Super-resolution frequency estimation method, system and equipment for circulating off-grid closed compensation and medium

Abstract

The invention discloses a super-resolution frequency estimation method, system and device for cyclic off-grid closed compensation and a medium. The method comprises the following steps: sampling a received signal according to a sampling frequency, a sampling point number and a sampling duration; performing coarse estimation on the signal frequency to obtain a frequency initial estimation value; carrying out Taylor expansion on the roughly estimated signal, simplifying an expansion formula, and establishing a matrix equation; compensating the initial frequency estimation value by using a total least square method; the total least square constraint optimization problem uses singular value decomposition to solve an approximate solution of total least square so as to obtain an estimation value of a difference value between a frequency initial estimation value and a real frequency value, and the value is used to compensate a frequency estimation initial value; and taking the compensated value as the initial frequency estimation value of the next cycle again, and performing cycle compensation for N times to obtain a frequency estimation value. According to the invention, high-precision signal frequency estimation is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal frequency estimation, and in particular relates to a super-resolution frequency estimation method, system, device and medium for cyclic off-grid closed-type compensation. Background Art

[0002] Signal frequency estimation is widely used in many fields such as communication, radar, sonar and satellite navigation. Signal frequency estimation refers to accurately estimating the frequency of the transmitted signal from the received signal containing noise and interference signals in order to perform signal analysis, detection or prediction. In wireless communication systems, frequency estimation is crucial for carrier synchronization and signal demodulation. However, due to factors such as channel noise, frequency offset and Doppler effect, the frequency of the transmitted signal may shift. Frequency estimation corrects the frequency offset through precise measurement, so that the receiving end synchronizes the transmitted signal carrier, thereby reducing errors and interference in the demodulation process. In radar and sonar systems, frequency estimation can detect the movement speed of the target, especially when the target moves at high speed, frequency estimation can help the system identify the dynamic characteristics of the target. In satellite navigation and positioning systems, the frequency characteristics of the signal can be used for accurate positioning. Due to the relative motion between the satellite and the radiation source, the signal undergoes frequency shift due to the Doppler effect during propagation. The frequency or frequency change rate of the signal at the receiving end is measured to obtain accurate position information and speed information.

[0003] With the increasing demand for high spectrum efficiency in various modern communication systems, traditional frequency estimation methods face the problem of insufficient resolution. The frequency estimation method based on fast Fourier transform (FFT) is one of the common frequency estimation techniques in signal processing. Applying the FFT method to the sampled signal, the time domain signal is converted into a frequency domain signal. The spectrum search of the frequency domain signal can obtain a rough estimate of the signal frequency according to the position index at the maximum amplitude. However, due to the limitations of the sampling rate and the number of sampling points, the frequency resolution of this method is limited. The Root-MUSIC (Root Multiple Signal Classification) algorithm is an improved algorithm of the MUSIC (Multiple Signal Classification) algorithm. It estimates the frequency of the signal based on the subspace decomposition of the signal. The MUSIC algorithm obtains the signal subspace and the noise subspace by performing eigenvalue decomposition on the signal covariance matrix. The Root-MUSIC method is a polynomial root-finding form of the MUSIC method. By solving the roots of the constructed polynomial, the direction, frequency and other parameters of the signal are estimated. The ESPRIT method uses the rotational invariance of the array signal in the spatial domain to estimate the parameters of the signal, avoiding frequency search and is suitable for array signal processing. However, the above traditional frequency estimation methods have limitations such as low frequency resolution and strong dependence on signal model and array structure.

[0004] Therefore, it is urgent to solve the above problems. Summary of the invention

[0005] Purpose of the invention: The first purpose of the present invention is to provide a super-resolution frequency estimation method with cyclic off-grid closed-type compensation to achieve high-precision signal frequency estimation.

[0006] A second object of the present invention is to provide a super-resolution frequency estimation system with cyclic off-grid closed-type compensation.

[0007] A third object of the present invention is to provide an electronic device.

[0008] A fourth object of the present invention is to provide a computer storage medium.

[0009] Technical solution: To achieve the above objectives, the present invention discloses a super-resolution frequency estimation method for cyclic off-grid closed-form compensation, comprising the following steps: (1) Sample the received signal according to the sampling frequency, number of sampling points, and sampling duration; (2) Make a rough estimate of the signal frequency and obtain the initial frequency estimate f ini ; (3) Perform Taylor expansion on the roughly estimated signal, simplify the expansion, and establish a matrix equation; (4) Applying the total least squares method to compensate for the initial frequency estimate; using the singular value decomposition (SVD) to solve the total least squares constrained optimization problem, the approximate solution of the total least squares method is obtained, and then the estimated value of the difference between the initial frequency estimate and the true frequency value is obtained, and the difference is used to compensate for the initial frequency estimate; (5) Use the compensated value as the initial frequency estimate in step (3) and repeat steps (3) to (4) to perform cyclic compensation. N times, to obtain frequency estimates f out .

[0010] Optionally, step (1) includes the following specific steps: (1.1) Receive the signal, (1.2) Set the sampling frequency f s , the sampling frequency refers to the number of sampling times per unit time, set the number of sampling points N s The number of sampling points refers to the total number of data points collected during the sampling process. The total sampling time is calculated as t s , the calculation formula of the total sampling time is expressed as:

[0011] (1.3) According to the set sampling frequency f s The total sampling time is t s , sample the received signal, and get N s sampling points, and the signal is obtained after sampling s .

[0012] Optionally, step (3) includes the following specific steps: (3.1) When obtaining the initial estimate of the signal frequency, without considering the noise, the signal is approximated as a single complex sinusoidal signal, and the signal can be approximately expressed as:

[0013] in A represents the amplitude of the signal, f represents the frequency of the signal, n Represents the index of the sampling point, Indicates the initial phase of the signal; (3.2) Initial estimate of the signal at frequency f ini Taylor expansion is performed at:

[0014] (3.3) Taylor expansion expresses the signal as f ini Infinite series at f ini for f The approximate value of the Taylor series is negligible. The first two terms of the Taylor series are taken to approximate the original function. The approximate signal is expressed as:

[0015] (3.4) The simplified Taylor expansion can be written as the multiplication of two matrices:

[0016] Among them, Δ f=ff ini , represents the difference between the initial frequency estimate and the true frequency value; (3.5) Establish the matrix equation: .

[0017] Optionally, step (4) includes the following specific steps: (4.1) According to the established matrix equation, the overall least squares constrained optimization problem is established, and the matrix equation is considered to be:

[0018] The above equation can also be written as:

[0019] Among them, the augmented matrix B and the perturbation matrix D are defined as:

[0020] (4.2) The overall least squares problem can be expressed as a constrained optimization problem:

[0021] in represents the Frobenius norm; Range Defined as: ; (4.3) Use the SVD-TLS algorithm to solve the approximate solution of total least squares. First, calculate the SVD decomposition of the augmented matrix B and store the right singular matrix V:

[0022] (4.4) Determine the effective rank of B p , the dimension of B is m*(n+1); (4.5) Calculate ( p +1)*( p +1) Matrix S (p) :

[0023] in, v ( i, j ) represents the element in the i-th row and k-th column of the matrix V; Seeking S (p) The inverse matrix S -(p) , find the approximate solution:

[0024] Based on the obtained approximate solution, the difference between the true frequency and the initial estimated frequency can be estimated to achieve compensation.

[0025] Based on the same inventive concept, the present invention discloses a super-resolution frequency estimation system with cyclic off-grid closed-form compensation, comprising: A signal sampling module is used to sample the received signal according to the sampling frequency, the number of sampling points and the sampling duration; The frequency rough estimation module is used to make a rough estimate of the signal frequency and obtain the initial frequency estimate value. f ini ; A matrix building module is used to perform Taylor expansion on the roughly estimated signal, simplify the expansion, and establish a matrix equation; The frequency compensation module is used to apply the total least squares method to compensate the initial frequency estimate. The total least squares constrained optimization problem uses the singular value decomposition SVD to solve the approximate solution of the total least squares, and then obtains the estimated value of the difference between the initial frequency estimate and the true frequency value, and uses this value to compensate the initial frequency estimate. The loop compensation module uses the compensated value as the initial frequency estimate in the matrix construction module, and repeatedly executes the matrix construction module and the frequency compensation module to perform loop compensation. N times, to obtain frequency estimates f out .

[0026] Optionally, the signal sampling module receives a signal and sets a sampling frequency f s , the sampling frequency refers to the number of sampling times per unit time, set the number of sampling points N s The number of sampling points refers to the total number of data points collected during the sampling process. The total sampling time is calculated as t s , the calculation formula of the total sampling time is expressed as:

[0027] According to the set sampling frequency f s The total sampling time is t s , sample the received signal, and get N s sampling points, and the signal is obtained after sampling s .

[0028] Optionally, when obtaining the initial estimated value of the signal frequency in the matrix construction module, the signal is approximated as a single complex sinusoidal signal without considering the noise. The signal can be approximately expressed as:

[0029] in A represents the amplitude of the signal, f represents the frequency of the signal, n Represents the index of the sampling point, Indicates the initial phase of the signal; An initial estimate of the signal at the frequency f ini Taylor expansion is performed at:

[0030] Taylor expansion expresses the signal as f ini Infinite series at f ini for f The approximate value of the Taylor series is negligible. The first two terms of the Taylor series are taken to approximate the original function. The approximate signal is expressed as:

[0031] The simplified Taylor expansion can be written as the multiplication of two matrices:

[0032] Among them, Δ f=ff ini , represents the difference between the initial frequency estimate and the true frequency value; Create the matrix equation: .

[0033] Optionally, in the frequency compensation module, according to the established matrix equation, a total least squares constrained optimization problem is established, and the matrix equation is considered to be:

[0034] The above equation can also be written as:

[0035] Among them, the augmented matrix B and the perturbation matrix D are defined as:

[0036] (4.2) The overall least squares problem can be expressed as a constrained optimization problem:

[0037] in represents the Frobenius norm; Range Defined as: ; (4.3) Use the SVD-TLS algorithm to solve the approximate solution of total least squares. First, calculate the SVD decomposition of the augmented matrix B and store the right singular matrix V:

[0038] (4.4) Determine the effective rank of B p , the dimension of B is m*(n+1); (4.5) Calculate ( p +1)*( p +1) Matrix S (p) :

[0039] in, v ( i, j ) represents the element in the i-th row and k-th column of the matrix V; Seeking S (p) The inverse matrix S -(p) , find the approximate solution:

[0040] Based on the obtained approximate solution, the difference between the true frequency and the initial estimated frequency can be estimated to achieve compensation.

[0041] Based on the same inventive concept, the present invention discloses an electronic device, including a processor and a memory, wherein the memory is connected to the processor and is used to store a computer program; when the processor is configured to execute the computer program stored in the memory, it implements the super-resolution frequency estimation method with cyclic off-grid closed-form compensation as described above.

[0042] Based on the same inventive concept, the present invention discloses a computer storage medium, characterized in that the computer storage medium stores a computer program, which is run by a processor to execute the above-mentioned super-resolution frequency estimation method with cyclic off-grid closed-form compensation.

[0043] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the present invention first obtains an initial frequency estimate, and performs frequency compensation using a total least squares method, and then cyclically compensates the initial frequency estimate to make it close to the true frequency value, thereby improving the frequency estimation accuracy; the present invention can ensure that the mean square error of frequency estimation can be effectively reduced under different signal-to-noise ratio conditions and different signal length conditions; it overcomes the problems of low frequency resolution and strong dependence on signal models and array structures in traditional frequency estimation methods, and realizes super-resolution frequency estimation through cyclic frequency compensation, and can effectively improve the robustness of frequency estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic diagram of the process of the present invention; Figure 2 A comparison diagram of RMSE of frequency estimation under different signal-to-noise ratios provided by an embodiment of the present invention; Figure 3 This is a graph comparing the RMSE results of frequency estimation under different signal lengths provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0045] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0046] Example 1: Figure 1 As shown, the present invention provides a super-resolution frequency estimation method with cyclic off-grid closed-type compensation, comprising the following steps: (1) Sample the received signal according to the sampling frequency, number of sampling points, and sampling duration; (1.1) Receive signals, receive actual signals or simulate and generate actual signals, and simulate the interference signals and noises that may be contained in the actual signals; (1.2) Set the sampling frequency f s , sampling frequency f s =40MHz, sampling frequency refers to the number of samples per unit time, set the number of sampling points N s =20*65536, the number of sampling points refers to the total number of data points collected during the sampling process, so the total sampling time can be calculated as t s , the calculation formula of the total sampling time is expressed as:

[0047] (1.3) According to the set sampling frequency f s The total sampling time is t s , sample the received signal, and get N s sampling points, and the signal is obtained after sampling s ; (2) Make a rough estimate of the signal frequency and obtain the initial frequency estimate f ini , the fast Fourier transform FFT can be used to roughly estimate the frequency value; (3) Perform Taylor expansion on the roughly estimated signal, simplify the expansion, and establish a matrix equation; (3.1) When obtaining the initial estimate of the signal frequency, without considering the noise, the signal is approximated as a single complex sinusoidal signal, and the signal can be approximately expressed as:

[0048] in A represents the amplitude of the signal, f represents the frequency of the signal, n Represents the index of the sampling point, Indicates the initial phase of the signal; (3.2) Initial estimate of the signal at frequency f ini Taylor expansion is performed at:

[0049] (3.3) Taylor expansion expresses the signal as f ini Infinite series at f ini for f The approximate value of the Taylor series is that the high-order derivatives in the Taylor series have little effect on the function value and can be ignored; so the first two terms of the Taylor series are taken to approximate the original function. After approximation, the signal can be expressed as:

[0050] (3.4) The simplified Taylor expansion can be written as the multiplication of two matrices:

[0051] Among them, Δ f=ff ini , represents the difference between the initial frequency estimate and the true frequency value; (3.5) Establish the matrix equation:

[0052] (4) Applying the total least squares method to compensate for the initial frequency estimate; using the singular value decomposition (SVD) to solve the total least squares constrained optimization problem, the approximate solution of the total least squares method is obtained, and then the estimated value of the difference between the initial frequency estimate and the true frequency value is obtained, and the difference is used to compensate for the initial frequency estimate; (4.1) Total Least Squares (TLS) is a regression analysis method that is widely used in situations where there is uncertainty or noise in both the independent and dependent variables. Unlike the traditional least squares method (OLS), which only considers the error of the dependent variable, TLS solves the model parameters by minimizing the errors of both the independent and dependent variables. Usually, TLS uses singular value decomposition (SVD) to solve the optimal solution. Total least squares considers A and b When there are errors, the matrix equation A x=b An approximate solution method; specifically, not only using the perturbation vector e De-interference vector b , and at the same time use the perturbation matrix E to interfere with the matrix A; According to the established matrix equation, the overall least squares can be established as a constrained optimization problem, considering the matrix equation:

[0053] The above equation can also be written as:

[0054] Among them, the augmented matrix B and the perturbation matrix D are defined as:

[0055] (4.2) The overall least squares problem can be expressed as a constrained optimization problem:

[0056] in represents the Frobenius norm; Range Defined as: ; (4.3) Use the SVD-TLS algorithm to solve the approximate solution of total least squares. First, calculate the SVD decomposition of the augmented matrix B and store the right singular matrix V:

[0057] (4.4) Determine the effective rank of B p , the dimension of B is m*(n+1); (4.5) Calculate ( p +1)*( p +1) Matrix S (p) :

[0058] in, v ( i, j ) represents the element in the i-th row and k-th column of the matrix V; Seeking S (p) The inverse matrix S -(p) , find the approximate solution:

[0059] Based on the obtained approximate solution, the difference between the true frequency and the initial estimated frequency can be estimated to achieve compensation; (5) Off-grid closed-loop compensation: cyclically compensate the initial frequency estimate to obtain a more accurate frequency estimate; the compensated result is used as the initial estimate in step (3), and steps (3) to (4) are repeated to perform cyclic compensation. The number of repetitions is set to N , N =5, loop compensation N After that, a more accurate frequency estimate can be obtained. f out .

[0060] The present invention first obtains an initial frequency estimation value, and then, based on this, compensates the initial frequency estimation value cyclically through frequency compensation to make it close to the real frequency value, thereby improving the frequency estimation accuracy and ensuring the system performance. The signal in the present invention may refer to a communication signal, a radar signal, a sonar signal or a satellite signal.

[0061] like Figure 2 As shown, a comparison result diagram of frequency estimation RMSE under different signal-to-noise ratios is described, and simulation is performed using MATLAB tools, including the method proposed in the present invention, the FFT algorithm, the Root-MUSIC algorithm, and the ESPRIT algorithm. In this embodiment, the signal-to-noise ratio range is set between -5dB and 20dB, and simulation is performed at intervals of 5dB, and the root mean square error RMSE is calculated. At the same time, the simulation results are compared with the FFT algorithm, the Root-MUSIC algorithm, and the ESPRIT algorithm. It can be seen that with the increase of the signal-to-noise ratio, the frequency estimation performance of the embodiment of the present invention is significantly improved, wherein the embodiment of the present invention shows good performance under all signal-to-noise ratio conditions; like Figure 3 As shown, a comparison result diagram of frequency estimation RMSE under different signal lengths is described, and simulation is performed using MATLAB tools, including the method proposed in the present invention, FFT algorithm, Root-MUSIC algorithm, and ESPRIT algorithm. In this embodiment, the signal length range is set to between 0.001s and 0.022s, and simulation is performed every 0.003s, and the root mean square error RMSE is calculated. At the same time, the simulation results are compared with the FFT algorithm, Root-MUSIC algorithm, and ESPRIT algorithm. It can be seen that the embodiment of the present invention shows good performance under all signal length conditions.

[0062] Embodiment 2: Based on the same inventive concept, the present invention discloses a super-resolution frequency estimation system with cyclic off-grid closed-form compensation, comprising: The signal sampling module is used to sample the received signal according to the sampling frequency, the number of sampling points and the sampling duration.

[0063] Receive the signal in the signal sampling module and set the sampling frequency f s , the sampling frequency refers to the number of sampling times per unit time, set the number of sampling points N s The number of sampling points refers to the total number of data points collected during the sampling process. The total sampling time is calculated as t s , the calculation formula of the total sampling time is expressed as:

[0064] According to the set sampling frequency f s The total sampling time is t s , sample the received signal, and get N s sampling points, and the signal is obtained after sampling s.

[0065] The frequency rough estimation module is used to make a rough estimate of the signal frequency and obtain the initial frequency estimate value. f ini .

[0066] The matrix building module is used to perform Taylor expansion on the roughly estimated signal, simplify the expansion, and establish a matrix equation.

[0067] In the case of obtaining the initial estimate of the signal frequency in the matrix building module, when the noise is not considered, the signal is approximated as a single complex sinusoidal signal, and the signal can be approximately expressed as:

[0068] in A represents the amplitude of the signal, f represents the frequency of the signal, n Represents the index of the sampling point, Indicates the initial phase of the signal; An initial estimate of the signal at the frequency f ini Taylor expansion is performed at:

[0069] Taylor expansion expresses the signal as f ini Infinite series at f ini for f The approximate value of the Taylor series is negligible. The first two terms of the Taylor series are taken to approximate the original function. The approximate signal is expressed as:

[0070] The simplified Taylor expansion can be written as the multiplication of two matrices:

[0071] Among them, Δ f=ff ini , represents the difference between the initial frequency estimate and the true frequency value; Create the matrix equation: .

[0072] The frequency compensation module is used to apply the total least squares method to compensate the initial frequency estimate. The total least squares constrained optimization problem uses the singular value decomposition SVD to solve the approximate solution of the total least squares, and then obtains the estimated value of the difference between the initial frequency estimate and the true frequency value, and uses this value to compensate the initial frequency estimate.

[0073] In the frequency compensation module, according to the established matrix equation, the overall least squares constrained optimization problem is established, and the matrix equation is considered to be:

[0074] The above equation can also be written as:

[0075] Among them, the augmented matrix B and the perturbation matrix D are defined as:

[0076] The total least squares problem can be expressed as a constrained optimization problem:

[0077] in represents the Frobenius norm; Range Defined as: ; Use the SVD-TLS algorithm to solve the approximate solution of total least squares. First, calculate the SVD decomposition of the augmented matrix B and store the right singular matrix V:

[0078] Determine the effective rank of B p , the dimension of B is m*(n+1); calculate( p +1)*( p +1) Matrix S (p) :

[0079] in, v ( i, j ) represents the element in the i-th row and k-th column of the matrix V; Seeking S (p) The inverse matrix S -(p) , find the approximate solution:

[0080] Based on the obtained approximate solution, the difference between the true frequency and the initial estimated frequency can be estimated to achieve compensation.

[0081] The loop compensation module uses the compensated value as the initial frequency estimate in the matrix construction module, and repeatedly executes the matrix construction module and the frequency compensation module to perform loop compensation. N times, to obtain frequency estimates f out .

[0082] Embodiment 3: Corresponding to the method of Embodiment 1 of the present invention, Embodiment 3 of the present invention further provides an electronic device, In this embodiment 3, the electronic device includes: at least one communication bus, at least one processor, at least one memory, at least one network interface, and at least one peripheral interface. The memory contains programs and data.

[0083] A communication bus may be a communication device that transmits data between components inside an electronic device, such as an internal bus (CPU and memory bus), an external bus (Universal Serial Bus port, Peripheral Component Interconnect Express port, etc.).

[0084] The memory may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0085] The processor calls the program and data stored in the memory to execute a super-resolution frequency estimation method with cyclic off-grid closed-form compensation provided in Embodiment 1 of the present invention.

[0086] The peripheral interface is used to connect to peripherals, which are external devices. External devices may include but are not limited to keyboards, displays, cursor control devices (such as mice, touch pads or touch screens), video input devices, etc.

[0087] A network interface is used to provide wired or wireless communication with an external network (eg, the Internet, an intranet, a local area network, a mobile communication network, etc.).

[0088] Example 4: Corresponding to the method of Example 1 of the present invention, Example 4 of the present invention further provides a computer storage medium for data acquisition and reception, wherein the computer storage medium stores a computer program, and the computer program is run by a processor to execute a super-resolution frequency estimation method for cyclic off-grid closed-type compensation provided in Example 1 of the present invention.

[0089] Each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware, or in the form of software functional unit, or in the form of a combination of software and hardware.

[0090] If the integrated unit 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 all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, server or network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: a mobile hard disk, a USB flash drive, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a disk or an optical disk, and other media that can store program codes.

[0091] The present invention provides a super-resolution frequency estimation method, system, device and storage medium for closed-loop off-grid compensation. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the protection scope of the present invention. All components not specified in this embodiment can be implemented by existing technologies.

Claims

1. A super-resolution frequency estimation method with cyclic off-grid closed-form compensation, characterized in that: The following steps are involved: (1) Sample the received signal according to the sampling frequency, number of sampling points, and sampling duration; (2) Make a rough estimate of the signal frequency and obtain the initial frequency estimate f ini ; (3) Perform Taylor expansion on the roughly estimated signal, simplify the expansion, and establish a matrix equation; (4) Applying the total least squares method to compensate for the initial frequency estimate; using the singular value decomposition (SVD) to solve the total least squares constrained optimization problem, the approximate solution of the total least squares method is obtained, and then the estimated value of the difference between the initial frequency estimate and the true frequency value is obtained, and the difference is used to compensate for the initial frequency estimate; (5) Use the compensated value as the initial frequency estimate in step (3) and repeat steps (3) to (4) to perform cyclic compensation. N times, to obtain frequency estimates f out .

2. The super-resolution frequency estimation method with cyclic off-grid closed-form compensation according to claim 1 is characterized in that: The step (1) comprises the following specific steps: (1.1) Receive the signal, (1.2) Set the sampling frequency f s , the sampling frequency refers to the number of sampling times per unit time, set the number of sampling points N s The number of sampling points refers to the total number of data points collected during the sampling process. The total sampling time is calculated as t s , the calculation formula of the total sampling time is expressed as: ， (1.3) According to the set sampling frequency f s The total sampling time is t s , sample the received signal, and get N s sampling points, and the signal is obtained after sampling s .

3. The super-resolution frequency estimation method with cyclic off-grid closed-form compensation according to claim 1 is characterized in that: The step (3) comprises the following specific steps: (3.1) When obtaining the initial estimate of the signal frequency, without considering the noise, the signal is approximated as a single complex sinusoidal signal, and the signal can be approximately expressed as: ， in A represents the amplitude of the signal, f represents the frequency of the signal, n Represents the index of the sampling point, Indicates the initial phase of the signal; (3.2) Initial estimate of the signal at frequency f ini Taylor expansion is performed at: ， (3.3) Taylor expansion expresses the signal as f ini Infinite series at f ini for f The approximate value of the Taylor series is negligible. The first two terms of the Taylor series are taken to approximate the original function. The approximate signal is expressed as: ， (3.4) The simplified Taylor expansion can be written as the multiplication of two matrices: ， Among them, Δ f=ff ini , represents the difference between the initial frequency estimate and the true frequency value; (3.5) Establish the matrix equation: 。 4. The super-resolution frequency estimation method with cyclic off-grid closed-form compensation according to claim 1 is characterized in that: The step (4) comprises the following specific steps: (4.1) According to the established matrix equation, the overall least squares constrained optimization problem is established, and the matrix equation is considered to be: ， The above equation can also be written as: ， Among them, the augmented matrix B and the perturbation matrix D are defined as: ， (4.2) The overall least squares problem can be expressed as a constrained optimization problem: ， in represents the Frobenius norm; Range Defined as: ； (4.3) Use the SVD-TLS algorithm to solve the approximate solution of total least squares. First, calculate the SVD decomposition of the augmented matrix B and store the right singular matrix V: ， (4.4) Determine the effective rank of B p , the dimension of B is m*(n+1); (4.5) Calculate ( p +1)*( p +1) Matrix S (p) : ， in, v ( i, j ) represents the element in the i-th row and k-th column of the matrix V; Seeking S (p) The inverse matrix S -(p) , find the approximate solution: ， Based on the obtained approximate solution, the difference between the true frequency and the initial estimated frequency can be estimated to achieve compensation.

5. A super-resolution frequency estimation system with cyclic off-grid closed-type compensation, characterized in that: include: A signal sampling module is used to sample the received signal according to the sampling frequency, the number of sampling points and the sampling duration; The frequency rough estimation module is used to make a rough estimate of the signal frequency and obtain the initial frequency estimate value. f ini ; A matrix building module is used to perform Taylor expansion on the roughly estimated signal, simplify the expansion, and establish a matrix equation; The frequency compensation module is used to apply the total least squares method to compensate the initial frequency estimate. The total least squares constrained optimization problem uses the singular value decomposition SVD to solve the approximate solution of the total least squares, and then obtains the estimated value of the difference between the initial frequency estimate and the true frequency value, and uses this value to compensate the initial frequency estimate. The loop compensation module uses the compensated value as the initial frequency estimate in the matrix construction module, and repeatedly executes the matrix construction module and the frequency compensation module to perform loop compensation. N times, to obtain frequency estimates f out .

6. The super-resolution frequency estimation system with cyclic off-grid closed-type compensation according to claim 5, characterized in that: The signal sampling module receives the signal and sets the sampling frequency f s , the sampling frequency refers to the number of sampling times per unit time, set the number of sampling points N s The number of sampling points refers to the total number of data points collected during the sampling process. The total sampling time is calculated as t s , the calculation formula of the total sampling time is expressed as: ， According to the set sampling frequency f s The total sampling time is t s , sample the received signal, and get N s sampling points, and the signal is obtained after sampling s .

7. The super-resolution frequency estimation system with cyclic off-grid closed-type compensation according to claim 5 is characterized in that: When obtaining the initial estimated value of the signal frequency in the matrix building module, the signal is approximated as a single complex sinusoidal signal without considering the noise. The signal can be approximately expressed as: ， in A represents the amplitude of the signal, f represents the frequency of the signal, n Represents the index of the sampling point, Indicates the initial phase of the signal; An initial estimate of the signal at the frequency f ini Taylor expansion is performed at: ， Taylor expansion expresses the signal as f ini Infinite series at f ini for f The approximate value of the Taylor series is negligible. The first two terms of the Taylor series are taken to approximate the original function. The approximate signal is expressed as: ， The simplified Taylor expansion can be written as the multiplication of two matrices: ， Among them, Δ f=ff ini , represents the difference between the initial frequency estimate and the true frequency value; Create the matrix equation: 。 8. The super-resolution frequency estimation system with cyclic off-grid closed-type compensation according to claim 5, characterized in that: In the frequency compensation module, according to the established matrix equation, the overall least squares constrained optimization problem is established, and the matrix equation is considered to be: ， The above equation can also be written as: ， Among them, the augmented matrix B and the perturbation matrix D are defined as: ， (4.2) The overall least squares problem can be expressed as a constrained optimization problem: ， in represents the Frobenius norm; Range Defined as: ； (4.3) Use the SVD-TLS algorithm to solve the approximate solution of total least squares. First, calculate the SVD decomposition of the augmented matrix B and store the right singular matrix V: ， (4.4) Determine the effective rank of B p , the dimension of B is m*(n+1); (4.5) Calculate ( p +1)*( p +1) Matrix S (p) : ， in, v ( i, j ) represents the element in the i-th row and k-th column of the matrix V; Seeking S (p) The inverse matrix S -(p) , find the approximate solution: ， Based on the obtained approximate solution, the difference between the true frequency and the initial estimated frequency can be estimated to achieve compensation.

9. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory is connected to the processor and is used to store a computer program; when the processor is configured to execute the computer program stored in the memory, the method according to any one of claims 1 to 4 is implemented.

10. A computer storage medium, characterized in that: The computer storage medium stores a computer program, which is executed by a processor to perform the method according to any one of claims 1 to 4.

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