A method for detecting radar signals with the minimum anti-eigenvalue using stochastic resonance preprocessing

Abstract

The present invention discloses a minimum inverse eigenvalue radar signal detection method using stochastic resonance preprocessing, which compresses the frequency of the signal to match the stochastic resonance system by performing secondary sampling on the received signal, thereby expanding the adaptability of the stochastic resonance system to higher frequency signals. Subsequently, the signal is subjected to stochastic resonance preprocessing to enhance the signal energy under low signal-to-noise ratio, obtain the processed signal information, send the processed signal to a constant false alarm (CFAR) signal detector, and construct the covariance matrix of the reference unit and the detection unit signal, perform eigenvalue decomposition on the covariance matrix to obtain the minimum inverse eigenvalue, and compare the minimum inverse eigenvalue of the detection unit with the average minimum inverse eigenvalue of the reference unit to determine the existence of the signal. This method solves the problem that the matrix constant false alarm detector based on the maximum eigenvalue is easily affected by noise uncertainty and the constant false alarm detector based on information geometry has high computational complexity.

Description

Technical Field

[0001] The present invention belongs to the field of radar signal detection, and particularly relates to a method for detecting radar signals with the minimum anti-eigenvalue by using stochastic resonance preprocessing. Background Art

[0002] A constant false alarm rate detector (CFAR) can effectively maintain a constant false alarm rate in a complex interference environment. Especially, detecting weak radar signals in a low signal-to-noise ratio environment is an important and difficult task, which is of great significance for both military and civilian fields. Conventional CFAR detection methods include the cell-averaging CFAR detection algorithm (CA-CFAR) that uses the original radar signal data, but its false alarm rate is relatively high at the clutter edge. In recent years, CFAR detectors based on the signal covariance matrix have received extensive attention, namely, matrix CFAR detectors (Matrix-CFAR). The covariance matrix can process multi-dimensional signals, which makes it have strong adaptability when dealing with complex signal systems. Whether in the fields of communication, radar or other signal processing, the covariance matrix can provide an effective analysis tool. By analyzing the covariance matrix, it can be understood whether there is a linear correlation between signals. This analysis of the linear relationship is crucial for signal detection and helps to identify the interaction and potential interference between signals.

[0003] Some matrix CFAR detectors based on the covariance matrix have been successively proposed. The CFAR detector based on the maximum eigenvalue of the covariance matrix is vulnerable to noise uncertainty. The classical information geometric CFAR detector has a high computational complexity, which limits the detection scenario. Moreover, in a low signal-to-noise ratio environment, signals are easily submerged by noise, resulting in a decrease in the detection efficiency of the above detection methods. The stochastic resonance system has been successfully applied to the field of signal detection, but the stochastic resonance system with fixed parameters cannot adapt to complex signal detection scenarios. Therefore, a new technical solution is needed to solve the above problems. Summary of the Invention

[0004] To overcome the deficiencies of the above-mentioned prior art, the present invention provides a minimum anti-eigenvalue radar signal detection method using stochastic resonance preprocessing. By performing secondary sampling on the received signal and compressing the frequency of the signal to match the stochastic resonance system, the adaptability of the stochastic resonance system to higher-frequency signals is extended. Subsequently, the signal is preprocessed by stochastic resonance to enhance the signal energy under low signal-to-noise ratio, and the processed signal information is obtained. The processed signal is sent to a constant false alarm rate (CFAR) signal detector, and the covariance matrices of the reference unit and the detection unit signals are constructed. The eigenvalue decomposition is performed on the covariance matrix to obtain the minimum anti-eigenvalue. The minimum anti-eigenvalue of the detection unit is compared with the average minimum anti-eigenvalue of the reference unit to determine the presence of the signal. This method solves the problems that the matrix CFAR detector based on the maximum eigenvalue is vulnerable to noise uncertainty and the CFAR detector based on information geometry has a high computational complexity.

[0005] The technical solution adopted by the present invention is as follows:

[0006] In a first aspect, the present invention provides a minimum anti-eigenvalue radar signal detection method using stochastic resonance preprocessing, and the method includes:

[0007] The receiver captures the radar signal and performs secondary sampling on the radar signal to obtain a sampled signal;

[0008] Perform adaptive stochastic resonance preprocessing on the sampled signal;

[0009] Perform adaptive stochastic resonance preprocessing on the detection unit and each reference unit of the constant false alarm rate detector, and calculate the covariance matrices of the detection unit and each reference unit respectively using the average value of the output signals of the stochastic resonance preprocessing;

[0010] Perform eigenvalue decomposition on the covariance matrix of each detection unit and reference unit, and calculate the minimum anti-eigenvalues of the covariance matrix of the detection unit and the covariance matrices of each reference unit;

[0011] The detection statistic composed of the minimum anti-eigenvalues of the covariance matrix of the detection unit and the covariance matrices of each reference unit , and is compared with a preset threshold . If is greater than , it is determined that the radar signal does not exist. If is less than , it is determined that the radar signal exists.

[0012] Preferably, the implementation process of the secondary sampling is:

[0013] Perform scale transformation on the radar signal, and introduce a scale transformation factor , which is specifically expressed as:

[0014] Equation (1)

[0015] where represents the sampled signal after scale transformation, represents the signal amplitude, represents the discrete time series, represents the sampling interval, represents the radar signal frequency.

[0016] Preferably, the implementation process of the adaptive stochastic resonance preprocessing is as follows:

[0017] The form of the stochastic resonance Langevin equation is defined as:

[0018] Equation (2)

[0019] In the equation, represents the output signal of the stochastic resonance preprocessing, represents time, is additive white Gaussian noise;

[0020] is the potential function of the bistable system, and the specific form is as follows:

[0021] Equation (3)

[0022] where and are the potential function parameters.

[0023] An approximate solution of the stochastic resonance Langevin equation is obtained to get each sampled value in the output signal of the stochastic resonance preprocessing.

[0024] Preferably, in the potential function of the bistable system , , ; represents the energy of the noise.

[0025] Preferably, the implementation process of performing eigenvalue decomposition on the covariance matrices of each detection unit and reference unit and calculating the minimum anti-eigenvalue of the covariance matrix of the detection unit and the covariance matrices of each reference unit is as follows:

[0026] Denote the covariance matrices of the detection unit and reference units as , represents the covariance matrix of the detection unit, represents the covariance matrices of the reference units;

[0027] Inverse eigenvalue of the covariance matrix and the eigenvalue satisfy the relationship:

[0028] Equation (4)

[0029] where , represents the dimension of the covariance matrix ;

[0030] Furthermore, the relationship between the inverse eigenvalues of the covariance matrix of the reference unit satisfies: ;

[0031] The minimum inverse eigenvalue of the covariance matrix of the reference unit is further obtained as:

[0032] Equation (5)

[0033] where and represent the maximum eigenvalue and the minimum eigenvalue of the covariance matrix of the reference unit, respectively;

[0034] Without loss of generality, let the minimum inverse eigenvalue of the detection unit be , and the minimum inverse eigenvalues of the reference unit be respectively. All the minimum inverse eigenvalues are independent and follow distribution, denoted as: Therefore, the joint probability density function of the minimum inverse eigenvalue is expressed as:

[0035] Equation (6)

[0036] Preferably, the -th inverse eigenvalue of the covariance matrix is denoted as:

[0037] Equation (7)

[0038] where is the inverse eigenvector corresponding to the -th inverse eigenvalue of the covariance matrix, is the covariance matrix and the vector ; represents the inner product of the vectors, represents the norm of the vector.

[0039] Preferably, the calculation process of the detection statistic is:

[0040]

[0041] wherein is the minimum inverse eigenvalue of the detection unit, is the minimum inverse eigenvalue of the M reference units.

[0042] In a second aspect, the present invention provides a radar signal detection system, including:

[0043] A data acquisition module, responsible for acquiring radar signals and performing secondary sampling on the radar signals to obtain sampled signals;

[0044] A first calculation module, responsible for performing adaptive stochastic resonance preprocessing on the sampled signals;

[0045] A second calculation module, responsible for performing adaptive stochastic resonance preprocessing on the detection unit and each reference unit of the constant false alarm detector respectively, calculating the covariance matrices of the detection unit and each reference unit by using the average value of the output signals of the first calculation module; performing eigenvalue decomposition on the covariance matrices of each detection unit and reference unit, and calculating the minimum inverse eigenvalues of the covariance matrices of the detection unit and each reference unit; and forming a detection statistic from the minimum inverse eigenvalues of the covariance matrices of the detection unit and each reference unit ;

[0046] A detection module, responsible for comparing the detection statistic with a preset threshold . If is greater than , it is determined that the radar signal does not exist. If is less than , it is determined that the radar signal exists.

[0047] In a third aspect, the present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed in a computer, the computer is made to execute the method.

[0048] In a fourth aspect, the present invention provides a computing device, including a memory and a processor. An executable code is stored in the memory, and when the processor executes the executable code, the method is implemented.

[0049] Compared with the prior art, the beneficial effects of the present invention:

[0050] The present invention rationally utilizes noise through adaptive stochastic resonance, transfers the noise energy to the energy of weak signals, and solves the problem of high signal leakage detection rate of traditional algorithms directly performing constant false alarm detection at low signal-to-noise ratios. The present invention constructs the covariance matrix of the preprocessed signal, and uses the minimum anti-eigenvalue of the covariance matrix to replace the original data of the detection unit and the reference unit of the constant false alarm detector, solving the problems of performance degradation of the maximum eigenvalue algorithm in the face of noise uncertainty and high complexity of the information geometry algorithm, enabling the method of the present invention to obtain better signal detection performance. Brief Description of the Drawings

[0051] Figure 1 is a schematic diagram of the matrix constant false alarm detector of the present invention.

[0052] Figure 2 is a schematic diagram of the output of the adaptive stochastic resonance signal of the present invention.

[0053] Figure 3 is a schematic diagram of the distribution of the minimum anti-eigenvalue after stochastic resonance preprocessing of the present invention, where (a) is without preprocessing and (b) is with preprocessing.

[0054] Figure 4 is a schematic diagram of the performance comparison of different algorithms under the conditions that the reference unit M = 16, the number of antennas G is set to 20, the number of sampling points N = 1000, and the false alarm probability is 0.001. Detailed Embodiment

[0055] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention.

[0056] This embodiment provides a method for detecting a constant false alarm signal of a minimum anti-eigenvalue matrix with stochastic resonance preprocessing. In a low signal-to-noise ratio environment, the noise intensity is much higher than the signal intensity. To address the possible problem of increased leakage detection probability, adaptive stochastic resonance is used to preprocess the signal, transfer the noise energy to the energy of weak signals, and improve the output signal-to-noise ratio of the system. To address the problems that the maximum eigenvalue is easily affected by noise uncertainty and the information geometry calculation complexity of the covariance matrix is high, a matrix constant false alarm detector with the minimum anti-eigenvalue of the covariance matrix is constructed, which can effectively detect signals while having a low calculation complexity. The specific steps are as follows:

[0057] Step S1: The receiver can capture radar signals through multi-antenna technology and perform secondary sampling on the radar signals to obtain sampling signals;

[0058] In one implementation, the number of antennas of the receiver is , sample the received radar signal, and use the frequency scaling technique to introduce a frequency scaling factor to equivalently reduce the frequency of the signal before random resonance preprocessing, expand the frequency range adapted by the random resonance system, and then send the sampled data into the adaptive random resonance system for signal preprocessing.

[0059] In one implementation, the process of the secondary sampling is as follows:

[0060] Perform a scale transformation on the radar signal frequency and introduce a scale transformation factor to reduce the frequency to of the original, and the sampled signal after scale transformation is expressed as:

[0061]

[0062] where represents the signal amplitude, represents the discrete time series, represents the sampling interval.

[0063] Step S2: Perform adaptive random resonance preprocessing on the sampled signal;

[0064] In one implementation, the process of the adaptive random resonance preprocessing is as follows:

[0065] The random resonance system does not require additional noise , and under the condition of low signal-to-noise ratio, the system transfers its own noise energy to the energy of the useful signal, thereby realizing signal enhancement.

[0066] The random resonance Langevin equation is defined as:

[0067]

[0068] In the formula, represents the output signal of the random resonance preprocessing, represents time, is the sampled signal obtained in step one, is the additive Gaussian white noise;

[0069] is the potential function of the bistable system, and the specific form is as follows:

[0070]

[0071] where and are the parameters of the potential function;

[0072] Parameter selection of the potential function: The potential barrier height of the potential function represents the potential energy value that the system needs to overcome to transition from one stable state to another. Let Two potential wells of the system potential function are obtained: , And the potential barrier height: . The adaptive stochastic resonance system can set appropriate system parameters according to the magnitude of the current noise power. When the system output has the maximum signal-to-noise ratio, the design criterion of the adaptive stochastic resonance system is: , , ; represents the energy of the noise, represents that the adaptive stochastic resonance system does not require additional noise;

[0073] For the stochastic resonance Langevin equation, the Runge-Kutta algorithm is used to find the approximate solution, and the sampled values in the stochastic resonance preprocessed output signal are obtained.

[0074] Further, the implementation process of using the Runge-Kutta algorithm to find the approximate solution for the stochastic resonance Langevin equation is as follows:

[0075]

[0076] Among them, is the -th sampled value in the stochastic resonance preprocessed output signal , is the calculation step size, is set to the reciprocal of the system sampling frequency, and the function , is -th sampled value in , is the average slope, .

[0077] Step S3: Perform adaptive stochastic resonance preprocessing on the detection unit and each reference unit of the constant false alarm detector, and calculate the covariance matrices of the detection unit and each reference unit respectively using the average value of the stochastic resonance preprocessed output signal;

[0078] The detection unit of the constant false alarm detector is represented by a -dimensional covariance matrix as , and the covariance matrix data of the reference unit . Figure 1 is the schematic diagram of the matrix constant false alarm detector of the present invention.

[0079] Step S4: Perform eigenvalue decomposition on the covariance matrices of each detection unit and reference unit, and calculate the minimum inverse eigenvalue of the covariance matrix of the detection unit and the covariance matrices of each reference unit.

[0080] In one implementation, the process of performing eigenvalue decomposition on the covariance matrices of each detection unit and reference unit and calculating the minimum inverse eigenvalue of the covariance matrix of the detection unit and the covariance matrices of each reference unit is as follows:

[0081] Denote the covariance matrix of the detection unit and reference units as , represents the covariance matrix of the detection unit, represents the covariance matrices of

[0082] Define the angle between the covariance matrix and the vector as . The scalar value that causes the largest change in direction when the matrix is multiplied by the vector is called the inverse eigenvalue. Using this feature, denote the -th inverse eigenvalue of the covariance matrix as:

[0083]

[0084] where is the inverse eigenvector corresponding to the -th inverse eigenvalue of the covariance matrix, represents the dimension of the covariance matrix , is the covariance matrix and the vector angle between; represents the inner product of the vectors, represents the norm of the vector;

[0085] The inverse eigenvalue can be solved using the eigenvalues of the covariance matrix. The relationship between the inverse eigenvalue and the eigenvalue of the covariance matrix satisfies:

[0086]

[0087] Furthermore, the relationship between the -th inverse eigenvalues of the covariance matrix satisfies: ;

[0088] Further obtain the minimum inverse eigenvalue of the covariance matrix as:

[0089]

[0090] where and respectively represent the maximum eigenvalue and the minimum eigenvalue of the covariance matrix;

[0091] Without loss of generality, let the minimum anti-eigenvalue of the detection unit be , and the minimum anti-eigenvalues of the reference units be , respectively. All the minimum anti-eigenvalues are independent of each other, and follow distribution, denoted as: . Therefore, the joint probability density function of the minimum anti-eigenvalues is expressed as:

[0092]

[0093] Step S5: The detection statistic formed by the minimum anti-eigenvalues of the covariance matrix of the detection unit and the covariance matrices of each reference unit, is compared with a preset threshold . If is greater than , it is determined that the radar signal does not exist, denoted as . If is less than , it is determined that the radar signal exists, denoted as .

[0094] In one implementation, the calculation process of the detection statistic is as follows:

[0095]

[0096] where is the minimum anti-eigenvalue of the detection unit, and are the minimum anti-eigenvalues of M reference units.

[0097] In one implementation, the threshold is determined according to the distribution of the minimum anti-eigenvalues. Generally, a value less than 1 is selected, and the value range determines the false alarm probability of the constant false alarm detector.

[0098] The probability density function of the detection statistic constructed by the present invention is independent of the noise parameter and can maintain the property of constant false alarm probability. The following joint probability density function is obtained by using the Jacobi transformation of the multi-dimensional conditional probability density function:

[0099]

[0100] Let be the inverse function of T, then there is:

[0101]

[0102] Therefore, the Jacobian matrix is as follows:

[0103]

[0104] where , so is an upper triangular matrix, and its determinant , so the joint probability density function can be further expressed as:

[0105]

[0106] Therefore, the probability density function of the detection statistic is as follows:

[0107]

[0108] Subsequently, the false alarm probability is:

[0109]

[0110] It can be seen from the above formula that the false alarm probability of the detection statistic proposed by the present invention is independent of the noise parameter and can maintain the constant false alarm probability property.

[0111] This embodiment is also compared with the following multiple constant false alarm detection methods: traditional Fourier transform constant false alarm detector (FFT-CFAR), maximum eigenvalue matrix constant false alarm detector (ME-MD), maximum minimum eigenvalue ratio matrix constant false alarm detector (MME-MD), Log-Euclidean mean detector (Log-Euclidean Mean), and minimum anti-eigenvalue matrix constant false alarm detector without preprocessing (MA-MD).

[0112] Figure 2 is under the condition of -10 dB. The signal to be detected is submerged in the background noise, and the periodic fluctuation of the signal cannot be observed in the time domain. After the output of the stochastic resonance process, the periodicity of the signal is significantly observed. Due to the transfer of noise energy to signal energy, its amplitude changes. Calculate the results of the minimum anti-eigenvalue difference before and after preprocessing under and conditions as shown in Figure 3 subfigure (a) - Figure 3 subfigure (b). The minimum anti-eigenvalue difference after the stochastic resonance preprocessing used in the present invention becomes larger compared to the direct detection difference, making it easier to distinguish and conditions, and improving the detection probability.

[0113] Figure 4 Under the conditions that the reference unit M = 16, the number of antennas G is set to 20, and the number of sampling points N = 1000, the performance of different algorithms is compared. The detection effect of the present invention is better than that of other detection methods under low signal-to-noise ratio.

[0114] In summary, from the analysis of the simulation effect diagram, it can be seen that the minimum anti-eigenvalue constant false alarm detection method based on adaptive bistable stochastic resonance proposed by the present invention improves the signal detection probability under low signal-to-noise ratio.

[0115] This embodiment also provides a radar signal detection system, including:

[0116] A data acquisition module, which is responsible for acquiring radar signals and performing secondary sampling on the radar signals to obtain sampling signals;

[0117] A first calculation module, which is responsible for performing adaptive stochastic resonance preprocessing on the sampling signals;

[0118] A second calculation module, which is responsible for performing adaptive stochastic resonance preprocessing on the detection unit and each reference unit of the constant false alarm detector respectively, calculating the covariance matrices of the detection unit and each reference unit by using the average value of the signals output by the first calculation module; performing eigenvalue decomposition on the covariance matrices of each detection unit and reference unit, and calculating the minimum anti-eigenvalues of the covariance matrices of the detection unit and each reference unit; and forming a detection statistic from the minimum anti-eigenvalues of the covariance matrices of the detection unit and each reference unit ;

[0119] A detection module, which is responsible for comparing the detection statistic with a preset threshold . If is greater than , it is determined that the radar signal does not exist. If is less than , it is determined that the radar signal exists.

[0120] This embodiment of the present invention provides an electronic device. Specifically, the electronic device includes a memory and a processor. An executable code is stored in the memory, and when the processor executes the executable code, the method described in any one of the above embodiments is implemented.

[0121] Among them, the memory may include a high-speed random access memory (RAM, Random Access Memory), and may also include a non-volatile memory (Non-volatile Memory), such as at least one disk memory. The communication connection between this system network element and at least one other network element is realized through at least one communication interface (which can be wired or wireless), and the Internet, wide area network, local area network, metropolitan area network, etc. can be used.

[0122] The bus can be an ISA bus, a PCI bus, an EISA bus, etc. The bus can be divided into an address bus, a data bus, a control bus, etc.

[0123] Among them, the memory is used to store a program. After receiving an execution instruction, the processor executes the program. The method executed by the device defined by the flow process disclosed in any embodiment of the foregoing embodiments of the present invention can be applied to or implemented by the processor.

[0124] The processor may be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method can be completed by the integrated logic circuit in the hardware of the processor or an instruction in the form of software. The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps and logic block diagrams disclosed in the embodiments of the present invention. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in combination with the embodiments of the present invention can be directly embodied as being executed and completed by a hardware decoding processor, or executed and completed by a combination of the hardware and software modules in the decoding processor. The software module can be located in a mature storage medium in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method.

[0125] The computer program product of the readable storage medium provided by the embodiments of the present invention includes a computer-readable storage medium storing program code. The instructions included in the program code can be used to execute the method described in the foregoing method embodiments. For the specific implementation, reference can be made to the foregoing method embodiments and will not be elaborated herein.

[0126] When the above-mentioned function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The foregoing storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (ROM), random access memories (RAM), magnetic disks, or optical discs.

[0127] Finally, it should be noted that the above-mentioned embodiments are only specific implementation manners of the present invention, used to illustrate the technical solutions of the present invention, rather than limiting them. The protection scope of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: any person skilled in the art within the technical scope disclosed by the present invention can still modify the technical solutions recorded in the foregoing embodiments, or can easily think of changes, or perform equivalent replacements on some of the technical features; and these modifications, changes, or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A minimum inverse eigenvalue radar signal detection method using stochastic resonance preprocessing, characterized in that: The method comprises: The receiver captures the radar signal and performs secondary sampling on the radar signal to obtain a sampling signal; The sampled signal is subjected to adaptive stochastic resonance preprocessing; The detection unit and each reference unit of the constant false alarm detector are respectively subjected to adaptive stochastic resonance preprocessing, and the covariance matrix of the detection unit and each reference unit is respectively calculated using the average value of the output signal after the sampling signal is subjected to adaptive stochastic resonance preprocessing; Perform eigenvalue decomposition on the covariance matrix of each detection unit and reference unit, and calculate the minimum inverse eigenvalue of the detection unit covariance matrix and the covariance matrix of each reference unit; The detection statistic is composed of the minimum inverse eigenvalue of the detection unit covariance matrix and the covariance matrix of each reference unit. ,Will With pre-set threshold For comparison, if Greater than It is determined that the radar signal does not exist. Less than It is determined that a radar signal exists.

2. The method according to claim 1, characterized in that: The secondary sampling implementation process is: Scale the radar signal and introduce the scale factor , specifically expressed as: Formula (1) in represents the sampled signal after scale transformation, represents the signal amplitude, represents a discrete time series, represents the sampling interval, Indicates the radar signal frequency.

3. The method according to claim 1, characterized in that: The adaptive stochastic resonance preprocessing implementation process is: The stochastic resonance Langevin equation is formally defined as: Formula (2) In the formula, represents the stochastic resonance preprocessing output signal, Indicates time, is additive Gaussian white noise; is the potential function of the bistable system, and its specific form is as follows: Formula (3) in, and is the potential function parameter; Find an approximate solution to the stochastic resonance Langevin equation and obtain the stochastic resonance preprocessing output signal Each sample value in .

4. The method according to claim 3, characterized in that: The potential function of the bistable system , , ; Represents the energy of the noise.

5. The method according to claim 1, characterized in that: The implementation process of performing eigenvalue decomposition on the covariance matrix of each detection unit and reference unit and calculating the minimum inverse eigenvalue of the detection unit covariance matrix and each reference unit covariance matrix is: Note: The covariance matrix of the reference units is , represents the detection unit covariance matrix, express The reference cell covariance matrix; Inverse eigenvalue of the covariance matrix With eigenvalue The relationship satisfies: Formula (4) in , Represents the covariance matrix The dimension of Then the covariance matrix of the reference unit is obtained The relationship between the inverse eigenvalues ​​satisfies: ; The minimum inverse eigenvalue of the covariance matrix of the reference unit is further obtained as: Formula (5) in, and denote the maximum eigenvalue and minimum eigenvalue of the covariance matrix of the reference unit, respectively; Without loss of generality, let the minimum inverse eigenvalue of the detection unit be , the minimum inverse eigenvalues ​​of the reference unit are , all the smallest inverse eigenvalues ​​are independent of each other, obey Distribution, denoted as: , so the joint probability density function of the minimum inverse eigenvalue is expressed as: Formula (6).

6. The method according to claim 5, characterized in that: The covariance matrix No. The inverse eigenvalues ​​are recorded as: Formula (7) in is the covariance matrix The inverse eigenvalues ​​correspond to the inverse eigenvectors, is the covariance matrix and vector The angle between represents the inner product of vectors, Represents the norm of a vector.

7. The method according to claim 1, characterized in that: The detection statistic The calculation process is: ； in is the minimum inverse eigenvalue of the detection unit, is the minimum inverse eigenvalue of the M reference units.

8. A radar signal detection system for implementing the method according to any one of claims 1 to 7, characterized in that: include: The data acquisition module is responsible for acquiring radar signals and performing secondary sampling on the radar signals to obtain sampling signals; The first calculation module is responsible for performing adaptive stochastic resonance preprocessing on the sampled signal; The second calculation module is responsible for performing adaptive stochastic resonance preprocessing on the detection unit and each reference unit of the constant false alarm detector, and calculating the covariance matrix of the detection unit and each reference unit respectively using the average value of the output signal of the first calculation module; Perform eigenvalue decomposition on the covariance matrix of each detection unit and reference unit, and calculate the minimum inverse eigenvalue of the detection unit covariance matrix and the covariance matrix of each reference unit; The detection statistic is formed by the minimum inverse eigenvalue of the detection unit covariance matrix and the covariance matrix of each reference unit ; The detection module is responsible for converting the detection statistics With pre-set threshold For comparison, if Greater than It is determined that the radar signal does not exist. Less than It is determined that a radar signal exists.

9. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to execute the method according to any one of claims 1 to 7.

10. A computing device, comprising a memory and a processor, wherein the memory stores executable code, and when the processor executes the executable code, the method according to any one of claims 1 to 7 is implemented.

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