, which solves the problem of clutter model mismatch when the existing sparse optimization method is applied to the ship's complex HRRP estimation under the background of non-Gaussian sea clutter, and significantly reduces the performance loss of the ship's complex HRRP estimation caused by the clutter model mismatch. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a flow chart of a method for sparse estimation of complex HRRP of a ship matching K distribution characteristics provided by an embodiment of the present invention;

[0020] Figure 2 The embodiment of the present invention provides a sparse estimation method for applying a matching K distribution characteristic to a vector matrix model of a radar echo signal to realize an estimation framework diagram of a ship complex HRRP;

[0021] FIG. 3 (a) and FIG. 3 (b) are curve diagrams showing the estimation error and variance of two methods provided by the embodiments of the present invention as the signal-to-noise ratio changes; FIG. 3( c ) and FIG. 3( d ) are curve diagrams showing the estimation errors and variances of the two methods provided by the embodiments of the present invention as the shape parameters change; FIG. 3 (e) and FIG. 3 (f) are curve diagrams showing the estimation error and variance of two methods provided by the embodiments of the present invention as the sparse parameters vary;

[0022] Figure 4 It is an experimental diagram of measured data provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0023] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0024] Embodiment 1

[0025] See also Figure 1 , Figure 1 1 is a flow chart of a method for sparse estimation of complex HRRP of a ship matching K distribution characteristics provided by an embodiment of the present invention, which includes:

[0026] Step 1: Get the raw radar echo data.

[0027] In this embodiment, it is assumed that the radar broadband pulse The bandwidth is , the carrier frequency is The down-converted signal of the received echo is . With interval right and Sampling can produce a discrete sequence and reference signal ,in is the width of the distance cell, is the speed of light. In order to reduce the range sidelobes, a window function is used in the frequency domain, and pulse compression is achieved in the frequency domain through Discrete Fourier Transform (DFT);

[0028]

[0029] in Indicates the inverse , Indicates the reference signal After performing DFT, take its conjugate complex number, Indicates the reference signal After performing DFT, take the square of its modulus, is the window function, and yes Length. is the point spread function to represent pulse compression.

[0030] When the high-resolution sea surveillance radar works in scanning mode, the radar echo of the ship is expressed as:

[0031]

[0032] in is the complex HRRP of the ship along the distance unit, For the For a high range resolution radar with a range cell of several meters, the time delay of a strong scatterer in a range cell is can be assumed to be an integer . , They are respectively the starting position and the ending position of the distance interval where the ship's complex HRRP is located.

[0033] Step 2: Use the threshold detection method to obtain the distance interval where the ship's complex HRRP is located on the original ship radar echo data.

[0034] In the application of target size feature extraction based on HRRP, in order to adapt to the range resolution capability of the radar and the scale characteristics of the target, the window pane of the radar receiving echo is usually discretized in units of radar range resolution units. The length of the intercepted window pane of the radar receiving echo needs to be greater than the length of the target echo. Therefore, in addition to the echo signal of the target, the one-dimensional range image of the radar also includes information such as noise and sea clutter. Threshold detection can be used to obtain the distance interval where the ship's complex HRRP is located. That is, if the radar echo power of a certain range unit is greater than a certain value, it can be considered that the range unit may be located in the distance interval where the ship's complex HRRP is located.

[0035] In some embodiments, step 2 specifically includes:

[0036] Step 2-1: The threshold used is the average power of high-resolution sea clutter, specifically:

[0037] in, , are the shape parameters and scale parameters of the K distribution fitting sea clutter determined by the moment estimation method.

[0038] Step 2-2: Remember is the radar echo power at the kth distance unit, and records all The continuous interval .

[0039] Step 2-3: The distance interval where the ship's HRRP is located It is expressed as:

[0040]

[0041] in, Representation interval Length.

[0042] Step 3: Perform vector matrix representation on the radar echo data within the distance interval.

[0043] The radar echo data is expressed as a vector matrix, that is, the radar echo data is expressed as The purpose is to express the problem of estimating the complex HRRP of a ship from radar echoes as a sparse reconstruction problem that can be solved using sparse optimization methods, where is the observation vector, is the perception matrix, is the sparse vector to be estimated, is the clutter vector.

[0044] In some embodiments, step 3 specifically includes:

[0045] Step 3-1: The echo data of the radar within the distance interval is expressed as:

[0046]

[0047]

[0048] in, Indicates a single pulse radar echo, which is a ship echo and high resolution sea clutter The superposition results; , . For high-resolution sea clutter, K distribution is used to model it, namely:

[0049]

[0050] in, are the shape parameter and scale parameter of the K distribution, is the gamma function, express The modified Bessel function of the second kind.

[0051] Step 3-2: Convert the complex vector sequence Convert to a one-dimensional complex-valued sequence:

[0052]

[0053] in, It is a single pulse radar echo.

[0054] Step 3-3: Represent the one-dimensional complex-valued sequence in matrix-vector form:

[0055]

[0056] in, is the radar echo signal vector; represents the vector corresponding to the complex HRRP of the ship, represents the interference vector, whose probability density function is p(d(n)), and its nth value is ; is the extended point spread function (PSF) vector, which is expressed as:

[0057]

[0058] in, The length is All-zero vector of ; for Length;

[0059] is the distance unit shift matrix, which is expressed as:

[0060]

[0061] in; for The center of and Represents an all-0 row vector and an all-0 column vector of length N-1 respectively; represents the identity matrix of N-1 rows and N-1 columns; A is the size of The perception matrix, L is the distance interval where the ship's complex HRRP is located Length.

[0062] Step 4: Apply the sparse estimation method matching the K distribution characteristics to the vector matrix model of the radar echo signal to estimate the complex HRRP of the ship.

[0063] See also Figure 2 , Figure 2 The present invention provides a sparse estimation method for matching the K distribution characteristics of the vector matrix model of the radar echo signal to realize the estimation framework diagram of the ship's complex HRRP.

[0064] In the sparse estimation method matching the K distribution characteristics, since the sparse parameter q values ​​corresponding to different ships are different, it is necessary to select a suitable sparse parameter q value when performing sparse estimation on the vector matrix model, and then use the sparse estimation result corresponding to the value as the ship complex HRRP estimation result. The value range of the sparse parameter q is [0.02 0.05:0.05:1].

[0065] In some embodiments, step 4 specifically includes:

[0066] Step 4-1: Calculate the ship complex HRRP estimation results corresponding to each value in the q value interval:

[0067] In this embodiment, the estimation method is as follows: the sparse optimization method matching the K distribution characteristics uses the maximum a posteriori probability estimation (MAP) to estimate the ship's complex HRRP, that is:

[0068]

[0069] in, is the ship complex HRRP estimated using the maximum a posteriori probability; is the ship complex HRRP vector The joint probability density function of , which uses a single-parameter random distribution, is

[0070] , is the sparse parameter, is the ship complex HRRP vector The lth value of ; , N is the radar echo signal vector Length, for The nth value of is the row vector corresponding to the nth row of the perception matrix A.

[0071] Substituting the above formula into the following optimization problem:

[0072]

[0073] in, is the estimation result of the ship's complex HRRP when the sparse parameter is q; yes The lth value of .

[0074] The above optimization problem is solved by using the gradient decomposition method. Specifically, the steps include:

[0075] 4-1-1: Recover HRRP from a Ship To initialize:

[0076] In this embodiment, a matched filter is applied to initialize the algorithm, i.e.

[0077]

[0078] in, yes The lth value of is the ship complex HRRP vector Initialization vector of The perception matrix The column vector corresponding to the lth column of .

[0079] 4-1-2: Iterative update of ship HRRP :

[0080] In this embodiment, the ship restores HRRP The iteration formula is:

[0081]

[0082] in, , Ship complex HRRP k+1, the vector of the kth iteration;

[0083] , yes The lth value of ;

[0084] ;

[0085] .

[0086] 4-1-3: Determine the iteration termination condition:

[0087] In this embodiment, when the ship restores HRRP Iterate 20 times or satisfy Stop iteration when As the estimated value of the ship's complex HRRP corresponding to the sparse parameter q ,in is a small positive number.

[0088] Step 4-2: Calculate the AD test statistic corresponding to each sparse parameter q. Specifically, the steps include:

[0089] Step 4-2-1: Determine the residual sequence of the ship's complex HRRP estimate .

[0090] In this embodiment, let is the residual of the ship complex HRRP estimation when the sparse parameter is q, that is ; for vector Sort the absolute values ​​of the numbers in to get the sequence , This is the first n value.

[0091] Step 4-2-2: Calculate each sparse parameter q The corresponding AD test statistic .

[0092] In this embodiment, the statistic of the AD test corresponding to the sparse parameter q is:

[0093]

[0094] in, is the cumulative density function of the magnitude of the K distribution.

[0095] Step 4-3: The sparse parameter q of the ship complex HRRP is determined as:

[0096] .

[0097] Step 4-4: Sparse parameters The corresponding This is the final ship complex HRRP estimation vector.

[0098] Embodiment 2

[0099] Corresponding to the above-mentioned ship complex HRRP sparse estimation method matching the K distribution characteristics, the embodiment of the present application also provides a ship complex HRRP sparse estimation system matching the K distribution characteristics, and the above-mentioned ship complex HRRP sparse estimation system matching the K distribution characteristics includes:

[0100] A data acquisition module, used to acquire raw radar echo data;

[0101] The threshold detection module is used to perform threshold detection on the original radar echo data to determine the distance interval where the ship's complex HRRP is located;

[0102] A model building module, used for representing the radar echo signal within the distance interval as a vector matrix model;

[0103] The estimation module is used to estimate the complex HRRP of the ship by applying a sparse optimization method that matches the K distribution characteristics.

[0104] Embodiment 3

[0105] Corresponding to the above-mentioned method for sparse estimation of complex HRRP of a ship that matches the K distribution characteristics, an embodiment of the present application also provides a computer-readable storage medium on which program instructions are stored, and when the program instructions are executed, a method for sparse estimation of complex HRRP of a ship that matches the K distribution characteristics is implemented.

[0106] Embodiment 4

[0107] Corresponding to the above-mentioned method for sparse estimation of complex HRRP of a ship that matches the K distribution characteristics, an embodiment of the present application also provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements a method for sparse estimation of complex HRRP of a ship that matches the K distribution characteristics.

[0108] In addition, although the present application is described in the context of functional modules, it should be understood that, unless otherwise specified, one or more of the functions and / or features described may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the present application. More specifically, in view of the properties, functions, and internal relationships of the various functional modules in the device disclosed herein, the actual implementation of the module will be understood within the conventional skills of the engineer. Therefore, those skilled in the art can implement the present application set forth in the claims without excessive experimentation using ordinary techniques. It is also understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the present application, which is determined by the full scope of the attached claims and their equivalents.

[0109] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium and includes several instructions for enabling an electronic device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0110] More specific examples of computer-readable media (a non-exhaustive list) include the following: an electrical connection with one or more wires (electronic device), a portable computer disk case (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be a paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering or, if necessary, processing in another suitable manner, and then stored in a computer memory.

[0111] Verification example:

[0112] The beneficial effects of the present application are further illustrated below through simulation experiments.

[0113] 1. Simulation conditions:

[0114] The simulation experiment of this embodiment is carried out in an environment where the computer configuration is core i7 2.6GHZ, the memory is 8G, the WINDOWS 10 system and the computer software is configured as Matlab R2022b.

[0115] 2. Simulation content and result analysis:

[0116] The simulation experiment of this embodiment uses the sparse optimization method proposed in the present invention and the existing sparse optimization method to carry out ship complex HRRP estimation experiments in simulation data and measured data.

[0117] In this simulation experiment, it is assumed that the radar is an X-band high-resolution radar, which transmits a linear frequency modulated LFM (Linear Frequency Modulated, LFM) pulse with a time width of 43.2 microseconds and a bandwidth of 200MHz. The sampling frequency of the baseband signal is 200MHz, and the radar's pulse repetition frequency PRF (Pulse Repetition Frequency, PRF) is 1800Hz. The transmitted LFM waveform is positive frequency modulation. When the pulse is compressed, a Hamming window is added in the time domain, and pulse compression is realized in the frequency domain. The farther the position from the main lobe, the lower the level of the range side lobe. The first range side lobe is about -31.27dB. The scale parameter of the sea clutter is set to = 5, and the sparsity parameter q is in the interval [0.02 0.05:0.05:1]. 10000 independent experiments are performed in each specified parameter set of average signal-to-clutter ratio (SCR), sea clutter shape parameter and sparsity parameter to calculate the mean and variance of the relative error of each method estimating 10000 ship complex HRRPs.

[0118] Figure 3 (a) and Figure 3 (b) are shape parameters The average relative error and variance of the relative error of the complex HRPP estimation of the ship when the signal-to-noise ratio is set to 10, the sparsity parameter q is set to 0.2, and the signal-to-noise ratio is in the interval [10:2:50]. The horizontal axis is the variation range of the signal-to-noise ratio in dB, and the vertical axis is the average relative error and the variance of the relative error, respectively. Figure 3 (c) and Figure 3 (d) are the average relative error and variance of the relative error of the complex HRPP estimation of the ship when the signal-to-noise ratio is set to 20dB, the sparsity parameter is set to 0.2, and the shape parameter is in the interval [2:2:10]. The horizontal axis is the variation range of the shape parameter, and the vertical axis is the average relative error and the variance of the relative error, respectively. Figure 3 (e) and Figure 3 (f) are the average relative error and variance of the relative error of the complex HRPP estimation of the ship when the signal-to-noise ratio is set to 20dB, the sparsity parameter is set to 0.2, and the shape parameter is in the interval [2:2:10]. The horizontal axis is the variation range of the shape parameter, and the vertical axis is the average relative error and the variance of the relative error, respectively. The average relative error and variance of the relative error of the ship complex HRPP estimation when the sparse parameter q is set to 10 and takes values ​​in the interval [0.02 0.05:0.05:1], the horizontal axis is the variation range of the sparse parameter, and the vertical axis is the average relative error and the variance of the relative error. The green straight line in all the pictures in the figure is the variation curve of the average relative error and the variance of the relative error of the ship complex HRRP estimated by the sparse optimization method matching the K distribution characteristics in this application, and the red triangle line is the variation curve of the average relative error and the variance of the relative error of the ship complex HRRP estimated by the existing SLIM method.

[0119] It can be seen from Figure 3 (a) to Figure 3 (e): First, in all cases, the sparse optimization method for ship complex HRRP estimation proposed in this application has better estimation performance than the SLIM method. In fact, since most of the current sparse optimization methods use Gaussian distribution as the interference background, performance loss is inevitable when they are applied to ship complex HRRP estimation. However, the proposed sparse optimization method can significantly reduce the impact of non-Gaussian characteristics of sea clutter. Second, the sparse optimization method for ship complex HRRP estimation proposed in this application will improve the estimation performance as the signal-to-clutter ratio increases. Third, the sparse optimization method for ship complex HRRP estimation proposed in this application is little affected by the non-Gaussian characteristics of sea clutter, and the estimation performance remains basically unchanged as the shape parameters of sea clutter increase. Fourth, the sparse optimization method for ship complex HRRP estimation proposed in this application continuously improves its estimation performance as the sparse parameter q decreases, which means that the sparser the complex HRRP of the ship, the better the estimation performance of the sparse optimization method for ship complex HRRP estimation proposed in this application.

[0120] For further information, see Figure 4 , Figure 4 is an experimental diagram of measured data provided by an embodiment of the present invention, wherein: Figure 4(a) is the amplitude diagram of radar clutter data (unit: dB). Figure 4 (b) is the amplitude diagram of the ship complex HRRP estimation result using the sparse optimization method proposed in this application (unit: dB). Figure 4 (c) is the amplitude diagram of the ship complex HRRP estimation result using the SLIM method (unit: dB).

[0121] from Figure 4 It can be seen that when the method is applied to measured data, the SLIM method is almost completely ineffective and cannot estimate the complex HRRP of the ship. However, the sparse optimization method for ship complex HRRP estimation proposed in this application can effectively estimate both the strong scattering points and the weak scattering points of the ship.

[0122] In summary, compared with the SLIM method, the present invention can effectively estimate the complex HRRP of a ship from radar echoes, significantly reducing the impact of the non-Gaussian characteristics of sea clutter on the estimation of the complex HRRP of a ship. This result is of great significance for high-resolution sea surveillance radars.

[0123] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0124] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A sparse estimation method for complex HRRP of ships matching the K distribution characteristics, characterized by include: Get raw radar echo data; A threshold detection method is used to obtain the distance interval where the ship's complex HRRP is located on the original radar echo data; The radar echo signal within the distance interval is represented as a vector matrix model; A sparse optimization method matching the K distribution characteristics is applied to the vector matrix model of the radar echo signal to achieve the estimation of the ship's complex HRRP.

2. The method for sparse estimation of complex HRRP of a ship matching K distribution characteristics according to claim 1 is characterized by: The threshold detection method used for the raw radar echo data includes: The threshold is set to the average power of sea clutter; Compare the intervals of radar echo data where the power is greater than a threshold; The longest interval in the intervals is determined as the distance interval where the ship's complex HRRP is located.

3. The method for sparse estimation of complex HRRP of a ship matching K distribution characteristics according to claim 2 is characterized by: The vector matrix model of the radar echo signal is expressed as the radar echo signal vector is equal to the product of the perception matrix and the ship's complex HRRP vector plus the interference vector, wherein the statistical characteristics of the interference vector are modeled using K distribution.

4. The method for sparse estimation of complex HRRP of a ship matching K distribution characteristics according to claim 1, characterized in that: The sparse optimization method matching the K distribution characteristics uses maximum a posteriori probability estimation to estimate the ship's complex HRRP, and obtains the estimation result by maximizing the product of the conditional probability density function of the radar echo signal when the ship's complex HRRP vector is known and the prior probability density function of the ship's complex HRRP vector.

5. The method for sparse estimation of complex HRRP of a ship matching K distribution characteristics according to claim 4 is characterized by: The prior probability density function adopts a single-parameter random distribution, which constrains the sparsity of the ship's complex HRRP vector in the form of an exponential function, wherein the sparsity parameter is used to control the sparsity of the distribution.

6. The method for sparse estimation of complex HRRP of a ship matching K distribution characteristics according to claim 5 is characterized by: The sparse parameter is determined by searching for a parameter value that minimizes the AD test statistic within a preset value range, wherein the AD test statistic is used to measure the degree of matching between the estimation result and the K distribution characteristic.

7. The method for sparse estimation of complex HRRP of a ship matching K distribution characteristics according to claim 1, characterized in that: The method further comprises iteratively updating the estimation result until a preset termination condition is met.

8. The ship complex HRRP sparse estimation system matching the K distribution characteristics is characterized by: include: A data acquisition module, used to acquire raw radar echo data; The threshold detection module is used to perform threshold detection on the original radar echo data to determine the distance interval where the ship's complex HRRP is located; A model building module, used for representing the radar echo signal within the distance interval as a vector matrix model; The estimation module is used to estimate the complex HRRP of the ship by applying a sparse optimization method that matches the K distribution characteristics.

9. A computer-readable storage medium, characterized in that: Program instructions are stored thereon, and when the program instructions are executed, the method according to any one of claims 1 to 7 is implemented.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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