Broadband signal measurement method based on improved Prony

Abstract

The invention discloses a broadband signal measurement method based on improved Prony, and the method comprises the following steps: 1, carrying out the singular value decomposition of a broadband signal, determining an initial singular value demarcation point through an energy accumulation method, and introducing a Pearson correlation coefficient to distinguish the main frequency components and noise of the signal, thereby determining the model order of Prony; 2, preprocessing the broadband signal by using variational mode decomposition, solving a variational problem through iteration, decomposing the complex broadband signal into a plurality of intrinsic mode functions with narrowband frequency spectrums, and reducing the complexity of signal processing; step 3, introducing a disturbance matrix satisfying a Toeplitz structure, iteratively optimizing a linear prediction coefficient of a Prony algorithm, using the Prony algorithm after parameter optimization to identify each mode, obtaining frequency, amplitude and phase information of each mode, and realizing measurement of broadband signals; according to the method, the problem of insufficient measurement precision caused by noise interference and difficulty in model order selection in broadband signal measurement of a traditional Prony algorithm is solved.

Description

Technical Field

[0001] The present invention relates to the field of broadband oscillation of power systems, and in particular to a broadband signal measurement method based on improved Prony. Background Art

[0002] In recent years, the integration of high proportions of renewable energy and power electronic equipment into power systems has continued to expand. This "double high" feature has profoundly impacted the dynamic characteristics and operational stability of power systems. One of the most prominent issues is the frequent occurrence of broadband oscillations. These oscillations have a wide frequency range, ranging from a few hertz to several kilohertz, and are often accompanied by complex noise interference, posing unprecedented challenges to traditional oscillation monitoring and analysis methods.

[0003] Accurately measuring and analyzing broadband signals is crucial for understanding oscillation mechanisms, formulating effective control strategies, and ensuring the safe and stable operation of power grids. However, existing broadband signal measurement methods have many limitations. For example, although the Fourier transform is fast and easy to implement, it is susceptible to spectrum leakage and fence effects, resulting in reduced measurement accuracy. Although the empirical mode decomposition method can decompose non-stationary signals into multiple relatively stationary sub-signals, it suffers from problems such as modal aliasing, false modes, and endpoint effects. While the traditional Prony algorithm has high frequency resolution and can directly calculate signal parameters such as amplitude, phase, and frequency, it suffers from large measurement errors in the presence of noise interference and improper selection of model order, making it difficult to meet the requirements of high-precision measurement. Therefore, how to overcome the shortcomings of existing methods and develop a new method that can effectively reduce noise and accurately identify broadband signal parameters in complex noise environments has become a key issue that needs to be addressed. Summary of the Invention

[0004] The purpose of the present invention is to overcome the above-mentioned shortcomings and provide a broadband signal measurement method based on improved Prony, aiming to solve the problem of insufficient measurement accuracy of traditional Prony algorithm in broadband signal measurement due to noise interference and difficulty in selecting model order.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is: a broadband signal measurement method based on improved Prony, comprising the following steps:

[0006] Step 1: Perform singular value decomposition on the broadband signal, determine the initial singular value cutoff point by the cumulative energy method, introduce the Pearson correlation coefficient to distinguish the main frequency components of the signal from the noise, and thus determine the Prony model order;

[0007] Step 2: Preprocess the broadband signal using variational mode decomposition. By iteratively solving the variational problem, the complex broadband signal is decomposed into multiple intrinsic mode functions with narrowband spectra, reducing the complexity of signal processing.

[0008] Step 3: Introduce a perturbation matrix that satisfies the Toeplitz structure, iteratively optimize the linear prediction coefficient of the Prony algorithm, use the parameter-optimized Prony algorithm to identify each mode separately, obtain the frequency, amplitude, and phase information of each mode, and realize the measurement of broadband signals.

[0009] Preferably, the step 1 is specifically:

[0010] Step 1.1: Construct the sampling values of the broadband signal into an m×n matrix X, and perform singular value decomposition on the matrix X to obtain normalized matrices of order m×m and n×n, and an m×n singular value matrix;

[0011] Step 1.2: Determine an initial singular value cutoff point using the cumulative energy method, and divide the singular value into two parts: one corresponding to the signal of the main frequency, and the other corresponding to the noise and the signal component with an amplitude close to the noise;

[0012] Step 1.3: Select the eigenvector corresponding to the first singular value and calculate the Pearson correlation coefficient between the eigenvector corresponding to each singular value after k and the first eigenvector;

[0013] Step 1.4: Determine the model order of the Prony algorithm by taking the value of the Pearson correlation coefficient. If the Pearson correlation coefficient is close to 0 or negative, it is considered to be a pure noise component. Count the number of singular values corresponding to the pure noise component, denoted as m, and the model order is rm.

[0014] Preferably, in step 1.1, the calculation formula for performing singular value decomposition on the matrix X to obtain normalized matrices of m×m and n×n orders and a singular value matrix of m×n order is as follows:

[0015] X=U m×m S m×n V n×n

[0016] Where U and V are normalized matrices of order m×m and n×n respectively, S is a singular value matrix of order m×n, S=[diag(σ1,σ2,…σ r ),0],σ i are singular values, all of which are non-zero and arranged in descending order, and r is the total number of singular values.

[0017] Preferably, the calculation formula corresponding to step 1.2 is as follows:

[0018]

[0019] Where r is the total number of singular values, η is 0.90, and k is the initial singular value cutoff point.

[0020] Preferably, in step 1.3, the Pearson correlation coefficient formula is expressed as:

[0021]

[0022] Where, v1=[v 1,1 ,v 1,2 ,...,v 1,i ] is the first eigenvector; v j =[v j,1 ,v j,2 ,...,v j,i ] is the jth eigenvector; and They are v1 and v j The mean of .

[0023] Preferably, the step 2 is specifically as follows:

[0024] Step 2.1: Decompose the broadband signal into multiple natural modes using VMD. Each mode is a finite bandwidth with a center frequency. Perform a Hilbert transform on each modal function to obtain the corresponding spectrum.

[0025]

[0026] Where δ(t) is the pulse function, j represents the imaginary part, and u k (t) represents the mode function, t represents the sampling time;

[0027] Step 2.2: Adjust the spectrum of each mode to the corresponding baseband, calculate the bandwidth of the modal signal, and construct a mathematical model for the variational constraint problem;

[0028]

[0029] Where, ω k Represents the modal function u k The center frequency, e jωkt is a complex exponential function, indicating a frequency of ω k The modulation signal, represents the partial derivative with respect to t, represents the square of the L2 norm, which is used to measure the difference between the modal component and the original signal tone. K represents the total number of modes, that is, the number of modal components into which the signal is decomposed.

[0030] Step 2.3: Introduce the Lagrangian operator λ(t) and the penalty factor α to transform the constrained problem into the corresponding unconstrained problem. Use the alternating direction multiplier method to solve the unconstrained problem, and continuously update the mode function, center frequency, and Lagrangian multiplier. The update formula is shown below.

[0031]

[0032] Where, L({u k},{ω k},λ) represents the Lagrangian optimization function, λ represents the Lagrangian operator, α represents the penalty factor, f(t) represents the original signal, represents the sum of all modal components, represents the inner product of the Lagrangian operator and the reconstruction error;

[0033] Step 2.4: Use the alternating direction multiplier method to solve the unconstrained problem. Update the mode function, center frequency, and Lagrange multiplier iteratively. The update formula is as follows:

[0034]

[0035] Where n represents the number of iterations, γ represents the noise tolerance parameter, represents the Fourier transform of the original signal f(t), represents the frequency domain update value of the kth modal component in the n+1th iteration, represents the sum of the modal components except the kth mode in the frequency domain, represents the i-th modal component u i The Fourier transform of (t), represents the Fourier transform of the Lagrange multiplier λ(t), ω represents the frequency component, represents the updated value of the center frequency of the kth mode in the n+1th iteration, Respectively represent the frequency domain update values of the Lagrange multiplier in the nth and n+1th iterations, represents the frequency domain sum of all modal components in the n+1th iteration;

[0036] The above iterative process is terminated when the following conditions are met:

[0037]

[0038] In the formula, ε represents the discrimination accuracy, and ε>0, represents the frequency domain updated value of the kth modal component in the nth iteration.

[0039] Preferably, the step three is specifically:

[0040] Step 3.1: Introduce the perturbation matrix to reduce the influence of noise on the linear prediction coefficient matrix, and construct the perturbation matrix E and the augmented matrix [g|E] of the perturbation matrix to satisfy the Toeplitz structure;

[0041] The linear prediction coefficient matrix a, data matrix Y, prediction matrix y and disturbance matrix E satisfy the following relationship expression:

[0042] (Y+E)a=y+g

[0043] Where a represents the linear prediction coefficient matrix, y represents the prediction matrix, both of which are used to construct the prediction model of the signal, and Y represents the data matrix, which is composed of the sample values of the input signal;

[0044] Step 3.2: Select the noise sampling value at a certain moment as the initial value of the perturbation matrix, and iteratively optimize the linear prediction coefficient of the Prony algorithm;

[0045] The constraints and objective function of the iterative process are set as follows:

[0046]

[0047] Where, F-norm represents the Frobenius norm of the matrix, i.e., the square root of the sum of the squares of the matrix elements, ||g|E|| F The norm of the augmented matrix [g|E] representing the perturbation matrix is used to measure the total energy of noise and perturbation, min||g|E|| F It represents the objective function of minimizing the Frobenius norm of the noise vector g and the disturbance matrix, that is, reducing the influence of noise and disturbance to make the model more stable. W(a) represents the objective function of the linear prediction coefficient.

[0048] Step 3.3: Use the optimized linear prediction coefficients to construct the characteristic polynomial of each modal function;

[0049] Step 3.4: Calculate the modal amplitude A by solving the equations based on the roots of the characteristic polynomial. i , phase θ i , frequency f i and the attenuation factor α i Parameter information to achieve measurement of broadband signals.

[0050] Preferably, the calculation formula corresponding to step 3.1 is as follows:

[0051]

[0052] Where k(n) represents the noise sample value, where n = 0, 1, 2, ..., N-1; E represents the (Np) × p-dimensional perturbation matrix composed of the noise sample values, and [g|E] represents the augmented matrix of the perturbation matrix, [g] = [k(p), k(p+1), ..., k(N-1)] T Represents the noise vector consisting of the pth to N-1th noise sampling values.

[0053] Preferably, the calculation formula corresponding to step 3.3 is as follows:

[0054] z i p +a1z i p-1 +a2z i p-2 +…+a p-1 z i +a p =0

[0055] Where z i is the root of the characteristic polynomial, a j＝ [a1,a2,...,a p ] represents the linear prediction coefficient, and p is the model order.

[0056] Preferably, the calculation formula corresponding to step 3.4 is as follows:

[0057]

[0058] Where b i is a complex parameter, Δt is the sampling interval, Im represents the imaginary part, and Re represents the real part.

[0059] Beneficial effects of the present invention:

[0060] 1. The present invention can effectively distinguish the main frequency components and noise of the signal by combining singular value decomposition (SVD) and Pearson correlation coefficient, so that the order of the model can be accurately determined when applying the Prony algorithm, thereby optimizing the signal measurement process.

[0061] 2. The present invention introduces variational mode decomposition (VMD) to preprocess broadband signals, which can decompose complex broadband signals into multiple intrinsic mode functions with narrowband spectra, thereby simplifying the subsequent processing steps of the signal and improving the efficiency of the algorithm.

[0062] 3. By introducing a perturbation matrix that satisfies the Toeplitz structure and iteratively optimizing the linear prediction coefficients of the Prony algorithm, the present invention can effectively reduce the interference of noise on signal measurement and further improve the robustness of the algorithm in noisy environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is a flow chart of the broadband signal measurement method of the present invention;

[0064] Figure 2 is a total vector error diagram of each method under Gaussian noise interference in an embodiment of the present invention;

[0065] Figure 3 is a total vector error diagram of each method under random pulse noise interference in an embodiment of the present invention;

[0066] Figure 4 3 is a total vector error diagram of each method under power frequency noise interference in an embodiment of the present invention. DETAILED DESCRIPTION

[0067] The present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

[0068] Example 1:

[0069] like Figure 1 As shown, a broadband signal measurement method based on improved Prony includes the following steps:

[0070] Step 1: Perform singular value decomposition (SVD) on the broadband signal, determine the initial singular value cutoff point by the cumulative energy method, introduce the Pearson correlation coefficient to distinguish the main frequency components of the signal from the noise, and thus determine the Prony model order;

[0071] Step 2: Preprocess the broadband signal using variational mode decomposition (VMD). By iteratively solving the variational problem, the complex broadband signal is decomposed into multiple intrinsic mode functions (IMFs) with narrowband spectra, reducing the signal processing cost.

[0072] The complexity of the

[0073] Step 3: Introduce the perturbation matrix that satisfies the Toeplitz structure and iteratively optimize the linear prediction system of the Prony algorithm.

[0074] The Prony algorithm with optimized parameters is used to identify each mode separately, obtain the frequency, amplitude, phase and other information of each mode, and realize the measurement of broadband signals.

[0075] Furthermore, the step 1 is specifically as follows:

[0076] Step 1.1: Construct the sampling values of the broadband signal into an m×n matrix X, and perform singular value decomposition on the matrix X to obtain normalized matrices of order m×m and n×n, and an m×n singular value matrix;

[0077] X=U m×m S m×n V n×n(1)

[0078] Where U and V are normalized matrices of order m×m and n×n respectively, S is a singular value matrix of order m×n, S=[diag(σ1,σ2,…σ r ),0],σ i are singular values, all singular values are non-zero and arranged in descending order, and r is the total number of singular values;

[0079] Step 1.2: Determine an initial singular value cutoff point using the cumulative energy method, and divide the singular value into two parts: one corresponding to the signal of the main frequency, and the other corresponding to the noise and the signal component with an amplitude close to the noise;

[0080]

[0081] Where r is the total number of singular values, η is 0.90, and k is the initial singular value cutoff point;

[0082] Step 1.3: Select the eigenvector corresponding to the first singular value and calculate the Pearson correlation coefficient between the eigenvector corresponding to each singular value after k and the first eigenvector;

[0083] The Pearson correlation coefficient formula can be expressed as:

[0084]

[0085] Where, v1=[v 1,1 ,v 1,2 ,...,v 1,i ] is the first eigenvector; v j =[v j,1 ,v j,2 ,...,v j,i ] is the jth eigenvector; and They are v1 and v j The mean of

[0086] Step 1.4: Determine the model order of the Prony algorithm by taking the value of the Pearson correlation coefficient. If the Pearson correlation coefficient is close to 0 or negative, it is considered to be a pure noise component. Count the number of singular values corresponding to the pure noise component, denoted as m, and the model order is rm.

[0087] Furthermore, the step 2 is specifically as follows:

[0088] Step 2.1: Decompose the broadband signal into multiple natural modes using VMD. Each mode is a finite bandwidth with a center frequency. Perform a Hilbert transform on each modal function to obtain the corresponding spectrum.

[0089]

[0090] Where δ(t) is the pulse function, j represents the imaginary part, and u k (t) represents the mode function, t represents the sampling time;

[0091] Step 2.2: Adjust the spectrum of each mode to the corresponding baseband, calculate the bandwidth of the modal signal, and construct a mathematical model for the variational constraint problem;

[0092]

[0093] Where, ω k Represents the modal function u k The center frequency, e jωkt is a complex exponential function, indicating a frequency of ω k The modulation signal, represents the partial derivative with respect to t, represents the square of the L2 norm, which is used to measure the difference between the modal component and the original signal tone. K represents the total number of modes, that is, the number of modal components into which the signal is decomposed.

[0094] Step 2.3: Introduce the Lagrangian operator λ(t) and the penalty factor α to transform the constrained problem into the corresponding unconstrained problem. Use the alternating direction multiplier method to solve the unconstrained problem, and continuously update the mode function, center frequency, and Lagrangian multiplier. The update formula is shown below.

[0095]

[0096] Where, L({u k},{ω k},λ) represents the Lagrangian optimization function, λ represents the Lagrangian operator, α represents the penalty factor, f(t) represents the original signal, represents the sum of all modal components, represents the inner product of the Lagrangian operator and the reconstruction error;

[0097] Step 2.4: Use the alternating direction multiplier method to solve the unconstrained problem. Update the mode function, center frequency, and Lagrange multiplier iteratively. The update formula is as follows:

[0098]

[0099] Where n represents the number of iterations, γ represents the noise tolerance parameter, represents the Fourier transform of the original signal f(t), represents the frequency domain update value of the kth modal component in the n+1th iteration, represents the sum of the modal components except the kth mode in the frequency domain, represents the i-th modal component u i The Fourier transform of (t), represents the Fourier transform of the Lagrange multiplier λ(t), ω represents the frequency component, represents the updated value of the center frequency of the kth mode in the n+1th iteration, Respectively represent the frequency domain update values of the Lagrange multiplier in the nth and n+1th iterations, represents the frequency domain sum of all modal components in the n+1th iteration;

[0100] The above iterative process is terminated when the following conditions are met:

[0101]

[0102] In the formula, ε represents the discrimination accuracy, and ε>0, represents the frequency domain updated value of the kth modal component in the nth iteration.

[0103] Furthermore, the step three is specifically as follows:

[0104] Step 3.1: Introduce the perturbation matrix to reduce the influence of noise on the linear prediction coefficient matrix, and construct the perturbation matrix E and the augmented matrix [g|E] of the perturbation matrix to satisfy the Toeplitz structure;

[0105]

[0106]

[0107] Where k(n) represents the noise sample value, where n = 0, 1, 2, ..., N-1; E represents the (Np) × p-dimensional perturbation matrix composed of the noise sample values, and [g|E] represents the augmented matrix of the perturbation matrix, [g] = [k(p), k(p+1), ..., k(N-1)] T represents the noise vector consisting of the pth to N-1th noise sampling values;

[0108] The linear prediction coefficient matrix a, data matrix Y, prediction matrix y and disturbance matrix E satisfy the following relationship expression:

[0109] (Y+E)a=y+g (14)

[0110] Where a represents the linear prediction coefficient matrix, y represents the prediction matrix, both of which are used to construct the prediction model of the signal, and Y represents the data matrix, which is composed of the sample values of the input signal;

[0111] Step 3.2: Select the noise sampling value at a certain moment as the initial value of the perturbation matrix, and iteratively optimize the linear prediction coefficient of the Prony algorithm;

[0112] The constraints and objective function of the iterative process are set as follows:

[0113]

[0114] Where, F-norm represents the Frobenius norm of the matrix, i.e., the square root of the sum of the squares of the matrix elements, ||g|E|| F express

[0115] The norm of the augmented matrix [g|E] of the perturbation matrix is used to measure the total energy of noise and perturbation, min||g|E|| F Indicates minimum

[0116] Optimize the Frobenius norm of the noise vector g and the perturbation matrix, that is, reduce the impact of noise and perturbation, making the model more stable

[0117] , W(a) represents the objective function of the linear prediction coefficient;

[0118] Step 3.3: Use the optimized linear prediction coefficients to construct the characteristic polynomial of each modal function;

[0119] z i p +a1z i p-1 +a2z i p-2 +…+a p-1 z i +a p =0 (16)

[0120] Where z i is the root of the characteristic polynomial, a j＝ [a1,a2,...,a p ] represents the linear prediction coefficient, and p is the model order;

[0121] Step 3.4: Calculate the modal amplitude A by solving the equations based on the roots of the characteristic polynomial. i , phase θ i , frequency f i and the attenuation factor α i And other parameter information to achieve the measurement of broadband signals;

[0122]

[0123] Where b i is a complex parameter, Δt is the sampling interval, Im represents the imaginary part, and Re represents the real part.

[0124] Example 2:

[0125] In order to verify the effectiveness of the improved method proposed in this paper, a broadband signal model is established with reference to the broadband signal characteristics. The amplitude, phase angle and frequency of each component in the signal model are all constants.

[0126] To illustrate the advantages of the proposed method, the proposed method is compared with traditional broadband measurement algorithms such as Prony, TLS-Prony, EMD-Prony and CWT. According to the characteristics of broadband signals, a signal model including the fundamental wave and three oscillation frequencies is set. The signal sampling frequency f s The frequency is set to 2560Hz, the simulation time t is set to 0.5s, the fundamental frequency f1 is set to 50Hz, the three oscillation frequencies are 113.5Hz, 294.7Hz and 780Hz respectively, and the amplitude of each frequency component is set to 1. The test signal model is shown in the formula:

[0127]

[0128] Where x(t) is the test signal, A i is the amplitude of the i-th signal component, f i is the frequency of the i-th signal component. To more specifically evaluate the performance of each broadband measurement algorithm, frequency error (FE) and total vector error (TVE) are used for evaluation. Table 1 shows the frequency error measured by different methods.

[0129] Table 1 Frequency errors measured by different methods

[0130]

[0131] Table 1 shows the frequency errors of several methods for measuring four frequency components. While the traditional Prony method accurately estimates the first few low-frequency components, it cannot accurately measure frequencies above 780 Hz. EMD-Prony and CWT perform poorly for measuring the frequency of static signals. TLS-Prony and the proposed method both accurately measure all four frequency components, with frequency errors much lower than those of the other methods.

[0132] Example 3:

[0133] Considering that the actual broadband signal contains noise interference, Gaussian white noise, impulse noise, and power frequency noise are added to the signal model to simulate the actual noise environment. The signal model containing noise is designed as follows:

[0134]

[0135] Where N 50 , N G and N Iare power frequency noise, Gaussian white noise and impulse noise respectively; a, b, c are selection coefficients, with values of 0 or 1, used to select the noise type in the signal model.

[0136] The proposed method is used together with three broadband measurement algorithms, namely EMD-Prony, TLS-Prony and CWT, to measure a signal model containing a single noise type. The total vector error of each method under the interference of Gaussian noise, random pulse noise and power frequency noise is shown as follows: Figure 2 、 Figure 3 and Figure 4 shown.

[0137] from Figure 2 、 Figure 3 and Figure 4 It can be seen that in a high noise environment with a signal-to-noise ratio (SNR) of 1 to 30 dB, the improved Prony algorithm proposed in this paper can ensure accurate measurement of the signal for different types of noise interference, and the measurement accuracy of this method is significantly higher than that of other methods.

[0138] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions set forth in the claims, including equivalent alternatives to the technical features of the technical solutions set forth in the claims. In other words, equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A broadband signal measurement method based on improved Prony, characterized by: The following steps are involved: Step 1: Perform singular value decomposition on the broadband signal, determine the initial singular value cutoff point by the cumulative energy method, introduce the Pearson correlation coefficient to distinguish the main frequency components of the signal from the noise, and thus determine the Prony model order; Step 2: Preprocess the broadband signal using variational mode decomposition. By iteratively solving the variational problem, the complex broadband signal is decomposed into multiple intrinsic mode functions with narrowband spectra, reducing the complexity of signal processing. Step 3: Introduce a perturbation matrix that satisfies the Toeplitz structure, iteratively optimize the linear prediction coefficient of the Prony algorithm, use the parameter-optimized Prony algorithm to identify each mode separately, obtain the frequency, amplitude, and phase information of each mode, and realize the measurement of broadband signals.

2. The broadband signal measurement method based on improved Prony according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1.1: Construct the sampling values of the broadband signal into an m×n matrix X, and perform singular value decomposition on the matrix X to obtain normalized matrices of order m×m and n×n, and an m×n singular value matrix; Step 1.2: Determine an initial singular value cutoff point using the cumulative energy method, and divide the singular value into two parts: one corresponding to the signal of the main frequency, and the other corresponding to the noise and the signal component with an amplitude close to the noise; Step 1.3: Select the eigenvector corresponding to the first singular value and calculate the Pearson correlation coefficient between the eigenvector corresponding to each singular value after k and the first eigenvector; Step 1.4: Determine the model order of the Prony algorithm by taking the value of the Pearson correlation coefficient. If the Pearson correlation coefficient is close to 0 or negative, it is considered to be a pure noise component. Count the number of singular values corresponding to the pure noise component, denoted as m, and the model order is rm.

3. The broadband signal measurement method based on improved Prony according to claim 2, characterized in that: In step 1.1, the calculation formulas for performing singular value decomposition on the matrix X to obtain normalized matrices of m×m and n×n orders and a singular value matrix of m×n order are as follows: X=U m×m S m×n V n×n Where U and V are normalized matrices of order m×m and n×n respectively, S is a singular value matrix of order m×n, S=[diag(σ1,σ2,…σ r ),0],σ i are singular values, all of which are non-zero and arranged in descending order, and r is the total number of singular values.

4. The broadband signal measurement method based on improved Prony according to claim 2, characterized in that: The corresponding calculation formula in step 1.2 is as follows: Where r is the total number of singular values, η is 0.90, and k is the initial singular value cutoff point.

5. The broadband signal measurement method based on improved Prony according to claim 2, characterized in that: In step 1.3, the Pearson correlation coefficient formula is expressed as: Where, v1=[v 1,1 ,v 1,2 ,...,v 1,i ] is the first eigenvector; v j =[v j,1 ,v j,2 ,...,v j,i ] is the jth eigenvector; and They are v1 and v j The mean of .

6. The broadband signal measurement method based on improved Prony according to claim 1, characterized in that: The step 2 is specifically as follows: Step 2.1: Decompose the broadband signal into multiple natural modes using VMD. Each mode is a finite bandwidth with a center frequency. Perform a Hilbert transform on each modal function to obtain the corresponding spectrum. Where δ(t) is the pulse function, j represents the imaginary part, and u k (t) represents the mode function, t represents the sampling time; Step 2.2: Adjust the spectrum of each mode to the corresponding baseband, calculate the bandwidth of the modal signal, and construct a mathematical model for the variational constraint problem; Where, ω k Represents the modal function u k The center frequency, e jωkt is a complex exponential function, indicating a frequency of ω k The modulation signal, represents the partial derivative with respect to t, represents the square of the L2 norm, which is used to measure the difference between the modal component and the original signal tone. K represents the total number of modes, that is, the number of modal components into which the signal is decomposed. Step 2.3: Introduce the Lagrangian operator λ(t) and the penalty factor α to transform the constrained problem into the corresponding unconstrained problem. Use the alternating direction multiplier method to solve the unconstrained problem, and continuously update the mode function, center frequency, and Lagrangian multiplier. The update formula is shown below. Where, L({u k },{ω k },λ) represents the Lagrangian optimization function, λ represents the Lagrangian operator, α represents the penalty factor, f(t) represents the original signal, represents the sum of all modal components, represents the inner product of the Lagrangian operator and the reconstruction error; Step 2.4: Use the alternating direction multiplier method to solve the unconstrained problem. Update the mode function, center frequency, and Lagrange multiplier iteratively. The update formula is as follows: Where n represents the number of iterations, γ represents the noise tolerance parameter, represents the Fourier transform of the original signal f(t), represents the frequency domain update value of the kth modal component in the n+1th iteration, represents the sum of the modal components except the kth mode in the frequency domain, represents the i-th modal component u i The Fourier transform of (t), represents the Fourier transform of the Lagrange multiplier λ(t), ω represents the frequency component, represents the updated value of the center frequency of the kth mode in the n+1th iteration, Respectively represent the frequency domain update values of the Lagrange multiplier in the nth and n+1th iterations, represents the frequency domain sum of all modal components in the n+1th iteration; The above iterative process is terminated when the following conditions are met: In the formula, ε represents the discrimination accuracy, and ε>0, represents the frequency domain updated value of the kth modal component in the nth iteration.

7. The broadband signal measurement method based on improved Prony according to claim 1, characterized in that: The step three is specifically as follows: Step 3.1: Introduce the perturbation matrix to reduce the influence of noise on the linear prediction coefficient matrix, and construct the perturbation matrix E and the augmented matrix [g|E] of the perturbation matrix to satisfy the Toeplitz structure; The linear prediction coefficient matrix a, data matrix Y, prediction matrix y and disturbance matrix E satisfy the following relationship expression: (Y+E)a=y+g Where a represents the linear prediction coefficient matrix, y represents the prediction matrix, both of which are used to construct the prediction model of the signal, and Y represents the data matrix, which is composed of the sample values of the input signal; Step 3.2: Select the noise sampling value at a certain moment as the initial value of the perturbation matrix, and iteratively optimize the linear prediction coefficient of the Prony algorithm; The constraints and objective function of the iterative process are set as follows: Where, F-norm represents the Frobenius norm of the matrix, i.e., the square root of the sum of the squares of the matrix elements, ||g|E|| F The norm of the augmented matrix [g|E] representing the perturbation matrix is used to measure the total energy of noise and perturbation, min||g|E|| F It represents the objective function of minimizing the Frobenius norm of the noise vector g and the disturbance matrix, that is, reducing the influence of noise and disturbance to make the model more stable. W(a) represents the objective function of the linear prediction coefficient. Step 3.3: Use the optimized linear prediction coefficients to construct the characteristic polynomial of each modal function; Step 3.4: Calculate the modal amplitude A by solving the equations based on the roots of the characteristic polynomial. i , phase θ i , frequency f i and the attenuation factor α i Parameter information to achieve measurement of broadband signals.

8. The broadband signal measurement method based on improved Prony according to claim 7, characterized in that: The calculation formula corresponding to step 3.1 is as follows: Where k(n) represents the noise sample value, where n = 0, 1, 2, ..., N-1; E represents the (Np) × p-dimensional perturbation matrix composed of the noise sample values, and [g|E] represents the augmented matrix of the perturbation matrix, [g] = [k(p), k(p+1), ..., k(N-1)] T Represents the noise vector consisting of the pth to N-1th noise sampling values.

9. The broadband signal measurement method based on improved Prony according to claim 7, characterized in that: The calculation formula corresponding to step 3.3 is as follows: z i p +a1z i p-1 +a2z i p-2 +…+a p-1 z i +a p =0 Where z i is the root of the characteristic polynomial, a j＝ [a1,a2,...,a p ] represents the linear prediction coefficient, and p is the model order.

10. The broadband signal measurement method based on improved Prony according to claim 7, characterized in that: The calculation formula corresponding to step 3.4 is as follows: Where b i is a complex parameter, Δt is the sampling interval, Im represents the imaginary part, and Re represents the real part.

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