Single-bit radar sparse imaging method and system based on variable threshold

Abstract

The present invention discloses a single-bit radar sparse imaging method and system based on variable threshold, the method comprising: obtaining radar echo signal, generating radar echo signal matrix; representing the process of adding single-frequency threshold to radar echo signal, obtaining single-bit radar echo real matrix of single-frequency threshold; generating probability density function of single-frequency threshold radar echo according to Gaussian random variable representing noise, obtaining likelihood function of single-bit radar echo real matrix of single-frequency threshold according to probability density function of single-frequency threshold radar echo; generating probability density function of scattering point intensity based on Laplace distribution, generating target function according to Bayesian formula, solving target function, obtaining range compression matrix, compressing range compression matrix in azimuth and imaging, obtaining target imaging result. The present invention can improve imaging quality of single-bit radar, and obtain fine single-bit radar imaging.

Description

Technical Field

[0001] The present invention relates to the technical field of single-bit radar imaging, and in particular to a single-bit radar sparse imaging method and system based on variable threshold. Background Art

[0002] Synthetic Aperture Radar (SAR / Inverse Synthetic Aperture Radar, ISAR) has all-day and all-weather imaging capabilities and is an indispensable electronic device at present. However, a large amount of echo data will cause the corresponding system of synthetic aperture radar to have a heavy burden of data collection, storage, transmission and processing, making the system complexity and cost high. The use of single-bit radar imaging technology can solve the above problems. This technology can not only reduce the amount of data that the system needs to process, but also reduce the cost of the system.

[0003] However, since single-bit quantization is a typical nonlinear mapping, single-bit radar imaging has the problem of reduced imaging quality compared to traditional radar imaging.

[0004] Therefore, the prior art still needs to be improved and developed. Summary of the invention

[0005] The main purpose of the present invention is to provide a single-bit radar sparse imaging method, system, terminal and computer-readable storage medium based on variable threshold, aiming to solve the problem in the prior art that single-bit radar imaging has reduced imaging quality compared with traditional radar imaging because single-bit quantization is a typical nonlinear mapping.

[0006] To achieve the above object, the present invention provides a single-bit radar sparse imaging method based on a variable threshold, and the single-bit radar sparse imaging method based on a variable threshold comprises the following steps:

[0007] Acquire a radar echo signal, and generate a radar echo signal matrix according to the radar echo signal;

[0008] The radar echo signal is represented by adding a single-frequency threshold according to the radar echo signal matrix and the preset single-frequency threshold, so as to obtain a single-bit radar echo real matrix of the single-frequency threshold;

[0009] The probability density function of the noise is represented according to the Gaussian random variable, the probability density function of the single-frequency threshold radar echo is generated according to the probability density function of the noise and the real matrix of the single-bit radar echo of the single-frequency threshold, and the likelihood function of the real matrix of the single-bit radar echo of the single-frequency threshold is obtained according to the probability density function of the single-frequency threshold radar echo;

[0010] Based on Laplace distribution, a probability density function of the scattering point intensity is generated according to the radar echo signal matrix, a target function is generated according to the Bayesian formula, and the target function is solved according to the likelihood function of the single-bit radar echo real matrix of the single-frequency threshold and the probability density function of the scattering point intensity to obtain a range compression matrix, and the range compression matrix is ​​compressed in azimuth and imaged to obtain a target imaging result.

[0011] Optionally, the acquiring of radar echo signals and generating a radar echo signal matrix according to the radar echo signals specifically includes:

[0012] Acquire a radar echo signal, and construct an echo signal model according to the radar echo signal;

[0013] Generate a specific expression of each echo in the radar echo signal according to the echo signal model, and remove the carrier frequency from the specific expression of each echo to obtain a matrix expression of each echo in the radar echo signal;

[0014] The radar echo signal matrix of each echo is generated according to the matrix expression of each echo.

[0015] Optionally, the step of representing a single-frequency threshold adding process of the radar echo signal according to the radar echo signal matrix and a preset single-frequency threshold to obtain a single-bit radar echo real matrix of the single-frequency threshold specifically includes:

[0016] The preset single frequency threshold is converted into a vector form to obtain a single frequency threshold vector, and a single frequency threshold parameter is obtained according to the single frequency threshold vector and the radar echo signal matrix, wherein the single frequency threshold is expressed as , is the single frequency threshold, is the amplitude, is the frequency, is the phase, is an imaginary unit, For fast time;

[0017] According to the single frequency threshold adding parameter, a single frequency threshold adding process model of the radar echo signal is constructed;

[0018] The single-frequency threshold adding parameter is expressed as a radar echo real matrix form of the single-frequency threshold to obtain the radar echo real matrix of the single-frequency threshold; and a single-bit radar echo real matrix of the single-frequency threshold is generated according to the radar echo real matrix of the single-frequency threshold and the single-frequency threshold adding process model.

[0019] Optionally, the generating a probability density function of noise according to a Gaussian random variable, and generating a probability density function of a single-frequency threshold radar echo according to the probability density function of noise and a single-bit radar echo real matrix of a single-frequency threshold, specifically includes:

[0020] Representing a probability density function of noise in a radar echo signal according to the Gaussian random variable;

[0021] According to the probability density function of the radar echo real matrix of the single-frequency threshold and the noise in the single-bit radar echo real matrix of the single-frequency threshold, under the condition of the first parameter in the radar echo real matrix of the single-frequency threshold, the probability density function of the single-frequency threshold radar echo of the radar echo real matrix of the single-frequency threshold is generated.

[0022] Optionally, obtaining the likelihood function of the real matrix of the single-bit radar echo of the single-frequency threshold in the real matrix of the single-bit radar echo of the single-frequency threshold according to the probability density function of the single-frequency threshold radar echo specifically includes:

[0023] Generate a distribution law representation of elements in the real matrix of single-bit radar echo of the single-frequency threshold according to the real matrix of single-bit radar echo of the single-frequency threshold, the real matrix of radar echo of the single-frequency threshold and the first parameter;

[0024] According to the distribution law representation, a likelihood function of a real matrix of a single-bit radar echo of a single-frequency threshold under the condition of the first parameter is obtained.

[0025] Optionally, the method of generating a probability density function of the scattering point intensity based on the Laplace distribution according to the radar echo signal matrix, generating a target function according to the Bayesian formula, and solving the target function according to the likelihood function of the single-bit radar echo real matrix of the single-frequency threshold and the probability density function of the scattering point intensity to obtain the range compression matrix specifically includes:

[0026] Based on the Laplace distribution, a probability density function of the scattering point intensity is generated according to the radar echo signal matrix;

[0027] According to the Bayesian formula, a first probability density function is constructed, and an objective function is generated according to the first probability density function, wherein the objective function is a maximum a posteriori probability formula of the first parameter;

[0028] Solving the objective function according to the likelihood function of the real matrix of the single-bit radar echo of the single-frequency threshold and the probability density function of the scattering point intensity to obtain a simplified objective function;

[0029] The simplified objective function is solved according to a first-order primal-dual algorithm to obtain the distance compression matrix.

[0030] Optionally, compressing the range compression matrix in azimuth and imaging it to obtain a target imaging result specifically includes:

[0031] According to the maximum a posteriori probability and the Bayesian criterion, the distance compression matrix is ​​compressed in the azimuth direction to obtain a two-dimensional compression matrix;

[0032] The two-dimensional compression matrix is ​​imaged to obtain the target imaging result.

[0033] In addition, to achieve the above-mentioned object, the present invention further provides a single-bit radar sparse imaging system based on a variable threshold, wherein the single-bit radar sparse imaging system based on a variable threshold comprises:

[0034] A signal acquisition module, used to acquire radar echo signals and generate a radar echo signal matrix according to the radar echo signals;

[0035] A single-bit radar echo real matrix generation module with a single-frequency threshold is used to represent the single-frequency threshold adding process of the radar echo signal according to the radar echo signal matrix and the preset single-frequency threshold to obtain a single-bit radar echo real matrix with a single-frequency threshold;

[0036] A function generation module, used for representing the probability density function of noise according to Gaussian random variables, generating the probability density function of the single-frequency threshold radar echo according to the probability density function of noise and the real matrix of the single-bit radar echo of the single-frequency threshold, and obtaining the likelihood function of the real matrix of the single-bit radar echo of the single-frequency threshold according to the probability density function of the single-frequency threshold radar echo;

[0037] The result generation module is used to generate a probability density function of the scattering point intensity according to the radar echo signal matrix based on Laplace distribution, generate a target function according to the Bayesian formula, and solve the target function according to the likelihood function of the single-bit radar echo real matrix of the single-frequency threshold and the probability density function of the scattering point intensity to obtain a range compression matrix, perform azimuth compression and imaging on the range compression matrix, and obtain a target imaging result. In addition, to achieve the above purpose, the present invention also provides a terminal, wherein the terminal includes: a memory, a processor, and a single-bit radar sparse imaging program based on a variable threshold stored in the memory and executable on the processor, wherein the single-bit radar sparse imaging program based on a variable threshold implements the steps of the single-bit radar sparse imaging method based on a variable threshold as described above when executed by the processor.

[0038] In addition, to achieve the above-mentioned purpose, the present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a single-bit radar sparse imaging program based on a variable threshold, and when the single-bit radar sparse imaging program based on a variable threshold is executed by a processor, the steps of the single-bit radar sparse imaging method based on a variable threshold as described above are implemented.

[0039] In the present invention, a radar echo signal is acquired, and a radar echo signal matrix is ​​generated according to the radar echo signal; a single-frequency threshold adding process of the radar echo signal is represented according to the radar echo signal matrix and a preset single-frequency threshold, and a single-bit radar echo real matrix of the single-frequency threshold is obtained; a probability density function of noise is represented according to a Gaussian random variable, a probability density function of a single-frequency threshold radar echo is generated according to the probability density function of noise and the single-bit radar echo real matrix of the single-frequency threshold, and a likelihood function of the single-bit radar echo real matrix of the single-frequency threshold is obtained according to the probability density function of the single-frequency threshold radar echo; based on Laplace distribution, a probability density function of scattering point intensity is generated according to the radar echo signal matrix, a target function is generated according to a Bayesian formula, and the target function is solved according to the likelihood function of the single-bit radar echo real matrix of the single-frequency threshold and the probability density function of the scattering point intensity, and a range compression matrix is ​​obtained, and the range compression matrix is ​​compressed in azimuth and imaged to obtain a target imaging result. The present invention utilizes single-bit quantization to reduce the amount of echo data received by the radar system, and the single-bit quantization can be implemented by a comparator, thereby reducing the cost of the radar system. At the same time, the data after single-bit quantization is in binary form, which can be implemented by simple logical operations, and the hardware cost is low. In addition, the present invention introduces a variable threshold value, which can effectively restore the intensity of the scattering point, thereby improving the imaging quality of the single-bit radar. At the same time, a sparse imaging algorithm is used in both the range and azimuth directions, which can effectively suppress the harmonics and intermodulation generated by the single-bit quantization, thereby realizing fine imaging of the single-bit radar. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of a preferred embodiment of the single-bit radar sparse imaging method based on variable threshold value of the present invention;

[0041] Figure 2 It is a schematic diagram of one-dimensional range envelope results based on FFT method under high-precision data in the single-bit radar sparse imaging method based on variable threshold of the present invention;

[0042] Figure 3 It is a schematic diagram of a one-dimensional range envelope result based on an FFT method under zero-threshold single-bit data in a single-bit radar sparse imaging method based on a variable threshold in the present invention;

[0043] Figure 4 It is a schematic diagram of a one-dimensional range envelope result based on a sparse imaging method under zero threshold single-bit data in a single-bit radar sparse imaging method based on a variable threshold in the present invention;

[0044] Figure 5 It is a schematic diagram of a one-dimensional range envelope result based on a sparse imaging method under a variable threshold single-bit data in a single-bit radar sparse imaging method based on a variable threshold of the present invention;

[0045] Figure 6 It is a schematic diagram of the imaging result of target sparse imaging under high-precision data in the single-bit radar sparse imaging method based on variable threshold value of the present invention;

[0046] Figure 7 It is a schematic diagram of the imaging result of target sparse imaging under zero threshold single-bit data in the single-bit radar sparse imaging method based on variable threshold of the present invention;

[0047] Figure 8 It is a schematic diagram of the imaging result of target sparse imaging under variable threshold single-bit data in the variable threshold single-bit radar sparse imaging method of the present invention;

[0048] Fig. 9 It is a structural diagram of a preferred embodiment of a single-bit radar sparse imaging system based on a variable threshold value according to the present invention;

[0049] Fig.10 It is a structural diagram of a preferred embodiment of the terminal of the present invention. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solution and advantages of the present invention clearer and more specific, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0051] Synthetic aperture radar has the ability to image all day and all weather, and is an indispensable electronic equipment at present. At present, the application of synthetic aperture radar generally requires the corresponding imaging to have a high resolution to obtain detailed information of the target scene. Synthetic aperture radar achieves high resolution in the range by transmitting a large bandwidth signal, and increases the virtual array aperture by increasing the echo pulse coherent processing time to achieve high resolution in the azimuth. In order to avoid aliasing in the range and azimuth, the radar system needs to have a high temporal and spatial sampling rate at the same time. It can be seen that fine imaging is based on high-bit sampling quantization, high sampling rate, and large-scale data calculation. However, a large amount of echo data will cause the system to have a heavy burden of data acquisition, storage, transmission and processing, making the system complexity and cost high.

[0052] At present, single-bit radar imaging technology can solve the above problems. The corresponding technology can not only reduce the amount of data that the system needs to process, but also reduce the cost of the system. However, since single-bit quantization is a typical nonlinear mapping, single-bit radar imaging has a problem of reduced imaging quality compared to traditional radar imaging.

[0053] In response to one or more of the above problems, the present application obtains a radar echo signal and generates a radar echo signal matrix according to the radar echo signal; represents the single-frequency threshold adding process of the radar echo signal according to the radar echo signal matrix and a preset single-frequency threshold, and obtains a single-bit radar echo real matrix of the single-frequency threshold; generates a probability density function of noise according to a Gaussian random variable, generates a probability density function of a single-frequency threshold radar echo according to the probability density function of noise and the single-bit radar echo real matrix of the single-frequency threshold, and obtains a likelihood function of the single-bit radar echo real matrix of the single-frequency threshold according to the probability density function of the single-frequency threshold radar echo; based on the Laplace distribution, generates a probability density function of the scattering point intensity according to the radar echo signal matrix, generates a target function according to the Bayesian formula, and solves the target function according to the likelihood function of the single-bit radar echo real matrix of the single-frequency threshold and the probability density function of the scattering point intensity, obtains a range compression matrix, compresses the range compression matrix in azimuth and images it, and obtains a target imaging result.

[0054] The single-bit radar sparse imaging method based on variable threshold according to the preferred embodiment of the present invention is as follows: Figure 1 As shown, the single-bit radar sparse imaging method based on variable threshold comprises the following steps:

[0055] Step S10: Acquire a radar echo signal, and generate a radar echo signal matrix according to the radar echo signal.

[0056] It should be noted that in the present application, the radar echo signal is a linear frequency modulation (LFM) signal transmitted by the radar. After receiving the radar echo signal, the present application constructs a corresponding model according to the received radar echo signal, that is, a radar echo signal matrix.

[0057] Further, the acquiring of the radar echo signal and generating a radar echo signal matrix according to the radar echo signal specifically includes:

[0058] Acquire a radar echo signal, and construct an echo signal model according to the radar echo signal;

[0059] Generate a specific expression of each echo in the radar echo signal according to the echo signal model, and remove the carrier frequency from the specific expression of each echo to obtain a matrix expression of each echo in the radar echo signal;

[0060] The radar echo signal matrix of each echo is generated according to the matrix expression of each echo.

[0061] Specifically, a radar echo signal is acquired, and an echo signal model is constructed according to the radar echo signal, wherein the echo signal model The expression of is shown in the following formula (1):

[0062] ; (1)

[0063] in, For quick time, is the pulse width, To adjust the frequency, is the carrier frequency, is an imaginary unit, ;

[0064] and is the unit rectangular function, and its expression is shown in the following formula (2):

[0065] ; (2)

[0066] in, Represents a variable in a function.

[0067] is the first function, let , the cumulative number of echoes used for imaging is The number of sampling points for each pulse is , the imaging result is grid points; For the m The echo n The scattering point intensity at the grid point, that is, the scattering intensity of the scattering point, corresponds to the m Echo The specific expression of can be expressed as shown in the following formula (3):

[0068] ; (3)

[0069] in, , , For the n The time delay of the scattering point intensity corresponding to each grid point, For the m The noise of an echo.

[0070] By removing the carrier frequency from the specific expression of each echo, we can obtain the matrix expression of each echo in the radar echo signal, as shown in the following equation (4):

[0071] ; (4)

[0072] in, Indicates m The pulse echo at the first grid point in the echo, Indicates mThe pulse echo at the second grid point in the echo, Indicates m Echo N The pulse echo of grid points, Indicates m The fast time corresponding to the first grid point in an echo, Indicates m The fast time corresponding to the second grid point in the echo, Indicates m Echo N The fast time corresponding to each grid point is Indicates m The time delay of the intensity of the scattering point corresponding to the first grid point in the echo, Indicates m The time delay of the intensity of the scattering point corresponding to the second grid point in the echo, Indicates m Echo N The time delay of the scattering point intensity corresponding to each grid point, Indicates m The scattering point intensity at the first grid point of the echo, Indicates m The scattering point intensity at the second grid point of the echo, Indicates m The echo N The scattering point intensity at each grid point is For the m The noise at the first grid point of the echo, For the m The noise at the second grid point of the echo, For the m The echo N The noise at the grid points, , , , , , , , and The independent variables are , , , , , , , and , the corresponding value of the first function.

[0073] Furthermore, the matrix in formula (4) is expressed as the following formula (6), formula (7), formula (8) and formula (9), and the radar echo signal matrix of each echo can be obtained from formula (4). Specifically, it is shown in the following formula (5):

[0074] ; (5)

[0075] in, is the first matrix parameter, is the second matrix parameter, is the third matrix parameter, is the fourth matrix parameter, and the corresponding matrices in formula (4) are respectively represented. The matrices or vectors representing complex numbers, the specific expressions of these matrices are shown in the following formulas (6), (7), (8) and (9):

[0076] ; (6)

[0077] ; (7)

[0078] ; (8)

[0079] ; (9)

[0080] T represents transpose. The matrix expression of each echo can be converted into a radar echo signal matrix of each echo through formula (6), formula (7), formula (8) and formula (9).

[0081] Step S20: representing the single-frequency threshold adding process of the radar echo signal according to the radar echo signal matrix and the preset single-frequency threshold, and obtaining a single-bit radar echo real matrix of the single-frequency threshold.

[0082] Specifically, in the present application, a single-frequency threshold is introduced as a variable threshold to effectively restore the scattering point intensity, thereby obtaining a single-bit radar echo real matrix corresponding to the single-frequency threshold.

[0083] Further, the process of adding a single-frequency threshold to the radar echo signal is represented according to the radar echo signal matrix and the preset single-frequency threshold to obtain a single-bit radar echo real matrix of the single-frequency threshold, specifically including:

[0084] The preset single frequency threshold is converted into a vector form to obtain a single frequency threshold vector, and a single frequency threshold parameter is obtained according to the single frequency threshold vector and the radar echo signal matrix, wherein the single frequency threshold is expressed as , is the single frequency threshold, is the amplitude, is the frequency, is the phase, is an imaginary unit, For fast time;

[0085] According to the single frequency threshold adding parameter, a single frequency threshold adding process model of the radar echo signal is constructed;

[0086] The single-frequency threshold adding parameter is expressed as a radar echo real matrix form of the single-frequency threshold to obtain the radar echo real matrix of the single-frequency threshold; and a single-bit radar echo real matrix of the single-frequency threshold is generated according to the radar echo real matrix of the single-frequency threshold and the single-frequency threshold adding process model.

[0087] In this application, a single-frequency threshold is pre-set, and the single-frequency threshold is added to the echo signal, and the radar echo real matrix form of the single-frequency threshold is obtained. Among them, the single-frequency threshold has three important parameters, namely, amplitude ,frequency , and the phase , the corresponding single frequency threshold can be expressed as the following formula (10):

[0088] ; (10)

[0089] Then, the single frequency threshold is converted into a vector form to obtain a single frequency threshold vector , as shown in formula (11):

[0090] ; (11)

[0091] Wherein, T represents transpose, and the corresponding single-frequency threshold parameter is obtained according to the single-frequency threshold vector and the radar echo signal matrix. , as shown in formula (12):

[0092] ; (12)

[0093] According to the single-frequency threshold adding parameter, a single-frequency threshold adding process based on the single-frequency threshold for each pulse can be constructed, that is, a single-frequency threshold adding process model of the radar echo signal, as shown in formula (13):

[0094] ; (13)

[0095] in, It means taking the real part of the data. It means taking the imaginary part of the data. represents single-bit quantization, is a single-bit radar echo with a single-frequency threshold.

[0096] Correspondingly, the single-frequency threshold parameter is expressed as a radar echo real matrix of a single-frequency threshold, and a radar echo real matrix of a single-frequency threshold is obtained. Specifically, the radar echo real matrix of a single-frequency threshold is expressed as formula (14):

[0097] ; (14)

[0098] in, is the radar echo real matrix of single frequency threshold, is the second parameter, is the first parameter, is the third parameter, is the fourth parameter, and the corresponding , , , and The corresponding real matrix representation is, Represented as a matrix or vector of real numbers, the radar echo real matrix of the single-frequency threshold and its corresponding matrix are specifically expressed as follows: Formula (15), Formula (16), Formula (17), Formula (18) and Formula (19):

[0099] ; (15)

[0100] ; (16)

[0101] ; (17)

[0102] ; (18)

[0103] ; (19)

[0104] The single-frequency threshold adding process model is represented by the radar echo real matrix of the single-frequency threshold, and the single-bit radar echo real matrix of the single-frequency threshold is obtained. That is, the single-bit radar echo real matrix of the single-frequency threshold can be obtained by formula (12), formula (13) and formula (14), which is specifically expressed as the following formula (20):

[0105] ; (20)

[0106] in, , is the real matrix of single-bit radar echo with single-frequency threshold, and its specific expression is shown in the following formula (21):

[0107] ;(twenty one)

[0108] Step S30, generating a probability density function of noise according to a Gaussian random variable, generating a probability density function of a single-frequency threshold radar echo according to the probability density function of noise and a real matrix of a single-bit radar echo of a single-frequency threshold, and obtaining a likelihood function of a real matrix of a single-bit radar echo of a single-frequency threshold according to the probability density function of the single-frequency threshold radar echo.

[0109] It should be noted that in the present application, on the basis of obtaining the real matrix of single-bit radar echo with a single-frequency threshold, multiple density functions are calculated to obtain the likelihood function of the real matrix of single-bit radar echo with a single-frequency threshold in the real matrix of single-bit radar echo with a single-frequency threshold, and the probability density function can be used to solve the corresponding objective function to obtain the range compression matrix.

[0110] Further, the method of representing the probability density function of noise according to the Gaussian random variable and generating the probability density function of the single-frequency threshold radar echo according to the probability density function of the noise and the single-bit radar echo real matrix of the single-frequency threshold specifically includes:

[0111] Representing a probability density function of noise in a radar echo signal according to the Gaussian random variable;

[0112] According to the probability density function of the radar echo real matrix of the single-frequency threshold and the noise in the single-bit radar echo real matrix of the single-frequency threshold, under the condition of the first parameter in the radar echo real matrix of the single-frequency threshold, the probability density function of the single-frequency threshold radar echo of the radar echo real matrix of the single-frequency threshold is generated.

[0113] Specifically, the noise in the radar echo signal obtained in this application obeys an independent and identically distributed Gaussian random variable with a mean of 0 and a variance of , then the probability density function of noise can be represented by a Gaussian random variable, and correspondingly, the probability density function of noise is It is expressed as the following formula (22):

[0114] ;(twenty two)

[0115] in, The first parameter in the radar echo real matrix of the single-frequency threshold is generated according to the probability density function of the radar echo real matrix of the single-bit radar echo real matrix of the single-frequency threshold and the noise. Under the condition of single frequency threshold radar echo real matrix The probability density function of the single-frequency threshold radar echo can be obtained from formula (14) and formula (22): Under the conditions The probability density function of the single-frequency threshold radar echo, the probability density function of the single-frequency threshold radar echo Specifically, as shown in formula (23):

[0116] ;(twenty three)

[0117] Furthermore, the likelihood function of the real matrix of the single-bit radar echo of the single-frequency threshold in the real matrix of the single-bit radar echo of the single-frequency threshold is obtained according to the probability density function of the single-frequency threshold radar echo, specifically comprising:

[0118] Generate a distribution law representation of elements in the real matrix of single-bit radar echo of the single-frequency threshold according to the real matrix of single-bit radar echo of the single-frequency threshold, the real matrix of radar echo of the single-frequency threshold and the first parameter;

[0119] According to the distribution law representation, a likelihood function of a real matrix of a single-bit radar echo of a single-frequency threshold under the condition of the first parameter is obtained.

[0120] Specifically, according to the real matrix of the single-bit radar echo of the single-frequency threshold, the real matrix of the radar echo of the single-frequency threshold and the first parameter, the distribution law representation of the elements in the single-bit radar echo of the single-frequency threshold can be obtained, wherein is the real matrix of single-bit radar echo with single-frequency threshold No. elements, then , is the radar echo real matrix of single frequency threshold No. elements, yes No. elements, is the first parameter No. elements, among which , represents a specific value; then the element in the real matrix of the single-bit radar echo of the single-frequency threshold The distribution law of is shown in Table 1 below.

[0121] Table 1 The distribution law of

[0122]

[0123] in, represents the probability, for The probability of for The probability of time.

[0124] When When , according to the probability density function of the single-frequency threshold radar echo, that is, formula (23), It can be expressed as the following formula (24):

[0125] ;(twenty four)

[0126] in, for No. OK, Variance The corresponding standard deviation is , then formula (24) can be simplified to the following formula (25):

[0127] ; (25)

[0128] in, , Variables representing functions, dt represents the differential in this function.

[0129] Correspondingly, when When , we can get the following formula (26):

[0130] ; (26)

[0131] According to formula (25) and formula (26), The distribution law of can be further expressed as shown in Table 2 below.

[0132] Table 2, after simplification The distribution law of

[0133]

[0134] Depend on The distribution law indicates that in the first parameter The real matrix of single-bit radar echo with single-frequency threshold under the condition of The likelihood function can be expressed as follows:

[0135] ; (27)

[0136] Here, Π represents cumulative multiplication.

[0137] Step S40: Based on the Laplace distribution, a probability density function of the scattering point intensity is generated according to the radar echo signal matrix, a target function is generated according to the Bayesian formula, and the target function is solved according to the likelihood function of the single-bit radar echo real matrix of the single-frequency threshold and the probability density function of the scattering point intensity to obtain a range compression matrix, and the range compression matrix is ​​compressed in azimuth and imaged to obtain a target imaging result.

[0138] Specifically, in order to achieve distance compression in the present application, the generated probability density function should be used to solve the corresponding objective function, thereby obtaining the distance compression matrix.

[0139] Further, the method of generating a probability density function of the scattering point intensity based on the Laplace distribution according to the radar echo signal matrix, generating a target function according to the Bayesian formula, and solving the target function according to the likelihood function of the single-bit radar echo real matrix of the single-frequency threshold and the probability density function of the scattering point intensity to obtain a range compression matrix specifically includes:

[0140] Based on the Laplace distribution, a probability density function of the scattering point intensity is generated according to the radar echo signal matrix;

[0141] According to the Bayesian formula, a first probability density function is constructed, and an objective function is generated according to the first probability density function, wherein the objective function is a maximum a posteriori probability formula of the first parameter;

[0142] Solving the objective function according to the likelihood function of the real matrix of the single-bit radar echo of the single-frequency threshold and the probability density function of the scattering point intensity to obtain a simplified objective function;

[0143] The simplified objective function is solved according to a first-order primal-dual algorithm to obtain the distance compression matrix.

[0144] Specifically, in the radar echo signal matrix of each echo, the scattering point intensity Obeying independent and identically distributed Laplace distribution, the scattering point intensity The corresponding probability density function It is expressed as the following formula (28):

[0145] ; (28)

[0146] Among them, Replace with , then the corresponding vector Elements The probability density function of can be expressed as the following formula (29):

[0147] ; (29)

[0148] in, ( ) is the scale factor, Indicates taking the absolute value, and due to , X n Indicates the first parameter No. n elements,X n+N Indicates the first parameter No. n + N elements, then the first parameter The probability density function of the scattering point intensity can be expressed as follows (30):

[0149] ; (30)

[0150] In this application, according to the Bayesian formula, the first probability density function can be obtained: , expressed as the following formula (31):

[0151] ; (31)

[0152] in, is the probability density function of the real matrix of single-bit radar echo with single-frequency threshold, is the joint probability density function of the single-bit radar echo real matrix of the first parameter and the single-frequency threshold, and That is ; Then the corresponding objective function can be generated, that is, the first parameter The MAP (maximum a posteriori probability) is specifically expressed as the following formula (32):

[0153] ; (32)

[0154] in, In order to find a solution that maximizes the expression, the likelihood function of the real matrix of the single-bit radar echo with a single-frequency threshold and the probability density function of the scattering point intensity are substituted into the objective function to obtain the simplified objective function, that is, substitute formula (27) and formula (30) into formula (32), and perform the first simplification to obtain the first simplified objective function, as shown in the following formula (33):

[0155] ; (33)

[0156] The first simplified objective function is simplified by removing brackets and changing the multiplication in the ln function to accumulation. The second simplified objective function is obtained, which is expressed as the following formula (34):

[0157] ; (34)

[0158] because and Usually the value is small. In order to avoid the appearance of singular values ​​in the second simplified objective function, in this application, it is set as follows: , and substitute it into the second simplified objective function to perform the third simplification, and obtain the simplified objective function, which is expressed as the following formula (35):

[0159] ; (35)

[0160] Corresponding to the simplified objective function, the simplified objective function can be solved using the first-order primal-dual algorithm, which can realize the range compression of radar data and obtain the range compression matrix.

[0161] Furthermore, the step of compressing the range compression matrix in azimuth and imaging the matrix to obtain a target imaging result specifically includes:

[0162] According to the maximum a posteriori probability and the Bayesian criterion, the distance compression matrix is ​​compressed in the azimuth direction to obtain a two-dimensional compression matrix;

[0163] The two-dimensional compression matrix is ​​imaged to obtain the target imaging result.

[0164] After obtaining the range compression matrix, the range compression matrix is ​​compressed in azimuth according to the maximum a posteriori probability and the Bayesian criterion to obtain a two-dimensional compression matrix, that is, the azimuth is written into a matrix form as shown in the above formula (5) according to the range compression matrix; then the corresponding objective function is obtained by the maximum a posteriori probability criterion and the Bayesian criterion; finally, the first-order primal-dual algorithm is used to solve the corresponding objective function to obtain a two-dimensional compression matrix, and the two-dimensional compression matrix is ​​imaged to obtain the target imaging result.

[0165] Furthermore, the present invention further demonstrates the effect of the present invention through experiments. Specifically, in the first experiment, the experimental conditions of the simulation point target are: carrier frequency is 10 GHz, pulse repetition frequency is 400 Hz, bandwidth is 400 MHz, pulse width is The number of sampling points in the range direction is 256, the amplitude is 0.6, the frequency is 1.35MHz, the signal-to-noise ratio is 10dB, and three point targets are set in this experiment, and the scattering intensities of the three point targets are 0.6, 0.8 and 1 respectively. Figure 2 It is the one-dimensional range envelope result based on the Fast Fourier Transform (FFT) method under high-precision data. Since the FFT method can more accurately give the scattering point intensity of the target under high-precision data, the experimental results are used as a control in this section to illustrate the effectiveness of the method in the present invention; Figure 3 is the one-dimensional distance envelope result based on FFT method under zero threshold single bit data, from Figure 3 It can be seen that the FFT method cannot accurately give the scattering point intensity under single-bit data. This is because single-bit data is nonlinearly quantized. Figure 3A large number of harmonics and intermodulation components appear in the Figure 4 is the one-dimensional range envelope result based on the sparse imaging method under zero threshold single-bit data. Figure 4 It can be seen that the maximum a posteriori probability estimation method based on zero threshold can suppress the harmonics and intermodulation generated by single-bit data, as well as background noise, but cannot restore the scattering point intensity; Figure 5 is the one-dimensional range envelope result based on sparse imaging method under time-varying threshold single-bit data. Figure 5 It can be seen that the single-bit radar sparse imaging method based on variable threshold proposed in this application can suppress harmonics, intermodulation and background noise, and can restore the scattering point intensity.

[0166] In the second experiment, the experimental conditions for simulating an aircraft point target were: carrier frequency 10 GHz, pulse repetition frequency 400 Hz, bandwidth 400 MHz, pulse width , the number of sampling points in the distance direction is 128, the number of accumulated pulses is 128, and the target rotation speed is , the amplitude is 1.4, the frequency is 1.35MHz, the signal-to-noise ratio is 10dB, and the scattering point intensity of the aircraft target is 0.5. Figure 6 The imaging result of sparse imaging of the target under high-precision data, where the colored columns in the figure represent the scattering point intensity. Since the MAP method can more accurately give the scattering point intensity of the target under high-precision data, the experimental results are used as a control in this section to illustrate the effectiveness of the method of this application; Figure 7 The imaging result of the target sparse imaging under zero threshold single bit data, where the colored columns in the figure represent the intensity of the scattering points. Figure 7 It can be seen that the target sparse imaging method based on single-bit data loses the intensity of each scattering point; Figure 8 The imaging result of target sparse imaging under variable threshold single-bit data, where the colored columns in the figure represent the intensity of the scattering points. Figure 8 It can be seen from the figure that the single-bit radar sparse imaging method based on variable threshold proposed in the present invention can effectively restore the intensity of each scattering point.

[0167] The present invention obtains a radar echo signal, and generates a radar echo signal matrix according to the radar echo signal; represents the single-frequency threshold adding process of the radar echo signal according to the radar echo signal matrix and a preset single-frequency threshold, and obtains a single-bit radar echo real matrix of the single-frequency threshold; represents the probability density function of noise according to a Gaussian random variable, generates the probability density function of the single-frequency threshold radar echo according to the probability density function of noise and the single-bit radar echo real matrix of the single-frequency threshold, and obtains the likelihood function of the single-bit radar echo real matrix of the single-frequency threshold according to the probability density function of the single-frequency threshold radar echo; based on Laplace distribution, generates the probability density function of the scattering point intensity according to the radar echo signal matrix, generates the target function according to the Bayesian formula, and solves the target function according to the likelihood function of the single-bit radar echo real matrix of the single-frequency threshold and the probability density function of the scattering point intensity, obtains a range compression matrix, compresses the range compression matrix in azimuth and images it, and obtains a target imaging result. The present invention utilizes single-bit quantization to reduce the amount of echo data received by the radar system, and the single-bit quantization can be implemented by a comparator, thereby reducing the cost of the radar system. At the same time, the data after single-bit quantization is in binary form, which can be implemented by simple logical operations, and the hardware cost is low. In addition, the present invention introduces a variable threshold value, which can effectively restore the intensity of the scattering point, thereby improving the imaging quality of the single-bit radar. At the same time, a sparse imaging algorithm is used in both the range and azimuth directions, which can effectively suppress the harmonics and intermodulation generated by the single-bit quantization, thereby realizing fine imaging of the single-bit radar.

[0168] Furthermore, if Fig. 9 As shown, based on the above-mentioned single-bit radar sparse imaging method based on variable threshold, the present invention also provides a single-bit radar sparse imaging system based on variable threshold, wherein the single-bit radar sparse imaging system based on variable threshold includes:

[0169] A signal acquisition module 91, used to acquire a radar echo signal and generate a radar echo signal matrix according to the radar echo signal;

[0170] A single-bit radar echo real matrix generating module 92 for a single-frequency threshold is used to represent a single-frequency threshold adding process of a radar echo signal according to the radar echo signal matrix and a preset single-frequency threshold, so as to obtain a single-bit radar echo real matrix for a single-frequency threshold;

[0171] A function generation module 93 is used to represent the probability density function of noise according to a Gaussian random variable, generate the probability density function of the single-frequency threshold radar echo according to the probability density function of the noise and the real matrix of the single-bit radar echo of the single-frequency threshold, and obtain the likelihood function of the real matrix of the single-bit radar echo of the single-frequency threshold according to the probability density function of the single-frequency threshold radar echo;

[0172] The result generating module 94 is used to generate a probability density function of the scattering point intensity according to the radar echo signal matrix based on Laplace distribution, generate a target function according to the Bayesian formula, and solve the target function according to the likelihood function of the single-bit radar echo real matrix of the single-frequency threshold and the probability density function of the scattering point intensity to obtain a range compression matrix, perform azimuth compression on the range compression matrix and image it to obtain a target imaging result.

[0173] Furthermore, if Fig.10 As shown, based on the above-mentioned variable threshold-based single-bit radar sparse imaging method and system, the present invention also provides a terminal accordingly, and the terminal includes a processor 10, a memory 20 and a display 30. Fig.10 Only some components of the terminal are shown, but it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0174] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard disk or memory of the terminal. In other embodiments, the memory 20 may also be an external storage device of the terminal, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (SecureDigital, SD) card, a flash card (Flash Card), etc. equipped on the terminal. Further, the memory 20 may also include both an internal storage unit of the terminal and an external storage device. The memory 20 is used to store application software and various types of data installed on the terminal, such as the program code of the installation terminal. The memory 20 may also be used to temporarily store data that has been output or is to be output. In one embodiment, a single-bit radar sparse imaging program 40 based on a variable threshold is stored on the memory 20, and the single-bit radar sparse imaging program 40 based on a variable threshold can be executed by the processor 10, thereby realizing the single-bit radar sparse imaging method based on a variable threshold in the present application.

[0175] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor or other data processing chip, used to run the program code or process data stored in the memory 20, such as executing the variable threshold-based single-bit radar sparse imaging method.

[0176] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch device, etc. The display 30 is used to display information on the terminal and to display a visual user interface. The components 10-30 of the terminal communicate with each other via a system bus.

[0177] In one embodiment, when the processor 10 executes the variable threshold-based single-bit radar sparse imaging program 40 in the memory 20 , the steps of the above variable threshold-based single-bit radar sparse imaging method are implemented.

[0178] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a single-bit radar sparse imaging program based on a variable threshold, and when the single-bit radar sparse imaging program based on a variable threshold is executed by a processor, the steps of the single-bit radar sparse imaging method based on a variable threshold as described above are implemented.

[0179] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or terminal including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or terminal. In the absence of further restrictions, an element defined by the sentence "includes a ..." does not exclude the existence of other identical elements in the process, method, article or terminal including the element.

[0180] Of course, those skilled in the art can understand that all or part of the processes in the above-mentioned embodiments can be implemented by instructing related hardware (such as a processor, a controller, etc.) through a computer program, and the program can be stored in a computer-readable storage medium that can be read by a computer, and the program can include the processes of the above-mentioned method embodiments when executed. The computer-readable storage medium can be a memory, a disk, an optical disk, etc.

[0181] It should be understood that the application of the present invention is not limited to the above examples. For ordinary technicians in this field, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.

Claims

1. A single-bit radar sparse imaging method based on variable threshold, characterized in that: The single-bit radar sparse imaging method based on variable threshold comprises: Acquire a radar echo signal, and generate a radar echo signal matrix according to the radar echo signal; The radar echo signal is represented by adding a single-frequency threshold according to the radar echo signal matrix and the preset single-frequency threshold, so as to obtain a single-bit radar echo real matrix of the single-frequency threshold; The probability density function of the noise is represented according to the Gaussian random variable, the probability density function of the single-frequency threshold radar echo is generated according to the probability density function of the noise and the real matrix of the single-bit radar echo of the single-frequency threshold, and the likelihood function of the real matrix of the single-bit radar echo of the single-frequency threshold is obtained according to the probability density function of the single-frequency threshold radar echo; Based on the Laplace distribution, a probability density function of the scattering point intensity is generated according to the radar echo signal matrix, a target function is generated according to the Bayesian formula, and the target function is solved according to the likelihood function of the single-bit radar echo real matrix of the single-frequency threshold and the probability density function of the scattering point intensity to obtain a range compression matrix, and the range compression matrix is ​​compressed in azimuth and imaged to obtain a target imaging result; The acquiring of the radar echo signal and generating a radar echo signal matrix according to the radar echo signal specifically includes: Acquire a radar echo signal, and construct an echo signal model according to the radar echo signal; Generate a specific expression of each echo in the radar echo signal according to the echo signal model, and remove the carrier frequency from the specific expression of each echo to obtain a matrix expression of each echo in the radar echo signal; Generate the radar echo signal matrix of each echo according to the matrix expression of each echo; Echo signal model ; in, is the echo signal model, For quick time, is the pulse width, To adjust the frequency, is the carrier frequency, is an imaginary unit, , is the unit rectangle function; The step of expressing the process of adding a single-frequency threshold to the radar echo signal according to the radar echo signal matrix and the preset single-frequency threshold to obtain a single-bit radar echo real matrix of the single-frequency threshold specifically includes: The preset single frequency threshold is converted into a vector form to obtain a single frequency threshold vector, and a single frequency threshold parameter is obtained according to the single frequency threshold vector and the radar echo signal matrix, wherein the single frequency threshold is expressed as , is the single frequency threshold, is the amplitude, is the frequency, is the phase, is an imaginary unit, For fast time; According to the single frequency threshold adding parameter, a single frequency threshold adding process model of the radar echo signal is constructed; The single-frequency threshold adding parameter is expressed as a radar echo real matrix form of the single-frequency threshold to obtain a radar echo real matrix of the single-frequency threshold, and a single-bit radar echo real matrix of the single-frequency threshold is generated according to the radar echo real matrix of the single-frequency threshold and the single-frequency threshold adding process model; Add single frequency threshold parameter ,in, To add a single frequency threshold parameter, , is the single frequency threshold vector, is the first matrix parameter, is the second matrix parameter, is the third matrix parameter, is the fourth matrix parameter; Single-bit radar echo real matrix with single-frequency threshold ,in, is the second parameter, is the first parameter, is the third parameter, is the fourth parameter, and the corresponding , , , and The corresponding real matrix representation is, represents single-bit quantization; The method of representing the probability density function of noise according to Gaussian random variables and generating the probability density function of the single-frequency threshold radar echo according to the probability density function of noise and the single-bit radar echo real matrix of the single-frequency threshold specifically includes: Representing a probability density function of noise in a radar echo signal according to the Gaussian random variable; According to the probability density function of the radar echo real matrix of the single-frequency threshold and the noise in the single-bit radar echo real matrix of the single-frequency threshold, under the condition of the first parameter in the radar echo real matrix of the single-frequency threshold, the probability density function of the single-frequency threshold radar echo of the radar echo real matrix of the single-frequency threshold is generated; Probability density function of noise ,in, is the probability density function of the noise, and the variance is , is the two-norm, is the number of sampling points for each pulse; Probability density function of single frequency threshold radar echo , is the probability density function of the single-frequency threshold radar echo, is the radar echo real matrix of single frequency threshold.

2. The single-bit radar sparse imaging method based on variable threshold according to claim 1, characterized in that: The method of obtaining the likelihood function of the real matrix of the single-bit radar echo of the single-frequency threshold in the real matrix of the single-bit radar echo of the single-frequency threshold according to the probability density function of the single-frequency threshold radar echo specifically includes: Generate a distribution law representation of elements in the real matrix of single-bit radar echo of the single-frequency threshold according to the real matrix of single-bit radar echo of the single-frequency threshold, the real matrix of radar echo of the single-frequency threshold and the first parameter; According to the distribution law representation, a likelihood function of a real matrix of a single-bit radar echo of a single-frequency threshold under the condition of the first parameter is obtained.

3. The single-bit radar sparse imaging method based on variable threshold according to claim 1, characterized in that: The method of generating a probability density function of the scattering point intensity based on the Laplace distribution according to the radar echo signal matrix, generating a target function according to the Bayesian formula, and solving the target function according to the likelihood function of the single-bit radar echo real matrix of the single-frequency threshold and the probability density function of the scattering point intensity to obtain a range compression matrix specifically includes: Based on the Laplace distribution, a probability density function of the scattering point intensity is generated according to the radar echo signal matrix; According to the Bayesian formula, a first probability density function is constructed, and an objective function is generated according to the first probability density function, wherein the objective function is a maximum a posteriori probability formula of the first parameter; Solving the objective function according to the likelihood function of the real matrix of the single-bit radar echo of the single-frequency threshold and the probability density function of the scattering point intensity to obtain a simplified objective function; The simplified objective function is solved according to a first-order primal-dual algorithm to obtain the distance compression matrix.

4. The single-bit radar sparse imaging method based on variable threshold according to claim 1, characterized in that: The step of compressing the range compression matrix in azimuth and imaging the matrix to obtain a target imaging result specifically includes: According to the maximum a posteriori probability and the Bayesian criterion, the distance compression matrix is ​​compressed in the azimuth direction to obtain a two-dimensional compression matrix; The two-dimensional compression matrix is ​​imaged to obtain the target imaging result.

5. A single-bit radar sparse imaging system based on variable threshold, characterized in that: The single-bit radar sparse imaging system based on variable threshold comprises: A signal acquisition module, used to acquire radar echo signals and generate a radar echo signal matrix according to the radar echo signals; A single-bit radar echo real matrix generation module with a single-frequency threshold is used to represent the single-frequency threshold adding process of the radar echo signal according to the radar echo signal matrix and the preset single-frequency threshold to obtain a single-bit radar echo real matrix with a single-frequency threshold; A function generation module, used for representing the probability density function of noise according to Gaussian random variables, generating the probability density function of the single-frequency threshold radar echo according to the probability density function of noise and the real matrix of the single-bit radar echo of the single-frequency threshold, and obtaining the likelihood function of the real matrix of the single-bit radar echo of the single-frequency threshold according to the probability density function of the single-frequency threshold radar echo; A result generation module is used to generate a probability density function of the scattering point intensity according to the radar echo signal matrix based on Laplace distribution, generate a target function according to the Bayesian formula, and solve the target function according to the likelihood function of the single-bit radar echo real matrix of the single-frequency threshold and the probability density function of the scattering point intensity to obtain a range compression matrix, perform azimuth compression on the range compression matrix and image it to obtain a target imaging result; The acquiring of the radar echo signal and generating a radar echo signal matrix according to the radar echo signal specifically includes: Acquire a radar echo signal, and construct an echo signal model according to the radar echo signal; Generate a specific expression of each echo in the radar echo signal according to the echo signal model, and remove the carrier frequency from the specific expression of each echo to obtain a matrix expression of each echo in the radar echo signal; Generate the radar echo signal matrix of each echo according to the matrix expression of each echo; Echo signal model ; in, is the echo signal model, For quick time, is the pulse width, To adjust the frequency, is the carrier frequency, is an imaginary unit, , is the unit rectangle function; The step of expressing the process of adding a single-frequency threshold to the radar echo signal according to the radar echo signal matrix and the preset single-frequency threshold to obtain a single-bit radar echo real matrix of the single-frequency threshold specifically includes: The preset single frequency threshold is converted into a vector form to obtain a single frequency threshold vector, and a single frequency threshold parameter is obtained according to the single frequency threshold vector and the radar echo signal matrix, wherein the single frequency threshold is expressed as , is the single frequency threshold, is the amplitude, is the frequency, is the phase, is an imaginary unit, For fast time; According to the single frequency threshold adding parameter, a single frequency threshold adding process model of the radar echo signal is constructed; The single-frequency threshold adding parameter is expressed as a radar echo real matrix form of the single-frequency threshold to obtain a radar echo real matrix of the single-frequency threshold, and a single-bit radar echo real matrix of the single-frequency threshold is generated according to the radar echo real matrix of the single-frequency threshold and the single-frequency threshold adding process model; Add single frequency threshold parameter ,in, To add a single frequency threshold parameter, , is the single frequency threshold vector, is the first matrix parameter, is the second matrix parameter, is the third matrix parameter, is the fourth matrix parameter; Single-bit radar echo real matrix with single-frequency threshold ,in, is the second parameter, is the first parameter, is the third parameter, is the fourth parameter, and the corresponding , , , and The corresponding real matrix representation is, represents single-bit quantization; The method of representing the probability density function of noise according to Gaussian random variables and generating the probability density function of the single-frequency threshold radar echo according to the probability density function of noise and the single-bit radar echo real matrix of the single-frequency threshold specifically includes: Representing a probability density function of noise in a radar echo signal according to the Gaussian random variable; According to the probability density function of the radar echo real matrix of the single-frequency threshold and the noise in the single-bit radar echo real matrix of the single-frequency threshold, under the condition of the first parameter in the radar echo real matrix of the single-frequency threshold, the probability density function of the single-frequency threshold radar echo of the radar echo real matrix of the single-frequency threshold is generated; Probability density function of noise ,in, is the probability density function of the noise, and the variance is , is the two-norm, is the number of sampling points for each pulse; Probability density function of single frequency threshold radar echo , is the probability density function of the single-frequency threshold radar echo, is the radar echo real matrix of single frequency threshold.

6. A terminal, characterized in that: The terminal includes: a memory, a processor, and a single-bit radar sparse imaging program based on a variable threshold stored in the memory and executable on the processor. When the single-bit radar sparse imaging program based on a variable threshold is executed by the processor, the steps of the single-bit radar sparse imaging method based on a variable threshold are implemented.

7. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a single-bit radar sparse imaging program based on a variable threshold. When the single-bit radar sparse imaging program based on a variable threshold is executed by a processor, the steps of the single-bit radar sparse imaging method based on a variable threshold as described in any one of claims 1 to 4 are implemented.

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