CN111985426A - Sea clutter hybrid denoising algorithm based on variational modal decomposition - Google Patents

Abstract

The invention discloses a sea clutter mixing denoising algorithm based on variational modal decomposition, which comprises the steps of firstly adopting a C-C method to carry out phase space reconstruction, determining embedded dimension and delay time, realizing the preprocessing of chaotic signals, then carrying out variation modal decomposition on the sea clutter signal containing the target signal to obtain a limited number of simple Intrinsic Mode Functions (IMF), analyzing the autocorrelation characteristic of the decomposed signal, performing wavelet hard threshold filtering on the modal component containing the noise characteristics, reconstructing the filtered component and residual component to obtain a denoised signal, finally establishing a chaotic time series prediction model by combining with an LSSVM (least squares support vector machine), detecting a weak signal submerged in sea clutter from a prediction error, comparing the root mean square error before and after denoising, the root mean square error is used as an evaluation standard of the denoising effect, and an experimental result shows that the denoising effect is good, and the predicted root mean square error after denoising is 0.00055, which is two orders of magnitude lower than the predicted root mean square error without denoising by 0.0125.

Description

Sea clutter hybrid denoising algorithm based on variational modal decomposition

Technical Field

The invention belongs to the technical field of radar data processing, and particularly relates to a sea clutter hybrid denoising algorithm based on variational modal decomposition.

Background

In civil or military applications, the reliability of radar detection technology is increasingly dependent, however, the radar is easily interfered by internal and external noise in actual work, and therefore, denoising becomes an inevitable step for radar signal processing. When the sea radar works, the sea radar can be influenced by the self-measuring noise of the radar and external dynamic noise such as sea clutter, and the influence on the work of the sea radar is the largest due to the fact that the physical mechanism of the sea clutter is complex and changeable, and the characteristics of non-Gaussian, non-linear and non-stable are obvious. Therefore, sea clutter denoising becomes a primary problem for sea radar target detection.

The weak signal detection under the background of the sea clutter is a hotspot in the field of signal processing, and the denoising problem is taken as an indispensable step for the research of the weak signal detection, and is highly valued by scholars at home and abroad. In 1997, Haykin and the like adopt a three-point moving average method to denoise when researching the chaos characteristic of sea clutter, and the denoise method can change the performance of signals, so that some scholars question the research on the chaos characteristic. Hunag proposes an Empirical Mode Decomposition (EMD) algorithm to process non-stationary, nonlinear signals, Flandrin et al decomposed fractal gaussian noise in 2004 using the EMD method, and found that EMD Decomposition can be equivalent to a narrow band filter bank to filter signals. Salim proposed that the EMD be replaced by a Variational Modal Decomposition (VMD) in order to easily separate similar frequencies when studying economic and financial time series, and that EMD be superior to the Mean Absolute Error (MAE), the mean percent absolute error (MAPE), and the mean square error (RMSE) among the three evaluation indexes. In China, Zhang Ji firstly provides a decomposition layer number determining method based on white noise detection and a threshold value determining method based on 3 sigma rule thought in order to solve the problems of threshold value selection and signal decomposition layer number when a wavelet denoising algorithm is researched. In 2006, the filtering and denoising method based on EMD is applied to the research of the GPS multipath effect by Daohu, and the result shows that the EMD can effectively remove instantaneous strong noise and extract a more accurate multipath effect repeatability error improvement model compared with the wavelet method. In 2015, in order to accurately and stably extract the fault features of the rolling bearing, the Liuchang good is subjected to VMD and singular value decomposition and is applied to fault feature signal extraction, and compared with an EMD method, the method has better classification performance and can accurately and stably extract the fault features. Therefore, in order to improve the detection precision of the weak signal under the background of the chaotic sea clutter, the research of a feasible denoising algorithm has great significance.

Disclosure of Invention

The technical problem to be solved by the invention is to provide a sea clutter mixing denoising algorithm based on variational modal decomposition aiming at the defects of the prior art.

In order to achieve the technical purpose, the technical scheme adopted by the invention is as follows:

a sea clutter mixing denoising algorithm based on variational modal decomposition is disclosed, wherein: comprises the following steps;

step S1: performing phase space reconstruction on the sea clutter signals x (n) to be detected by adopting a C-C method, and determining a key parameter embedding dimension m and a delay time tau of a phase space;

step S2: preliminarily determining the number of variable mode decomposition layers by using an EMD algorithm;

step S3: setting the number of EMD decomposition layers as an initial layer, and decomposing the sea clutter signal containing the target by using a variational modal decomposition algorithm to obtain a limited number of intrinsic modal functions IMF;

step S4: classifying the decomposed signal by utilizing the autocorrelation characteristic, and dividing the decomposed signal into a noise component and a signal component;

step S5: filtering a signal containing a noise component by combining a wavelet threshold denoising method;

step S6: reconstructing the signal component and the denoised noise component to obtain a denoised signal, establishing a chaotic time sequence prediction model by combining with an LSSVM (least squares support vector machine), comparing the predicted root mean square error before and after denoising, and judging the denoising effect according to the root mean square error.

In order to optimize the technical scheme, the specific measures adopted further comprise:

further, step S1 is specifically:

s11: dividing a sea clutter signal x (N) to be detected into t disjoint time sequences with the length of N/t, rounding off the N/t, and calculating the statistic S (m, N, r, tau) of each subsequence

Wherein, C_lIs the correlation integral of the ith subsequence, N is the length of the data set, and r is the search radius in the reconstruction space;

s12: selecting the maximum and minimum radiuses r of the corresponding value of the local maximum interval to calculate the difference

ΔS(m，t)＝max[S(m，N，r_i，t)]-min[S(m，N，r_i，t)]，i≠j

m∈(2，5)

r∈(σ/2，2σ)

Wherein σ is the mean square error of the time series;

s13: computing a time series delay time window

Wherein the content of the first and second substances,

is the mean of the statistics of all sub-sequences,

corresponds to the minimum value of the first local maximum time, S_ωr(t_i) And solving the embedding dimension and the delay time by utilizing the delay time window corresponding to the first integral maximum value time window independent from the time sequence, namely the delay time window.

Further, step S2 is specifically:

performing Empirical Mode Decomposition (EMD) algorithm processing on the sea clutter signals x (n) to be detected to obtain a decomposition layer number K, determining the decomposition layer number as a variation modal decomposition layer number, and obtaining a formula of the sum of modal components

Wherein, C_i(N) is the ith modal component, N is the total number of modal components, and R (N) is the remainder.

Further, step S3 is specifically:

s31: after the VMD carries out modal separation on the input signals, the frequency center and the bandwidth of each modal component are determined through continuous iteration to obtain a set { u ] of K inherent modal function components_k}＝{u₁，u₂，...，u_k}，k＝1，2，...，K；

S32: performing Hilbert-Huang transformation on each modal component to obtain each modal component u_kThe single-sided spectrum of the analytic signal of (3) is:

wherein, (t) represents an impact function, and j represents an imaginary unit in a complex number;

s33: mixing an estimated center frequency for each modal component's analytic signal

Converting the frequency spectrum of the modal component to a corresponding baseband to obtain a demodulation signal:

s34: carrying out H1 Gaussian smoothing processing on the demodulated signal, and estimating the bandwidth of each modal signal to obtain the following variational constraint model expression:

wherein, { w_k}＝{w₁，w₂，...，w_kAre the respective modal components u_kThe center frequency of (d);

s34: calculating an optimal solution of a variational constraint model by combining a secondary penalty factor alpha and a Lagrange multiplication operator lambda, and converting the variational constraint problem into a variational unconstrained problem to obtain the following expression:

wherein, (t) is dirichlet distribution, f (t) represents original input signal;

alternately updating u by using multiplication operator alternate direction method_k，w_k，λ_k，u_k，w_k，λ_kThe update formula of (2) is as follows:

wherein:

representing the values in the iterative process.

Further, step S6 is specifically:

s61: reconstructing a sea clutter denoising signal, and obtaining a denoised sea clutter signal by using a superposed signal component and a denoised noise component;

s62: establishing LSSVM chaos time sequence prediction model

For a given sea clutter training data set:

{(x_i，y_i)|i＝1，2，...，l，x_i∈Rⁿ，y_i∈R}

in the formula: x is the number of_iN-dimensional input of model training data for weak signal predictionEntering; y is_iAn output value predicted for the target signal; l is the number of samples for collecting training;

calculating a regression estimation function:

wherein the weight of the hyperplane is omega, the bias constant is b,

converting the nonlinear relation between the training sample of the weak signal prediction model under the input sea clutter background and the output prediction value into

And y.

Optimizing the target value by using an optimization function of the support vector machine to obtain the following formula:

constraint conditions are as follows:

wherein C is a penalty coefficient of a support vector machine model, and C is more than 0; xi_iξ relaxation variable for allowing data deviation_i ^*Is expressed as xi_iThe conjugate function of (a);

the regression model of the support vector machine is

In the formula, alpha_i，α_i ^*Is Lagrange multiplier, K (x)_iAnd x) is the Gaussian radial basis kernel function of the training process

S63: comparing predicted root mean square error to judge denoising effect

The method comprises the steps of constructing a chaotic sea clutter time sequence prediction model based on an LSSVM model, selecting 2000 sample points in IPIX radar data, selecting the first 1000 points as a training sample set, selecting the second 1000 points as a prediction verification set, comparing the prediction set obtained by the prediction model with the prediction verification set, analyzing signal waveforms, calculating root mean square errors of the prediction set and the prediction verification set, and using the root mean square errors as an evaluation index of a denoising effect.

The invention has the beneficial effects that:

the invention provides a sea clutter mixing denoising algorithm based on variational modal decomposition, which is characterized in that a VMD is utilized to decompose a sea clutter signal into a limited Intrinsic Mode Function (IMF) with different center frequencies and limited bandwidths, the autocorrelation characteristic of the decomposed signal is analyzed, wavelet hard threshold filtering is carried out on a mode component with noise characteristics, and the filtered component and residual component are reconstructed to obtain a denoised signal. And establishing a sea clutter prediction model based on the LSSVM, comparing the prediction effects before and after denoising, and using the predicted root mean square error as an evaluation criterion. Experimental results show that the VMD denoising method provided by the method is feasible, and the predicted root mean square error after denoising is 0.00055, which is two orders of magnitude lower than the non-denoised predicted root mean square error of 0.0125.

Drawings

FIG. 1 is a flow chart of a sea clutter mixing denoising algorithm based on variational modal decomposition according to the present invention;

FIG. 2 is a comparison graph of the true value and the predicted value of the non-denoised sea clutter;

FIG. 3 is a prediction error spectrum plot;

FIG. 4 is an exploded view of a VMD based sea clutter signal;

FIG. 5 is a graph of autocorrelation characteristics of a noise component;

FIG. 6 is a graph of the original signal and a denoised clutter map;

FIG. 7 is a comparison graph of real values and predicted values after denoising;

fig. 8 is a prediction error spectrum diagram.

Detailed Description

Embodiments of the present invention are described in further detail below with reference to the accompanying drawings.

As shown in fig. 1, the present invention provides a sea clutter mixing denoising algorithm based on variational modal decomposition, which includes the following steps:

step S1: performing phase space reconstruction on the sea clutter signals x (n) to be detected by adopting a C-C method, and determining a key parameter embedding dimension m and a delay time tau of a phase space;

s11: dividing a sea clutter signal x (N) to be detected into t disjoint time sequences with the length of N/t, rounding off the N/t, and calculating the statistic S (m, N, r, tau) of each subsequence

Wherein, C_lIs the correlation integral of the ith subsequence, N is the length of the data set, and r is the search radius in the reconstruction space;

s12: selecting the maximum and minimum radii r corresponding to the local maximum interval to calculate the difference, wherein the local maximum interval can be the zero point of S (-) or the time point of the minimum difference between all radii r, and the embodiment selects

ΔS(m，t)＝max[S(m，N，r_i，t)]-min[S(m，N，r_i，t)]，i≠j

m∈(2，5)

r∈(σ/2，2σ)

Where σ is the mean square error of the time series and t represents t disjoint time series;

s13: calculating the mean of the statistics of all subsequences

Wherein the content of the first and second substances,

is the mean of the statistics of all sub-sequences,

corresponds to the minimum value of the first local maximum time, S_ωr(t_i) And solving the embedding dimension and the delay time by utilizing the delay time window corresponding to the first integral maximum value time window independent from the time sequence, namely the delay time window.

Step S2: preliminarily determining the number of variable mode decomposition layers by using an EMD algorithm;

the method specifically comprises the following steps: EMD algorithm processing is carried out on the sea clutter signals x (n) to be detected, the number of variable-fraction modal decomposition layers is determined, the number of decomposition layers is obtained and determined as the number of variable-fraction modal decomposition layers, and then the formula of the sum of modal components is

Wherein, C_i(N) is the ith modal component, N is the total number of modal components, and R (N) is the remainder.

Step S3: setting the EMD decomposition layer number as a variational modal decomposition initial layer number, and decomposing the sea clutter signal containing the target by using a variational modal decomposition algorithm to obtain a limited number of intrinsic mode functions IMF;

s31: after the input signal is subjected to modal separation by variational modal decomposition, the frequency center w and the bandwidth of each modal component are determined by continuous iteration to obtain a set { u } of K inherent modal function components_k}＝{u₁，u₂，...，u_k}，k＝1，2，...，K；

S32: performing Hilbert-Huang transformation on each modal component to obtain each modal component u_kThe single-sided spectrum of the analytic signal of (3) is:

wherein, (t) represents an impact function, and j represents an imaginary unit in a complex number;

s33: mixing an estimated center frequency for each modal component's analytic signal

Converting the frequency spectrum of the modal component to a corresponding baseband to obtain a demodulation signal:

s34: carrying out H1 Gaussian smoothing processing on the demodulated signal, and estimating the bandwidth of each modal signal to obtain the following variational constraint model expression:

wherein, { w_k}＝{w₁，w₂，...，w_kAre the respective modal components u_kThe center frequency of (c).

S35: calculating an optimal solution of a variational constraint model by combining a secondary penalty factor alpha and a Lagrange multiplication operator lambda, and converting the variational constraint problem into a variational unconstrained problem to obtain the following expression:

wherein, (t) is dirichlet distribution, f (t) represents original input signal;

alternately updating u by using multiplication operator alternate direction method_k，w_k，λ_k，u_k，w_k，λ_kThe update formula of (2) is as follows:

wherein:

representing the values in the iterative process.

Step S4: classifying the decomposed signal by utilizing the autocorrelation characteristic, and dividing the decomposed signal into a noise component and a signal component;

step S5: filtering a signal containing a noise component by combining a wavelet threshold denoising method;

step S6: reconstructing the signal component and the denoised noise component to obtain a denoised signal, establishing a chaotic time sequence prediction model by combining with an LSSVM (least squares support vector machine), comparing the predicted root mean square error before and after denoising, and judging the denoising effect according to the root mean square error.

S61: reconstructing a sea clutter denoising signal, and obtaining a denoised sea clutter signal by using a superposed signal component and a denoised noise component;

s62: establishing LSSVM chaos time sequence prediction model

For a given training data set:

{(x_i，y_i)|i＝1，2，...，l，x_i∈Rⁿ，y_i∈R}

in the formula: x is the number of_iPredicting n-dimensional input of model training data for weak signals; y is_iAn output value predicted for the target signal; l is the number of samples for collecting training;

the regression estimation function was calculated as:

wherein the weight of the hyperplane is omega, the bias constant is b,

converting the nonlinear relation between the training sample of the weak signal prediction model under the input sea clutter background and the output prediction value into

And y.

Optimizing the target value by using an optimization function of the support vector machine to obtain the following formula:

constraint conditions are as follows:

wherein C is a penalty coefficient of a support vector machine model, and C is more than 0; xi_iξ relaxation variable for allowing data deviation_i ^*Is expressed as xi_iThe conjugate function of (a);

the regression model of the support vector machine is

In the formula, alpha_i，α_i ^*Is Lagrange multiplier, K (x)_iAnd x) is the kernel function of the training process, and we use the Gaussian radial basis kernel function as

S63: comparing predicted root mean square error to judge denoising effect

Constructing a time sequence prediction model of the chaotic sea clutter based on an LSSVM model, and selecting an IPIX radar54 ^#2000 sample points in the data are selected, the first 1000 points are used as a training sample set, and the second 1000 points are used as a prediction verification set. And analyzing the signal waveforms by comparing the prediction set obtained by the prediction model with the prediction verification set, calculating the root mean square error of the prediction set and the prediction verification set, and using the root mean square error as an evaluation index of the denoising effect.

In order to illustrate the effectiveness of the method, the sea clutter data is subjected to chaotic phase space reconstruction and single-step prediction based on the LSSVM, the detection capability of an LSSVM prediction model on a small target in the sea clutter background before and after denoising is compared, and the predicted root mean square error is used as a judgment standard. The experiment before denoising is firstly 54^#The sea clutter target distance unit comprises 2000 sample points, the first 1000 points are selected as a training sample set, the second 1000 points are selected as a prediction verification set, phase space reconstruction and LSSVM prediction are carried out on the two groups of data, the experimental result is shown in figures 2 and 3, an obvious peak exists in the prediction Error, the LSSVM model can detect weak signals submerged in the sea clutter background, and the Root Mean Square Error (RMSE) of the prediction result is 0.0125.

The denoising experiment adopts a VMD method based on autocorrelation and wavelet hard threshold filtering to process the sea clutter data, FIG. 4 is a sea clutter signal exploded view based on a VMD algorithm, and the sea clutter signal is divided into 12 modal components of C0-C11. As can be seen from the exploded view, the first four modal components contain signals, and the last eight modal components are directly discarded. In combination with an exploded view of a sea clutter signal, in order to reduce denoising workload, the autocorrelation characteristic functions of the first four modal components are analyzed, as shown in fig. 5, the C2 and C3 modal components have good noise component characteristics, so that wavelet hard threshold filtering is performed on the two modal components of C2 to C3, and then the filtered components and the two components of C0 and C1 are reconstructed to obtain a denoised sea clutter signal, as shown in fig. 6. In order to verify the denoising effect of the VMD algorithm, normalization processing is firstly carried out on the denoised sea clutter data according to the experimental steps of experiment one, then phase space reconstruction and LSSVM single-step prediction are carried out, and the experimental result is shown in FIG. 7. As can be seen from FIG. 8, the prediction error has an obvious peak, which indicates that a target small signal exists at the position, and the LSSVM model is proved to be capable of detecting a weak signal submerged in the error, and the obtained prediction result RMSE is 0.00055, which is two orders of magnitude lower than the RMSE of 0.0125 obtained before denoising.

The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (5)

1. A sea clutter mixing denoising algorithm based on variational modal decomposition is characterized by comprising the following steps:

step S1: performing phase space reconstruction on the sea clutter signals x (n) to be detected by adopting a C-C method, and determining a key parameter embedding dimension m and a delay time tau of a phase space;

step S2: preliminarily determining the number of variable-mode decomposition layers by using an Empirical Mode Decomposition (EMD) algorithm;

step S3: setting the number of EMD decomposition layers as an initial layer, and decomposing the sea clutter signal containing the target by using a variational modal decomposition algorithm to obtain a limited number of Intrinsic Modal Functions (IMF);

step S4: classifying the decomposed signal by utilizing the autocorrelation characteristic, and dividing the decomposed signal into a noise component and a signal component;

step S5: filtering a signal containing a noise component by combining a wavelet threshold denoising method;

step S6: reconstructing the signal component and the denoised noise component to obtain a denoised signal, establishing a chaotic time sequence prediction model by combining with an LSSVM (least squares support vector machine), comparing the predicted root mean square error before and after denoising, and judging the denoising effect according to the root mean square error.

2. The sea clutter mixing denoising algorithm based on variational modal decomposition according to claim 1, wherein the step S1 is specifically:

s11: dividing a sea clutter signal x (N) to be detected into t disjoint time sequences with the length of N/t, rounding off the N/t, and calculating the statistic S (m, N, r, tau) of each subsequence

Wherein, C_lIs the correlation integral of the ith subsequence, N is the length of the data set, and r is the search radius in the reconstruction space;

s12: selecting the maximum and minimum radiuses r of the corresponding value of the local maximum interval to calculate the difference

ΔS(m,t)＝max[S(m,N,r_i,t)]-min[S(m,N,r_i,t)],i≠j

m∈(2,5)

r∈(σ/2,2σ)

Wherein σ is the mean square error of the time series;

s13: computing a time series delay time window

Wherein the content of the first and second substances,

is the mean of the statistics of all sub-sequences,

corresponds to the minimum value of the first local maximum time, S_ωr(t_i) And solving the embedding dimension and the delay time by utilizing the delay time window corresponding to the first integral maximum value time window independent from the time sequence, namely the delay time window.

3. The sea clutter mixing denoising algorithm based on variational modal decomposition of claim 2, wherein: the step S2 specifically includes: performing empirical mode decomposition algorithm processing on the sea clutter signals x (n) to be detected to obtain a decomposition layer number K, determining the decomposition layer number as a variation mode decomposition layer number, wherein the formula of the sum of each mode component is

Wherein, C_i(N) is the ith modal component, N is the total number of modal components, and R (N) is the remainder.

4. The sea clutter mixing denoising algorithm based on variational modal decomposition of claim 3, wherein: the step S3 specifically includes:

s31: after the VMD carries out modal separation on the input signals, the frequency center and the bandwidth of each modal component are determined through continuous iteration to obtain a set { u ] of K inherent modal function components_k}＝{u₁,u₂,...,u_k},k＝1,2,...,K；

S32: performing Hilbert-Huang transformation on each modal component to obtain each modal component u_kThe single-sided spectrum of the analytic signal of (3) is:

wherein, (t) represents an impact function, and j represents an imaginary unit in a complex number;

s33: for each modal component u_kMixing the analytic signals with an estimated center frequency

Converting the frequency spectrum of the modal component to a corresponding baseband to obtain a demodulation signal:

s34: carrying out H1 Gaussian smoothing processing on the demodulated signal, and estimating the bandwidth of each modal signal to obtain the following variational constraint model expression:

wherein, { w_k}＝{w₁,w₂,...,w_kAre the respective modal components u_kThe center frequency of (d);

s34: calculating the optimal solution of the variational constraint model by combining the secondary penalty factor alpha and the Lagrange multiplication operator lambda,

transforming the variational constraint problem into a variational unconstrained problem to obtain the following expression:

wherein, (t) is dirichlet distribution, f (t) represents original input signal;

alternately updating u by using multiplication operator alternate direction method_k,w_k,λ_k，u_k,w_k,λ_kThe update formula of (2) is as follows:

wherein:

representing numbers in an iterative processThe value is obtained.

5. The sea clutter mixing denoising algorithm based on variational modal decomposition of claim 4, wherein: the step S6 specifically includes:

s61: reconstructing a sea clutter denoising signal, and obtaining a denoised sea clutter signal by using a superposed signal component and a denoised noise component;

s62: establishing LSSVM chaos time sequence prediction model

For a given sea clutter training data set:

{(x_i,y_i)|i＝1,2,...,l,x_i∈Rⁿ,y_i∈R}

in the formula: x is the number of_iPredicting n-dimensional input of model training data for weak signals; y is_iAn output value predicted for the target signal; l is the number of samples for collecting training;

calculating a regression estimation function:

wherein the weight of the hyperplane is omega, the bias constant is b,

converting the nonlinear relation between the training sample of the weak signal prediction model under the input sea clutter background and the output prediction value into

A linear relationship with y;

optimizing the regression estimation function by using the optimization function of the support vector machine to obtain the following formula:

constraint conditions are as follows:

wherein C is a penalty coefficient of the support vector machine model, C>0；ξ_iξ relaxation variable for allowing data deviation_i ^*Is expressed as xi_iThe conjugate function of (a);

the regression model of the support vector machine is

In the formula, alpha_i，α_i ^*Is Lagrange multiplier, K (x)_iAnd x) is the Gaussian radial basis kernel function of the training process

S63: comparing predicted root mean square error to judge denoising effect

The method comprises the steps of constructing a chaotic sea clutter time sequence prediction model based on an LSSVM model, selecting 2000 sample points in IPIX radar data, selecting the first 1000 points as a training sample set, selecting the second 1000 points as a prediction verification set, comparing the prediction set obtained by the prediction model with the prediction verification set, analyzing signal waveforms, calculating root mean square errors of the prediction set and the prediction verification set, and using the root mean square errors as an evaluation index of a denoising effect.

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