Radar signal preprocessing method for adaptive filtering and noise reduction

Abstract

The invention provides a radar signal preprocessing method for adaptive filtering and noise reduction. The method comprises the following steps: decomposing a radar signal into a multi-order IMF by performing CEEMDAN on the radar signal, then judging the selection of the IMF through a fuzzy entropy and a cross correlation coefficient, then performing noise positioning and noise reduction processing on the selected IMF through a normalized correlation coefficient, and finally obtaining a noise-reduced signal through signal reconstruction. According to the method, the background noise can be effectively suppressed to the maximum extent while effective signal energy is reserved, and the precision of radar signal characteristic analysis is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of radar signal processing, and in particular relates to a radar signal preprocessing method of adaptive filtering and noise reduction. Background Art

[0002] As the electromagnetic environment becomes increasingly complex, the signals received by the electronic reconnaissance system become a superposition of multiple signals in the time domain and frequency domain. The signal radiation source types include radar, communication and other equipment. Among them, the radar echo signal has non-stationary discrete mathematical characteristics, and effective information is often hidden in the subtleties of the signal, making it more complicated to distinguish the target information from the clutter. These characteristics make traditional radar signal processing methods, such as matching filter theory, time-space domain filtering theory, and wavelet theory, etc., which will cause distortion of the radar signal after denoising to a certain extent.

[0003] The advantage of modal decomposition methods over the above denoising methods is that they do not require prior knowledge and do not have fixed basis functions, so they can adaptively decompose the signal modally. At the same time, this type of method can effectively separate signals of different components during the decomposition process, so this type of method can effectively separate different components of the input signal while performing denoising. A typical example is the Empirical Mode Decomposition (EMD) method, which decomposes signals based on the time scale characteristics of the data itself without presetting any basis functions, so it can adaptively process nonlinear and non-stationary signals. The EMD method decomposes complex signals into a finite number of intrinsic mode functions (IMFs), and these IMF components contain local characteristic signals of different time scales of the original signal. This method has significant advantages in processing non-stationary data. Summary of the invention

[0004] In order to overcome the shortcomings of existing noise reduction methods such as limited applicability, modal aliasing, and poor noise reduction effect when facing radar signals, the present invention provides a radar signal preprocessing method for adaptive filtering and noise reduction. The radar signal is decomposed into multi-order IMFs by performing adaptive noise complete set empirical mode decomposition (CEEMDAN) on the radar signal, and then the selection of IMFs is determined by fuzzy entropy and mutual correlation coefficients, and then the selected IMFs are noise-located and noise-reduced by normalized correlation coefficients, and finally the noise-reduced signal is obtained by signal reconstruction. The present invention can effectively suppress the background noise to the greatest extent while retaining the effective signal energy, thereby improving the accuracy of radar signal characteristic analysis.

[0005] A radar signal preprocessing method for adaptive filtering and noise reduction, characterized by the following steps:

[0006] Step 1: Use the CEEMDAN algorithm to perform modal decomposition on the radar signal to obtain the IMF components of each order from high to low frequency;

[0007] Step 2: Calculate the fuzzy entropy and mutual correlation coefficient of each order IMF component, and calculate the mean of all fuzzy entropies and the mean of all mutual correlation coefficients. Keep the IMF components whose fuzzy entropy is less than the mean of all fuzzy entropies and whose mutual correlation coefficient is greater than the mean of all mutual correlation coefficients, and eliminate other components.

[0008] Step 3: Calculate the normalized correlation coefficient between the retained IMF components of each order and the radar signal, and compare the normalized correlation coefficient with the threshold. If the normalized correlation coefficient is greater than the threshold, the location is determined to be useful information and the component value of the IMF component at that location is retained. Otherwise, the location is determined to be random noise and the component value of the IMF component at that location is set to zero.

[0009] Step 4: Perform signal accumulation and reconstruction on the IMF components processed in step 3 to obtain the denoised signal.

[0010] Specifically, the specific steps of the CEEMDAN algorithm are as follows:

[0011] Step 1.1: Decompose each radar signal sequence x by EMD i (t) = x(t) + ε0n i (t), and the first CEEMDAN modal component is calculated as follows:

[0012]

[0013] Where I represents the number of noise sequences, x i (t) represents the i-th radar signal sequence, IMF i1 Represents the radar signal sequence x i (t) is the intrinsic mode function obtained by EMD decomposition, x(t) represents the pure radar signal, ε0 is the noise coefficient, n i (t) represents different Gaussian white noises, i = 1, 2, ..., I;

[0014] Step 1.2: Let j = 1, and calculate the first residual signal r1(t) as follows:

[0015]

[0016] Step 1.3: Calculate the second CEEMDAN modal component as follows:

[0017]

[0018] Where E1(·) represents the first-order IMF component after EMD decomposition, ε1 represents n i (t) Noise coefficient of the first-order IMF component obtained after EMD decomposition;

[0019] Step 1.4: For j = 2, 3, ..., N, calculate the jth residual signal r as follows: j (t):

[0020]

[0021] Where N is the total number of modal components; the jth CEEMDAN modal component The calculation formula is as follows:

[0022]

[0023] Among them, E j-1 (·) represents the j-1th order IMF component after EMD decomposition;

[0024] All the above obtained j=1,2,3,…,N, which are the IMF components of each order from high to low frequency.

[0025] Specifically, the calculation formula of the fuzzy entropy is as follows:

[0026] FuzzyEn(m,r,N)=lnφ m (r)-lnφ m+1 (r) (6)

[0027] Wherein, FuzzyEn(m,r,N) represents the value of fuzzy entropy, m is the pattern dimension, which is equal to the order of IMF component, r is the similarity tolerance parameter, which is calculated according to r=R×δ, δ is the standard deviation of the m-th order IMF component, R is a coefficient ranging from 0.1 to 0.2, and N is the length of radar signal data;

[0028] φ m (r) represents the average value of all similarities except itself, calculated as follows:

[0029]

[0030] in, Represents the average value of similarity, and the calculation formula is as follows:

[0031]

[0032] in, Represents similarity, and the calculation formula is as follows:

[0033]

[0034] in, is the maximum absolute value of the difference between any elements i and j of the m-th order IMF component.

[0035] Specifically, the normalized correlation coefficient refers to the normalized coefficient of the correlation coefficient, and the calculation formula of the correlation coefficient is as follows:

[0036]

[0037] Among them, R m (n) represents the correlation coefficient between the m-th order IMF component and the radar signal x(n), L represents the data length of the radar signal, and IMF m (n) represents the discrete form of the m-th order IMF component, and x(n+l) represents the discrete form of the radar signal;

[0038] The normalized correlation coefficient is calculated as follows:

[0039]

[0040] Among them, NR m (n) represents the correlation coefficient R m (n) Normalization coefficient.

[0041] Specifically, the threshold in step 3 is an adaptive threshold, which varies according to different order IMFs, and its calculation formula is as follows:

[0042]

[0043] Among them, T m represents the adaptive threshold, m represents the order of the IMF component, L represents the data length of the radar signal, σ m is the noise variance of the m-th order IMF component, which is calculated as follows:

[0044]

[0045] Among them, H is the number of signals formed by equally dividing each order IMF component, and IMF m (n) represents the discrete form of the m-th order IMF component.

[0046] The beneficial effects of the present invention are as follows: since the CEEMDAN algorithm is used for signal decomposition, the modal aliasing problem in the signal decomposition can be effectively suppressed; at the same time, since a signal selection and denoising method based on adaptive parameters is used, a better denoising effect can be obtained; and the denoising effect of the method can be effectively changed by only debugging the parameters; the operation is simple and the applicability is good; since signals with different meanings in the radar signal can be effectively separated, the modal aliasing phenomenon can be effectively avoided from affecting the characteristic analysis of signals with different meanings; the present invention can maximize the retention of the energy of the effective signal and can suppress the background noise of the radar signal as much as possible. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is a flow chart of a radar signal preprocessing method for adaptive filtering and noise reduction of the present invention.

[0048] Figure 2 is a radar signal of a simulation example of the present invention;

[0049] Figure 3 is the signal obtained after the simulation example of the present invention is processed by the CEEMDAN method;

[0050] Figure 4 It is the signal obtained after the simulation example of the present invention is processed by the inventive method. DETAILED DESCRIPTION

[0051] The present invention is further described below in conjunction with the accompanying drawings and embodiments. The present invention includes but is not limited to the following embodiments.

[0052] The present invention provides a radar signal preprocessing method for adaptive filtering and noise reduction, such as Figure 1 As shown, the specific implementation process is as follows:

[0053] 1. Use the CEEMDAN algorithm to perform modal decomposition on the radar signal and obtain the IMF components of each order from high to low frequency.

[0054] The present invention adopts a Complete Ensemble Empirical Mode Decomposition of Adaptive Noise (CEEMDAN) method to decompose radar signals into multi-order Intrinsic Mode Functions (IMFs). The specific process is as follows:

[0055] Step 1.1: Decompose each radar signal sequence x by EMD i (t) = x(t) + ε0n i(t), and the first CEEMDAN modal component is calculated as follows:

[0056]

[0057] Where I represents the number of noise sequences, x i (t) represents the i-th radar signal sequence, IMF i1 Represents the radar signal sequence x i (t) is the intrinsic mode function obtained by EMD decomposition, x(t) represents the pure radar signal, ε0 is the noise coefficient, n i (t) represents different Gaussian white noises, i = 1, 2, ..., I;

[0058] Step 1.2: Let j = 1, and calculate the first residual signal r1(t) as follows:

[0059]

[0060] Step 1.3: Calculate the second CEEMDAN modal component as follows:

[0061]

[0062] Where E1(·) represents the first-order IMF component after EMD decomposition, ε1 represents n i (t) Noise coefficient of the first-order IMF component obtained after EMD decomposition;

[0063] Step 1.4: For j = 2, 3, ..., N, calculate the jth residual signal r as follows: j (t):

[0064]

[0065] Where N is the total number of modal components; the jth CEEMDAN modal component The calculation formula is as follows:

[0066]

[0067] Among them, E j-1 (·) represents the j-1th order IMF component after EMD decomposition;

[0068] All the above obtained j=1,2,3,…,N, which are the IMF components of each order from high to low frequency.

[0069] 2. Calculate the fuzzy entropy and mutual correlation coefficient of each order IMF component, and calculate the mean of all fuzzy entropies and the mean of all mutual correlation coefficients. Keep the IMF components whose fuzzy entropy is less than the mean of all fuzzy entropies and whose mutual correlation coefficient is greater than the mean of all mutual correlation coefficients, and eliminate other components.

[0070] The calculation formula of the fuzzy entropy is as follows:

[0071]

[0072] Wherein, FuzzyEn(m,r,N) represents the value of fuzzy entropy, m is the pattern dimension, which is equal to the order of IMF component, r is the similarity tolerance parameter, which is calculated according to r=R×δ, δ is the standard deviation of the m-th order IMF component, R is a coefficient ranging from 0.1 to 0.2, and N is the length of radar signal data;

[0073] φ m (r) represents the average value of all similarities except itself, calculated as follows:

[0074]

[0075] in, Represents the average value of similarity, and the calculation formula is as follows:

[0076]

[0077] in, Represents similarity, and the calculation formula is as follows:

[0078]

[0079] in, is the maximum absolute value of the difference between any elements i and j of the m-th order IMF component.

[0080] 3. Calculate the normalized correlation coefficient between the retained IMF components of each order and the radar signal, and compare the normalized correlation coefficient with the threshold. If the normalized correlation coefficient is greater than the threshold, the location is determined to be useful information and the component value of the IMF component at that location is retained. Otherwise, the location is determined to be random noise and the component value of the IMF component at that location is set to zero.

[0081] The normalized correlation coefficient refers to the normalized coefficient of the correlation coefficient. The calculation formula of the correlation coefficient is as follows:

[0082]

[0083] Among them, R m(n) represents the correlation coefficient between the m-th order IMF component and the radar signal x(n), L represents the data length of the radar signal, and IMF m (n) represents the discrete form of the m-th order IMF component, and x(n+l) represents the discrete form of the radar signal;

[0084] The normalized correlation coefficient is calculated as follows:

[0085]

[0086] Among them, NR m (n) represents the correlation coefficient R m (n) Normalization coefficient.

[0087] The threshold is an adaptive threshold, which varies according to different order IMFs, and its calculation formula is as follows:

[0088]

[0089] Among them, T m represents the adaptive threshold, m represents the order of the IMF component, L represents the data length of the radar signal, σ m is the noise variance of the m-th order IMF component, which is calculated as follows:

[0090]

[0091] Among them, H is the number of signals formed by equally dividing each order IMF component, and IMF m (n) represents the discrete form of the m-th order IMF component.

[0092] 4. Perform signal accumulation and reconstruction on the IMF components processed in step 3 to obtain the denoised signal.

[0093] In order to verify the effectiveness of the present invention, a noise reduction simulation experiment was carried out on the radar signal. Figure 2 The time domain waveform of the radar signal of the simulation example is shown in Figure 2. Figure 3 This is the time domain waveform of the result signal obtained after the radar signal is denoised only by the CEEMDAN method. Figure 4 This is the time domain waveform diagram of the result signal obtained after the radar signal is denoised by the method of the present invention. Figure 3 and Figure 4 It can be seen that the waveforms of the radar signals obtained after denoising are basically the same, but the background noise of the signal denoised only by the CEEMDAN method will fluctuate slightly in some time periods, while the result of denoising by the method of the present invention can hardly see the existence of background noise from the time domain waveform, which proves that the method of the present invention has a better denoising effect.

Claims

1. A radar signal preprocessing method for adaptive filtering and noise reduction, characterized in that Here are the steps: Step 1: Use the CEEMDAN algorithm to perform modal decomposition on the radar signal to obtain the IMF components of each order from high to low frequency; Step 2: Calculate the fuzzy entropy and mutual correlation coefficient of each order IMF component, and calculate the mean of all fuzzy entropies and the mean of all mutual correlation coefficients. Keep the IMF components whose fuzzy entropy is less than the mean of all fuzzy entropies and whose mutual correlation coefficient is greater than the mean of all mutual correlation coefficients, and eliminate other components. Step 3: Calculate the normalized correlation coefficient between the retained IMF components of each order and the radar signal, and compare the normalized correlation coefficient with the threshold. If the normalized correlation coefficient is greater than the threshold, the location is determined to be useful information and the component value of the IMF component at that location is retained. Otherwise, the location is determined to be random noise and the component value of the IMF component at that location is set to zero. Step 4: Perform signal accumulation and reconstruction on the IMF components processed in step 3 to obtain the denoised signal.

2. The radar signal preprocessing method of adaptive filtering and noise reduction according to claim 1, characterized in that: The specific steps of the CEEMDAN algorithm are as follows: Step 1.1: Decompose each radar signal sequence x by EMD i (t) = x(t) + ε0n i (t), and the first CEEMDAN modal component is calculated as follows: Where I represents the number of noise sequences, x i (t) represents the i-th radar signal sequence, IMF i1 Represents the radar signal sequence x i (t) is the intrinsic mode function obtained by EMD decomposition, x(t) represents the pure radar signal, ε0 is the noise coefficient, n i (t) represents different Gaussian white noises, i = 1, 2, ..., I; Step 1.2: Let j = 1, and calculate the first residual signal r1(t) as follows: Step 1.3: Calculate the second CEEMDAN modal component as follows: Where E1(·) represents the first-order IMF component after EMD decomposition, ε1 represents n i (t) Noise coefficient of the first-order IMF component obtained after EMD decomposition; Step 1.4: For j = 2, 3, ..., N, calculate the jth residual signal r as follows: j (t): Where N is the total number of modal components; the jth CEEMDAN modal component The calculation formula is as follows: Among them, E j-1 (·) represents the j-1th order IMF component after EMD decomposition; All the above obtained j=1,2,3,…,N, which are the IMF components of each order from high to low frequency.

3. The radar signal preprocessing method of adaptive filtering and noise reduction according to claim 1, characterized in that: The calculation formula of the fuzzy entropy is as follows: FuzzyEn(m,r,N)=lnφ m (r)-lnφ m+1 (r) (6) Wherein, FuzzyEn(m,r,N) represents the value of fuzzy entropy, m is the pattern dimension, which is equal to the order of IMF component, r is the similarity tolerance parameter, which is calculated according to r=R×δ, δ is the standard deviation of the m-th order IMF component, R is a coefficient ranging from 0.1 to 0.2, and N is the length of radar signal data; φ m (r) represents the average value of all similarities except itself, calculated as follows: in, Represents the average value of similarity, and the calculation formula is as follows: in, Represents similarity, and the calculation formula is as follows: in, is the maximum absolute value of the difference between any elements i and j of the m-th order IMF component.

4. The radar signal preprocessing method of adaptive filtering and noise reduction according to claim 1, characterized in that: The normalized correlation coefficient refers to the normalized coefficient of the correlation coefficient. The calculation formula of the correlation coefficient is as follows: Among them, R m (n) represents the correlation coefficient between the m-th order IMF component and the radar signal x(n), L represents the data length of the radar signal, and IMF m (n) represents the discrete form of the m-th order IMF component, and x(n+l) represents the discrete form of the radar signal; The normalized correlation coefficient is calculated as follows: Among them, NR m (n) represents the correlation coefficient R m (n) Normalization coefficient.

5. The radar signal preprocessing method of adaptive filtering and noise reduction according to claim 1, characterized in that: The threshold described in step 3 is an adaptive threshold, which varies according to different order IMFs. Its calculation formula is as follows: Among them, T m represents the adaptive threshold, m represents the order of the IMF component, L represents the data length of the radar signal, σ m is the noise variance of the m-th order IMF component, which is calculated as follows: Among them, H is the number of signals formed by equally dividing each order IMF component, and IMF m (n) represents the discrete form of the m-th order IMF component.

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