A super-resolution frequency estimation method, system, device, and medium for cyclic off-grid closed-loop compensation.

Abstract

This invention discloses a super-resolution frequency estimation method, system, device, and medium for cyclic off-grid closed-loop compensation, comprising the following steps: sampling the received signal according to the sampling frequency, number of sampling points, and sampling duration; performing a coarse estimation of the signal frequency to obtain an initial frequency estimate; performing a Taylor expansion on the coarsely estimated signal and simplifying the expansion to establish a matrix equation; applying the overall least squares method to compensate the initial frequency estimate; solving the overall least squares constrained optimization problem using singular value decomposition to obtain an approximate solution for the overall least squares method, thereby obtaining an estimate of the difference between the initial frequency estimate and the true frequency value, and using this value to compensate the initial frequency estimate; and using the compensated value as the initial frequency estimate for the next cycle for cyclic compensation. N This invention achieves high-precision signal frequency estimation by obtaining a frequency estimate.

Description

Technical Field

[0001] This invention belongs to the field of signal frequency estimation technology, and particularly relates to a super-resolution frequency estimation method, system, device and medium with cyclic off-grid closed-loop compensation. Background Technology

[0002] Signal frequency estimation is widely used in various fields such as communications, radar, sonar, and satellite navigation. It refers to accurately estimating the frequency of a transmitted signal from a received signal containing noise and interference, enabling 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 the Doppler effect, the frequency of the transmitted signal may shift. Frequency estimation corrects this frequency offset through precise measurement, ensuring synchronized transmission of the signal carrier at the receiver, thereby reducing errors and interference during demodulation. In radar and sonar systems, frequency estimation can detect the velocity of moving targets, especially at high speeds, helping the system identify the target's dynamic characteristics. In satellite navigation and positioning systems, the frequency characteristics of signals can be used for precise positioning. Due to the relative motion between the satellite and the radiation source, the signal frequency shifts during propagation due to the Doppler effect. Measuring the frequency or rate of change of the received signal yields accurate position and velocity information.

[0003] With the increasing demand for high spectral efficiency in various modern communication systems, traditional frequency estimation methods face the problem of insufficient resolution. Frequency estimation based on the Fast Fourier Transform (FFT) is one of the common frequency estimation techniques in signal processing. Applying the FFT method to the sampled signal converts the time-domain signal into a frequency-domain signal. A spectrum search is then performed on the frequency-domain signal, and a coarse estimate of the signal frequency can be obtained based on the index of the position of the amplitude maximum. However, due to limitations in 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 version of the MUSIC (Multiple Signal Classification) algorithm, estimating the signal frequency based on the subspace decomposition of the signal. The MUSIC algorithm obtains the signal subspace and 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, constructing the roots of the polynomial to estimate parameters such as the signal direction and frequency. The ESPRIT method utilizes the rotation invariance of array signals in the spatial domain to estimate signal parameters, avoiding frequency search and making it suitable for array signal processing. However, the above-mentioned traditional frequency estimation methods have limitations such as low frequency resolution and strong dependence on signal models and array structures.

[0004] Therefore, the above problems urgently need to be solved. Summary of the Invention

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

[0006] The second objective of this invention is to provide a super-resolution frequency estimation system with cyclic off-grid closed-loop compensation.

[0007] A third objective of this invention is to provide an electronic device.

[0008] A fourth objective of this invention is to provide a computer storage medium.

[0009] Technical Solution: To achieve the above objectives, this invention discloses a super-resolution frequency estimation method for cyclic off-grid closed-loop compensation, comprising the following steps:

[0010] (1) Sample the received signal according to the sampling frequency, number of sampling points, and sampling duration;

[0011] (2) Perform a coarse estimation of the signal frequency to obtain an initial frequency estimate. f ini ;

[0012] (3) Perform Taylor expansion on the coarsely estimated signal, simplify the expansion, and establish a matrix equation;

[0013] (4) Apply the overall least squares method to compensate for the initial frequency estimate; the overall least squares constrained optimization problem uses singular value decomposition (SVD) to solve the overall least squares approximate solution, 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 for the initial frequency estimate.

[0014] (5) Use the compensated value as the initial frequency estimate in step (3) again, and repeat steps (3) to (4) to perform cyclic compensation. N This time, the frequency estimate is obtained. f out .

[0015] Optionally, step (1) includes the following specific steps:

[0016] (1.1) Receiving signals,

[0017] (1.2) Set the sampling frequency f s Sampling frequency refers to the number of samples taken per unit time. The number of sampling points is set. N sThe number of sampling points refers to the total number of data points collected during the sampling process. The total sampling time is calculated as follows: t s The formula for calculating the total sampling time is as follows:

[0018]

[0019] (1.3) Based on the set sampling frequency f s The total sampling time is t s The received signal is sampled, and the sampled signal is obtained. N s Each sampling point is used to obtain the signal. s .

[0020] Optionally, step (3) includes the following specific steps:

[0021] (3.1) Given the initial estimate of the signal frequency, and without considering noise, the signal can be approximated as a single complex sinusoidal signal, which can be approximately represented as:

[0022]

[0023] in A Indicates the amplitude of the signal. f Indicates the frequency of the signal. n Indicates the index of the sampling point. Indicates the initial phase of the signal;

[0024] (3.2) Initial frequency estimate of the signal f ini Perform Taylor expansion at this point:

[0025]

[0026] (3.3) The Taylor expansion represents the signal as f ini An infinite series at a given point, f ini for f The approximation is obtained by neglecting the higher-order derivatives in the Taylor series and taking the first two terms of the Taylor series to approximate the original function. The approximated signal is expressed as:

[0027]

[0028] (3.4) The simplified Taylor expansion can be written as the product of two matrices:

[0029]

[0030] Where, Δf=ff ini , representing the difference between the initial frequency estimate and the actual frequency value;

[0031] (3.5) Establish the matrix equation:

[0032] .

[0033] Optionally, step (4) includes the following specific steps:

[0034] (4.1) Based on the established matrix equation, a total least squares constrained optimization problem is established, considering the matrix equation as follows:

[0035]

[0036] The above equation can also be written as:

[0037]

[0038] Here, the augmented matrix B and the perturbation matrix D are defined as follows:

[0039]

[0040] (4.2) The overall least squares problem can be expressed as a constrained optimization problem:

[0041]

[0042] in Denotes the Frobenius norm; Range Defined as:

[0043] ;

[0044] (4.3) The SVD-TLS algorithm is used to solve the approximate solution of the total least squares. First, the SVD decomposition of the augmented matrix B is calculated and the right singular matrix V is stored:

[0045]

[0046] (4.4) Determine the effective rank of B p The dimension of B is m*(n+1);

[0047] (4.5) Calculate ( p +1)*( p +1) Matrix S (p) :

[0048]

[0049] in, v ( i, j() represents the element in the i-th row and k-th column of matrix V;

[0050] Find S (p) The inverse matrix S -(p) Find an approximate solution:

[0051]

[0052] Based on the approximate solution obtained, the difference between the true frequency and the initial frequency estimate can be estimated, thus achieving compensation.

[0053] Based on the same inventive concept, this invention discloses a super-resolution frequency estimation system with cyclic off-grid closed-loop compensation, comprising:

[0054] 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;

[0055] The frequency coarse estimation module is used to perform a coarse estimation of the signal frequency and obtain an initial frequency estimate. f ini ;

[0056] The matrix construction module is used to perform Taylor expansion on the coarsely estimated signal, simplify the expansion, and establish the matrix equation.

[0057] The frequency compensation module is used to compensate the initial frequency estimate by applying the total least squares method. The total least squares constrained optimization problem uses 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. This value is used to compensate the initial frequency estimate.

[0058] The cyclic 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 cyclic compensation. N This time, the frequency estimate is obtained. f out .

[0059] Optionally, the signal sampling module receives signals and sets the sampling frequency. f s Sampling frequency refers to the number of samples taken per unit time. The number of sampling points is set. 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 follows: t s The formula for calculating the total sampling time is as follows:

[0060]

[0061] According to the set sampling frequency f s The total sampling time is t s The received signal is sampled, and the sampled signal is obtained. N s Each sampling point is used to obtain the signal. s .

[0062] Optionally, when obtaining the initial estimate of the signal frequency in the matrix construction module, without considering noise, the signal is approximated as a single complex sine signal, which can be approximately represented as:

[0063]

[0064] in A Indicates the amplitude of the signal. f Indicates the frequency of the signal. n Indicates the index of the sampling point. Indicates the initial phase of the signal;

[0065] For the initial frequency estimate of the signal f ini Perform Taylor expansion at this point:

[0066]

[0067] Taylor expansion represents the signal as f ini An infinite series at a given point, f ini for f The approximation is obtained by neglecting the higher-order derivatives in the Taylor series and taking the first two terms of the Taylor series to approximate the original function. The approximated signal is expressed as:

[0068]

[0069] The simplified Taylor expansion can be written as the product of two matrices:

[0070]

[0071] Where, Δ f=ff ini , representing the difference between the initial frequency estimate and the actual frequency value;

[0072] Establish the matrix equation:

[0073] .

[0074] Optionally, in the frequency compensation module, based on the established matrix equation, a total least squares constrained optimization problem is established, considering the matrix equation as follows:

[0075]

[0076] The above equation can also be written as:

[0077]

[0078] Here, the augmented matrix B and the perturbation matrix D are defined as follows:

[0079]

[0080] (4.2) The overall least squares problem can be expressed as a constrained optimization problem:

[0081]

[0082] in Denotes the Frobenius norm; Range Defined as:

[0083] ;

[0084] (4.3) The SVD-TLS algorithm is used to solve the approximate solution of the total least squares. First, the SVD decomposition of the augmented matrix B is calculated and the right singular matrix V is stored:

[0085]

[0086] (4.4) Determine the effective rank of B p The dimension of B is m*(n+1);

[0087] (4.5) Calculate ( p +1)*( p +1) Matrix S (p) :

[0088]

[0089] in, v ( i, j () represents the element in the i-th row and k-th column of matrix V;

[0090] Find S (p) The inverse matrix S -(p) Find an approximate solution:

[0091]

[0092] Based on the approximate solution obtained, the difference between the true frequency and the initial frequency estimate can be estimated, thus achieving compensation.

[0093] Based on the same inventive concept, this 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 a super-resolution frequency estimation method for cyclic off-grid closed-loop compensation as described above.

[0094] Based on the same inventive concept, this invention discloses a computer storage medium, characterized in that the computer storage medium stores a computer program, which is executed by a processor to perform the above-described super-resolution frequency estimation method for cyclic off-grid closed-loop compensation.

[0095] 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 then uses the overall least squares method to perform frequency compensation, and then iteratively compensates the initial frequency estimate to make it close to the true frequency value, thereby improving the frequency estimation accuracy; The present invention can effectively reduce the mean square error of frequency estimation 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 model and array structure in traditional frequency estimation methods. Through cyclic frequency compensation, it achieves super-resolution frequency estimation and can effectively improve the robustness of frequency estimation. Attached Figure Description

[0096] Figure 1 This is a schematic flowchart of the method of the present invention;

[0097] Figure 2 This is a comparison chart of frequency estimation RMSE results under different signal-to-noise ratios provided in the embodiments of the present invention;

[0098] Figure 3 The graph shows the comparison results of frequency estimation RMSE under different signal lengths provided in the embodiments of the present invention. Detailed Implementation

[0099] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0100] Example 1: Figure 1 As shown, the present invention provides a super-resolution frequency estimation method for cyclic off-grid closed-loop compensation, comprising the following steps:

[0101] (1) Sample the received signal according to the sampling frequency, number of sampling points, and sampling duration;

[0102] (1.1) Receive signal, receive actual signal or simulate to generate actual signal, and simulate the interference signal and noise that the actual signal may contain;

[0103] (1.2) Set the sampling frequencyf s sampling frequency f s =40MHz, sampling frequency refers to the number of samples taken per unit time, setting the number of sampling points. N s =20*65536, where the number of sampling points refers to the total number of data points collected during the sampling process. Therefore, the total sampling time can be calculated as: t s The formula for calculating the total sampling time is as follows:

[0104]

[0105] (1.3) Based on the set sampling frequency f s The total sampling time is t s The received signal is sampled, and the sampled signal is obtained. N s Each sampling point is used to obtain the signal. s ;

[0106] (2) Perform a coarse estimation of the signal frequency to obtain an initial frequency estimate. f ini The frequency value can be roughly estimated using the Fast Fourier Transform (FFT).

[0107] (3) Perform Taylor expansion on the coarsely estimated signal, simplify the expansion, and establish a matrix equation;

[0108] (3.1) Given the initial estimate of the signal frequency, and without considering noise, the signal can be approximated as a single complex sinusoidal signal, which can be approximately represented as:

[0109]

[0110] in A Indicates the amplitude of the signal. f Indicates the frequency of the signal. n Indicates the index of the sampling point. Indicates the initial phase of the signal;

[0111] (3.2) Initial frequency estimate of the signal f ini Perform Taylor expansion at this point:

[0112]

[0113] (3.3) The Taylor expansion represents the signal as f ini An infinite series at a given point, fini for f The higher-order derivatives in the Taylor series have a negligible effect on the function value; therefore, the first two terms of the Taylor series are used to approximate the original function. The approximate signal can be expressed as:

[0114]

[0115] (3.4) The simplified Taylor expansion can be written as the product of two matrices:

[0116]

[0117] Where, Δ f=ff ini , representing the difference between the initial frequency estimate and the actual frequency value;

[0118] (3.5) Establish the matrix equation:

[0119]

[0120] (4) Apply the overall least squares method to compensate for the initial frequency estimate; the overall least squares constrained optimization problem uses singular value decomposition (SVD) to solve the overall least squares approximate solution, 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 for the initial frequency estimate.

[0121] (4.1) Total Least Squares (TLS) is a regression analysis method widely used when both independent and dependent variables in the data have uncertainty or noise. Unlike traditional Ordinary Least Squares (OLS), which only considers the error of the dependent variable, TLS solves for the model parameters by simultaneously minimizing the errors of both independent and dependent variables. Typically, TLS uses Singular Value Decomposition (SVD) to find the optimal solution. Total Least Squares considers both A and B. b When errors exist simultaneously, matrix equation A x=b An approximate solution method; specifically, not only using the perturbation vector e De-interference vector b Furthermore, the perturbation matrix E is used to perturb the matrix A at the same time;

[0122] Based on the established matrix equation, a total least squares constrained optimization problem can be established. Consider the matrix equation:

[0123]

[0124] The above equation can also be written as:

[0125]

[0126] Here, the augmented matrix B and the perturbation matrix D are defined as follows:

[0127]

[0128] (4.2) The overall least squares problem can be expressed as a constrained optimization problem:

[0129]

[0130] in Denotes the Frobenius norm; Range Defined as:

[0131] ;

[0132] (4.3) The SVD-TLS algorithm is used to solve the approximate solution of the total least squares. First, the SVD decomposition of the augmented matrix B is calculated and the right singular matrix V is stored:

[0133]

[0134] (4.4) Determine the effective rank of B p The dimension of B is m*(n+1);

[0135] (4.5) Calculate ( p +1)*( p +1) Matrix S (p) :

[0136]

[0137] in, v ( i, j () represents the element in the i-th row and k-th column of matrix V;

[0138] Find S (p) The inverse matrix S -(p) Find an approximate solution:

[0139]

[0140] Based on the approximate solution obtained, the difference between the true frequency and the initial frequency estimate can be estimated, thereby achieving compensation;

[0141] (5) Off-grid closed-loop compensation: The initial frequency estimate is compensated cyclically to obtain a more accurate frequency estimate; the compensated result is used again as the initial estimate in step (3), and steps (3) to (4) are repeated for cyclic compensation. The number of repetitions is set to N , N =5, cyclic compensation N After this, a more accurate frequency estimate can be obtained. f out .

[0142] This invention first obtains an initial frequency estimate. Based on this estimate, frequency compensation is performed cyclically to continuously compensate the initial frequency estimate, bringing it closer to the true frequency value. This improves the frequency estimation accuracy while ensuring system performance. The signal in this invention can refer to communication signals, radar signals, sonar signals, or satellite signals, etc.

[0143] like Figure 2 The figure shows a comparison of the RMSE of frequency estimation under different signal-to-noise ratios (SNRs). Simulations were performed using MATLAB, including the method proposed in this invention, the FFT algorithm, the Root-MUSIC algorithm, and the ESPRIT algorithm. In this embodiment, the SNR range was set between -5dB and 20dB, and simulations were performed at 5dB intervals. The root mean square error (RMSE) was calculated, and the simulation results were compared with those of the FFT algorithm, the Root-MUSIC algorithm, and the ESPRIT algorithm. It can be seen that the frequency estimation performance of this embodiment is significantly improved with the increase of the SNR. In particular, this embodiment exhibits good performance under all SNR conditions.

[0144] like Figure 3 The figure shows a comparison of the RMSE (Root Mean Square Error) of frequency estimation under different signal lengths. Simulations were performed using MATLAB, including the method proposed in this invention, the FFT algorithm, the Root-MUSIC algorithm, and the ESPRIT algorithm. In this embodiment, the signal length range was set to 0.001s to 0.022s, with simulations performed every 0.003s, and the RMSE was calculated. The simulation results were compared with those of the FFT algorithm, the Root-MUSIC algorithm, and the ESPRIT algorithm. It can be seen that the embodiment of this invention exhibits better performance under all signal length conditions.

[0145] Example 2: Based on the same inventive concept, this invention discloses a super-resolution frequency estimation system with cyclic off-grid closed-loop compensation, comprising:

[0146] 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.

[0147] The signal sampling module receives signals and sets the sampling frequency. f s Sampling frequency refers to the number of samples taken per unit time. The number of sampling points is set. 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 follows: t s The formula for calculating the total sampling time is as follows:

[0148]

[0149] According to the set sampling frequency f s The total sampling time is t s The received signal is sampled, and the sampled signal is obtained. N s Each sampling point is used to obtain the signal. s .

[0150] The frequency coarse estimation module is used to perform a coarse estimation of the signal frequency and obtain an initial frequency estimate. f ini .

[0151] The matrix construction module is used to perform Taylor expansion on the coarsely estimated signal, simplify the expansion, and establish the matrix equation.

[0152] When obtaining the initial estimate of the signal frequency in the matrix construction module, and neglecting noise, the signal is approximated as a single complex sinusoidal signal, which can be approximately represented as:

[0153]

[0154] in A Indicates the amplitude of the signal. f Indicates the frequency of the signal. n Indicates the index of the sampling point. Indicates the initial phase of the signal;

[0155] For the initial frequency estimate of the signal f ini Perform Taylor expansion at this point:

[0156]

[0157] Taylor expansion represents the signal as f ini An infinite series at a given point, f ini for f The approximation is obtained by neglecting the higher-order derivatives in the Taylor series and taking the first two terms of the Taylor series to approximate the original function. The approximated signal is expressed as:

[0158]

[0159] The simplified Taylor expansion can be written as the product of two matrices:

[0160]

[0161] Where, Δ f=ffini , representing the difference between the initial frequency estimate and the actual frequency value;

[0162] Establish the matrix equation:

[0163] .

[0164] The frequency compensation module is used to compensate the initial frequency estimate by applying the total least squares method. The total least squares constrained optimization problem uses 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. This value is used to compensate the initial frequency estimate.

[0165] In the frequency compensation module, based on the established matrix equation, a total least squares constrained optimization problem is established, considering the following matrix equation:

[0166]

[0167] The above equation can also be written as:

[0168]

[0169] Here, the augmented matrix B and the perturbation matrix D are defined as follows:

[0170]

[0171] The overall least squares problem can be represented as a constrained optimization problem:

[0172]

[0173] in Denotes the Frobenius norm; Range Defined as:

[0174] ;

[0175] The SVD-TLS algorithm is used to find an approximate solution for total least squares. First, the SVD decomposition of the augmented matrix B is calculated and the right singular matrix V is stored:

[0176]

[0177] Determine the effective rank of B p The dimension of B is m*(n+1);

[0178] calculate( p +1)*( p +1) Matrix S (p) :

[0179]

[0180] in, v ( i, j () represents the element in the i-th row and k-th column of matrix V;

[0181] Find S (p) The inverse matrix S -(p) Find an approximate solution:

[0182]

[0183] Based on the approximate solution obtained, the difference between the true frequency and the initial frequency estimate can be estimated, thus achieving compensation.

[0184] The cyclic 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 cyclic compensation. N This time, the frequency estimate is obtained. f out .

[0185] Example 3: Corresponding to the method of Example 1 of the present invention, Example 3 of the present invention also provides an electronic device.

[0186] 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.

[0187] A communication bus can be a communication device that transmits data between components within an electronic device, such as an internal bus (CPU and memory bus) or an external bus (Universal Serial Bus port, Peripheral Component Interconnect Fast Port, etc.).

[0188] The memory may include high-speed RAM, and may also include non-volatile memory, such as at least one disk storage device.

[0189] The processor calls the program and data stored in the memory to execute the super-resolution frequency estimation method for cyclic off-grid closed-loop compensation provided in Embodiment 1 of the present invention.

[0190] Peripheral interfaces are used to connect to peripherals, which are external devices. External devices may include, but are not limited to, keyboards, monitors, cursor control devices (such as mice, touchpads or touch screens), video input devices, etc.

[0191] A network interface provides wired or wireless communication with external networks (e.g., the Internet, intranets, local area networks, mobile communication networks, etc.).

[0192] Example 4: Corresponding to the method of Example 1 of the present invention, Example 4 of the present invention also provides a computer storage medium for data acquisition and reception. The computer storage medium stores a computer program, which is executed by a processor to perform a super-resolution frequency estimation method for cyclic off-grid closed-loop compensation provided in Example 1 of the present invention.

[0193] The functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware, as a software functional unit, or in a combination of software and hardware.

[0194] If the integrated unit is implemented as 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. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as portable hard drives, USB flash drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0195] This invention provides a super-resolution frequency estimation method, system, device, and storage medium for cyclic off-grid closed-loop compensation. The above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A super-resolution frequency estimation method with cyclic off-grid closed-loop compensation, characterized in that, Includes the following steps: (1) Sample the received signal according to the sampling frequency, number of sampling points, and sampling duration; Step (1) includes the following specific steps: (1.1) Receiving signals, (1.2) Set the sampling frequency f s Sampling frequency refers to the number of samples taken per unit time. The number of sampling points is set. 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 follows: t s The formula for calculating the total sampling time is as follows: ， (1.3) Based on the set sampling frequency f s The total sampling time is t s The received signal is sampled, and the sampled signal is obtained. N s Each sampling point is used to obtain the signal. s ; (2) Perform a coarse estimation of the signal frequency to obtain an initial frequency estimate. f ini ; (3) Perform Taylor expansion on the coarsely estimated signal, simplify the expansion, and establish a matrix equation; Step (3) includes the following specific steps: (3.1) Given the initial estimate of the signal frequency, and without considering noise, the signal can be approximated as a single complex sinusoidal signal, which can be approximately represented as: ， in A Indicates the amplitude of the signal. f Indicates the frequency of the signal. n Indicates the index of the sampling point. Indicates the initial phase of the signal; (3.2) Initial frequency estimate of the signal f ini Perform Taylor expansion at this point: ， (3.3) The Taylor expansion represents the signal as f ini An infinite series at a given point, f ini for f The approximation is obtained by neglecting the higher-order derivatives in the Taylor series and taking the first two terms of the Taylor series to approximate the original function. The approximated signal is expressed as: ， (3.4) The simplified Taylor expansion can be written as the product of two matrices: ， Where, Δ f=ff ini , representing the difference between the initial frequency estimate and the actual frequency value; (3.5) Establish the matrix equation: ； (4) Based on the established matrix equation, establish the overall least squares as a constrained optimization problem, and apply the overall least squares method to compensate the initial frequency estimate; the overall least squares constrained optimization problem uses singular value decomposition (SVD) to solve the overall least squares approximate solution, 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. Step (4) includes the following specific steps: (4.1) Based on the established matrix equation, a total least squares constrained optimization problem is established, considering the matrix equation as follows: ， The above equation can also be written as: ， Here, the augmented matrix B and the perturbation matrix D are defined as follows: ， (4.2) The overall least squares problem can be expressed as a constrained optimization problem: ， in Denotes the Frobenius norm; Range Defined as: ； (4.3) The SVD-TLS algorithm is used to solve the approximate solution of the total least squares. First, the SVD decomposition of the augmented matrix B is calculated and the right singular matrix V is stored: ， (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 matrix V; Find S (p) The inverse matrix S -(p) Find an approximate solution: ， Based on the approximate solution obtained, the difference between the true frequency and the initial frequency estimate can be estimated, thereby achieving compensation; (5) Use the compensated value as the initial frequency estimate in step (3) again, and repeat steps (3) to (4) to perform cyclic compensation. N This time, the frequency estimate is obtained. f out .

2. A super-resolution frequency estimation system with cyclic off-grid closed-loop compensation, characterized in that, include: 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; The signal sampling module receives signals and sets the sampling frequency. f s Sampling frequency refers to the number of samples taken per unit time. The number of sampling points is set. 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 follows: t s The formula for calculating the total sampling time is as follows: ， According to the set sampling frequency f s The total sampling time is t s The received signal is sampled, and the sampled signal is obtained. N s Each sampling point is used to obtain the signal. s ; The frequency coarse estimation module is used to perform a coarse estimation of the signal frequency and obtain an initial frequency estimate. f ini ; The matrix construction module is used to perform Taylor expansion on the coarsely estimated signal, simplify the expansion, and establish the matrix equation. In the matrix construction module, when obtaining the initial estimate of the signal frequency, and without considering noise, the signal is approximated as a single complex sinusoidal signal, which can be approximately represented as: ， in A Indicates the amplitude of the signal. f Indicates the frequency of the signal. n Indicates the index of the sampling point. Indicates the initial phase of the signal; For the initial frequency estimate of the signal f ini Perform Taylor expansion at this point: ， Taylor expansion represents the signal as f ini An infinite series at a given point, f ini for f The approximation is obtained by neglecting the higher-order derivatives in the Taylor series and taking the first two terms of the Taylor series to approximate the original function. The approximated signal is expressed as: ， The simplified Taylor expansion can be written as the product of two matrices: ， Where, Δ f=ff ini , representing the difference between the initial frequency estimate and the actual frequency value; Establish the matrix equation: ； The frequency compensation module is used to establish a total least squares constrained optimization problem based on the established matrix equation, and apply the total least squares method to compensate the initial frequency estimate. The total least squares constrained optimization problem uses singular value decomposition (SVD) to solve the total least squares approximate solution, and then obtains the estimate of the difference between the initial frequency estimate and the true frequency value. This value is used to compensate the initial frequency estimate. The frequency compensation module establishes a total least squares constrained optimization problem based on the established matrix equation, considering the following matrix equation: ， The above equation can also be written as: ， Here, the augmented matrix B and the perturbation matrix D are defined as follows: ， (4.2) The overall least squares problem can be expressed as a constrained optimization problem: ， in Denotes the Frobenius norm; Range Defined as: ； (4.3) The SVD-TLS algorithm is used to solve the approximate solution of the total least squares. First, the SVD decomposition of the augmented matrix B is calculated and the right singular matrix V is stored: ， (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 matrix V; Find S (p) The inverse matrix S -(p) Find an approximate solution: ， Based on the approximate solution obtained, the difference between the true frequency and the initial frequency estimate can be estimated, thereby achieving compensation; The cyclic 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 cyclic compensation. N This time, the frequency estimate is obtained. f out .

3. An electronic device, characterized in that, The system includes a processor and a memory, wherein the memory is connected to the processor for storing computer programs; when the processor is configured to execute the computer programs stored in the memory, it implements the method as described in claim 1.

4. A computer storage medium, characterized in that, The computer storage medium stores a computer program that is executed by a processor to perform the method of claim 1.

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