Parameter estimation method for multi-component linear frequency modulated signals based on incomplete spectrum reconstruction

Abstract

This invention belongs to the field of radar communication technology, specifically relating to a method for estimating parameters of multi-component linear frequency modulated (LFM) signals based on incomplete spectrum reconstruction. The method includes: performing a short-time Fourier transform on the discretized multi-component LFM signal and initializing it as the observed spectrum; extracting the amplitude peaks and corresponding frequency coordinates from the observed spectrum and performing correction and updates; estimating single-component signals and performing parameter checks; performing an incomplete reconstructed signal and performing a short-time Fourier transform; subtracting the spectra to obtain the residual spectrum and updating it as the observed spectrum; repeating the parameter estimation iteratively; and ending the loop when the parameter robustness index is less than a set threshold standard, ultimately obtaining the parameter estimation results for the multi-component signals. This invention performs spectral separation of multi-component signals in the time-frequency domain, employing a successive analysis approach. In noisy environments, it effectively suppresses interference from strong component signals on the detection of weak components, achieving the goal of rapid and accurate estimation of multi-component LFM signals.

Description

Technical Field

[0001] This invention belongs to the field of radar communication technology, specifically relating to a method for estimating parameters of multi-component linear frequency modulated signals based on incomplete spectrum reconstruction. Background Technology

[0002] Linear Frequency Modulated Signal (LFM), as a low-intercept signal with a large time-bandwidth product, is widely used in military radar. With further research, its applications have expanded to various civilian fields such as meteorological satellites, seismic surveys, and navigation systems. Compared to single-component LFM signals, multi-component LFM signals suffer from cross-term interference, which severely affects the identification of the signal's true time and frequency. Therefore, suppressing cross-terms is a crucial problem to be solved in time-frequency analysis applications. For non-stationary signals, the most direct approach is to use time-frequency analysis methods. Traditional time-frequency analysis methods include linear transforms and quadratic transforms. Typical quadratic time-frequency transforms include Cohen-type (Born-Jordan distribution, Choi-Williams distribution, smoothed pseudo-Wigner-Ville, etc.) and ambiguity functions. These time-frequency distributions use different kernel functions to suppress cross-terms. However, for signals with different time-varying frequency characteristics, the selection of the kernel function must be adaptive.

[0003] The patent "Parameter Estimation Method for Multi-Component Linear Frequency Modulation Signals Based on Fractional Fourier Domain Filtering" (Application No. 201911085593.5, Publication No. CN 110764062 A) provides a parameter estimation method that establishes a parameter template library for linear frequency modulation signals and matches the real-time observation frames to the parameter template library based on fractional Fourier transform. This method can obtain accurate parameters of multi-component linear frequency modulation signals, but the implementation process is relatively complex and its engineering applicability is limited.

[0004] The patent "Adaptive Multi-Component Linear Frequency Modulation Signal Parameter Estimation Method" (application number 202110209363.6, publication number CN 112559973 A) provides an adaptive multi-component linear frequency modulation signal parameter estimation method based on short-time fractional Fourier transform (STFrFT). This method can adaptively determine whether parameter estimation should be terminated and determine the number of LFM component signals in the signal, but it has the disadvantages of too much computation, too complicated steps, and long time consumption.

[0005] In summary, existing technologies for estimating parameters of multi-component linear frequency modulated signals suffer from shortcomings such as cross-term interference and computational complexity, thus limiting their practicality. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a method for estimating parameters of a multi-component linear frequency modulated signal based on incomplete spectrum reconstruction, comprising the following steps:

[0007] S1. Discretize the input multi-component linear frequency modulated signal;

[0008] S2. Obtain the full-component time-frequency spectrum through short-time Fourier transform and initialize it as the observed spectrum, then enter the loop;

[0009] S3. Extract the amplitude peak points and corresponding frequency coordinates from the observed spectrum;

[0010] S4. Use a Gaussian function to correct and update the amplitude peak points and corresponding frequency coordinates in the extracted observed spectrum;

[0011] S5. Fit the single-component signal estimation result based on the least squares method, and perform parameter verification of the single-component signal using a set threshold. If the parameters meet the component characteristics of the linear frequency modulated signal, save the component estimation parameters and proceed to the signal reconstruction step.

[0012] S6. Based on the component estimation parameters, perform incomplete reconstruction of the signal and then perform short-time Fourier transform to obtain the reconstructed spectrum;

[0013] S7. Subtract the observed spectrum from the reconstructed spectrum to obtain the residual spectrum. Update the residual spectrum to the observed spectrum through spectrum readjustment. Repeat steps S3-S7. When the parameter robustness index is less than the set threshold standard, the loop ends and the multi-component parameter estimation results are finally obtained.

[0014] The beneficial effects of this invention are:

[0015] This invention employs the short-time Fourier transform, a linear time-frequency analysis method. Based on the characteristic that multi-component linear frequency modulated signals satisfy the principle of linear superposition under linear transformation conditions, it overcomes the interference of cross terms and is computationally simple. At the same time, based on the incomplete reconstruction of multi-component signals in the time domain, it requires less prior information, further reducing the complexity of the algorithm.

[0016] This invention performs spectral separation of multi-component signals in the time-frequency domain and adopts a successive analysis approach. In noisy environments, it effectively suppresses the interference of strong component signals on the detection of weak components, and achieves the goal of fast and accurate estimation of multi-component linear frequency modulated signals. Attached Figure Description

[0017] Figure 1 This is a flowchart of the present invention;

[0018] Figure 2 A three-dimensional time-frequency plot of a multi-component linear frequency modulated signal;

[0019] Figure 3 A two-dimensional time-frequency diagram of a multi-component linear frequency modulated signal;

[0020] Figure 4 This is the result of the first peak extraction.

[0021] Figure 5 This is the residual spectrum after the first spectrum subtraction;

[0022] Figure 6 This is the result of the second peak extraction.

[0023] Figure 7 This is the residual spectrum after the second spectrum subtraction;

[0024] Figure 8 This is the result of the third peak extraction.

[0025] Figure 9 This is the residual spectrum after the third spectrum subtraction;

[0026] Figure 10 This is the result of the fourth peak extraction. Detailed Implementation

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] A parameter estimation method for multi-component linear frequency modulated signals based on incomplete spectrum reconstruction, such as... Figure 1 As shown, it includes:

[0029] S1. Discretize the input multi-component linear frequency modulated signal;

[0030] S2. Obtain the full-component time-frequency spectrum through short-time Fourier transform and initialize it as the observed spectrum, then enter the loop;

[0031] S3. Extract the amplitude peak points and corresponding frequency coordinates from the observed spectrum;

[0032] S4. Use a Gaussian function to correct and update the amplitude peak points and corresponding frequency coordinates in the extracted observed spectrum;

[0033] S5. Fit the single-component signal estimation result based on the least squares method, and perform parameter verification of the single-component signal using a set threshold. If the parameters meet the component characteristics of the linear frequency modulated signal, save the component estimation parameters and proceed to the signal reconstruction step.

[0034] S6. Based on the component estimation parameters, perform incomplete reconstruction of the signal and then perform short-time Fourier transform to obtain the reconstructed spectrum;

[0035] S7. Subtract the observed spectrum from the reconstructed spectrum to obtain the residual spectrum. Update the residual spectrum to the observed spectrum through spectrum readjustment. Repeat steps S3-S7. When the parameter robustness index is less than the set threshold standard, the loop ends and the multi-component parameter estimation results are finally obtained.

[0036] The multi-component linear frequency modulated signal includes:

[0037]

[0038] Where s(t) is a multi-component linear frequency modulated signal sequence; i = 1, 2, ..., I are the signal component indices, and I is the total number of components; A i f is the amplitude; i The initial frequency; μ i φ is the frequency modulation slope. i ν is the initial phase; ν(t) is the noise; t is the time.

[0039] Discretization of multi-component linear frequency modulated signals includes:

[0040]

[0041] Where s(n) is a discretized multi-component linear frequency modulated signal sequence; i = 1, 2, ..., I are the signal component indices, and I is the total number of components; A i f is the amplitude; i The initial frequency; μ i φ is the frequency modulation slope. i The initial phase; T s T is the sampling time interval. s =1 / f s f s ν is the sampling frequency; n is the sample number; ν(n) is the discretized noise.

[0042] The full-component time-frequency spectrum is obtained through short-time Fourier transform and initialized with the observed spectrum. The process then enters a loop, including:

[0043] S21: A Gaussian window with a window length of L and a sliding step of L′ is selected as the analysis window. The signal s(n) is divided into R frame sub-signals according to the Gaussian window with a window length of L, denoted as... Where r=1,2,...,R represents the frame sequence number;

[0044] S22: For R-frame sub-signals Perform interpolation and zero-padding operations, in The sub-signal is then filled with L zero-value samples to extend it to 2L.

[0045] S23: Perform a Fast Fourier Transform on the interpolated and zero-padded sub-signal to obtain its spectrum, denoted as... R-frame sub-signals can form a complete full-component time-frequency spectrum, denoted as S(f);

[0046] S24: Initialize S(f): Use it as the observed spectrum for loop analysis.

[0047] Extract the amplitude peak points and corresponding frequency coordinates from the observed spectrum, including:

[0048] Extracting the neutron signal spectrum from the observed spectrum The maximum peak value in and its corresponding frequency coordinates The maximum peak value of the R-frame signal and its corresponding frequency coordinates can form a peak vector. and frequency coordinate vector Right now and in, This represents the amplitude of the maximum peak value of the signal in the Rth frame; This represents the frequency coordinate corresponding to the maximum peak value of the signal in frame R.

[0049] The amplitude peaks and corresponding frequency coordinates in the extracted observed spectrum are corrected and updated using a Gaussian function, including:

[0050] The peak points are corrected using the method of undetermined coefficients, and the sub-signal spectrum is obtained. The maximum peak value in and its two neighboring values The corresponding frequencies for the data analyzed are as follows: Substitute them into the Gaussian function expression respectively. They were obtained respectively Where f is the independent variable, G(f) is the dependent variable, and a, b, and c are the first, second, and third parameters to be determined, respectively.

[0051] When f = b, the maximum value of the dependent variable G(f) of the Gaussian function is a, the corrected amplitude peak size is a, the corresponding frequency size is b, and the corrected amplitude peak vector is... The corrected frequency vector is in, This represents the amplitude of the maximum peak value of the corrected R-th frame signal. This represents the frequency corresponding to the maximum peak value of the corrected R-th frame signal.

[0052] The single-component signal estimation result is obtained by fitting using the least squares method. A set threshold σ0 is used to check the parameters of the single-component signal. If the parameters conform to the component characteristics of a linear frequency modulated signal, the component estimation parameters are saved, including:

[0053] With frame number as the x-axis, frequency vector Using the ordinate as the sample data, a linear regression method is employed, and the parameter estimation results of the single-component signal are obtained based on least squares fitting: the estimated initial frequency is denoted as... The estimated frequency modulation slope is denoted as The robustness index σ returned by the fitting is used as the test result. If the robustness index σ is greater than the set threshold σ0, it is determined that it has the component characteristics of a linear frequency modulated signal, and the estimated parameters are saved.

[0054] The signal is incompletely reconstructed based on the component estimation parameters, and the reconstructed spectrum is obtained by performing a short-time Fourier transform, including:

[0055] S61: Extract the corrected and updated amplitude peak vector The largest element in the equation is used to calculate the amplitude estimate. Where λ represents the reconstruction coefficient, ε represents the amplitude gain (typically 1.5), and phase information is ignored, the component signal is incompletely reconstructed in the time domain.

[0056] S62: For the reconstructed signal Perform a short-time Fourier transform to obtain the reconstructed spectrum of the component signal, denoted as .

[0057] Ignoring phase information, the component signals are incompletely reconstructed in the time domain, including:

[0058]

[0059] in, The component signal is not fully reconstructed. Here is the amplitude estimate, where, The component signal is not fully reconstructed. This is an estimate of the amplitude. The initial frequency is T, where n is the sample number and T is the initial frequency. s The sampling time interval, This is the estimated frequency modulation slope.

[0060] The residual spectrum is obtained by subtracting the observed spectrum from the reconstructed spectrum. The residual spectrum is then updated to reflect the observed spectrum through spectrum readjustment, including:

[0061] The signal is separated by subtracting the full-component time-frequency spectrum from the reconstructed spectrum of the component signals. Obtain the residual spectrum of the remaining components. Where S(f) represents the full-component time-frequency spectrum, This represents the reconstructed spectrum of the component signal;

[0062] The residual spectrum is nonnegated by setting all values ​​less than zero in the residual spectrum to zero. The nonnegated residual spectrum is then used as the observation spectrum for the next cycle. in, This represents the residual spectrum after nonnegation.

[0063] Example 1: Under the conditions of I=3 signal components and SNR=-5dB, a parameter estimation method for multi-component linear frequency modulated signals based on spectrum separation is simulated and analyzed using MATLAB. The specific implementation steps are as follows:

[0064] The first step is to initialize the parameters;

[0065] Preferably, the parameters of component signal one are set as follows: amplitude: A1 = 3; initial frequency: f1 = 610.2 Hz; frequency modulation slope: μ1 = 383.8 Hz / s; initial phase:

[0066] Preferably, the parameters of component signal two are set as follows: amplitude: A3=2; initial frequency: f3=3333.3Hz; frequency modulation slope: μ3=-298.1Hz / s; initial phase:

[0067] Preferably, the parameters of component signal three are set as follows: amplitude: A2 = 1.5; initial frequency: f2 = 4326.6 Hz; frequency modulation slope: μ2 = -755.5 Hz / s; initial phase:

[0068] The second step is signal sampling;

[0069] Preferably, the sampling frequency is 10000Hz, the signal duration is t=5s, and the number of sampling points is N=50000. The linear frequency modulated signal of the above three components is combined with random noise and sampled to obtain the analysis sample.

[0070] The third step is the short-time Fourier transform;

[0071] Preferably, the length of the Gaussian window is set to L = 1000, the sliding step size is L′ = 200, the signal is divided into R = 250 frames, and zeros are padded to make the length 2000. The short-time Fourier transform of the signal is performed to obtain the spectrum of the signal, denoted as S(f).

[0072] like Figure 2 As shown, the three-dimensional time spectrum of a multi-component linear frequency modulated signal consists of three straight lines of varying heights arranged in a dorsal fin pattern. Figure 3 for Figure 2 The projection onto the time-frequency plane appears as three intersecting straight lines.

[0073] The fourth step is to extract the maximum peak value and obtain the corresponding frequency coordinates;

[0074] Preferably, the strongest component signal s1(n) is first labeled, and the maximum peak value in the spectrum of each frame of the signal is extracted. and its corresponding frequency coordinates The peak amplitude vector is obtained as follows Frequency vector is

[0075] Step 5: Gaussian function peak and frequency correction;

[0076] The peak points were corrected using the method of undetermined coefficients. and its two neighboring values As the data for analysis, the corresponding frequencies are as follows: Substituting into the Gaussian function expression, we obtain the corrected amplitude peak value as a and the corresponding frequency value as b;

[0077] Corrected amplitude peak vector is

[0078] The corrected frequency vector is

[0079] Step 6: Least squares linear fitting;

[0080] Preferably, the frame number is used as the horizontal axis. Using the ordinate as the sample data, the parameter estimation results of the single-component signal are obtained based on least squares fitting, and the robustness index threshold is set to 0.5.

[0081] initial frequency FM slope The robustness indicator σ = 0.98;

[0082] like Figure 4 As shown, the time-frequency curve calculated by least squares linear regression is a linear function of time.

[0083] Step 7: Incomplete signal reconstruction;

[0084] Preferably, extraction The largest element in the equation is used to calculate the amplitude estimate. Where λ represents the reconstruction coefficient, calculated using a window function, and is approximately 2.7, and ε represents the amplitude gain, which is 1.5. This results in the incomplete reconstruction of the strongest component signal in the time domain.

[0085]

[0086] Performing a short-time Fourier transform on the above equation yields the reconstructed spectrum, denoted as .

[0087] Step 8: Subtract the spectra;

[0088] Preferably, the reconstructed spectrum is subtracted from the original time-frequency spectrum S(f). Obtain the residual spectrum

[0089] like Figure 5 As shown, canceling the original signal spectrum with the incompletely reconstructed signal completely eliminates the previous component signal, suppressing the interference of the strong component signal on the weak component signal; non-negating the residual spectrum, i.e., setting all values ​​less than zero to zero, and using the new data as the observation spectrum for the next cycle, i.e. Return to step 4 and repeat the above process, estimating each component sequentially until the robustness index is less than the threshold; according to Figure 5 After readjustment, the residual spectrum shown can be used for a second loop to extract the maximum peak value and its corresponding frequency coordinates, as follows. Figure 6 As shown. The parameter values ​​of the second component and the robustness index can be estimated through least-squares fitting. Simultaneously, the second residual spectrum can be obtained by subtracting the readjusted spectrum from the second incomplete reconstruction of the signal, as shown. Figure 7 As shown. Similarly, the third loop can Figure 8 The maximum peak value and its corresponding frequency coordinates shown in the figure are Figure 9 The third residual spectrum is shown in the figure. In the fourth iteration, the extracted maximum peak value and its corresponding frequency coordinates are shown in the figure. Figure 10 As shown. Least squares fitting yields the fourth component parameter values ​​and robustness index. Since the robustness index is less than the set threshold, the cyclic median is used. The final estimation results are as follows:

[0090] Signal 1: Initial Frequency FM slope The robustness indicator σ = 0.99;

[0091] Signal 2: Initial Frequency FM slope The robustness indicator σ = 0.98;

[0092] Signal 3: Initial Frequency FM slope The robustness indicator σ = 0.93;

[0093] Signal 4: Initial Frequency FM slope The robustness indicator σ = 0.12;

[0094] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for parameter estimation of multi-component linear frequency modulated signals based on incomplete spectrum reconstruction, characterized in that, The method comprises the following steps: S1, discretizing the input multi-component linear frequency modulation signal; S2, obtaining a full-component time-frequency spectrum by short-time Fourier transform and initializing the full-component time-frequency spectrum as an observation spectrum, and entering a loop; S3, extracting amplitude peak points and corresponding frequency coordinates in the observation spectrum; S4, correcting and updating the extracted amplitude peak points and corresponding frequency coordinates in the observation spectrum by using a Gaussian function; S5, fitting a single-component signal estimation result based on a least square method, setting a threshold for parameter inspection of the single-component signal, saving component estimation parameters if the parameters meet the component characteristics of the linear frequency modulation signal, and entering a signal reconstruction step; S6, incompletely reconstructing a signal according to the component estimation parameters, and obtaining a reconstructed spectrum by short-time Fourier transform; S7, obtaining a residual spectrum by subtracting the reconstructed spectrum from the observation spectrum, updating the residual spectrum to the observation spectrum by spectrum re-adjustment, repeating steps S3-S7, ending the loop when a parameter robustness index is less than a set threshold, and finally obtaining a multi-component parameter estimation result.

2. The method of claim 1, wherein, The multi-component linear frequency modulation signal comprises: wherein, is a sequence of multi-component linear frequency modulated signals; is a signal component number, I is the total number of components; is an amplitude; is an initial frequency; is a frequency modulation slope; is an initial phase; is a noise; is a time.

3. The method of claim 1, wherein, The discretization of the multi-component linear frequency modulation signal comprises: wherein is a sequence of discretized multi-component chirp signals; is a signal component number, I is a total number of components; is an amplitude; is an initial frequency; is a frequency modulation slope; is an initial phase; is a sampling time interval, , is a sampling frequency; is a sample number; is a discretized noise.

4. The method of claim 1, wherein, The obtaining of the full-component time-frequency spectrum by short-time Fourier transform and the initialization of the full-component time-frequency spectrum as the observation spectrum, and the entering of the loop comprise: S21: Select a window length of... The sliding step size is A Gaussian window is used as the analysis window, based on the window length... Gaussian window will signal Divided into Frame signal, denoted as ,in, Indicates the frame number; S22: interpolate and fill zeros to the sub-signal frame sub-signal perform an interpolation and zero filling operation to the sub-signal fill zeros after extend the sub-signal to ; S23: performing fast Fourier transform on the interpolated and zero-padded sub-signal to obtain a frequency spectrum of the sub-signal, denoted as , and the R-frame sub-signals can constitute a complete full-component time-frequency spectrum, denoted as . S24: The complete full-complexion time-frequency spectrum is obtained The observed spectrum enters the cycle of analysis.

5. The method of claim 4, wherein, The extraction of the amplitude peak points and the corresponding frequency coordinates in the observation spectrum comprises: Extracting the neutron signal spectrum from the observed spectrum The maximum peak value in and its corresponding frequency coordinates The maximum peak value of the R-frame signal and its corresponding frequency coordinates constitute the peak vector. and frequency coordinate vector ,Right now and ,in, Indicates the first The amplitude of the maximum peak value of the frame signal; Indicates the first The frequency coordinates corresponding to the maximum peak value of the frame signal.

6. The method of claim 4, wherein, The correction and the update of the extracted amplitude peak points and the corresponding frequency coordinates in the observation spectrum by using the Gaussian function comprise: The peak points are corrected using the method of undetermined coefficients, and the sub-signal spectrum is obtained. The maximum peak value in and its two neighboring values , The corresponding frequencies for the data analyzed are as follows: , , Substitute them into the Gaussian function expression respectively. , respectively obtained ;in, As the independent variable, As the dependent variable, These are the first, second, and third parameters to be determined, respectively. When the maximum value of the dependent variable of the Gaussian function is , the corrected amplitude peak value is , the corresponding frequency size is , the corrected amplitude peak vector is , and the corrected frequency vector is , wherein represents the amplitude of the maximum peak value of the corrected frame signal, represents the frequency corresponding to the maximum peak value of the corrected frame signal.

7. The method of claim 6, wherein, The fitting of the single-component signal estimation result based on the least square method, the setting of the threshold for the parameter inspection of the single-component signal, and the saving of the component estimation parameters if the parameters meet the component characteristics of the linear frequency modulation signal comprise: With frame number as the horizontal coordinate, frequency vector As the longitudinal coordinate as sample data, using linear regression method, based on least square fitting to get the parameter estimation results of single component signal: the estimated initial frequency is recorded as , the estimated frequency modulation slope is recorded as ; And the robustness index returned by fitting As the test result, if the robustness index Is greater than the set threshold , it is determined that the component characteristics of the linear frequency modulation signal, and the estimated parameters are saved.

8. The method of claim 7, wherein, The incomplete reconstruction of the signal according to the component estimation parameters and the obtaining of the reconstructed spectrum by short-time Fourier transform comprise: S61: extract the maximum element in the corrected updated amplitude peak vector and compute the amplitude estimate while ignoring the phase information, the component signal is non-perfectly reconstructed in the time domain where denotes the recovery coefficient, denotes the amplitude gain; S62: performing a short-time Fourier transform on the reconstructed signal to obtain a reconstructed spectrum of the component signal, denoted as .

9. The method of claim 8, wherein, The incomplete reconstruction of the component signal in the time domain by ignoring the phase information comprises: wherein is a non-completely reconstructed component signal, is an amplitude estimate, is an estimated initial frequency, is a sample number, is a sampling time interval, is an estimated frequency modulation slope.

10. The method of claim 1, wherein, The obtaining of the residual spectrum by subtracting the reconstructed spectrum from the observation spectrum and the updating of the residual spectrum to the observation spectrum by spectrum re-adjustment comprise: Subtracting the full-component time-frequency spectrum from the component signal reconstruction spectrum separates the signal , obtaining the residual spectrum of the remaining components ; wherein, denotes the full-component time-frequency spectrum, denotes the component signal reconstruction spectrum; Residual spectrum non-negativity, all values less than zero in the residual spectrum are set to zero, and the non-negativity-processed residual spectrum is taken as the observation spectrum for the next cycle, that is wherein, denotes the non-negativity-processed residual spectrum.

Images