Accurate frequency estimation method combining amplitude ratio method and interpolation method

Abstract

The invention relates to the technical field of signal processing, in particular to an accurate frequency estimation method combining an amplitude ratio method and an interpolation method, which comprises the following steps of: generating a pulse single-frequency signal with zero filling, and setting a signal frequency value, a pulse width and a total signal length; performing M-point FFT calculation on the received signal to obtain a maximum spectral level position and an adjacent spectral line coefficient, and intercepting a noise segment to estimate noise power; performing coarse frequency estimation through a corrected amplitude ratio method; performing accurate estimation based on a zero-filling improved fractional Fourier coefficient interpolation method; and outputting a final accurate frequency estimation result. According to the method, the problems that the requirement of a fractional Fourier coefficient interpolation method for coarse estimation is high and estimation is inaccurate under the condition that the initial error of a signal frequency domain is large are solved, meanwhile, the problem that an amplitude ratio method does not consider noise power is corrected, and compared with a traditional amplitude ratio method, the accuracy is greatly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of signal processing, in particular to a precise frequency estimation method combining amplitude ratio method and interpolation method. BACKGROUND

[0002] In the field of signal processing, frequency estimation of sinusoidal signals is a fundamental and critical task, widely used in communication, radar, sonar, vibration analysis, and other fields. In particular, in underwater signal processing, single-frequency pulse signals are often used for target detection, Doppler shift measurement, and underwater acoustic communication synchronization. However, in actual engineering, due to factors such as signal truncation, noise interference, and zero-padding, the accuracy of traditional frequency estimation methods is often limited, making it difficult to meet the demand for high-precision measurement.

[0003] 1. Traditional frequency estimation methods and their limitations

[0004] Currently, frequency estimation methods based on Discrete Fourier Transform (DFT) mainly include:

[0005] Peak search method: directly selecting the frequency corresponding to the maximum amplitude of the DFT spectrum as the estimated value. This method is simple, but limited by the spectral resolution, has a "picket-fence effect", and has a large estimation error.

[0006] Interpolation correction method: such as Rife algorithm, Quinn algorithm, etc., using DFT spectral amplitude ratio for interpolation correction to improve estimation accuracy. However, these methods usually assume continuous sampling of the signal, and do not consider the impact of zero-padding on the spectral structure, and their performance decreases under zero-padding signals.

[0007] Iterative optimization method: such as Macleod algorithm, AM algorithm, etc., through iterative approximation of the true frequency, with high computational complexity and sensitivity to initial estimation value, and poor robustness in low signal-to-noise ratio (SNR) environment.

[0008] 2. Special nature of zero-padding signals and shortcomings of existing methods

[0009] Zero-padding is a common spectral refinement technique that increases the number of FFT points by padding zeros in the time domain to improve spectral display resolution. However, zero-padding changes the spectral characteristics of the signal, resulting in:

[0010] Increased spectral leakage: The spectral sidelobe attenuation characteristics of a zero-padding signal are different from those of the original signal, and the correction formula of traditional interpolation algorithms (such as the Rife algorithm) is no longer applicable.

[0011] Changes in noise power distribution: After zero-padding, the statistical characteristics of noise in the frequency domain change, and the traditional ratio method does not consider the impact of noise power, resulting in estimation bias.

[0012] The existing research such as Frequency Estimation for Zero-Padded Signal Based on the Amplitude Ratio of Two DFT Samples proposes a zero-padding signal frequency estimation method based on the DFT amplitude ratio, but still has the following problems:

[0013] Only applicable to high signal-to-noise ratio environment, and the noise power is not compensated;

[0014] The coarse estimation depends on the discrete spectrum line search, and the initial error is large, which affects the subsequent interpolation accuracy.

[0015] On the other hand, the fractional Fourier coefficient interpolation method proposed in Iterative frequency estimation by interpolation on Fourier coefficients has high estimation accuracy, but:

[0016] The spectral characteristics of the zero-padding signal are not considered, and the interpolation formula needs to be re-derived;

[0017] The dependence on coarse estimation is strong, and the initial error is large, which affects the iteration convergence.

[0018] The related technical problems have not been solved. SUMMARY

[0019] In view of the problems in the related art, the present application proposes a precise frequency estimation method combining amplitude ratio method and interpolation method to overcome the above technical problems existing in the prior art. The purpose of the present application is to overcome the problem that the fractional Fourier coefficient interpolation method requires high coarse estimation and is not accurate when the initial error in the signal frequency domain is large. At the same time, the problem of not considering the noise power in the amplitude ratio method is corrected, and the accuracy of the frequency estimation method is greatly improved compared with the traditional amplitude ratio method.

[0020] To achieve the above purpose, the present application provides the following technical scheme: a precise frequency estimation method combining amplitude ratio method and interpolation method, comprising the following steps:

[0021] S1, generate a pulse single-frequency signal with zero padding, set the signal frequency value f0, the pulse width N and the total signal length M;

[0022] S2, perform M-point FFT calculation on the received signal, obtain the maximum spectrum level position p and its adjacent spectrum line coefficients R(p-1), R(p+1), and intercept the noise section to estimate the noise power;

[0023] S3, coarse frequency estimation by modified amplitude ratio method:

[0024] ①Calculate the ratio function g(x) = |R(p+1) / R(p)| and g(x) = |R(p-1) / R(p)|;

[0025] ②Solve the equation in the interval x∈(0, 0.5) and x∈(-0.5, 0) respectively by Newton gradient descent method, get candidate solutions x_r and x_l;

[0026] ③Determine the real frequency direction by comparing the DTFT value, get the coarse estimation frequency Where is the selected solution;

[0027] S4, accurate estimation based on zero padding improved fractional Fourier coefficient interpolation method:

[0028] ①Take the coarse estimation result as the initial value, calculate the closed-form solution of the residual deviation δ:

[0029] δ = (|R(p+1)| - |R(p-1)|) / (4|R(p)| - 2|R(p-1)| - 2|R(p+1)|);

[0030] ②Iteratively correct the frequency estimation value until convergence;

[0031] S5, output the final accurate frequency estimation result

[0032] Preferably, in step S1, the zero padding signal model satisfies:

[0033] The transmitted signal s(t) = exp(j2πf0t) for 0≤t<N, s(t) = 0 for N≤t<M;

[0034] The received signal r(t) = s(t) + n(t), where n(t) is additive white Gaussian noise.

[0035] Preferably, in step S3, the modified amplitude ratio method includes a noise power compensation term, specifically:

[0036] The ratio function is modified to g(x) = (|R(p±1) 2 -σ 2 ) / (|R(p) 2 -σ 2 ), where σ 2 is the estimated noise power;

[0037] Determine the uniqueness interval of the solution by monotonicity analysis.

[0038] Preferably, in step S4, the improved interpolation method adjusts the Fourier coefficient expression for the zero-padding signal:

[0039] Introducing zero padding factor η = N / M, the modified interpolation coefficient is:

[0040]

[0041] The explicit solution of δ is derived by Taylor expansion retaining the first order term.

[0042] Preferably, in step S3, the DTFT value comparison is specifically implemented as:

[0043] Calculate the DTFT value corresponding to the candidate frequency:

[0044] |X(e^(jω))|=|sin(π(ω-ω0)N / fs) / sin(π(ω-ω0) / fs)|;

[0045] Select the direction that makes the DTFT value larger as the real frequency direction.

[0046] Preferably, in step S4, the iteration process includes:

[0047] Set the maximum number of iterations Q;

[0048] Recalculate the interpolation coefficient after updating δ each time;

[0049] Terminate the iteration in advance when |δ^(k+1)-δ^(k)|<ε.

[0050] Preferably, the application of the method in sonar line spectrum estimation includes:

[0051] Realize target Doppler frequency shift measurement through accurate frequency estimation;

[0052] Calculate the target radial velocity in combination with the pulse interval parameter.

[0053] Preferably, the application of the frequency estimation method in underwater acoustic communication Doppler estimation includes:

[0054] Perform frequency estimation on the pilot single-frequency pulse in the received signal;

[0055] Realize dynamic channel tracking through frequency offset compensation.

[0056] The present application also provides the following technical solutions:

[0057] A signal processing device, comprising:

[0058] A signal generation module for generating the zero-padding single-frequency pulse signal of claim 1;

[0059] a processing module configured to perform the frequency estimation method of any one of claims 1-8;

[0060] an output module for displaying or transmitting the estimation result.

[0061] The application also provides the following technical solutions:

[0062] A computer readable storage medium storing a computer program, the program being executed by a processor to implement the steps of the frequency estimation method of any one of claims 1-8.

[0063] Preferably, the two ends of the rotating rod are movably connected to the filter screen I and the filter screen II respectively through bearings.

[0064] Compared with the prior art, the application has the following beneficial effects:

[0065] (1) The application is a precise frequency estimation method combining the amplitude ratio method and the interpolation method, realizes high-precision estimation under zero-padding signals, solves the problem that traditional frequency estimation algorithms are mainly designed for continuous sampling signals and do not consider the influence of zero-padding on the spectrum structure, leading to a decrease in estimation accuracy, modifies the interpolation formula, so that the algorithm can adapt to the spectrum characteristics of zero-padding signals, and under the same signal-to-noise ratio condition, the estimation error is reduced by more than 30% compared with the traditional method, simulation experiments show that when the zero-padding ratio N / M is 1024 / 2048, the mean square error of the method is close to the theoretical Cramer-Rao lower bound, and the performance is better than that of the existing zero-padding special algorithm;

[0066] (2) The application is a precise frequency estimation method combining the amplitude ratio method and the interpolation method, has strong noise robustness, is suitable for low signal-to-noise ratio environments, introduces a noise power compensation mechanism to modify the calculation process of the amplitude ratio method, so that the coarse estimation stage can remain stable when SNR is greater than or equal to -10dB, compared with the ratio method without considering noise, the estimation variance of the method under low signal-to-noise ratio is reduced by about 40%, and in the Doppler estimation of pulse-type underwater acoustic communication signals, the frequency offset estimation error of the method when SNR is 0dB is less than 0.01Hz, meeting the demand for high-precision synchronization;

[0067] (3) The application is a precise frequency estimation method combining the amplitude ratio method and the interpolation method, and the generality of non-zero padding signals is considered, the difference between the MSE and the HAQSE algorithm is less than 5%, avoiding the implementation complexity caused by algorithm switching, and the calculation efficiency is high, suitable for engineering real-time processing, through the combination of coarse estimation and fine estimation, the overall calculation amount is reduced by about 50% compared with the pure iterative algorithm, in the embedded platform test, the time consumption of single frequency estimation is less than 0.5ms (M=2048), meeting the demand for real-time processing of sonar;

[0068] (4) The present application is a precise frequency estimation method combining amplitude ratio method and interpolation method. For single frequency component in ship radiated noise, the frequency resolution of the method under 50% zero padding condition can reach 0.005 Hz (fs=10 kHz), which is 10 times higher than traditional FFT peak value method. In mobile platform (such as AUV) communication, the estimation error of Doppler frequency offset is less than 0.1 Hz (v=5 m / s, carrier frequency 10 kHz), which is significantly better than traditional method based on autocorrelation. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 g (x) for several different parameters l (x), g r (x) ratio function schematic diagram

[0070] Figure 2 Basic idea diagram for solving by amplitude ratio method

[0071] Figure 3 Estimation error and signal-to-noise ratio relationship of different algorithms for non-zero padding signal (a) residual frequency offset 0.25, (b) residual frequency offset 0.45

[0072] Figure 4 Estimation error and residual frequency offset relationship of different algorithms for non-zero padding signal (a) signal-to-noise ratio is 10 dB, (b) signal-to-noise ratio is -10 dB

[0073] Figure 5 Estimation error and signal-to-noise ratio relationship of different algorithms for non-zero padding signal (a) residual frequency offset 0.25, N / M is 1500 / 2048, (b) residual frequency offset 0.45, N / M is 1500 / 2048, (c) residual frequency offset 0.25, N / M is 1024 / 2048, (d) residual frequency offset 0.45, N / M is 1024 / 2048

[0074] Figure 6 Estimation error and residual error relationship of different algorithms for non-zero padding signal (a) SNR=10 dB (b) SNR=-10 dB

[0075] Figure 7 The overall flowchart of the present application. DETAILED DESCRIPTION

[0076] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application.

[0077] EMBODIMENT

[0078] Please refer to Figures 1-7The application provides a precise frequency estimation method combining an amplitude ratio method and an interpolation method.

[0079] S1, generating a pulse single-frequency signal with zero padding, setting a signal frequency value f0, a pulse width N and a total signal length M;

[0080] S2, performing M-point FFT calculation on the received signal, obtaining a maximum spectrum level position p and adjacent spectrum line coefficients R(p-1) and R(p+1) of the position p, and intercepting a noise section to estimate a noise power;

[0081] S3, performing frequency coarse estimation by using a modified amplitude ratio method:

[0082] ① calculating ratio functions g(x)=|R(p+1) / R(p)| and g(x)=|R(p-1) / R(p)|;

[0083] ② solving equations in intervals x∈(0, 0.5) and x∈(-0.5, 0) respectively by using a Newton gradient descent method to obtain candidate solutions x_r and x_l;

[0084] ③ determining a real frequency direction by comparing DTFT values to obtain a coarse estimation frequency wherein is a selected solution;

[0085] S4, performing precise estimation based on a zero-padding improved fractional Fourier coefficient interpolation method:

[0086] ① taking the coarse estimation result as an initial value to calculate a closed-form solution of a residual deviation δ:

[0087] δ=(|R(p+1)|-|R(p-1)|) / (4|R(p)|-2|R(p-1)|-2|R(p+1)|);

[0088] ② iteratively correcting the frequency estimation value until convergence is achieved;

[0089] S5, outputting a final precise frequency estimation result

[0090] Further, in step S1, the zero-padding signal model satisfies:

[0091] a transmitting signal s(t)=exp(j2πf0t) for 0≤t<N, and s(t)=0 for N≤t<M;

[0092] a received signal r(t)=s(t)+n(t), wherein n(t) is additive white Gaussian noise.

[0093] Further, in step S3, the modified amplitude ratio method contains a noise power compensation term, specifically:

[0094] The ratio function is modified to g(x) = (|R(p±1)| 2 -σ 2 ) / (|R(p)| 2 -σ 2 ), where σ 2 is the estimated noise power;

[0095] The uniqueness interval of the solution is determined by monotonicity analysis.

[0096] Further, in step S4, the improved interpolation method adjusts the Fourier coefficient expression for zero-padding signals:

[0097] A zero-padding factor η = N / M is introduced, and the modified interpolation coefficient is:

[0098]

[0099] The explicit solution of δ is derived by Taylor expansion retaining the first-order term.

[0100] Further, in step S3, the DTFT value comparison is specifically implemented as:

[0101] The DTFT value corresponding to the candidate frequency is calculated:

[0102] |X(e^(jω))| = |sin(π(ω-ω0)N / fs) / sin(π(ω-ω0) / fs)|;

[0103] The direction that makes the DTFT value larger is selected as the real frequency direction.

[0104] Further, in step S4, the iterative process includes:

[0105] Set the maximum number of iterations Q;

[0106] After updating δ each time, the interpolation coefficient is recalculated;

[0107] When |δ^(k+1)-δ^(k)| < ε, the iteration is terminated in advance.

[0108] Further, the application of the method in sonar line spectrum estimation includes:

[0109] Accurate frequency estimation is achieved to measure the target Doppler shift;

[0110] The target radial velocity is calculated in combination with the pulse interval parameter.

[0111] Further, the frequency estimation method is applied in the Doppler estimation of underwater acoustic communication, and the application comprises the following technical solutions:

[0112] The frequency estimation method is applied in the Doppler estimation of underwater acoustic communication, and the application comprises the following technical solutions:

[0113] The frequency estimation method is applied in the Doppler estimation of underwater acoustic communication, and the application comprises the following technical solutions:

[0114] The application further provides the following technical solutions:

[0115] The application further provides the following technical solutions:

[0116] The application further provides the following technical solutions:

[0117] The application further provides the following technical solutions:

[0118] The application further provides the following technical solutions:

[0119] In the embodiment, a sine signal model with zero padding is provided based on the assumption of signal zero padding, and the signal model is as follows: M is the total length of the signal, and N is the length of the non-zero part.

[0120]

[0121] In the above formula, is a transmission signal with zero padding, is a received signal with zero padding, f0 is a signal frequency, p is a frequency index coefficient, is an integer, x is an initial deviation, and |x|≤0.5, so that the Fourier transform result of the received signal is as follows:

[0122]

[0123] Similarly, the Fourier transform result of the transmission signal is as follows:

[0124]

[0125] 2, frequency coarse estimation based on the ratio method

[0126] Ignoring the influence of noise, the signal is analyzed first, and the non-zero part of the signal is as follows: The FFT estimation result of the single-frequency signal with zero padding can be written as:

[0127]

[0128] The term unrelated to p is arranged out, φ is set as θ+πx(N-1) / (M-1), and the influence of the FFT coefficient is a constant value, and the above formula can be further simplified as:

[0129]

[0130] Here p is the index of the FFT coefficient, so it is an integer, so we can get:

[0131]

[0132] Then we can get the adjacent FFT coefficients of the signal peak value coefficient as:

[0133]

[0134] Note that the adjacent FFT coefficients of the signal peak value coefficient can be easily obtained, and according to and We can get:

[0135]

[0136] In the above formula, g(x) is the defined ratio function, and then two intervals get two different ratio functions respectively:

[0137]

[0138] For the FFT coefficient of the signal, it can be obtained by receiving the signal:

[0139]

[0140] Since the power of the Gaussian white noise at each frequency point is almost the same, we think that the value of at each frequency point is the same, and we assume that the signal-to-noise ratio SNR is known, so we assume it as a constant related to the signal-to-noise ratio as a correction term, so the problem is converted to solve the following two equations.

[0141]

[0142] However, the above formula is not a linear equation, and it is difficult to get a closed-form solution of the above formula, but according to the attached Figure 1 , we can see that when -0.5 < x < 0, g(x) is monotonically decreasing, and when 0 < x < 0.5, this function is monotonically increasing. In the corresponding interval, according to the characteristics of the function having monotone increasing or monotone decreasing, Newton gradient descent method can be used to solve the corresponding value. Then the problem shifts to how to obtain the corresponding function value and the corresponding function, that is, how to determine whether the true value is on the left side or the right side of the peak value.

[0143] According to the attached Figure 2It can be seen that, whether the real value is on the left or right of the peak, we can consider that the real frequency point is between the maximum FFT coefficient point and the second point, and we can get two different x values by assuming x in the two intervals respectively, and then we can get the corresponding xr or xl by substituting into (17) (18). So what we have to do is to calculate the x value according to the g(x) value obtained by the ratio. Obviously, the x solution corresponding to a g(x) is not unique, and according to this value, we can get two x values, one of which is in (-0.5, 0) and the other is in (0, 0.5). We can also naturally get two different frequency values f r And f l .

[0144] According to the definition of DTFT:

[0145]

[0146] And the calculated frequency value, the DTFT value corresponding to the received signal can be calculated, and the DTFT value corresponding to the received signal can be calculated from the appendix Figure 3 It can be seen that the real frequency value should be near the maximum value of DTFT, so by comparing the size of the two DTFT values, we can determine which direction the real frequency value is more consistent with. By comparing the calculated DTFT values, it is considered that the estimated frequency is in the direction where it is greater.

[0147] So far, the rough estimation of the received signal based on the amplitude ratio method has been completed.

[0148] 3. Frequency accurate estimation based on iterative interpolation of Fourier coefficients

[0149] In the literature "Iterative frequency estimation by interpolation on Fourier coefficients", the method of iterative interpolation of rough estimated signal to ±0.5 on both sides is used for accurate estimation. From the simulation, it can be seen that for zero padding signal, the improvement of the accurate estimation method for rough estimation is weak, and the method is improved on the basis of the method.

[0150] On the premise of rough estimation of frequency based on improved ratio method, the improved iterative FFT coefficient interpolation algorithm is used again to accurately estimate the frequency error compensation of the signal.

[0151]

[0152] Among them, is the rough estimated DFT coefficient, that is, p+x r or p+x l, δ is the residual error. As mentioned above, δ is generally in the range [-0.5, 0.5].

[0153] First, calculate the DFT coefficients at the coarse estimate of Δp:

[0154]

[0155] As mentioned above, when k is greater than N, s(k) = 0, and the value is adjusted for zero padding:

[0156]

[0157] Substitute s(k) into the above equation, and use the summation formula of a geometric sequence to obtain:

[0158]

[0159] Because δ - Δp · M, according to the principle of equivalent infinitesimal, (22) can be transformed into:

[0160]

[0161] In order to make independent of Δp, take Then we can get:

[0162] Let be b, we can get:

[0163]

[0164] Because Ignoring the effect of noise, we can get:

[0165]

[0166] Thus, we can get the accurate estimation of the residual frequency deviation.

[0167] 4. Overall algorithm flow

[0168] Combining the coarse estimate and the accurate estimate, we can get the complete frequency estimation method as follows:

[0169] Step 1: Perform M-point FFT calculation

[0170] First, we perform M-point FFT calculation on the received signal to obtain the maximum spectral level position, denoted as R(p), and record its adjacent spectral line coefficients R(p-1), R(p+1), and intercept a segment of noise signal to estimate the noise power W P ;

[0171] Step 2: Obtain a coarse frequency estimate using the modified amplitude ratio method.

[0172] The result was obtained using Newton's method. The solution is x. l , and f l =(p+x) l )Δf;

[0173] The result was obtained using Newton's method. The solution is x. r , and f r =(p+x) r )Δf;

[0174] Calculate D(f) respectively l ), D(f r And compare their sizes;

[0175] If |D(f l )|>|D(f r If |, then x c =x l ;

[0176] Otherwise x c =x r ;

[0177] A rough estimate is obtained: f c =(p+x) c )Δf, and the coarse index value is

[0178] Step 3: Obtain accurate frequency estimates using zero-padding-based iterative FFT interpolation.

[0179] Accurate frequency estimation based on FFT interpolation algorithm:

[0180] Assumption

[0181] Cycle from 1 to Q

[0182]

[0183] Step Four:

[0184] The accurate frequency estimation results are obtained:

[0185]

[0186] 5. Algorithm Performance Analysis

[0187] The method proposed in this paper is mainly aimed at the accurate frequency estimation of single frequency signal with zero padding, and two main DFT coefficient-based algorithms are modified and combined, which not only overcomes the shortcomings of traditional interpolation algorithm that can only perform well in the case of small residual frequency error, but also further improves the performance of the adjacent DFT coefficient ratio method to achieve higher estimation accuracy.

[0188] First, the data simulation experiment is carried out for the algorithm, and the comparison with other accurate estimators under the conditions of no zero padding and zero padding signal is discussed. In each Monte Carlo simulation, the simulation error obtained is:

[0189]

[0190] It is worth noting that in the case of zero padding, the theoretical CRLB does not have a closed-form solution given by related scholars, so the comparison results in this paper are the CRLB values of non-zero padding signals. Theoretically, the performance improvement of the interpolation algorithm should be related to the proportion of zero padding, and the calculated result is Substitute M and N, we can get:

[0191]

[0192] Assuming that the influence of this correction term is caused by zero padding, we can get the log ACRLB:

[0193]

[0194] As can be seen from the foregoing, the iterative interpolation frequency estimation algorithm based on amplitude ratio method proposed in this paper is based on the amplitude ratio method of two DFT samples in the literature, which is combined with the improved fractional Fourier coefficient interpolation algorithm. The amplitude ratio method algorithm is simple to calculate and easy to implement, but since the DTFT coefficient calculation uses Newton's method instead of the closed-form solution, there is a certain error. Therefore, we use the maximum spectrum line adjacent to the spectrum line to perform coarse estimation based on the amplitude ratio method, which is used as the initial value of the iterative algorithm. The fine estimation no longer uses the ratio method, but uses the improved fractional Fourier coefficient interpolation iterative method for accurate estimation. In this way, not only does it solve the problem of insufficient accuracy of the amplitude ratio method and the lack of theoretical error value, but it also compensates for the sensitivity of the interpolation iterative method to coarse estimation.

[0195] 5.1 Improved interpolation algorithm and commonly used algorithm applied to non-zero padding signal simulation

[0196] This section mainly carries out some common algorithm and the performance comparison of the algorithm proposed in this paper, in order to facilitate the expression, the algorithm proposed in this paper is represented by using the form of abbreviation (MARD-FFCI). Among them, the comparison algorithm includes the basic algorithm of this algorithm, fractional Fourier coefficient interpolation method (FFCI), amplitude interpolation method (MOI), classical iterative interpolation algorithm (AM), the estimation algorithm with good performance in recent years, QSE and HAQSE algorithm in the literature "A. Fast and efficient sinusoidal frequency estimation by using the DFT coefficients", and the amplitude ratio method algorithm (ARD) which is the best algorithm under the condition of zero padding at present.

[0197] Appendix Figure 3 The simulation parameters are as follows: SNR = -20:30dB, fs = 2048, FFT point number and signal length are N = 1024, initial phase is random, f = (16 + δ) * Δf, and Monte Carlo number is 50000.

[0198] Appendix Figure 3 It is for the simulation of different signal-to-noise ratios under the condition of fixed frequency deviation. It can be seen that under the condition of non-zero padding and small frequency residual, many algorithms have good estimation performance, and most of them can accurately estimate the frequency of the sinusoidal signal under the condition of signal-to-noise ratio above -10dB. The performance of the algorithm proposed in this paper is basically not inferior to the known frequency estimation algorithms. Figure 3 (a) Local magnification can be seen that the traditional non-iterative fractional interpolation algorithm has a performance difference compared with the later improved algorithm, but it is within an acceptable range. However, the fractional Fourier coefficient interpolation algorithm is more sensitive to residual frequency deviation compared with the later algorithm, that is, there is a significant performance difference under different δ values. The performance decreases obviously when the frequency residual is 0.45, and the signal-to-noise ratio performance of the algorithm proposed in this paper is basically not inferior to the known frequency estimation algorithms.

[0199] In order to verify the algorithm performance simulation of different δ values, the following parameters are simulated: δ = -0.5:0.05:0.5, fs = 2048, FFT point number and signal length are N = 1024, initial phase is random, f = (16 + δ) * Δf, and Monte Carlo number is 50000.

[0200] From the appendix Figure 4 It can be seen that under the condition of high signal-to-noise ratio, most of the frequency estimation algorithms can achieve relatively stable and accurate frequency estimation except the traditional non-iterative frequency domain interpolation algorithm. However, under the condition of low signal-to-noise ratio, few algorithms can achieve as stable as the algorithm proposed in this paper. It can be seen that the algorithm proposed in this paper has very good estimation performance even under the condition of non-zero padding signal.

[0201] 5.2 Improved interpolation algorithm and commonly used algorithm applied to zero padding signal simulation

[0202] In order to verify the performance of the algorithm proposed in this paper and part of the algorithm for zero padding signal, the algorithm simulation and performance analysis are carried out for zero padding signal. The basic parameters are consistent with the previous ones, but the zero padding signal with different duty cycles is used in this simulation. The simulation results are shown in the following figures. Figure 5 .

[0203] From the figures Figure 5 It can be seen that most of the current algorithms have poor frequency estimation effect for zero padding signal, while the MARD-FFCI algorithm can effectively estimate the zero padding signal, and the amplitude ratio method algorithm can estimate the zero padding signal to a certain extent, but the estimation performance is better under the condition of high duty cycle. Once the duty cycle of the signal is reduced, the gap with the algorithm proposed in this paper becomes more obvious.

[0204] The Figure 6 is the accurate frequency estimation result of the zero padding signal from the perspective of high signal-to-noise ratio and low signal-to-noise ratio. The basic simulation parameters are the same as before. From the figures, it can be seen that under the condition of low signal-to-noise ratio or high signal-to-noise ratio, the MARD-FFCI algorithm can effectively estimate the frequency value, and the MSE obtained by estimation is consistent with the error of non-zero padding signal and theoretical calculation. Correspondingly, other high-precision estimation algorithms are basically invalid under the condition of zero padding, and the defect of being sensitive to residual is exposed under the condition of zero padding. For the amplitude ratio method for zero padding signal, there is a significant performance difference with the present invention, and the performance is not very stable under the condition of low signal-to-noise ratio, which is more different from the present invention.

[0205] In summary, in various simulations, the accurate frequency estimation method for single-frequency pulse signal based on amplitude ratio method coarse estimation and fractional Fourier coefficient interpolation method proposed in the present invention can obtain good results.

[0206] In the description of the present invention, it should be understood that the terms "coaxial", "bottom", "one end", "top", "middle", "the other end", "upper", "one side", "top", "inner", "front", "central", "both ends" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present invention.

[0207] In the present application, unless otherwise explicitly specified and limited, the terms "mounting", "setting", "connecting", "fixing", "screwing" and the like should be understood in a broad sense, for example, can be fixed connection, can also be detachable connection, or integrated; can be mechanical connection, can also be electrical connection; can be directly connected, can also be indirectly connected through an intermediate medium, can be the internal communication of two elements or the interaction relationship of two elements, unless otherwise explicitly limited, the person skilled in the art can understand the specific meaning of the above-mentioned terms in the present application according to the specific circumstances.

[0208] Although the embodiments of the present application have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present application, and the scope of the present application is defined by the appended claims and their equivalents.

Claims

1. A method of accurate frequency estimation combining the amplitude-ratio method and the interpolation method, characterized by, The method comprises the following steps: S1, generating a pulse single-frequency signal with zero padding, setting signal frequency value f0, pulse width N and total signal length M; S2, performing M-point FFT calculation on the received signal to obtain the maximum spectral level position p and its adjacent spectral line coefficients R(p-1) and R(p+1), and intercepting the noise section to estimate the noise power; S3, performing frequency coarse estimation by the modified amplitude ratio method: ① Calculate the ratio function g(x)=|R(p+1) / R(p)| and g(x)=|R(p-1) / R(p)|; ②Solve the equation in the interval x∈(0, 0.5) and x∈(-0.5, 0) respectively by using Newton gradient descent method to obtain candidate solutions x_r and x_l; ③ Determine the real frequency direction by comparing the DTFT values, and get the coarse estimated frequency wherein is the selected solution; S4, performing accurate estimation based on the improved fractional Fourier coefficient interpolation method of zero padding: ① Based on the rough estimate Using the initial values, calculate the closed-form solution for the residual deviation δ: δ=(|R(p+1)|-|R(p-1)|) / (4|R(p)|-2|R(p-1)|-2|R(p+1)|); ②Iteratively correct the frequency estimation value until convergence; S5, output the final accurate frequency estimation result 2. The method of claim 1, wherein the method is characterized by: In step S1, the zero padding signal model satisfies: The transmitted signal s(t) = exp(j2πf0t) for 0≤t<N, s(t) = 0 for N≤t<M; The received signal r(t) = s(t) + n(t), where n(t) is additive white Gaussian noise.

3. The method of claim 1, wherein the method is characterized by: In step S3, the modified amplitude ratio method includes a noise power compensation term, specifically: The ratio function is modified to g(x) = (|R(p±1)|2- σ 2 ) / (|R(p)|2- σ 2 ), where σ 2 is the estimated noise power; Determine the uniqueness interval of the solution through monotonicity analysis.

4. The method of claim 1, wherein the method is characterized by: In step S4, the improved interpolation method adjusts the Fourier coefficient expression for the zero padding signal: Introduce the zero padding factor η = N / M, and modify the interpolation coefficient as: Deduce the explicit solution of δ by Taylor expansion retaining the first-order term.

5. The method of claim 1, wherein the method is characterized by: In step S3, the DTFT value comparison is specifically implemented as: Calculate the DTFT value corresponding to the candidate frequency: |X(e^(jω))|=|sin(π(ω-ω0)N / fs) / sin(π(ω-ω0) / fs)|; Select the direction that makes the DTFT value larger as the real frequency direction.

6. The method of claim 1, wherein the method is characterized by: In step S4, the iteration process includes: Set the maximum number of iterations Q; Update the interpolation coefficient after each iteration; Terminate the iteration in advance when |δ^(k+1)-δ^(k)|<ε.

7. The method of claim 1, wherein the method is characterized by: The application of the method in sonar line spectrum estimation includes: Realize target Doppler frequency shift measurement through accurate frequency estimation; Calculate the target radial velocity in combination with the pulse interval parameter.

8. The method of claim 1, wherein the method is characterized by: The application of the frequency estimation method in underwater acoustic communication Doppler estimation includes: Perform frequency estimation on the pilot single-frequency pulse in the received signal; Realize dynamic channel tracking through frequency offset compensation.

9. A signal processing device, characterized by It comprises: A signal generation module for generating the zero padding single-frequency pulse signal of claim 1; A processing module configured to perform the frequency estimation method of any one of claims 1-8; An output module for displaying or transmitting the estimation result.

10. A computer readable storage medium storing a computer program, characterized in that, The program is executed by the processor to realize the steps of the frequency estimation method of any one of claims 1-8.

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