A method for estimating parameters of a linear frequency modulation signal under low signal-to-noise ratio conditions

Abstract

The application belongs to the field of digital signal processing, and particularly relates to a linear frequency modulation signal parameter estimation method under a low signal-to-noise ratio condition, which comprises the following steps: collecting signals and discretizing the signals; dividing the discrete sequence into sub-signals by framing, performing an FFT operation after a windowing and zero padding operation, and obtaining a frame sequence vector; searching for a maximum spectral peak of the spectrum of each frame of signals, and correcting the maximum spectral peak by using a cubic spline interpolation method to obtain a corresponding frequency; performing an equal-step distance and successive rotation scanning of two groups of vectors in a plane; synchronously projecting frequency vectors at different rotation angles, dividing a frequency band, and recording a frequency quantity statistical result; eliminating a trend item by using a median filtering, obtaining a maximum value of a statistical quantity, and then obtaining a preliminary estimation value of a parameter; and obtaining a final estimation result of an initial frequency and a frequency modulation rate of the linear frequency modulation signal by using a least square method fitting. The application overcomes the problems of great difficulty, low precision and complex calculation of the linear frequency modulation signal parameter estimation under the low signal-to-noise ratio condition in the prior art, and has good engineering practicability.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of digital signal processing, and particularly relates to a method for estimating parameters of a linear frequency modulation signal under a low signal-to-noise ratio condition. BACKGROUND

[0002] The instantaneous frequency of a linear frequency modulation signal varies linearly with time, has a large time-bandwidth product, and has good pulse compression characteristics, and can meet the requirements of ensuring a certain detection distance and having good resolution at the same time, and is therefore widely applied in the fields of radar, sonar, satellite communication and the like. The instantaneous frequency information of the linear frequency modulation signal can be obtained by determining two parameters of an initial frequency and a frequency modulation rate, so as to realize accurate detection of a target, and therefore it is particularly important to accurately estimate the two parameters.

[0003] At present, time-frequency analysis methods are often used for analyzing the linear frequency modulation signal, including Wigner-Ville distribution (WVD), Radon-Ambiguity transform (RAT) and fractional Fourier transform (FRFT), and the like. These methods all utilize the good energy aggregation characteristics of the linear frequency modulation signal in the time-frequency aspect. Among them, the WVD distribution, as a quadratic time-frequency transform, has very good advantages for analyzing a single-component linear frequency modulation signal, but for a multi-component signal, serious cross-term interference is generated; the RAT has a slow operation speed, which limits its engineering application, and the RAT algorithm loses the initial frequency information of the signal and is only suitable for occasions where the frequency modulation rate is of interest; the fractional Fourier transform, as a newly emerging time-frequency analysis tool, although a variety of improved optimization algorithms have appeared at present, but the defect that the FRFT needs to be two-dimensionally searched and has a large amount of calculation cannot be avoided. Therefore, it is difficult to simultaneously meet the requirements of small amount of calculation, high precision and the like by only using the above time-frequency analysis methods to analyze the linear frequency modulation signal, and the application utilizes the good time-frequency aggregation advantage of the single-component linear frequency modulation signal, and adopts a design idea of jointly using a plurality of analysis methods, so as to better overcome the deficiencies of the above methods.

[0004] Affected by a plurality of uncontrollable factors, the echo signal received by a radar receiver will inevitably be mixed with a large amount of random noise, which seriously interferes with the detection of the signal, and when the frequency and energy of the noise reach a certain threshold, the useful signal will be submerged, the signal will be distorted, and even the signal detection work cannot be normally carried out. SUMMARY

[0005] To solve the above technical problems, the application provides a method for estimating parameters of a linear frequency modulation signal under a low signal-to-noise ratio condition, which comprises the following steps:

[0006] S1, collect the continuous linear frequency modulation signal containing random noise in the linear frequency modulation radar transmitting wave, and discretize the signal to obtain a discrete signal sequence;

[0007] S2, the discrete signal sequence is time domain truncated by a Gaussian window, and a series of continuous time-varying and frame-length-equal different sub-signals are formed after zero padding, and each frame of sub-signal is subjected to FFT transformation to convert it from time domain to time-frequency domain, and the sub-signals are named as frame sequence vectors in time sequence;

[0008] S3, the energy spectrum of the time-frequency domain sub-signal STFT is obtained, the maximum spectrum peak in each frame of signal spectrum is searched, the amplitude threshold is set, and all peak values greater than the given threshold in the spectrum are extracted;

[0009] S4, the extracted spectrum peak value is corrected by using cubic spline interpolation method to obtain accurate spectrum peak amplitude, and the corresponding frequency is extracted according to the accurate spectrum peak amplitude;

[0010] S5, the extracted frequency and frame sequence vector are projected to a two-dimensional time-frequency plane, a rotation equation is constructed, and an equal-step rotation scanning is carried out;

[0011] S6, the frequency vectors of different rotation angles are projected synchronously in turn, and the frequency number statistical results of the small frequency bands are recorded;

[0012] S7, the maximum statistical value of the frequency number is obtained by using median filter to eliminate the noise trend item, and the preliminary estimated value of the parameter is obtained;

[0013] S8, the sample points in the neighborhood of the preliminary estimated value are selected for fitting to eliminate the interference of abnormal data, and the final estimated results of the initial frequency and the frequency modulation rate are obtained.

[0014] The beneficial effects of the present application are:

[0015] The present application uses short-time Fourier transform to analyze the time-frequency of the signal, which is simple in operation and does not need to perform multi-dimensional search, and converts the parameter estimation problem of the signal into a peak value search problem, greatly reducing the operation amount and being easy to realize;

[0016] The present application uses the energy aggregation characteristics of the linear frequency modulation signal to construct a rotation equation, when the time-frequency line is orthogonal to the frequency axis, the energy aggregation of the signal is the strongest, the energy projection converges into a point, and the performance is in the form of impact, at this time, the energy aggregation characteristics of the noise is obviously not higher than that of the signal, the noise trend item is eliminated by using median filter, the interference of strong noise is effectively excluded, and the accurate estimation of the initial frequency and the frequency modulation rate of the linear frequency modulation signal under the condition of extremely low signal-to-noise ratio is realized.

[0017] The application adopts the design scheme of combined use of multiple methods, continuously optimizes sample data in the whole signal processing process, eliminates the influence of abnormal data points, and meets the requirement of high-precision parameter estimation. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 A flowchart of the application;

[0019] Figure 2 A schematic diagram of the original linear frequency modulation signal to be processed by the application;

[0020] Figure 3 A schematic diagram of the time-frequency distribution of the traditional short-time Fourier transform of the application;

[0021] Figure 4 A schematic diagram of the time-frequency distribution of the multi-peak extraction short-time Fourier transform of the application;

[0022] Figure 5 A schematic diagram of R-F plane rotation scanning of the application;

[0023] Figure 6 A frequency vector F of the application k Projection statistics schematic diagram;

[0024] Figure 7 A comparison diagram of the trend item removal result of the application;

[0025] Figure 8 The least square sample data distribution of the application;

[0026] Figure 9 The fitting result diagram of the parameter estimation of the application. DETAILED DESCRIPTION

[0027] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the application.

[0028] A linear frequency modulation signal parameter estimation method under low signal-to-noise ratio conditions, as shown in Figure 1 , comprises:

[0029] S1, collecting a continuous linear frequency modulation signal containing random noise in a linear frequency modulation radar transmitting wave, and discretizing the signal to obtain a discrete signal sequence;

[0030] S2, the discrete signal sequence is truncated in time domain by a Gaussian window, and after zero padding, a series of different sub-signals with continuous time variation and equal frame length are formed, and the FFT transformation is performed on each frame of sub-signal to convert it from time domain to time-frequency domain, and the sub-signals are named as frame sequence vectors in time sequence;

[0031] S3, the energy spectrum of the time-frequency domain sub-signal STFT is obtained, the maximum spectral peak in each frame of signal spectrum is searched, an amplitude threshold is set, and all peak values greater than the given threshold in the spectrum are extracted;

[0032] S4, the extracted spectral peak values are corrected by using a cubic spline interpolation method to obtain accurate spectral peak amplitudes, and the corresponding frequencies are extracted according to the accurate spectral peak amplitudes;

[0033] S5, the extracted frequencies and frame sequence vectors are projected onto a two-dimensional time-frequency plane, a rotation equation is constructed, and an equal-step rotation scanning is performed;

[0034] S6, the frequency vectors of different rotation angles are projected synchronously in sequence, and the fine frequency band is divided to record the frequency quantity statistical results;

[0035] S7, the median filter is used to eliminate the noise trend item, the maximum statistical value of the frequency quantity is obtained, and then the preliminary estimated value of the parameter is obtained;

[0036] S8, the sample points in the neighborhood of the preliminary estimated value are selected for fitting to eliminate the interference of abnormal data, and the final estimated results of the initial frequency and the frequency modulation rate are obtained.

[0037] The continuous linear frequency modulation signal containing random noise comprises:

[0038] x(t)=Acos[2π(f0t+0.5kt 2 )+θ0]+w(t)

[0039] Wherein, x(t) is a continuous linear frequency modulation signal containing random noise in the linear frequency modulation radar transmitted wave collected, A is the signal amplitude, f0 is the initial frequency to be estimated, k is the frequency modulation rate to be estimated, t is the time, θ0 is the initial phase, and w(t) is the random noise of the continuous linear frequency modulation signal.

[0040] In the embodiment, the initial signal parameters are: amplitude A=1, initial frequency f0=982.5Hz, frequency modulation rate k=202.5Hz / s, initial phase θ0=45°, time t=10s, sampling frequency f s =10000Hz, the number of sampling points N=100000, and the signal-to-noise ratio SNR=-19dB.

[0041] The discretization of a continuous linear frequency modulated signal containing random noise to obtain a discrete signal sequence includes:

[0042] x(n) = A cos{2π[f0nT]} s +0.5k(nT s ) 2 ]+θ0}+w(n)

[0043] Where x(n) is the discrete signal sequence after digital sampling discretization, A is the signal amplitude, f0 is the initial frequency to be estimated, k is the modulation frequency to be estimated, t is time, θ0 is the initial phase, and T s T is the sampling time interval. s =1 / f s f s denoted as the sampling frequency, n as the sample number, and w(n) as the noise of the discrete signal sequence.

[0044] like Figure 2 As shown, the amplitude of an ideal linear frequency modulated (LFM) signal is constant, but fluctuates after noise is added. Therefore, by truncating the discrete signal sequence in the time domain using a Gaussian window and padding with zeros to form a series of different sub-signals with continuous time variations and equal frame lengths, a local FFT is performed on each frame sub-signal to transform it from the time domain to the time-frequency domain, including:

[0045] S21. Select a Gaussian window as the analysis window, set the window length to M and the window sliding step size to L, move the window function on the time axis, and divide the discrete signal sequence x(n) after digital sampling discretization into R frames, denoted as xr(m), where r = 0, 1, ..., R-1 represents the frame number, and m = 0, 1, ..., M-1 represents the sample number in each frame of the signal;

[0046] S22. Zero-padding is performed on xr(m), adding (β-1)M zero-value data points after the original data, extending the signal in the time domain by a total of βM samples, to obtain a sub-signal sequence with continuous time variation and equal frame length. Then, the windowed and zero-padding signal is subjected to FFT transformation to obtain the time-frequency domain sub-signal sequence.

[0047] In this embodiment, the length of the Gaussian window is set to M = 2000, and the sliding step size is set to L = 100. Over the entire time span, i.e., t = 10s, the moving window function truncates the signal into R = 1000 frames, denoted as xr(m).

[0048] The number of samples is extended to 20,000 by adding zero-value data points after each frame of signal, and FFT is performed on the signal to transform xr(m) from the time domain to the time-frequency domain.

[0049] The linear frequency modulation signal instantaneous frequency expression is a first order curve in time-frequency domain, the vertical axis intercept is initial frequency, the slope is frequency modulation rate, and the formula is as follows:

[0050] f = f0 + kt

[0051] Wherein, f is linear frequency modulation signal instantaneous frequency, f0 is initial frequency, k is frequency modulation rate, and t is time.

[0052] As shown in Figure 3 , under the condition of low signal-to-noise ratio, the time-frequency line distribution of the traditional short-time Fourier transform is not clear when it is interfered by strong noise. Therefore, by obtaining the energy spectrum of the time-frequency domain sub-signal STFT, searching for the maximum spectral peak in each frame signal spectrum, setting the amplitude threshold, extracting all the peak values in the spectrum greater than the given threshold, including:

[0053] obtaining the energy spectrum X r (m) of each time-frequency domain sub-signal sequence, searching for the amplitude maximum spectral peak E r of each frame signal in the energy spectrum X r (m), setting the spectral peak threshold μE r (0 < μ ≤ 1), extracting all the peak values in X r (m) whose amplitude is greater than the given threshold, denoted as A r,s , the index peak frequency is denoted as f r,s ; the total number of extracted peak values in the R frame data of the discrete signal sequence is denoted as J, and the corresponding peak frequency vector is ordered according to the frame sequence number, denoted as F = (f0, f1,..., f j ,..., f J-2 ,f J-1 ), and the corresponding frame sequence number vector is denoted as R = (r0, r1,..., r j ,..., r J-2 ,r J-1 ).

[0054] As shown in Figure 4 , the short-time Fourier transform using multi-peak extraction obtains more peak frequencies, the cubic spline interpolation method is used to correct A r,s to obtain accurate peak amplitude and index frequency; denoted as and is updated in the peak frequency vector F.

[0055] The extracted frequency and frame sequence vector are projected to a two-dimensional time-frequency plane, a rotation equation is constructed for equidistant rotation scanning, including:

[0056] The corrected extracted peak frequency vector F and frame sequence number vector R are projected to a two-dimensional time-frequency plane, denoted as R-F plane, and a scanning equation is constructed: F k=F-xR, where x is the rotation amount; set the scanning step size to Δk, and the scanning range to [-KΔk, KΔk], so that the RF plane is rotated step by step to obtain the frequency vector F. k .

[0057] In this embodiment, the scanning range is set to K = 400, and the scanning step size is set to Δk = 1.

[0058] Construct the scanning equation: F k =F-xR, where x∈[-400,400];

[0059] This allows the RF plane to be rotated step by step to obtain the vector F. k .

[0060] like Figure 5 As shown, the signal energy concentration is strongest when the RF plane is rotated so that the time-frequency line is orthogonal to the frequency axis.

[0061] Frequency vectors at different rotation angles are projected synchronously in sequence, and the frequency count is recorded in small frequency bands, including:

[0062] Effective analysis of frequency band f s / 2 is divided into P equal parts of width f. Δ The refined frequency band, i.e., P = ceil{f s / (2fΔ)}, where ceil{·} represents the floor function; rotate the frequency vector F by different angles. k Projecting the data onto P smaller frequency bands, we count the number of frequencies in each band, and denot the maximum count and its corresponding frequency band as h. k and p k After completing the traversal scanning process, the vector H = (h) with the maximum statistical value is obtained. -K ,h -K+1 ,...,h0,...,h K-1 ,h K ) and the corresponding frequency band vector P = (p -K ,p -K+1 ,...,p0,...,p K-1 ,p K ).

[0063] In this embodiment, the statistical bandwidth is set to f. Δ =1H Z The entire effective bandwidth is divided into P = 5000 small frequency bands;

[0064] Rotate F at different angles k Projecting the frequency across 5000 smaller frequency bands, count the number of frequencies in each band, and denot the maximum count and its corresponding frequency band as h. k and pk ;

[0065] After the scan is complete, the vector of the maximum statistical value can be obtained: H = {h} -400 ,h -399 ,...,h0,,...,h 399 ,h 400} and the corresponding frequency band vector: P = {p -400 ,p -399 ,...,p0,,...,p 399 ,p 400}

[0066] like Figure 6 As shown, when the RF plane is rotated to the optimal angle, F k The peak values ​​of the projected frequency count are concentrated in the frequency band near the initial frequency value.

[0067] Median filtering is used to eliminate noise trend terms, and the maximum statistical value of the number of frequencies is obtained, thus yielding preliminary estimates of the parameters, including:

[0068] Median filtering algorithm is used for vector H=(h) -K ,h -K+1 ,...,h0,...,h K-1 ,h K After processing to eliminate the cumulative trend caused by noise interference, the vector H is obtained. f Find the vector H f The infinite norm h in max =|H f | ∞ And the corresponding rotation amount k max and statistical frequency band p max At this time, k max and p max These can be regarded as preliminary estimates of the frequency modulation and the initial frequency, respectively.

[0069] In this embodiment, the length of the median filter is set to 21, and the vector H is smoothed to obtain H. f Furthermore, the vector H can be obtained. f The infinite norm in: h max =|H f | ∞ ≈275; corresponding rotation amount: k max =202; Statistical bandwidth: p max =2982.4; At this point, the preliminary estimate of the linear frequency modulated signal can be expressed as:

[0070] like Figure 7As shown, the size of the trend item is positively correlated with the energy of the noise, and the smoothing filtering can eliminate the interference of the noise cumulative trend.

[0071] The sample points in the neighborhood of the preliminary estimation value are selected for fitting to eliminate the interference of abnormal data, and the final estimation results of the initial frequency and the frequency modulation rate are obtained, including:

[0072] According to the obtained linear frequency modulation signal parameter preliminary estimation value k max and p max , the discrete frequency points in the neighborhood range of the frequency band p max are selected as sample data, and the least square method is used for linear function estimation to obtain the intercept and the slope , and according to the intercept and the slope , the initial frequency estimation value and the frequency modulation rate estimation value of the linear frequency modulation signal are finally obtained.

[0073] According to the intercept and the slope , the initial frequency estimation value and the frequency modulation rate estimation value of the linear frequency modulation signal are finally obtained.

[0074]

[0075] wherein, is the final initial frequency estimation value of the linear frequency modulation signal, is the intercept; is the final frequency modulation rate estimation value of the linear frequency modulation signal, k max is the linear frequency modulation signal parameter preliminary estimation value, is the slope.

[0076] In this embodiment, the discrete frequency points in the neighborhood range of the frequency band p max = 2982.4, P ∈ [981.4, 983.4] are selected as sample data, the least square method is used for linear function estimation, and the discrete data points in the frequency band near Figure 8 are used for least square estimation; the intercept is obtained as: the slope is: the initial frequency estimation value and the frequency modulation rate estimation value of the linear frequency modulation signal are finally obtained.

[0077] As shown in Figure 9As shown, the initial frequency estimation of the chirp signal is the frequency value after linear fitting, and the estimation of the chirp rate is the rotation frequency value plus the slope value after linear fitting. The estimation errors of the chirp rate and the initial frequency can be calculated as follows under the condition of SNR=-19dB:

[0078] Although the embodiments of the present application have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, alternatives, and variations can be made thereto without departing from the principles and spirit of the application, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for estimating parameters of a linear frequency modulated signal under low signal-to-noise ratio conditions, characterized in that, include: S1. Collect the continuous linear frequency modulated signal containing random noise from the transmitted wave of the linear frequency modulated radar, and discretize it to obtain a discrete signal sequence. S2. The discrete signal sequence is truncated in the time domain through a Gaussian window and padded with zeros to form a series of different sub-signals with continuous time variation and equal frame length. Each frame sub-signal is transformed by FFT to convert it from the time domain to the time-frequency domain. At the same time, the sub-signals are named frame sequence vectors according to their time sequence. S3. Obtain the energy spectrum of the time-frequency domain sub-signal STFT, search for the maximum spectral peak in the spectrum of each frame of signal, set the amplitude threshold, and extract all peaks in the spectrum that are greater than the given threshold. S4. The extracted spectral peak values ​​are corrected using cubic spline interpolation to obtain accurate spectral peak amplitudes, and the corresponding frequencies are extracted based on the accurate spectral peak amplitudes. S5. Project the extracted frequency and frame sequence vector onto the two-dimensional time-frequency surface, construct the rotation equation and perform equidistant rotation scanning. S6. Simultaneously project frequency vectors at different rotation angles in sequence, divide into small frequency bands, and record the frequency count results. S7. Median filtering is used to eliminate the noise trend term, and the maximum statistical value of the frequency is obtained, thereby obtaining the preliminary estimate of the parameter. S8. Select sample points in the neighborhood of the preliminary estimate for fitting, eliminate the interference of abnormal data, and obtain the final estimate results of the initial frequency and the frequency modulation.

2. The method for estimating parameters of a linear frequency modulated signal under low signal-to-noise ratio conditions according to claim 1, characterized in that, The continuous linear frequency modulated signal containing random noise includes: x(t)=Acos[2π(f0t+0.5kt 2 )+θ0]+w(t) Where x(t) is the continuous linear frequency modulated signal containing random noise in the acquired linear frequency modulated radar transmitted wave, A is the signal amplitude, f0 is the initial frequency to be estimated, k is the modulation frequency to be estimated, t is the time, θ0 is the initial phase, and w(t) is the random noise of the continuous linear frequency modulated signal.

3. The method for estimating parameters of a linear frequency modulated signal under low signal-to-noise ratio conditions according to claim 1, characterized in that, The process of discretizing a continuous linear frequency modulated signal containing random noise to obtain a discrete signal sequence, and performing a local FFT on each frame sub-signal to transform it from the time domain to the time-frequency domain includes: x(n)=Acos{2π[f0nT s +0.5k(nT s ) 2 ]+θ0}+w(n) Where x(n) is the discrete signal sequence after digital sampling discretization, A is the signal amplitude, f0 is the initial frequency to be estimated, k is the modulation frequency to be estimated, t is time, θ0 is the initial phase, and T s T is the sampling time interval. s =1 / f s f s denoted as the sampling frequency, n as the sample number, and w(n) as the noise of the discrete signal sequence.

4. The method for estimating parameters of a linear frequency modulated signal under low signal-to-noise ratio conditions according to claim 1, characterized in that, Discrete signal sequences are truncated in the time domain using a Gaussian window and padded with zeros to form a series of different sub-signals with continuous time variations and equal frame lengths, including: S21. Select a Gaussian window as the analysis window, set the window length to M and the window sliding step size to L, and move the window function on the time axis to divide the discrete signal sequence x(n) after digital sampling discretization into R frames, denoted as x. r (m), where r = 0, 1, ..., R-1 represents the frame number, and m = 0, 1, ..., M-1 represents the sample number in each frame of the signal; S22, regarding x r (m) Zero padding is performed, adding (β-1)M zero data points after the original data, extending the signal in the time domain by a total of βM samples, to obtain a sub-signal sequence with continuous time variation and equal frame length, and then performing FFT transformation on the windowed and zero-padded signal to obtain the time-frequency domain sub-signal sequence.

5. The method for estimating parameters of a linear frequency modulated signal under low signal-to-noise ratio conditions according to claim 1, characterized in that, Obtain the energy spectrum of the time-frequency domain sub-signal STFT, search for the maximum spectral peak in the spectrum of each frame of the signal, set an amplitude threshold, and extract all peaks in the spectrum that are greater than the given threshold, including: Obtain the energy spectrum X of each time-frequency domain sub-signal sequence r (m), Search energy spectrum X r The maximum amplitude peak E of each frame of the signal in (m) r Set the spectral peak threshold μE r (0 < μ ≤ 1), extract X r (m) All peak values ​​with amplitudes greater than a given threshold are denoted as A. r,s Its index peak frequency is denoted as f. r,s The total number of peak values ​​extracted from R frames of a discrete signal sequence is denoted as J, and the corresponding peak frequency vectors are ordered by frame number and denoted as F = (f0, f1, ..., f2). j ,...,f J-2 ,f J-1 The corresponding frame sequence number vector is denoted as R = (r0, r1, ..., r...). j ,...,r J-2 ,r J-1 ).

6. The method for estimating parameters of a linear frequency modulated signal under low signal-to-noise ratio conditions according to claim 1, characterized in that, The extracted frequency and frame sequence vectors are projected onto a two-dimensional time-frequency surface, and a rotation equation is constructed to perform a step-by-step rotation scan, including: The corrected extracted peak frequency vector F and frame number vector R are projected onto the two-dimensional time-frequency surface, denoted as the RF plane, and the scanning equation is constructed as follows: F k =F-xR, where x is the rotation amount; set the scanning step size to Δk, and the scanning range to [-KΔk, KΔk], so that the RF plane is rotated step by step to obtain the frequency vector F. k .

7. The method for estimating parameters of a linear frequency modulated signal under low signal-to-noise ratio conditions according to claim 1, characterized in that, Frequency vectors at different rotation angles are projected synchronously in sequence, and the frequency count is recorded in small frequency bands, including: Effective analysis of frequency band f s / 2 is divided into P equal parts of width f. Δ The refined frequency band, i.e., P = ceil{f s / (2fΔ)}, where ceil{·} represents the floor function; rotate the frequency vector F by different angles. k Projecting the data onto P smaller frequency bands, we count the number of frequencies in each band, and denot the maximum count and its corresponding frequency band as h. k and p k After completing the traversal scanning process, the vector H = (h) with the maximum statistical value is obtained. -K ,h -K+1 ,...,h0,...,h K-1 ,h K ) and the corresponding frequency band vector P = (p -K ,p -K+1 ,...,p0,...,p K-1 ,p K ).

8. The method for estimating parameters of a linear frequency modulated signal under low signal-to-noise ratio conditions according to claim 1, characterized in that, Median filtering is used to eliminate noise trend terms, and the maximum statistical value of the number of frequencies is obtained, thus yielding preliminary estimates of the parameters, including: The median filtering algorithm is used to filter the vector H = (h -K ,h -K+1 ,...,h0,...,h K-1 ,h K After processing to eliminate the cumulative trend caused by noise interference, the vector H is obtained. f Find the vector H f The infinite norm h in max =|H f | ∞ And the corresponding rotation amount k max and statistical frequency band p max At this time, k max and p max These can be regarded as preliminary estimates of the frequency modulation and the initial frequency, respectively.

9. The method for estimating parameters of a linear frequency modulated signal under low signal-to-noise ratio conditions according to claim 1, characterized in that, Sample points within the neighborhood of the initial estimate are selected for fitting to eliminate interference from outliers, resulting in the final estimates of the initial frequency and frequency modulation (FM), including: Based on the preliminary estimate of the linear frequency modulated signal parameters k max and p max Select frequency band p max Discrete frequency points within the neighborhood are used as sample data, and the least squares method is used to estimate the linear function to obtain the intercept. and slope And based on the intercept and slope Finally, the initial frequency estimate of the linear frequency modulated signal is obtained. Harmony frequency estimate 10. The method for estimating parameters of a linear frequency modulated signal under low signal-to-noise ratio conditions according to claim 9, characterized in that, According to the intercept and slope Finally, the initial frequency estimate of the linear frequency modulated signal is obtained. Harmony frequency estimate include: in, This is the initial frequency estimate for the final linear frequency modulated signal. The intercept; k is the final frequency modulation estimate of the linear frequency modulated signal. max These are preliminary estimates of the parameters for the linear frequency modulated signal. The slope is denoted as .

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