Frequency spectrum correction method based on sinc function fitting

Abstract

The invention provides a spectrum correction method based on sinc function fitting, which is suitable for a wind speed measurement scene of a coherent wind lidar. According to the method, firstly, zero-padding FFT and frequency spectrum accumulation operation are carried out on echo signals, and the distinguishability of signal frequency spectrums is enhanced through double means; secondly, for an echo signal corresponding to each range gate, background noise deduction operation is further executed, and superimposed interference of background noise on spectrum features is effectively weakened; the distribution characteristic of the processed signal spectrum is highly matched with the sinc function. Based on the characteristic, least square fitting is carried out on the frequency spectrum by adopting a sinc function, and through deviation compensation and accurate correction, the frequency estimation error is remarkably reduced, and finally the estimation accuracy of Doppler frequency shift is improved. The method mainly solves the technical bottleneck of poor correction effect of a frequency spectrum correction algorithm under the condition of low signal-to-noise ratio, and remarkably improves the wind speed measurement accuracy of the coherent wind lidar in a complex signal environment.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of measurement test technology, and in particular to a spectrum correction method based on sinc function fitting. BACKGROUND

[0002] In the key fields of low-altitude meteorological support, aircraft take-off and landing safety, wind farm operation and maintenance, etc., wind measurement radar is the core equipment for obtaining high-precision wind field information. Its work is based on the Doppler effect, and the accurate extraction and frequency measurement of the echo signal spectrum are the core link of high-precision inversion of wind field parameters, which directly determines the overall measurement error of the wind measurement radar. However, in actual application, due to the limitations of radar hardware performance, atmospheric environmental interference, etc., the traditional spectrum estimation method represented by FFT faces two major problems: first, the signal energy spreads and the main peak broadens due to spectrum leakage; second, the real frequency may fall between the resolution interval and cannot be captured due to the fence effect. Both of them together cause insufficient frequency estimation accuracy, which ultimately increases the wind field velocity measurement error.

[0003] To solve this defect, the industry has developed various spectrum correction algorithms to improve the accuracy of real frequency estimation by correcting the preliminary results of FFT, among which the energy centroid method and the ratio correction method are widely used: The energy centroid method: the spectrum of the Doppler time domain signal multiplied by the window function is equivalent to the shift of the window function spectrum to the Doppler frequency. By using the energy centroid characteristics of the window function, the main lobe center position can be accurately obtained through several spectral lines with larger power spectrum values in the main lobe, and then the Doppler shift is obtained.

[0004] The ratio correction method: an equation is constructed by the ratio of the amplitudes of the two adjacent frequency spectra at the top of the main lobe of the window function spectrum, the correction amount of frequency estimation is solved, and then the center frequency value is calculated.

[0005] The former has simple principle and small calculation amount, and can quickly realize preliminary correction in the scene of high signal-to-noise ratio and obvious spectrum main peak characteristics; the latter can still maintain high correction accuracy in the scene of low signal-to-noise ratio and serious spectrum interference, and is suitable for complex observation environment.

[0006] At present, the two types of algorithms have become an important part of wind measurement radar signal processing, but there is still room for optimization in actual application: the energy centroid method is sensitive to the selection range of the spectrum main peak, and improper selection may increase the correction error; the ratio correction method depends on the assumption of a specific spectrum model, and when the echo spectrum deviates from the ideal model due to multi-target scattering, non-stationary interference, etc., the correction accuracy decreases significantly.

[0007] Therefore, a new type of spectrum correction algorithm with higher accuracy suitable for wind measurement laser radar is needed. SUMMARY

[0008] The present application is to solve the problem of wind measurement laser radar spectrum correction accuracy, provide a kind of based on the spectrum correction method of sinc function fitting, by introducing sinc function fitting model, can be targeted to solve the technical pain point of insufficient spectrum correction accuracy in low signal-to-noise ratio scene, effectively optimize the wind field detection accuracy of coherent wind measurement laser radar.

[0009] The present application provides a kind of based on the spectrum correction method of sinc function fitting, comprising the following steps: S1, the echo signal of coherent wind measurement laser radar is sampled to obtain discrete signal, and the time domain signal is converted to frequency domain by FFT for spectrum estimation processing; When the sampling length does not satisfy 2 p , the total length satisfies 2 p by zero padding preprocessing, and p is a positive integer; S2, when non-coherent accumulation, only the amplitude information of echo signal is used to accumulate and average to obtain the frequency domain amplitude after non-coherent accumulation; S3, the echo signal of the last range gate is used as substrate noise, and the power spectrum of the echo signal of each range gate is subtracted from the power spectrum of the substrate noise, background noise removal is carried out, and preprocessed discrete spectrum point is obtained; S4, the least square method is fitted to all preprocessed discrete spectrum points to obtain parameters , , is the discrete index of spectrum, and the discrete spectrum point index corresponding to the spectrum peak value , correction amount , the corrected Doppler frequency .

[0010] The spectrum correction method based on sinc function fitting provided by the present application, as a preferred mode, only the frequency domain amplitude of L pulses accumulated in the same range gate is accumulated and averaged in step S2: ; Wherein, is the frequency domain amplitude of single pulse echo signal after FFT, .

[0011] The spectrum correction method based on sinc function fitting provided by the present application, as a preferred mode, in step S3, ; Wherein, is the power spectrum of the Lth range gate after accumulation and average, , , is the total number of range gates, is frequency variable, .

[0012] The spectrum correction method based on sinc function fitting, as a preferred mode, in step S3, the pre-processed discrete spectrum points are signal spectrum with sinc function distribution characteristics.

[0013] The spectrum correction method based on sinc function fitting, as a preferred mode, in step S4, ; Wherein, is the discrete spectrum point index corresponding to the spectrum peak, is the sampling frequency, The number of points of FFT, N is 2 p ; .

[0014] The spectrum correction method based on sinc function fitting, as a preferred mode, in step S4, the least square fitting method is: calculating the discrete inner product between sinc base functions, constructing the coefficient matrix of normal equation group ; calculating the discrete inner product between sinc base functions and spectrum data, constructing vector ; solving the normal equation group , obtaining the parameters a, b, c, d of the sinc model; Wherein, , is the undetermined parameter column vector; , is the column vector composed of the inner product between base functions and target functions; , Undetermined fitting parameters, is the fitted base function, is the number of base functions.

[0015] The spectrum correction method based on sinc function fitting, as a preferred mode, using residual sum of squares to measure the fitting effect: ; Wherein, n is the total number of discrete data ; ; The smaller the value is, the smaller the deviation between the fitting result and the actual data is, and the better the fitting effect is; For Regarding each undetermined parameter , the partial derivative is solved and set to 0, that is , gTo find the specific coefficients of the partial derivative, .

[0016] The spectral correction method based on sinc function fitting described in this invention, as a preferred embodiment, uses the discrete inner product between sinc basis functions as follows: ; It is a matrix composed of the inner products of basis functions.

[0017] The spectral correction method based on sinc function fitting described in this invention, as a preferred embodiment, uses the discrete inner product of the sinc basis function and the spectral data as follows: ; Wherein, objective function .

[0018] This invention provides a spectrum correction algorithm based on sinc function fitting, applicable to wind speed measurement scenarios in coherent wind lidar. First, the invention performs zero-padding FFT and spectrum accumulation operations on the echo signal, enhancing the distinguishability of the signal spectrum through these two methods. Second, for the echo signal corresponding to each range gate, a background noise subtraction operation is further performed, effectively reducing the superposition interference of background noise on the spectral characteristics. The signal spectrum after the above processing exhibits distribution characteristics that highly match the sinc function. Based on this characteristic, the spectrum is fitted using the least squares method with the sinc function, and through deviation compensation and precise correction, the frequency estimation error is significantly reduced, ultimately improving the estimation accuracy of Doppler frequency shift. This invention mainly solves the technical bottleneck of poor correction effect of spectrum correction algorithms under low signal-to-noise ratio conditions, significantly improving the wind speed measurement accuracy of coherent wind lidar in complex signal environments.

[0019] In low signal-to-noise ratio (SNR) scenarios, the spectral correction performance of the energy centroid method and ratio correction method significantly decreases. Therefore, this invention proposes a novel spectral correction algorithm suitable for coherent wind lidar. This algorithm is simple to implement, has a fast computation speed, and maintains high frequency estimation accuracy even under low SNR conditions. After zero-padded FFT and cumulative averaging, the echo signal exhibits a sinc function-like spectrum. The discrete points of the spectrum can be fitted using the sinc function with the least squares method (preferably, the magnitudes of the seven points at the center of the spectral peaks are fitted). The center frequency position is then calculated using the fitted sinc function model, which is subsequently converted into radial wind speed.

[0020] This invention performs zero-padding FFT and cumulative denoising on the echo signal, resulting in a spectrum with sinc function-like distribution characteristics. The sinc function is then used for least squares fitting, and through bias compensation and precise correction, the estimated Doppler frequency shift value is obtained.

[0021] The present application has the following advantages: (1) The present application carries out zero padding FFT processing, which not only solves the limitation of FFT on sampling length and realizes flexible adaptation, but also relieves the "fence effect" by reducing the spectral line interval and improves the initial accuracy of frequency estimation; (2) The present application uses multi-pulse power spectrum accumulation and average, utilizes non-phase accumulation characteristics, effectively suppresses noise random interference, enhances weak signal detection capability, and adapts to signal changes caused by aerosol particle density fluctuations; (3) The present application is based on the last distance gate noise denoising, which accurately and effectively filters out the background noise in the power spectrum, improves the spectral purity, and lays a foundation for subsequent fitting correction; (4) The present application provides a spectrum correction method based on sinc function fitting, which can still maintain high frequency estimation accuracy under low signal-to-noise ratio conditions, and is simple to implement, fast in operation, and significantly improves the wind field detection accuracy and reliability of coherent wind lidar. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 A flowchart of a spectrum correction method based on sinc function fitting; Figure 2a An original signal diagram; Figure 2b A signal diagram after the original signal is subjected to FFT transformation in a spectrum correction method based on sinc function fitting; Figure 2a Figure 3a A spectrum diagram before zero padding FFT processing in a spectrum correction method based on sinc function fitting; Figure 3b An FFT spectrum diagram after the spectrum diagram in the middle is zero padded to 256 points in a spectrum correction method based on sinc function fitting; Figure 3a Figure 3c An FFT spectrum diagram after the spectrum diagram in the middle is zero padded to 512 points in a spectrum correction method based on sinc function fitting; Figure 3a Figure 3d An FFT spectrum diagram after the spectrum diagram in the middle is zero padded to 1024 points in a spectrum correction method based on sinc function fitting; Figure 3a Figure 4a A spectrum diagram before accumulation in a spectrum correction method based on sinc function fitting; Figure 4b A spectrum diagram after the spectrum is accumulated 100 times in a spectrum correction method based on sinc function fitting; Figure 4a Figure 4c A spectrum diagram after the spectrum is accumulated 1000 times in a spectrum correction method based on sinc function fitting; Figure 4a ​​​​​​Figure 4d A spectrum correction method based on sinc function fitting is used to correct the spectrum Figure 4a Spectrum after 10000 times of spectrum accumulation Figure 5a A spectrum correction method based on sinc function fitting 80MHz-55dBm spectrum graph without deducting noise Figure 5b A spectrum correction method based on sinc function fitting 80MHz-55dBm spectrum graph after deducting noise Figure 5c A spectrum correction method based on sinc function fitting 80MHz-65dBm spectrum graph without deducting noise Figure 5d A spectrum correction method based on sinc function fitting 80MHz-65dBm spectrum graph after deducting noise Figure 6a A spectrum correction method based on sinc function fitting Error simulation condition diagram of three spectrum correction algorithms when SNR is-5dB Figure 6b A spectrum correction method based on sinc function fitting Error simulation condition diagram of three spectrum correction algorithms when SNR is-20dB Figure 7a A spectrum correction method based on sinc function fitting Error simulation condition diagram of three spectrum correction algorithms when SNR is-50dBm Figure 7b A spectrum correction method based on sinc function fitting Error simulation condition diagram of three spectrum correction algorithms when SNR is-70dBm DETAILED DESCRIPTION

[0023] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, not all embodiments. Embodiment 1

[0024] As shown in the drawings, Figure 1 A spectrum correction method based on sinc function fitting includes the following steps: Step S1, sample the coherent wind measurement laser radar echo signal to obtain a discrete signal, and convert the time domain signal to the frequency domain by FFT for spectrum estimation processing.

[0025] FFT conversion, according to the dimension extraction is divided into time extraction and frequency extraction two kinds, through the sequence decomposition into shorter sub-sequence to simplify the operation; According to the number of butterfly unit can be further divided into base-2, base-4, base-8 method, the total operation amount is consistent. But FFT has "fence effect" - only when the signal frequency is an integer multiple of FFT frequency resolution, the frequency estimate value is accurate.

[0026] In order to improve the precision, reduce the interval between adjacent spectral lines, the echo signal needs to be zero-filled. After zero padding, the sampling length increases and the spectral line interval decreases, which not only improves the frequency estimation accuracy, but also makes the sampling length selection more flexible.

[0027] When the sampling length does not satisfy 2 p (p is a positive integer), the total length satisfies 2 p by zero padding preprocessing, which not only reduces the interval between adjacent spectral lines to improve the initial accuracy of frequency estimation, but also widens the range of sampling length selection to achieve flexible adaptation.

[0028] Step S2, in order to enhance the signal-to-noise ratio of weak signal detection, the power spectrum of multiple pulses needs to be accumulated and averaged. In theory, the coherent accumulation of L pulses can improve the signal-to-noise ratio by L times, and the performance is better than that of non-coherent accumulation, but the radar receiver often receives the echo of many moving targets. Due to the fluctuation of moving target echo signal, the coherence of the phase between signals is difficult to maintain, and the coherent accumulation is difficult to achieve ideal effect.

[0029] In view of the low signal-to-noise ratio problem of echo signal caused by environmental noise, circuit noise and other factors, the frequency spectrum of multiple pulse echo data of the same range gate is calculated and accumulated and averaged, and the non-coherent superposition of multi-pulse energy is used to improve the signal detection probability.

[0030] Non-coherent accumulation only uses the amplitude information of echo signal, which can be realized by accumulating the frequency spectrum of echo signal, and is more suitable for real-time monitoring of wind speed of coherent wind measurement laser radar. Spectrum accumulation is the core step of non-coherent accumulation, and after eliminating the phase information, only the frequency domain amplitude of multi-pulse echo is accumulated and averaged.

[0031] Let the frequency domain amplitude of single pulse echo signal after FFT be , The number of accumulated pulses is , and the frequency variable is The frequency domain amplitude after non-coherent accumulation is Due to the large fluctuation of aerosol particle density in the air, the echo signals of different laser pulses are significantly different. In single echo detection, the Doppler signal is weak and the noise is random, and after FFT, the noise amplitude at a certain frequency may be higher than the signal amplitude at the true Doppler frequency, so the cumulative average is crucial to suppress noise. Through the cumulative average of the multi-pulse power spectrum, random noise can be suppressed and signal components can be highlighted.

[0032] Step S3, due to the fluctuation of atmospheric aerosol particle density, the echo signals of different pulses and noise exist jitter, resulting in strong fluctuation of the spectrum distribution estimated by single power spectrum. Therefore, on the basis of step 2 cumulative average, the background noise in the power spectrum still needs to be filtered out - the power spectrum after cumulative average still carries noise power spectrum information, which cannot be directly used for frequency spectrum estimation. Generally, the coherent wind measurement laser radar considers that there is no effective Doppler signal in the last distance gate, i.e. the highest detection distance of the radar, and only contains background noise, so the echo signal of the distance gate is taken as the substrate noise; by subtracting the substrate noise power spectrum from the power spectrum of the echo signal of each distance gate, the background noise removal is completed, that is, the "last distance gate noise reduction", which can effectively remove the background noise interference and improve the purity of the signal spectrum.

[0033] The signal power spectrum of the last distance gate in the detection range is selected as the noise reference (it is assumed that the distance gate has no effective Doppler signal and only contains noise), and the power spectrum of other distance gates is subtracted from the reference to eliminate noise components and complete noise reduction.

[0034] Let the power spectrum of the first distance gate after cumulative average be , , , the total number of distance gates be , the frequency variable be , and the cumulative average power spectrum of the last distance gate (the first ) be the substrate noise power spectrum , then the power spectrum of the first distance gate after noise reduction is , and the calculation formula is: .

[0035] Step S4, the signal spectrum processed by the above method has a sinc function distribution characteristic, a least square fitting is performed on the sinc function, the frequency estimation error is reduced through deviation compensation and accurate correction, and the accuracy of Doppler frequency shift estimation is improved.

[0036] In order to solve the problem that the correction effect of the spectrum correction algorithm is poor at low signal-to-noise ratio, the present application provides a new spectrum correction algorithm suitable for coherent wind measurement laser radar. The algorithm is simple to implement and fast to operate, and has high frequency estimation accuracy at low signal-to-noise ratio.

[0037] The specific process of the spectrum correction algorithm based on sinc function fitting is as follows: After the echo signal is zero-padded FFT in step 1 and accumulated and averaged in step 2, its spectrum exhibits sinc function-like distribution characteristics. The least squares method can be used to fit all discrete spectrum points by sinc function, and the modulus function is fitted by selecting 7 points at the center of the spectrum peak. Through deviation compensation and accurate correction, the frequency estimation error is reduced, and thus the accurate radial wind speed is obtained.

[0038] Given discrete data , , For the number of data points, This refers to the discrete index of the spectrum, such as the location number of a spectral point. for Spectral magnitude, Starting node, This is the end node.

[0039] Its fitting function can be expressed as: ; in, These are the undetermined fitting parameters. The basis functions for fitting, m is the number of basis functions. <n。

[0040] Using residual sum of squares The formula for measuring the fit is: , The smaller the value, the smaller the deviation between the fitting result and the actual data, and the better the fitting effect.

[0041] According to the necessary condition for finding the minimum value of a multivariable function, Regarding each undetermined parameter Find the partial derivative and set it to 0, that is... , where g is the specific coefficient for the current partial derivative calculation. For example, when g=0, the current partial derivative is... Find the partial derivative.

[0042] The derivation process is as follows: , resolved For basis functions Define its discrete inner product as For functions ( Function representation and The dependency relationship, that is Define inner product Organized ,Right now Therefore, for each The above equation constitutes a linear equation group, and a normal equation group is obtained The equation is written in matrix form as Wherein, is a matrix composed of inner products of basis functions, that is, a coefficient matrix of the normal equation group, is a column vector of undetermined parameters, is a column vector composed of inner products of basis functions and target functions. By solving the above normal equation group, the undetermined parameters , can be obtained, and the fitting of data is completed.

[0043] Based on the above least square fitting principle, combined with the sinc-like distribution characteristics of the spectrum, a sinc model function for spectrum fitting is defined: Wherein, is the parameter to be fitted. The sinc model is substituted into the above least square fitting process, the discrete inner product between the sinc basis functions is calculated, the coefficient matrix of the normal equation group is constructed, the discrete inner product between the sinc basis function and the spectrum data (target function ) is calculated, the vector is constructed, the normal equation group is solved, and the parameters a, b, c, d of the sinc model are obtained, so that the fitting of the spectrum data is completed. The peak value of the sinc function appears at the position of the independent variable 0, that is, when , the peak value is obtained. Assuming that the discrete spectrum point index corresponding to the spectrum peak value is X (that is, the initial estimated frequency point), and the correction amount is (for correcting the initial estimation deviation), the corrected peak position satisfies . Solving the equation can obtain:

[0044] By least square fitting, the is obtained, and then the correction amount is obtained, and the corrected Doppler frequency is . Wherein is the sampling frequency, is the number of FFT points (the length of FFT after zero padding).

[0045] The present application realizes Doppler shift estimation through a three-stage process of "preprocessing-rough estimation-fine correction". First, the frequency shift preprocessing and rough estimation are realized through zero padding FFT, the signal characteristics are enhanced by combining spectrum accumulation and denoising, and finally the fine correction is completed based on the sinc function fitting. The scheme is superior to the traditional correction algorithm in the weak signal processing scene, and effectively solves the problem of insufficient accuracy of Doppler shift estimation in a low signal-to-noise ratio environment.

[0046] The specific implementation is as follows: Reference Figure 1 The spectrum correction algorithm based on the sinc function fitting includes the following steps Step 1, sampling the coherent wind lidar echo signal to obtain a discrete signal, and converting the time domain signal into a frequency domain signal for signal processing through FFT. As shown in Figure 2a 、 2b , the FFT transform is performed on the echo signal with a sampling frequency of 500MHz and a sampling point number of 512, and the spectral characteristics of the original signal and the signal after the FFT transform can be directly observed. However, since the FFT output is a discrete frequency value, the frequency estimation value obtained by the FFT is accurate only when the signal frequency is an integer multiple of the FFT frequency resolution, that is, the "fence effect" of the FFT.

[0047] Further, to verify the effect of zero padding, ideal cosine signals with frequencies of 68MHz and 69MHz are taken as examples for simulation, as shown in Figure 3a 、 3b , 3c, 3d. The distance resolution is set to 30m, the sampling frequency is 500MHz, and the discrete point number corresponding to one distance gate is 100. When zero padding is not performed, the Doppler frequency shift error caused by the FFT is 5MHz, and due to the fence effect, the spectral peaks of 68MHz and 69MHz are both located at the 14th spectral line, and cannot be distinguished. When zero padding is performed to 256 points, the two frequencies cannot be effectively separated. When zero padding is performed to 512 points, the frequency shift error is reduced to 0.98MHz, and the two frequency peaks are located at the 69th and 70th spectral lines, respectively, achieving separation. When zero padding is performed to 1024 points, the frequency shift error is further reduced to 0.49MHz, and the peaks are located at the 139th and 141st spectral lines, respectively.

[0048] It should be noted that zero padding is a kind of spectrum refinement, and zero padding makes the spectrum smoother and closer to the true spectrum. Although it cannot improve the spectral resolution, it can refine the spectrum, so that the spectral envelope shape is closer to the original continuous spectrum, which is beneficial to subsequent spectrum correction. Too much zero padding will increase the computational load, and will make the spectrum spread and the sidelobe effect more obvious, so it is not necessarily the more the better. In actual application, factors such as the data characteristics and index requirements of the signal and noise need to be considered, and the appropriate number of zero padding is selected for data processing.

[0049] Step 2, in order to solve the problem of low signal-to-noise ratio caused by environmental noise, circuit noise and the like, the power spectrum of multiple pulse echo data of the same distance gate is calculated respectively and then is accumulated and averaged, and the signal detection probability is improved through the energy superposition of multiple pulses. In order to more intuitively present the improvement of the spectrum accumulation number on the spectrum, the improvement of the spectrum quality by different spectrum accumulation numbers is simulated based on MATLAB. The sampling frequency is set to 500 MHz, the signal frequency is set to 80 MHz, the signal-to-noise ratio is set to -20 dB, and the sampling point number is set to 512. As shown in Figure 4a , Figure 4b 、 4c , 4d, 100, 1000 and 10000 times of accumulation and averaging are respectively performed. Since the frequency of the Doppler signal is always at a certain frequency and does not change, and the noise is random, after the accumulation and averaging of the frequency domain amplitude, the sharp peak noise will not be increased, and the noise amplitudes at different frequency points will be maintained at an average level. Finally, the amplitude at the Doppler signal frequency is significantly higher than the noise amplitude, the signal and the noise are effectively distinguished, and the detection accuracy of the laser radar system is greatly improved.

[0050] Step 3, in the coherent wind measurement laser radar system, by default, there is no effective Doppler signal in the last distance gate corresponding to the highest detection distance, and only background noise is contained, so the echo signal power spectrum of the distance gate can be used as a noise reference. The specific denoising process is as follows: the signal power spectrum of the last distance gate is extracted as a noise reference, the power spectrum of all other distance gates in the detection range is respectively subtracted from the noise power spectrum, the common background noise component is offset, and finally the signal is denoised. The denoising effect is shown in Figure 5a 、 5b , 5c, 5d.

[0051] Step 4, the signal spectrum processed by the above method has a distribution characteristic similar to a sinc function, a least square fitting is performed on the sinc function, all discrete points are collected, 7 points around the center of the spectrum peak value are taken, a modulus function is fitted, a frequency estimation error is reduced through deviation compensation and accurate correction, and the accuracy of Doppler shift estimation is improved.

[0052] The fitting method is as shown above.

[0053] Further, in order to verify the performance of the spectrum correction algorithm based on the sinc function fitting proposed in the application, two types of experiments are respectively simulated and analyzed, and the frequency estimation error of the energy gravity method, the ratio correction method and the spectrum correction algorithm based on the sinc function fitting of the application are compared. The specific process and results are as follows: 1. Simulation performance analysis based on MATLAB The simulation environment is built by using MATLAB software, and error characteristics of the three algorithms under different signal-to-noise ratios are compared. In the experiment, the black line represents the original error without correction, the blue line represents the correction error of the energy gravity method, the green line represents the correction error of the ratio correction method, and the red line represents the correction error of the spectrum correction algorithm based on the sinc function fitting of the application, as shown in Figure 6a 、 6b At-5dB, the maximum error of the spectrum correction algorithm based on the sinc function fitting is 0.0816MHz, and the average error is 0.0326MHz. At-20dB, the errors of the energy gravity method and the ratio correction method are larger, while the maximum error of the spectrum correction algorithm based on the sinc function fitting is 0.0952MHz, and the average error is 0.0582MHz, which is obviously smaller than the first two algorithms. The simulation results show that the algorithm of the application has stronger ability to process weak signals, and can maintain high frequency estimation accuracy in a wide signal-to-noise ratio range.

[0054] 2. Hardware platform-based actual measurement verification To further verify the engineering applicability of the algorithm, an actual measurement platform is built by using a "signal acquisition and processing module + vector signal generator + MATLAB host computer", and the specific experimental settings are as follows: the sampling frequency is 400MHz, the sampling point number is 512, the distance resolution is 30m, and the non-coherent accumulation number is 10000. The vector signal generator outputs an analog signal with a frequency of 40MHz-120MHz and a signal strength of-50dBm and-70dBm. The electrical signal detected by the analog detector has only the noise of the device and the board card itself, and in order to be closer to the actual measurement environment, the signal strength is set to a lower value.

[0055] After the signal acquisition and processing module performs zero padding FFT and accumulation average preprocessing on the analog signal, the three algorithms are called in the host computer by using MATLAB to perform spectrum correction, and the correction error results are shown in Figure 7a 、 7b The legend definition is consistent with the simulation experiment. By comparing the actual measurement data, it can be seen that when the signal strength is low, the correction effect of the energy gravity method and the ratio correction method decreases obviously, while the spectrum correction algorithm based on the sinc function fitting of the application still maintains high accuracy and stable error level, which is consistent with the conclusion of the simulation experiment.

[0056] The above is only a preferred specific embodiment of the application, but the protection scope of the application is not limited thereto, and any person skilled in the art can make equivalent substitutions or changes to the technical solutions and inventive concepts of the application within the technical scope disclosed by the application, which should be covered within the protection scope of the application.

Claims

1. A spectrum correction method based on sinc function fitting, characterized in that: Includes the following steps: S1. Sample the echo signal of the coherent wind lidar to obtain a discrete signal, and use FFT to convert the time domain signal to the frequency domain for spectrum estimation. When the sampling length does not meet 2 p At that time, zero-padding preprocessing is used to ensure that the total length meets the requirement of 2. p p is a positive integer; S2. In noncoherent accumulation, the frequency domain amplitude after noncoherent accumulation is obtained by averaging only the amplitude information of the echo signal. S3. Using the echo signal of the last distance gate as the base noise, subtract the power spectrum of the base noise from the power spectrum of the echo signals of the other distance gates respectively to remove background noise and obtain the preprocessed discrete spectrum points. S4. Using the sinc function The parameters are obtained by least-squares fitting of all the preprocessed discrete spectral points. , For discrete indexes of the spectrum; indexed by discrete spectral points corresponding to spectral peaks. Correction amount Obtain the corrected Doppler frequency .

2. The spectrum correction method based on sinc function fitting according to claim 1, characterized in that: In step S2, only the frequency domain amplitudes of the L pulses accumulated in the same distance gate are summed and averaged: ； in, The frequency domain amplitude of a single pulse echo signal after FFT. .

3. The spectral correction method based on sinc function fitting according to claim 1, characterized in that: In step S3, ； in, The th after cumulative averaging The power spectrum of a distance gate, , This represents the total number of doors at a distance. For frequency variables, .

4. The spectrum correction method based on sinc function fitting according to claim 1, characterized in that: In step S3, the preprocessed discrete spectral points are signal spectra with sinc function-like distribution characteristics.

5. The spectral correction method based on sinc function fitting according to claim 1, characterized in that: In step S4, ； in, Sampling frequency, N is the number of points in the FFT, and N is 2. p ; 。 6. The spectrum correction method based on sinc function fitting according to claim 1, characterized in that: In step S4, the least squares fitting method is as follows: calculate the discrete inner product between the sinc basis functions and construct the coefficient matrix of the normal equation system. Calculate the discrete inner product of the sinc basis function and the spectral data, and construct a vector. Solving the normal equations The parameters a, b, c, d of the sinc model are obtained. in, , which is a column vector of parameters to be determined; , is a column vector composed of the inner product of basis functions and objective function; , For the undetermined fitting parameters, Let be the basis functions for fitting. The number of basis functions; It is a matrix composed of the inner products of basis functions.

7. The spectral correction method based on sinc function fitting according to claim 6, characterized in that: Using the sum of squared residuals Measuring the fit: ； Where n is discrete data The total number, ; The smaller the value, the smaller the deviation between the fitting result and the actual data, and the better the fitting effect. right Regarding each undetermined parameter Find the partial derivative and set it to 0, that is , g To find the specific coefficients of the partial derivative, .

8. The spectral correction method based on sinc function fitting according to claim 7, characterized in that: The discrete inner product between the sinc basis functions is: 。 9. The spectral correction method based on sinc function fitting according to claim 7, characterized in that: The discrete inner product of the sinc basis function and the spectral data is: ； Wherein, objective function .

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