CN110109080B - Weak signal detection method based on IA-SVM model - Google Patents
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Abstract
The invention discloses a weak signal detection method based on an IA-SVM model, which comprises the steps of firstly adopting a C-C method to carry out phase space reconstruction, determining embedding dimension and delay time, realizing the preprocessing of chaotic signals, then establishing a single-step prediction model based on a Support Vector Machine (SVM) and optimized by an Immune Algorithm (IA), carrying out the training and prediction of the prediction model under a Lorenz chaotic background and an IPIX actual measurement radar sea clutter background, detecting a weak signal submerged in the chaotic system from the spectrum analysis of prediction errors, and finally judging whether a weak target signal exists or not.
Description
Technical Field
The invention relates to the field of radar data processing, in particular to a weak signal detection method based on an IA-SVM model.
Background
The sea clutter is a backscattering echo of a sea surface radar, is influenced by various external natural factors such as wind power, tides, ocean currents, humidity and surges, has a complex and changeable physical mechanism and obvious non-Gaussian, non-linear and non-stable characteristics, and can interfere with radar target detection. The method starts from the requirement of radar for detecting the sea level target, and further develops the research on the characteristics of the sea clutter. With the deep research of sea wave mechanism and sea clutter characteristics, researchers find that sea clutter has chaos characteristics. The chaos is irregular and random-like motion generated by the nonlinear action in a nonlinear determination system, and the chaos theory is mutually staggered with discipline theories in other fields, so that the chaos characteristic is greatly amplified and varied in the weak signal detection field, and particularly weak signal detection under the sea clutter background becomes a hot research subject of signal processing and detection. The research on the sea clutter for weak signal detection of background noise has very important theoretical and practical application significance for the identification and detection of small targets on the sea level.
In 1997, mukherjee applies a support vector machine to the prediction of the chaotic time sequence, and promotes the prediction research of the chaotic sequence. In 2005, leaf beauty and the like proposed a prediction method of chaotic time series based on LS-SVM regression, and were verified under Chenl's chaotic system, rossler chaotic system, henon mapping and electroencephalogram (EEG) as chaotic time series, respectively. In 2010, golden Tianli provides sea clutter background weak signal detection based on a novel LS-SVM model when a complex nonlinear system phase space reconstruction theory is researched, and compared with a traditional neural network method and an LS-SVM, prediction accuracy and a detection threshold value are improved, but certain limitations exist. Therefore, the method for detecting the weak signal with higher precision and efficiency has great significance.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a weak signal detection method based on an IA-SVM model, aiming at solving the problems of low detection precision and low efficiency of the weak signal detection method under the traditional sea clutter background.
The technical scheme is as follows: the invention relates to a weak signal detection method based on an IA-SVM model, which comprises the following steps of (1) carrying out phase space reconstruction on a sea clutter signal x (n) to be detected by adopting a C-C method, and determining the embedding dimension and delay time of key parameters of a phase space;
(2) The method comprises the steps that a support vector machine is utilized to better process complex nonlinear problems and better classification regression capacity, and a sea clutter single-step prediction model based on the support vector machine is established;
(3) The punishment coefficient, the kernel function and the insensitive loss parameter which affect the prediction capability of the support vector machine are optimized by using an immune algorithm, so that the prediction effect of the model is optimal;
(4) And substituting the optimal parameters C, sigma and epsilon obtained by using the immune algorithm into a single-step prediction model of the support vector machine for prediction to obtain a final prediction result.
(5) And calculating a prediction error, performing time domain and frequency domain analysis on the error, and detecting a weak signal submerged in the chaotic sea clutter from the prediction error.
Has the advantages that: the invention provides a weak signal detection model based on an IA-SVM model, a single-step prediction model is carried out on a sequence after chaos phase space reconstruction, a weak signal submerged in a sea clutter background is detected from a prediction error, and compared with a root mean square error in a traditional detection method, the root mean square error is smaller under the condition of higher signal to noise ratio (the signal to noise ratio is minus 104.2473. The root mean square error is 0.0001463), and the effectiveness and superiority of the invention are proved.
Drawings
FIG. 1 is a flow chart of a method for detecting weak signals in a sea clutter background according to the present invention;
FIG. 2 shows the real and predicted values of transient signals in the Lornez system;
FIG. 3 is a graph of the prediction error for a Lornez system with transient signals;
FIG. 4 is a graph of the prediction error of a periodic signal in the Lornez system;
FIG. 5 is a predicted error spectrum with periodic signals under the Lornez system;
FIG. 6 is a predicted value and a true value under a sea clutter background;
FIG. 7 is an error spectrum in the background of sea clutter.
Detailed Description
As shown in fig. 1, the present invention provides a method for detecting a weak target signal under a sea clutter background, which comprises the following steps:
(1) Performing phase space reconstruction on the sea clutter signal x (n) to be detected by adopting a C-C method, and determining the key parameter embedding dimension and delay time of the phase space;
(1.2) dividing the sea clutter signals x (N), N =1, 2.. And N to be detected into t disjoint time columns, rounding the time columns with the length of N/t, and calculating the statistic S (m, N, r, tau) of each subsequence
In the formula, C l Is the correlation integral of the ith subsequence.
(1.2) the local maximum separation can be taken to be the zero point of S (-) or the point in time where the mutual difference is minimal for all radii r. Selecting two radii r with maximum and minimum corresponding values, and defining the difference as
ΔS(m,t)＝max[S(m,N,r i ,t)]-min[S(m,N,r i ,t)],i≠j (2)
According to the statistical principle, the value of m is between 2 and 5, and the value of r is between sigma/2 and 2 sigma. σ is the mean square error of the time series, and the equation is as follows:
in the formula (I), the compound is shown in the specification,
are the mean of the statistics of all subsequences; s ωr (t i ) Corresponds to the minimum of the first local maximum time and simultaneously corresponds to the time window of the first overall maximum time independent of the time series, i.e. the delay time window.
(2) The method comprises the steps that a support vector machine is utilized to better process complex nonlinear problems and better classification regression capacity, and a sea clutter single-step prediction model based on the support vector machine is established;
(2.1) for a given training data set:
{(x i ,y i )|i＝1,2,...,l,x i ∈R n ,y i epsilon R } (4) in the formula:
x i inputting weak signal prediction model training data in n dimensions; y is i An output value predicted for the target signal; l is the number of samples for training acquisition.
The regression estimation function is:
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 valueInto
And y.
(2.2) optimizing the target value by 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 the support vector machine model, and C>0；ξ i For the relaxation variables, the intervals at which the data are allowed to deviate are as small as possible based on the original target. The lagrange multiplier method can be used for solving the quadratic programming problem with the constraint condition to obtain a regression model of the support vector machine
In the formula, alpha i ，α i * Is Lagrange multiplier, K (x) i And x) is the kernel function of the training process, and we use the Gaussian radial basis kernel function as
The main parameters of the support vector machine comprise a penalty coefficient C, a kernel function parameter sigma and an insensitive loss parameter epsilon, and the parameters influence the generalization capability of the support vector machine, wherein the penalty coefficient C is too large in value, easy to over-fit, too small in value and easy to under-fit, and the generalization capability of the system is poor under the two conditions; the kernel function parameter sigma can reflect the distribution characteristics of the training data, if the value is too large, a complex optimal classification surface can be obtained, the confidence range is large, and vice versa; the insensitive loss parameter epsilon is preferably large, in which case the regression function is simpler and faster to calculate, but when epsilon is larger than a certain value, under-fitting occurs. Therefore, the optimization is carried out by adopting the step (3).
(3) The punishment coefficient, the kernel function and the insensitive loss parameter which affect the prediction capability of the support vector machine are optimized by using an immune algorithm, so that the prediction effect of the model is optimal, and the specific optimization steps are as follows:
(3.1) initializing parameters, creating an initial population: setting the respective parameter ranges of a support vector machine C, sigma and epsilon as [0.1,100], [0.01,1000] and [0.01,1000] respectively by taking an actual signal to be predicted as an antigen and a predicted signal as an antibody; setting the dimension of immune individuals as 3, the number of immune individuals as NP and the maximum immune algebra as G, and adopting binary coding because the number of parameters to be optimized is less
(3.2) affinity calculation: the affinity characterization is the binding strength between immune cells and antigen, similar to the fitness in genetic algorithm, the combination of antigen and the minimum root mean square error of the whole optimization model, and the reciprocal of the root mean square error is defined as the affinity function
Wherein, y i Is the actual value of the signal to be predicted,
is the predicted value of the signal, and l is the number of training samples.
(3.3) algorithm optimizing termination judgment condition: and judging whether the algorithm meets the termination condition, if so, stopping the algorithm optimization, and otherwise, continuing the optimization. Judging whether the affinity is maximum or not in the limited optimization iteration
(3.4) antibody concentration and stimulation calculation: the antibody concentration is characterized by the diversity of the antibody population, and the over-high concentration can lead to concentrated optimization and is not beneficial to global optimization, so that the over-high concentration of the antibody is inhibited. We define the antibody concentration as:
in the formula: n is the population size, S represents the similarity between antibodies, fit (y) i ,y j ) Indicates the affinity between the two antibodies, delta s Representing a similarity threshold.
The excitation degree is characterized by the final evaluation result of the antibody quality, and the calculation mode is that the antibody affinity and the antibody concentration are comprehensively considered
Sim ij (C,σ,ε)＝a·Fit ij (C,σ,ε)-b·Den ij (C,σ,ε) (13)
Wherein, a and b are calculation parameters, the excitation degree is in direct proportion to the affinity of the antibody and in inverse proportion to the concentration of the antibody, and considering that the affinity in the experiment is larger, the concentration of the antibody is less than 1, the a parameter is 1, and the b parameter is 1000.
(3.5) population refreshing: and (5) replacing the antibody with lower incentive in the population with the new antibody generated randomly to generate a new generation of antibody, and repeating the step (3.3) until the optimization process is finished.
(4) And substituting the optimal parameters C, sigma and epsilon obtained by using the immune algorithm into a single-step prediction model of a support vector machine for prediction to obtain a final prediction result.
(5) Calculating a prediction error, performing time domain and frequency domain analysis on the error, and detecting a weak signal submerged in the chaotic sea clutter from the prediction error; and then, performing spectrum analysis on the prediction error by adopting Fast Fourier Transform (FFT), and judging whether a weak target signal exists in a preset frequency range.
In order to illustrate the effectiveness of the method, a Lorenz system and an IPIX actual measurement radar sea clutter signal are used as chaotic background noise, when the system completely enters a chaotic state, normalization processing and phase space reconstruction are carried out, 2000 processed points are taken as experimental simulation data of a prediction model, the first 1000 data points are taken as a training sample set, the second 1000 data points are taken as a prediction verification set, and the existence of a weak target signal is judged through prediction errors and error frequency spectrums. FIG. 2 is a comparison of predicted values and true values of small signals added to samples 605-654 in Lorenz system, and the prediction error in the system of FIG. 3 can find the target signal position at samples 605-654.
Fig. 4 is a prediction error diagram of a periodic signal, where a weak target signal cannot be visually seen, FFT transformation is performed on the weak target signal, and spectral characteristics are analyzed, as shown in fig. 5, the position of the weak signal can be identified, and a peak occurs at a frequency of 0.0318, so as to preliminarily determine the position of the weak periodic signal.
Fig. 6 is a comparison between a predicted value and a true value of a prediction model in an actually measured sea clutter background, and fig. 7 is a spectrogram of a prediction error, and the obtained frequency shows an obvious peak value at 0.01442, so that a weak target signal can be preliminarily determined to exist in the sea clutter background, which indicates that the detection method provided herein has extremely high detection precision on the weak signal in the sea clutter.
Claims (5)
1. A weak signal detection method based on an IA-SVM model; the method is characterized by comprising the following steps:
(1) Performing phase space reconstruction on the sea clutter signal x (n) to be detected by adopting a C-C method, and determining the embedding dimension and delay time of key parameters of the phase space;
(2) The method comprises the steps that a support vector machine is utilized to better process complex nonlinear problems and better classification regression capability, and a sea clutter single-step prediction model based on the support vector machine is established;
(3) The punishment coefficient, the kernel function and the insensitive loss parameter which affect the prediction capability of the support vector machine are optimized by using an immune algorithm, so that the prediction effect of the model is optimal;
(4) Substituting the optimal parameters C, sigma and epsilon obtained by using the immune algorithm into a single-step prediction model of a support vector machine for prediction to obtain a final prediction result; c represents a penalty coefficient, sigma represents a kernel function parameter, and epsilon represents an insensitive loss parameter;
(5) And calculating a prediction error, performing time domain and frequency domain analysis on the error, and detecting a weak signal submerged in the chaotic sea clutter from the prediction error.
2. The weak signal detection method based on the IA-SVM model as claimed in claim 1, wherein in step 1, the C-C method phase space reconstruction comprises the steps of:
(1.1) dividing the sea clutter signals x (N), N =1, 2.. Times.N to be detected into t disjoint time columns with the length of N/t, rounding, and calculating the statistic S (m, N, r, tau) of each subsequence
In the formula, C l Is the correlation integral of the l-th subsequence;
(1.2) the local maximum separation can be taken to the zero point of S (-) or the point in time where the mutual difference is minimal for all radii r; selecting two radii r with maximum and minimum corresponding values, and defining the difference as
ΔS(m,t)＝max[S(m,N,r i ,t)]-min[S(m,N,r i ,t)],i≠j (2)
According to the statistical principle, m is between 2 and 5, r is between sigma/2 and 2 sigma, sigma is the mean square error of the time series, and the equation is as follows:
in the formula (I), the compound is shown in the specification,
are the mean of the statistics of all subsequences; s. the ωr (t i ) Corresponds to the minimum of the first local maximum time and simultaneously corresponds to the time window of the first overall maximum time independent of the time series, i.e. the delay time window.
3. The weak signal detection method based on the IA-SVM model of claim 1, wherein the step (2) comprises:
(2.1) for a given training data set:
{(x i ,y i )|i＝1,2,...,l,x i ∈R n ,y i epsilon R } (4) in the formula:
x i predicting n-dimensional input of model training data for weak signals; y is i An output value predicted for the target signal; l is the number of samples for collecting training;
the regression estimation function is:
wherein the weight of the hyperplane is omega, the bias constant is b,
converting the nonlinear relation between the input weak signal under the background of the sea clutter, the training sample of the prediction model and the output predicted value into
A linear relationship with y;
(2.2) optimizing the target value by 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 the support vector machine model, and C>0；ξ i For the slack variable, is the interval at which the data is allowed to deviate,
the size of the target is as small as possible on the basis of the original target; the lagrange multiplier method can be used for solving the quadratic programming problem with constraint conditions to obtain a regression model of the support vector machine
In the formula, alpha i ，α i * Is Lagrange multiplier, K (x) i And x) is a kernel function of the training process, which adopts a Gaussian radial basis kernel function of
4. The weak signal detection method based on the IA-SVM model of claim 1, wherein the step (3) comprises:
(3.1) initializing parameters, creating an initial population: setting respective parameters of a support vector machine C, sigma and epsilon by taking an actual signal to be predicted as an antigen and a predicted signal as an antibody;
(3.2) calculation of affinity: the affinity characterizes the binding strength between immune cells and antigen, is similar to the fitness in a genetic algorithm, and the root mean square error obtained by the whole optimization model is minimized while the antigen is bound, and the reciprocal of the root mean square error is defined as an affinity function
Wherein, y i Is the actual value of the signal to be predicted,
the predicted value of the signal is represented by l, and the number of training samples is represented by l;
(3.3) algorithm optimizing termination judgment condition: judging whether the algorithm meets a termination condition, if so, stopping optimizing the algorithm, otherwise, continuing optimizing the algorithm; judging whether the affinity is maximum in limited optimization iteration;
(3.4) antibody concentration and stimulation calculation: the antibody concentration is characterized by the diversity of the antibody population, and the concentration is too high to make optimization centralized and global optimization unfavorable, so the inhibition is performed on the antibody concentration, which is defined as:
in the formula: n is population size, S represents the similarity between antibodies, fit (y) i ,y j ) Indicates the affinity between the two antibodies, delta s Representing a similarity threshold;
the excitation degree is characterized by the final evaluation result of the antibody quality, and the calculation mode is that the antibody affinity and the antibody concentration are comprehensively considered
Sim ij (C,σ,ε)＝a·Fit ij (C,σ,ε)-b·Den ij (C,σ,ε) (13)
Wherein a and b are calculation parameters;
(3.5) population refreshing: and (5) replacing the antibody with lower incentive in the population with the new antibody generated randomly to generate a new generation of antibody, and repeating the step (3.3) until the optimization process is finished.
5. The weak signal detection method based on IA-SVM model of claim 4, wherein the respective parameter ranges of C, σ and ε of the support vector machine are [0.1,100], [0.01,1000]; setting the dimension of immune individuals as 3, the number of immune individuals as NP and the maximum immune algebra as G, and adopting binary coding because the quantity of parameters to be optimized is less.
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