A method for estimating parameters of a linear frequency modulation signal based on local iterative filtering

Abstract

The application belongs to the technical field of linear frequency modulation signal parameter estimation, and discloses a linear frequency modulation signal parameter estimation method based on local iterative filtering, which comprises the following steps: S1, carrying out denoising processing on the signal intercepted by an interference receiver; S2, decomposing each LFM component of the denoised signal to different IMF through a local iterative filtering algorithm; S3, carrying out time-frequency analysis on each component to obtain the instantaneous frequency corresponding to the linear frequency modulation signal; and S4, carrying out parameter estimation on each linear frequency modulation component according to the instantaneous frequency. The local iterative filtering algorithm can realize adaptive decomposition of the multi-component LFM signal by dynamically adjusting the filter length, and effectively solves the cross interference problem of the existing time-frequency analysis method when facing the multi-component linear frequency modulation signal. Compared with the prior art, the application can effectively remove noise, retain the characteristics of each LFM component, and has high estimation accuracy of the linear frequency modulation signal parameters, i.e. initial frequency and frequency modulation rate.

Description

Technical Field

[0001] This invention relates to the field of linear frequency modulated signal parameter estimation technology, specifically to a linear frequency modulated signal parameter estimation method based on local iterative filtering. Background Technology

[0002] Linear Frequency Modulation (LFM) signals are frequency-modulated signals whose frequency changes linearly with time, and are a typical type of non-stationary signal. They are characterized by long range and high resolution, and are widely used in radar, communications, seismic exploration, and other fields. Parameter estimation for LFM signals is a crucial problem in electronic countermeasures, passive radar, and synthetic aperture imaging. In electronic countermeasures, jamming systems generate corresponding jamming signals based on the parameters of the LFM radar's transmitted signals, forming coherent interference and significantly improving jamming efficiency. In synthetic aperture imaging, the Doppler signal generated by relative motion can be modeled as an LFM signal, and its parameters explain the target's motion characteristics and azimuth information. Therefore, accurate estimation of LFM signals, especially multi-component LFM signals, is of great significance and value for radar signal processing and radar countermeasures.

[0003] Commonly used methods for parameter estimation of LFM signals include: two-dimensional search methods based on maximum likelihood estimation, one-dimensional search methods based on fractional Fourier transform, and instantaneous frequency analysis methods based on time-frequency transform. Among these, search algorithms based on maximum likelihood estimation and fractional Fourier transform can achieve optimal estimation under white noise, but these algorithms require global search, resulting in high computational cost and poor real-time performance. Instantaneous frequency analysis methods based on time-frequency transform utilize tools such as Short-Time Fourier Transform (STFT), Wigner-Ville Distribution (WVD), and cubic phase functions to obtain the modulation parameters of the signal under test from its instantaneous frequency. WVD, in particular, can achieve high time and frequency resolution simultaneously and is currently the most commonly used time-frequency analysis tool for LFM signal parameter estimation. However, when the signal contains multiple LFM components with the same or similar modulation frequencies, WVD can produce severe crossover, leading to spurious components.

[0004] Regarding data-driven signal decomposition algorithms, existing algorithms such as Empirical Mode Decomposition (EMD) and Iterative Filtering (IF) have achieved great success in the field of signal time-frequency analysis. Among them, the IF algorithm, based on the EMD framework, uses a low-pass filter instead of cubic spline interpolation to extract individual Intrinsic Mode Functions (IMFs), making the algorithm more interpretable, with better convergence and stronger robustness. Based on the IF algorithm, the signal is adaptively decomposed into individual IMFs, and time-frequency analysis is performed through the IMFs to obtain estimated parameters, making it possible to use it for linear frequency modulated (LFM) signal parameter estimation. However, this method uses a fixed filter length M when decomposing the signal. Therefore, when processing large-bandwidth signals such as LFM signals, this can lead to the same signal being decomposed into different IMFs, resulting in low estimation accuracy of the initial frequency and modulation frequency parameters of LFM signals. Summary of the Invention

[0005] This invention aims to provide a parameter estimation method for linear frequency modulated (LFM) signals based on Local Iterative Filtering (LIF). It takes into account the impact of data noise on the algorithm's performance and proposes a denoising method based on second-order variational regularization, effectively reducing the influence of signal noise on the parameter estimation results. After receiving a noisy multi-component LFM signal, two variational regularization operations are used to reduce the noise's impact on the LFM decomposition algorithm. When performing time-frequency analysis on each IMF, instead of using the instantaneous frequency definition based on the global operator Hilbert transform, the method analyzes the Cicone instantaneous frequency definition of local frequencies, improving the analysis effect of local frequencies. This method achieves high estimation accuracy for the LFM signal parameters—initial frequency and frequency modulation frequency.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for estimating parameters of a linear frequency modulated signal based on local iterative filtering includes the following steps:

[0008] S1. The signal intercepted by the interference receiver is denoised using a second-order variational regularization algorithm; it first undergoes a second-order variational regularization and then a Wiener filter.

[0009] S2. The LIF algorithm is used to decompose each LFM component of the denoised signal in S1 into different IMFs. The algorithm contains two nested loops.

[0010] S3. Perform time-frequency analysis on each IMF obtained in S2 to obtain the instantaneous frequency of the corresponding LFM signal; wherein, the instantaneous frequency adopts the instantaneous frequency defined by Citone;

[0011] S4. Estimate the parameters of each LFM component based on the instantaneous frequency obtained in S3.

[0012] Furthermore, in S1, when the signal intercepted by the interference receiver contains I different LFM components, the expression for the intercepted signal is:

[0013]

[0014] When the intercepted signal carries noise, its expression is:

[0015]

[0016] Among them, A i a i and b i These represent the amplitude, initial frequency, and modulation frequency of the i-th LFM component, respectively, and N0(n) represents Gaussian white noise.

[0017] Furthermore, in S1, the Wiener filtering process is performed as follows:

[0018] Let s r Let the intercepted signal vector of the interfering receiver represent the signal denoising process, which can be represented by the following optimization problem:

[0019]

[0020] In the formula, λ1 represents the regularization parameter, and H represents the second derivative; it is solved by finding the extrema:

[0021]

[0022] To further remove residual noise components from the signal, the denoised signal is processed as follows:

[0023]

[0024] This process is known as Wiener filtering.

[0025] Furthermore, in S2, the instantaneous period is represented by the interval Per(n) between the two most recent extreme points of the signal at time n, and the filter length M(n) is dynamically adjusted according to the instantaneous period.

[0026] M(n) = Per(n)

[0027] The envelope extraction process of the local iterative filtering algorithm is represented as follows:

[0028]

[0029] Define s1(n) = s(n), and s in+1 (n)=s in (n)-LP[s in [n], then the first eigenmode function obtained by decomposition is expressed as:

[0030]

[0031] After obtaining IMF1(n), let s1(n) = s(n) - IMF1(n), and repeat the above process to obtain IMF2(n); after two inner and outer loops and satisfying the preset number of iterations or the iteration stopping condition, the original signal is finally decomposed into:

[0032] r(n)=s(n)-IMF1(n)-IMF2(n)…-IMF OU (n)

[0033] Where r(n) represents the residual trend component, and OU represents the number of iterations after the iteration conditions are met.

[0034] Furthermore, in S3, the analytical expression of the signal is:

[0035]

[0036] According to this expression, the instantaneous frequency of the signal is represented as:

[0037]

[0038] Furthermore, in S4, the parameters of the LFM component include the initial frequency and the modulation frequency; based on the definition of the instantaneous frequency of the signal, the initial frequency and modulation slope of the linear frequency modulated component are finally obtained as follows:

[0039] a i =f i (0)

[0040] b i (n)=f i (n)-f(n-1)

[0041] Among them, a i and b i These represent the initial frequency and modulation frequency of the i-th LFM component, respectively.

[0042] The principles and beneficial effects of the technical solution are as follows:

[0043] This invention provides a method for estimating linear frequency modulated (LFM) signal parameters based on local iterative filtering. Building upon the IF algorithm, it dynamically adjusts the filter length to decompose each LFM component of the signal into different IMFs, and obtains the modulation parameters of each LFM component based on the instantaneous frequency of the IMF. To avoid the influence of noise on the LIF algorithm, a second-order variational denoising method is designed; using the Citone instantaneous frequency definition, the estimation accuracy of the LFM signal parameters—initial frequency and modulation frequency—is high.

[0044] The effectiveness of the proposed method was verified by MATLAB simulation and experimental data. The results show that:

[0045] 1) The second-order variational denoising method can still effectively remove noise and preserve LFM signal characteristics even under a 0dB signal-to-noise ratio condition;

[0046] 2) The LIF algorithm can effectively decompose LFM components with the same slope into different IMFs;

[0047] 3) The method provided by this invention has a parameter estimation error of less than 0.1% under a signal-to-noise ratio of 0dB, and has significant advantages over traditional time-frequency analysis methods in estimating multi-component LFM signals. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating the parameter estimation method for linear frequency modulated signals based on local iterative filtering according to the present invention.

[0049] Figure 2 The diagram shows the effect of first-order variational regularization in the embodiments provided by the present invention.

[0050] Figure 3 The diagram shows the effect of second-order variational regularization in the embodiments provided by the present invention;

[0051] Figure 4 The waveform of the signal denoising algorithm provided in the embodiments of the present invention is shown in the figure.

[0052] Figure 5 The waveform diagram of the intercepted signal in the signal denoising algorithm provided in the embodiments of the present invention;

[0053] Figure 6 The above is a waveform diagram of the intercepted signal after second-order variational regularization processing in the signal denoising algorithm provided in the embodiments of the present invention.

[0054] Figure 7 The signal waveform obtained by Wiener filtering after second-order variational regularization in the embodiment provided by the present invention is shown.

[0055] Figure 8The filter length selection, i.e. the selection of the instantaneous period, is used in the embodiments provided by the present invention;

[0056] Figure 9 This is a signal decomposition effect diagram of the local iterative filtering algorithm in the embodiment of the present invention when the signal-to-noise ratio is 0dB;

[0057] Figure 10 The instantaneous frequency estimation results of each signal in the parameter estimation method provided in the embodiment of the present invention at a signal-to-noise ratio of 10dB are shown in the figure.

[0058] Figure 11 The instantaneous frequency estimation results of each signal in the parameter estimation method provided in the embodiment of the present invention when the signal-to-noise ratio is 0dB are shown in the figure.

[0059] Figure 12 The instantaneous frequency estimation results of each signal using the short-time Fourier transform method in the embodiments provided by the present invention at a signal-to-noise ratio of 10dB are shown in the figure.

[0060] Figure 13 The diagram shows the instantaneous frequency estimation results of each signal using the Wegener-Villi distribution method in the embodiments provided by the present invention when the signal-to-noise ratio is 10dB. Detailed Implementation

[0061] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments:

[0062] like Figure 1 As shown, a method for estimating parameters of a linear frequency modulated signal based on local iterative filtering includes the following steps:

[0063] S1. The signal intercepted by the interference receiver is denoised using a second-order variational regularization algorithm; it is first subjected to second-order variational regularization, and then to Wiener filtering (first-order variational regularization).

[0064] The second-order variational regularization denoising method is as follows: In this embodiment, a radar jammer is used as the application platform. Assuming the signal intercepted by the jamming receiver contains i different LFM components, the intercepted signal can be modeled as follows:

[0065]

[0066] Where A i a i and b i These represent the amplitude, initial frequency, and modulation frequency of the i-th LFM component, respectively.

[0067] When the intercepted signal carries noise, it is represented as follows:

[0068]

[0069] Where N0(n) represents Gaussian white noise; let s r Let the intercepted signal vector of the interfering receiver represent the signal denoising process, which can be represented by the following optimization problem:

[0070]

[0071] In the formula, λ1 represents the regularization parameter, and H represents the second derivative; it is solved by finding the extrema:

[0072]

[0073] To further remove residual noise components from the signal, Wiener filtering (first-order variational regularization) is applied to the denoised signal:

[0074]

[0075] like Figure 2 and Figure 3 As shown, the sine wave component is preserved and the influence of noise is removed through two variational regularizations. Compared with the first-order variational regularization, the second-order variational regularization makes the energy distribution of the sine wave component more concentrated and the difference from the noise distribution greater, which is more conducive to noise removal; however, the computational cost of the second-order variational regularization is greater than that of the first-order variational regularization. Therefore, the algorithm chooses the first-order variational regularization when further removing the noise components, and does not use the second-order variational regularization again.

[0076] like Figures 4 to 7 As shown, after receiving the signal under test, the jammer first removes environmental clutter and noise using a second-order variational regularization denoising algorithm. The results show the signal under test at a 0dB signal-to-noise ratio, the intercepted signal, second-order variational denoising, and Wiener filtering denoising. Figure 6 It can be seen that the second-order variational method removes most of the noise in the intercepted signal, but residual components still exist, which causes the signal extrema to not truly reflect the instantaneous period of the signal; from Figure 7 It can be seen that the signal is smoother after Wiener filtering and the noise residue is completely removed. Compared with the original signal, the high-frequency part of the denoised signal is attenuated due to the influence of Wiener filtering, but it retains the extreme point information of the original signal. That is, the denoising algorithm does not change the time-frequency characteristics of the intercepted signal.

[0077] S2. The LIF algorithm is used to decompose each LFM component of the denoised signal in S1 into different IMFs. The algorithm contains two nested loops.

[0078] The IF algorithm, based on the EMD algorithm framework, uses a low-pass filter instead of cubic spline interpolation to extract each IMF, making the algorithm more interpretable, with better convergence and stronger robustness. According to the IF algorithm principle, for any signal s(t), the algorithm removes the signal envelope mean through a low-pass filter w(t), and the extracted envelope mean is expressed as...

[0079]

[0080] Where w(t) is any low-pass filter with a compact structure, and in this embodiment, an FP low-pass filter based on the Fock-Planck equation is selected; M is the filter length, which is determined by the signal length N, the number of signal extrema e, and the constant κ.

[0081]

[0082] Define s1(n) = s(n), and s in+1 (n)=s in (n)-LP[s in [n], then the first eigenmode function obtained by decomposition is expressed as:

[0083]

[0084] After obtaining IMF1(n), let s1(n) = s(n) - IMF1(n), and repeat the above process to obtain IMF2(n); after two inner and outer loops and satisfying the preset number of iterations or the iteration stopping condition, the original signal is finally decomposed into

[0085] r(n)=s(n)-IMF1(n)-IMF2(n)…-IMF OU (n)

[0086] Where r(n) represents the residual trend component, and OU represents the number of iterations after the iteration conditions are met;

[0087] This invention proposes a LIF algorithm based on the IF algorithm framework. This algorithm avoids the same signal being decomposed into different IMFs by dynamically adjusting the filter length M(n), making it more suitable for time-frequency analysis of large-bandwidth signals. The filter length M(n) is determined based on the instantaneous period of the signal. Here, the instantaneous period is represented by the interval Per(n) between the two nearest extreme points of the signal at time n.

[0088] M(n) = Per(n)

[0089] The envelope extraction process of the LIF algorithm can then be expressed as follows:

[0090]

[0091] Similarly, after two inner and outer loops and meeting the iteration stopping condition, the original signal can be decomposed into multiple IMFs;

[0092] like Figure 8 As shown, according to the LIF algorithm principle, its core lies in the length of the low-pass filter. To obtain better decomposition results, the low-pass filter length M is equal to the local instantaneous period of the signal. However, in reality, the true instantaneous period of the signal is difficult to obtain, so the interval between the two extreme points of the signal is used to represent the instantaneous period. However, the instantaneous period represented by the interval between extreme points has large fluctuations. To improve the robustness of the algorithm, this embodiment selects the average of multiple local instantaneous periods as the filter length.

[0093] like Figure 9 The simulation results of the LIF algorithm under a 0dB signal-to-noise ratio are shown. The results indicate that the LFM 1 component of the original signal is decomposed into IMF 1, while the LFM 2 component is decomposed into IMF 2. That is, each LFM component of the signal under test is decomposed into a different IMF. Due to the influence of the Wiener filtering algorithm, the amplitudes of each IMF differ somewhat from the LFM components, but their frequency characteristics are basically consistent with the original signal.

[0094] like Figure 10 and Figure 11 As shown, estimating the instantaneous frequency of each IMF ultimately yields the estimated instantaneous frequency of each LFM component. Under different signal-to-noise ratios (SNRs), the instantaneous frequency variation trends of IMF 1 and IMF 2 are consistent with those of LFM 1 and LFM 2 components. Since the denoising algorithm cannot completely remove the influence of noise on the signal under test, the instantaneous frequencies of each IMF obtained by the LIF algorithm have a certain error compared to the true frequencies of their corresponding LFM components. This error is mainly reflected in the random perturbations in the instantaneous frequencies of the IMFs caused by noise, and these perturbations are more pronounced at lower SNRs. These perturbations can be removed using a simple smoothing algorithm. Based on the smoothed instantaneous frequencies of each IMF, the modulation parameters of each LFM component can finally be obtained.

[0095] like Figure 12 and Figure 13 As shown in the figure, for comparison, under a 10dB signal-to-noise ratio (SNR) condition, the simulation results of the short-time Fourier transform and the Wegener-Villi distribution of the intercepted signal show that the short-time Fourier transform only represents a single LFM signal in the time-frequency domain, and cannot distinguish the various LFM components in the original signal; while the Wegener-Villi distribution can distinguish the various components in the original signal, but it introduces a significant cross term, leading to the appearance of a non-existent LFM component. Therefore, the frequency modulation signal analysis and parameter estimation algorithm proposed in this invention has significant advantages over other time-frequency analysis methods when processing multi-component LFM signals with the same or similar slopes.

[0096] S3. Perform time-frequency analysis on each IMF obtained in S2 to obtain the instantaneous frequency of the corresponding LFM signal; wherein, the instantaneous frequency adopts the instantaneous frequency defined by Citone;

[0097] For a given intrinsic mode function IMF(n), assuming its cubic spline interpolation envelope E(n) and the cubic spline interpolation envelope E′(n) of its first-order difference function IMF′(n), then Citone's analytic expression for the signal is:

[0098]

[0099] The instantaneous frequency of the signal at this time can be expressed as:

[0100]

[0101] The instantaneous frequency defined by Citone is essentially achieved by normalizing the amplitude of the intrinsic mode function, thereby avoiding the influence of amplitude variations on the frequency.

[0102] S4. Based on the instantaneous frequency obtained in S3, estimate the parameters of each LFM component—initial frequency and frequency modulation frequency.

[0103] Based on the definition of instantaneous frequency of the signal, the initial frequency and modulation slope of the linear frequency modulated component are finally obtained as follows:

[0104] a i =f i (0)

[0105] b i (n)=f i (n)-f(n-1)

[0106] Under microwave anechoic chamber conditions, two digital RF signal sources, E8257D, were used to simulate the radar transmitter and ambient noise, respectively. An N5193 signal source and an M9203A digital receiver were used to simulate the interference receiver. The signals under test were collected, and the parameter estimation accuracy of the algorithm was analyzed. During the experiment, the simulated radar transmitter and simulated ambient noise were placed 6m away from the radar, with the antenna beam main lobes aligned with each other.

[0107] The center frequency of the simulated radar transmitted signals is 5.5 GHz, the power is 10 dBm, the modulation bandwidth is 250 MHz, and the modulation period is 1 ms. The ambient noise is a Gaussian noise frequency-modulated signal, with the power increased from 0 dBm to 10 dBm to meet the SNR of 0–10 dB. The jammer's down-conversion module has a center frequency of 5 GHz, and the digital receiver's A / D sampling rate is 5 GHz / s.

[0108] One hundred experiments were conducted under various signal-to-noise ratio (SNR) conditions, and the average of the experimental results was used as the test result to evaluate the algorithm's performance. The signal parameter estimation errors under different SNR conditions are shown in Table 1. According to the test results, the method still has high parameter estimation accuracy under a 0dB SNR condition, with an estimation error of less than 0.1%.

[0109] Table 1. Signal parameter estimation errors under different signal-to-noise ratios

[0110] 10 0.01 0.34 5 0.04 0.59 0 0.18 1.73

[0111] The above descriptions are merely embodiments of the present invention, and common knowledge regarding specific technical solutions or characteristics is not elaborated upon here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the technical solutions of the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the implementation of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A method for estimating parameters of a linear frequency modulated signal based on local iterative filtering, characterized in that, Includes the following steps: S1. The signal intercepted by the interference receiver is denoised using a second-order variational regularization algorithm; it first undergoes a second-order variational regularization and then a Wiener filter. S2. The LIF algorithm is used to decompose each LFM component of the denoised signal in S1 into different IMFs. The algorithm contains two nested loops. S3. Perform time-frequency analysis on each IMF obtained in S2 to obtain the instantaneous frequency of the corresponding LFM signal; wherein, the instantaneous frequency adopts the instantaneous frequency defined by Citone; S4. Estimate the parameters of each LFM component based on the instantaneous frequency obtained in S3. In S1, the signal intercepted by the interference receiver includes I The expression for the intercepted signal is as follows: (The expression is missing from the original text.) When the intercepted signal carries noise, its expression is: in, , and These represent the amplitude, initial frequency, and modulation frequency of the i-th LFM component, respectively. Indicates Gaussian white noise; The method for Wiener filtering is as follows: make Let the intercepted signal vector of the interfering receiver represent the signal denoising process, which can be represented by the following optimization problem: In the formula, Represents the regularization parameter. Denote the second derivative; solve for it using extrema: To further remove residual noise components from the signal, the denoised signal is processed as follows: This process is known as Wiener filtering. In S2, the instantaneous period is represented by the interval Per(n) between the two nearest extreme points of the signal at time n, and the filter length M(n) is dynamically adjusted according to the instantaneous period. The envelope extraction process of the local iterative filtering algorithm is represented as follows: definition ,and The first eigenmode function obtained from the decomposition is expressed as: get Afterwards, order By repeating the above process, you can obtain After two loops, inner and outer, and meeting the preset number of iterations or the iteration stopping condition, the original signal is finally decomposed into: in Represents the residual trend component. This indicates the number of iterations after the iteration condition is met; In S3, the analytical expression of the signal is: According to this expression, the instantaneous frequency of the signal is represented as: In S4, the parameters of the LFM component include the initial frequency and the modulation frequency; based on the definition of the instantaneous frequency of the signal, the initial frequency and modulation slope of the linear frequency modulated component are finally obtained as follows: in, and These represent the initial frequency and modulation frequency of the i-th LFM component, respectively.

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