CN112882012B - Radar target noise robust identification method based on signal-to-noise ratio matching and echo enhancement - Google Patents

Radar target noise robust identification method based on signal-to-noise ratio matching and echo enhancement Download PDF

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CN112882012B
CN112882012B CN202110032931.XA CN202110032931A CN112882012B CN 112882012 B CN112882012 B CN 112882012B CN 202110032931 A CN202110032931 A CN 202110032931A CN 112882012 B CN112882012 B CN 112882012B
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王鹏辉
司景元
刘宏伟
丁军
陈婷
陈渤
纠博
邵帅
赵希宇
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
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    • G01S13/52—Discriminating between fixed and moving objects or between objects moving at different speeds
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
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Abstract

The invention discloses a radar target noise steady recognition method based on signal-to-noise ratio matching and echo enhancement, which mainly solves the problem that the classification performance of a narrow-band radar target is reduced when the signal-to-noise ratio of a radar is very low. The method comprises the following steps: (1) generating a noisy data set; (2) carrying out template matching by utilizing the signal-to-noise ratio information; (3) generating a training feature matrix; (4) training an SVM classifier; (5) preprocessing a test set; (6) generating a test feature matrix; (7) and (4) target identification. The invention uses the signal-to-noise ratio information of the echo signal of the target to be identified to carry out template matching, and uses the orthogonal matching and tracking OMP method to carry out echo enhancement on the echo of the target to be identified, thereby effectively improving the identification accuracy of the narrow-band radar target under the condition of low signal-to-noise ratio and having certain noise robustness.

Description

Radar target noise robust identification method based on signal-to-noise ratio matching and echo enhancement
Technical Field
The invention belongs to the technical field of radars, and further relates to a radar target noise robust identification method based on signal-to-noise ratio matching and echo enhancement in the technical field of automatic target identification (RATR) of radars. The invention can identify different targets moving in the air and on the ground in real time under the scene of low signal-to-noise ratio.
Background
In actual military battles, radar target echoes always contain inevitable noise, and particularly for long-distance non-cooperative targets in a battlefield environment, the signal-to-noise ratio of the acquired target echoes is usually low. However, since the target inching component accounts for only a small portion of the total energy, the inching component is easily drowned by noise. In general, a training sample is obtained by recording or simulating a cooperative target, the signal-to-noise ratio is high, noise can be basically ignored, and the signal-to-noise ratio of an actual test sample is low, so that noise components cannot be ignored. The signal-to-noise ratio mismatch between the training sample and the test sample causes the performance deterioration of the target identification method, and even the identification capability is lost.
The Hangzhou electronic science and technology university provides a radar one-dimensional range profile target identification method in a patent document 'radar one-dimensional range profile target identification method based on a deep convolutional neural network' (patent application number: CN201810806078.0, application publication number: CN 109086700A). The method comprises the following specific steps: the first step is as follows: collecting a data set, preprocessing the collected data, extracting features from the preprocessed data, and setting a threshold to divide the collected radar HRRP signal into a low signal-to-noise ratio sample and a high signal-to-noise ratio sample; the second step is that: constructing a feature enhancement algorithm based on the robust Boltzmann; the third step: constructing HRRP target recognition models of a convolutional neural network and an LSTM-based bidirectional cyclic neural network; the fourth step: and fine-tuning parameters of the constructed network model by using a gradient descent algorithm to obtain an effective target identification model. The method has certain small sample robustness and noise robustness, but the method still has the defects that: the method divides the radar echo signal into two parts of a low signal-to-noise ratio sample and a high signal-to-noise ratio sample by using a threshold setting method, the signal-to-noise ratio of the echo signal in each part is changed greatly due to the division, the problem that the identification accuracy rate is obviously reduced due to the mismatch of the signal-to-noise ratio of a training sample and a test sample still occurs, and the noise robustness is poor.
The university of electronic science and technology of west ampere proposes an aircraft target classification method based on generalized matched filtering in the patent document "robust classification method of aircraft target noise based on generalized matched filtering" (patent application number: CN201410128512.6, application publication number: CN 103885043A). The method comprises the following specific steps: the first step is as follows: receiving the measured data by using a radar, and aiming at the received measured data; the second step is that: obtaining an autocorrelation matrix of an aircraft target echo sample; the third step: obtaining a whitening matrix of generalized matched filtering; the fourth step: obtaining an autocorrelation matrix of the aircraft target echo sample after clutter and noise are filtered; the fifth step: obtaining the 3-dimensional characteristic spectrum scattering characteristics of the actually measured data; and a sixth step: obtaining a training data characteristic matrix, and training a support vector machine classifier by using the training data characteristic matrix; the seventh step: and classifying the 3-dimensional characteristic spectrum scattering characteristics of the measured data by using the trained support vector machine classifier. The method has the following defects: according to the method, after clutter and noise filtering operation is carried out on radar echo data by using generalized matched filtering, a support vector machine classifier is trained by using an artificial feature extraction method, the classification performance of the method depends on the noise filtering effect and the artificial feature extraction effect, the calculated amount of the features extracted manually is large, and the real-time requirement of target identification cannot be met.
Disclosure of Invention
The invention aims to provide a radar target noise steady recognition method based on signal-to-noise ratio matching and echo enhancement aiming at the defects in the prior art, and the method is used for solving the problems that the performance of the target recognition method is deteriorated due to the fact that the signal-to-noise ratios of a training sample and a test sample are different and the problem that a complex model cannot meet the real-time requirement of target recognition in the prior art.
The idea for realizing the purpose of the invention is that for a target echo signal to be identified, an orthogonal matching tracking algorithm is utilized to carry out echo enhancement on the echo signal, and the noise energy in the echo signal is suppressed. And according to the characteristic that the radar identifies the target after detecting the target, the signal-to-noise ratio information of the target can be roughly estimated according to the related information such as the target track, and the signal-to-noise ratio information of the target echo signal to be identified is utilized to carry out template matching, so that the search range is narrowed, the calculation amount is reduced, and the real-time requirement is met.
The method comprises the following specific steps:
(1) generating a noisy data set:
(1a) p radar echo signals of D category targets are extracted, D is larger than or equal to 3, and P is larger than or equal to 2400;
(1b) performing clutter suppression on each echo signal by using a regional clear method;
(1c) separating micro-motion component echo signals from each echo signal subjected to clutter suppression by using a global CLEAN method, and forming a micro-motion target data set by using all the micro-motion component echo signals;
(1d) independently adding 30 times of Gaussian noise to each echo signal in the micro-motion target data set to obtain 30 groups of noise-added data sets, wherein the signal-to-noise ratio of each echo signal in the ith group of noise-added data sets is-10 + i, and i is more than or equal to 1 and less than or equal to 30;
(2) and (3) carrying out template matching by utilizing signal-to-noise ratio information:
(2a) f target echo signals to be identified which are continuously received in real time form a test set, wherein F is more than or equal to 1, and the signal-to-noise ratio of each echo signal in the test set is estimated;
(2b) calculating the mode of the signal-to-noise ratio of all echo signals in the test set by using the following formula
Figure GDA0003426942820000031
Figure GDA0003426942820000032
Where Mode (. cndot.) denotes a Mode operation, round (. cndot.) denotes a rounding operation, SNRηRepresenting the signal-to-noise ratio of the eta echo signal in the test set, wherein eta is more than or equal to 1 and less than or equal to F;
(2c) selecting the signal-to-noise ratio of the echo signal in the 30 noisy data sets to be equal to
Figure GDA0003426942820000033
The noisy training data set; performing echo enhancement processing on each echo signal in the noise-added data set by using an orthogonal matching and tracking OMP (orthogonal matching and tracking) method to obtain a training set;
(3) generating a training feature matrix:
(3a) performing fast Fourier transform on each echo signal in the training set to obtain each Doppler domain echo signal of the training set;
(3b) carrying out amplitude normalization on each Doppler domain echo signal;
(3c) respectively extracting frequency domain second moment, fourth moment, frequency domain waveform entropy and frequency domain amplitude variance characteristics of each Doppler domain echo signal with the normalized amplitude;
(3d) forming an N multiplied by 4 dimensional training sample characteristic matrix by the frequency domain second moment, the fourth moment, the frequency domain waveform entropy and the frequency domain amplitude variance characteristics of all signals in the training set, wherein the value of N is equal to the total number P of samples in the training data set;
(3e) normalizing the training sample feature matrix to obtain a training feature matrix;
(4) training an SVM classifier:
selecting an SVM classifier and setting a kernel function of the SVM classifier as a Gaussian kernel function, inputting a training sample feature matrix into the SVM classifier for training, and obtaining a trained SVM classifier;
(5) preprocessing a test set:
(5a) performing clutter suppression on each echo signal in the test set by using a regional CLEAN method;
(5b) removing a main component in each echo signal in the test set after clutter suppression by using a global CLEAN method;
(5c) carrying out analog-to-two norm normalization processing on the amplitude of each echo signal in the test set after the main component is removed;
(5d) carrying out echo enhancement processing on the echo signals in the normalized test set by using an orthogonal matching and tracking OMP (orthogonal matching and tracking) method;
(6) generating a test feature matrix:
(6a) performing fast Fourier transform on each echo signal in the test set to obtain each Doppler domain echo signal of the test set;
(6b) carrying out amplitude normalization on each Doppler domain echo signal;
(6c) respectively extracting frequency domain second moment, fourth moment, frequency domain waveform entropy and frequency domain amplitude variance characteristics of each Doppler domain echo signal with the normalized amplitude;
(6d) forming an M multiplied by 4 dimensional test sample characteristic matrix by the frequency domain second moment, the fourth moment, the frequency domain waveform entropy and the frequency domain amplitude variance characteristics of all signals in the test set, wherein the value of M is equal to the total number F of samples in the test set;
(6e) normalizing the characteristic matrix of the test sample to obtain a test characteristic matrix;
(7) target identification:
and inputting the test feature matrix into the trained SVM classifier to obtain a recognition result.
Compared with the prior art, the invention has the following advantages:
firstly, the invention uses the signal-to-noise ratio information to carry out template matching, so that the signal-to-noise ratio of the target sample in the test set is consistent with the signal-to-noise ratio of the target sample in the training set, the problems of model mismatch and incapability of meeting the real-time requirement of target identification due to the fact that the signal-to-noise ratio of the training sample is different from that of the test sample in the prior art are solved, and the intra-class distance is not changed but the inter-class distance can be increased when the characteristics of the target sample are extracted, so that the identification rate of the target is improved.
Secondly, the method enhances the target echo by using the orthogonal matching and tracking OMP method on the basis of performing template matching by using the signal-to-noise ratio information, so that the problem that the recognition rate is reduced due to model mismatch cannot be solved by performing echo enhancement processing on the echo signal by using the orthogonal matching and tracking OMP method in the prior art is solved, the method not only can effectively suppress noise, but also can enable the target echo to obtain more divisible features in the feature extraction process, and improve the recognition accuracy.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph showing the results of a simulation experiment according to the present invention.
Detailed Description
The present invention is described in further detail below with reference to the attached drawings.
The specific steps implemented by the present invention are described in further detail with reference to fig. 1.
Step 1, generating a noise-added data set.
P radar echo signals of D category targets are extracted, D is larger than or equal to 3, and P is larger than or equal to 2400.
And performing clutter suppression on each echo signal by using a regional clear method.
The method for area CLEAN comprises the following specific steps:
the method comprises the first step of estimating the ground clutter energy in radar echo according to radar working parameters.
And secondly, performing discrete Fourier transform on each echo signal to obtain a Doppler spectrum of the echo signal, and taking a region near zero frequency of the Doppler spectrum as a clutter region, wherein the region near zero frequency is determined by the type of clutter.
Thirdly, reconstructing a time domain signal corresponding to the maximum Doppler amplitude in the clutter region in each echo signal according to the following formula:
Figure GDA0003426942820000051
wherein, Ci(t) represents the signal amplitude of the reconstructed time domain signal corresponding to the maximum Doppler amplitude in the clutter region in the ith echo signal at the time t, YiDenotes the maximum Doppler amplitude of a clutter region in the Doppler spectrum of the ith echo signal, K denotes the number of points of discrete Fourier transform, exp denotes the peak amplitude in natureExponential operation with constant e as base, j representing imaginary unit symbol, pi representing circumferential ratio, xiiRepresents YiThe corresponding doppler frequency of the doppler frequency is,
Figure GDA0003426942820000052
represents YiThe corresponding phase.
And fourthly, subtracting the reconstructed time domain signal from each echo signal to obtain the echo processed signal.
And fifthly, calculating the energy of each processed echo signal in the clutter region.
Judging whether the energy of each processed echo signal in a clutter area is smaller than the energy of a ground clutter, if so, obtaining the echo signal after clutter suppression; otherwise, executing the second step of the step.
And separating a micro-motion component echo signal from each echo signal subjected to clutter suppression by using a global CLEAN method, and forming a micro-motion target data set by using all the micro-motion component echo signals.
The specific steps of the global CLEAN method are as follows:
firstly, estimating the energy of a main body component in a radar echo according to the radar working parameters.
And secondly, performing discrete Fourier transform on each echo signal to obtain the Doppler spectrum of the echo signal.
Thirdly, reconstructing a time domain signal corresponding to the main component in each echo signal according to the following formula:
Figure GDA0003426942820000061
wherein, Bodyi(t) represents the signal amplitude at time t of the main component echo signal reconstructed from the main component echo signal in the ith echo signal, RiIndicating the maximum Doppler amplitude, f, in the Doppler spectrum of the ith echo signaliRepresents RiCorresponding Doppler frequency, θiRepresents RiThe corresponding phase.
And fourthly, subtracting the reconstructed time domain signal from each echo signal subjected to clutter suppression to obtain an echo signal from which the main component is removed.
Independently adding 30 times of Gaussian noise to each echo signal in the micro-motion target data set to obtain 30 groups of noise-added data sets, wherein the signal-to-noise ratio of each echo signal in the ith group of noise-added data sets is-10 + i, i is more than or equal to 1 and less than or equal to 30, and the first group of noise-added data sets X1With a signal-to-noise ratio of-9 dB, and a second set of noisy data set X2Has a signal-to-noise ratio of-8 dB, and so on, and a thirtieth group of noisy data set X30Has a signal-to-noise ratio of 20 dB.
And 2, carrying out template matching by utilizing the signal-to-noise ratio information.
And (3) forming a test set by the echo signals of F radars continuously received in real time, wherein F is more than or equal to 1.
Calculating the mode of the signal-to-noise ratio of all echo signals in the test set by using the following formula
Figure GDA0003426942820000062
Figure GDA0003426942820000063
Where Mode (. cndot.) denotes a Mode operation, round (. cndot.) denotes a rounding operation, SNRηAnd representing the signal-to-noise ratio of the eta echo signal in the test set, wherein eta is more than or equal to 1 and less than or equal to F.
Selecting the signal-to-noise ratio of the echo signal in the 30 noisy data sets to be equal to
Figure GDA0003426942820000064
The noisy training data set; and performing echo enhancement processing on each echo signal in the noisy data set by using an orthogonal matching and tracking OMP (orthogonal matching and tracking) method to obtain a training set.
The steps of the orthogonal matching tracking OMP method are as follows:
firstly, an unselected echo signal is selected from the noise-added data set as an observation signal, and the noise energy of the observation signal is estimated.
And secondly, selecting a Gaussian function corresponding to the waveform characteristics of the observation signal to construct a dictionary matrix phi.
Third, let r0Obtaining initialized residual signals r, r0Representing the residual signal without iteration, initializing a candidate support set Γ, and causing
Figure GDA0003426942820000071
Γ0Representing the set of candidate supports that have not been iterated,
Figure GDA0003426942820000072
and (5) representing an empty set, initializing the current iteration number iter, and making iter equal to 1.
Fourthly, calculating the atom index to be selected by using the following formula, and selecting the atom phi corresponding to the atom index from the dictionary matrix phiindex：
Figure GDA0003426942820000073
Wherein G represents the total number of atoms in the dictionary matrix,<·，·>it is shown that the vector inner product operation is solved,
Figure GDA0003426942820000074
the function represents the subscript operation corresponding to the output when the value in the parentheses is maximized, riter-1Representing the residual signal of the last iteration.
Fifthly, updating the support set by using the following formula:
Γiter＝Γiter-1∪Φindex
wherein, U represents and operation, ΓiterCandidate support set, Γ, representing the current iterationiter-1Representing the candidate support set for the last iteration.
Sixthly, using Schmidt orthogonalization method to process phiindexAnd performing orthogonalization processing.
And seventhly, decomposing the observation signals by using the following formula, and solving the signals on the support set gamma:
sigiter＝((Γiter)TΓiter)-1(Γiter)T
wherein, sigiterRepresenting the signal of the observed signal decomposition on the support set Γ in the current iteration, and the superscript T representing the transpose operation.
Eighth, the residual signal is updated using the following equation:
riter＝obs-Γitersigiter
where obs denotes the observed signal in the current iteration.
And ninthly, judging whether the energy of the updated residual signal is lower than the noise energy of the observation signal, if so, obtaining the observation signal after the echo enhancement, and executing the tenth step, otherwise, adding one to the current iteration number, and executing the fourth step of the step.
And step ten, judging whether all echo signals in the noise-added data set are selected completely, if so, obtaining all enhanced echo signals, and otherwise, executing the first step of the step.
And 3, generating a training feature matrix.
And carrying out fast Fourier transform on each echo signal in the training set to obtain each Doppler domain echo signal of the training sample set.
Performing amplitude normalization on each Doppler domain echo signal, wherein the amplitude normalization on the Doppler domain echo signals of the training set is performed according to the following formula:
Figure GDA0003426942820000081
wherein, Xn(k) Indicating the n-th Doppler domain echo signal, U, in the training set after amplitude normalizationn(k) The amplitude normalization is represented by the nth Doppler domain echo signal of the training set before amplitude normalization, N is 1, 2.
And extracting the characteristics of frequency domain second moment, fourth moment, frequency domain waveform entropy and frequency domain amplitude variance of the Doppler domain echo signal after each amplitude is normalized.
The steps of extracting the characteristics of the frequency domain second moment, the frequency domain fourth moment, the frequency domain waveform entropy and the frequency domain amplitude variance are as follows:
firstly, extracting the frequency domain second moment characteristics of each Doppler domain echo signal in a training set after amplitude normalization according to the following formula:
Figure GDA0003426942820000082
wherein, MoTnRepresenting the frequency domain second moment characteristics of the amplitude normalized training set nth Doppler domain echo signals, AnRepresents Xn(k) The first moment characteristic of the frequency domain of (a),
Figure GDA0003426942820000083
k represents the total number of points of the fast fourier transform.
Secondly, extracting the frequency domain fourth moment characteristic of each Doppler domain echo signal in the training set after the amplitude normalization according to the following formula:
Figure GDA0003426942820000091
wherein, MoFnAnd representing the frequency domain fourth moment characteristic of the amplitude normalized training set nth Doppler domain echo signal.
Thirdly, extracting the frequency domain waveform entropy characteristics of echo signals of each Doppler domain in the training set after amplitude normalization according to the following formula:
Figure GDA0003426942820000092
wherein E isnRepresenting the frequency domain waveform entropy characteristic of the n-th Doppler domain echo signal of the amplitude normalized training set, | · | represents the operation of taking an absolute value, and log10Representing base 10 logarithmic operationDo this.
Fourthly, extracting the frequency domain amplitude variance characteristics of echo signals of each Doppler domain in the training set after amplitude normalization according to the following formula:
Figure GDA0003426942820000093
wherein, deltanRepresenting the frequency domain amplitude variance characteristic, mu, of the amplitude normalized training set nth Doppler domain echo signalnRepresents Xn(k) The average value of (a) of (b),
Figure GDA0003426942820000094
and (3) forming an N multiplied by 4 dimensional training sample characteristic matrix by the frequency domain second moment, fourth moment, frequency domain waveform entropy and frequency domain amplitude variance characteristics of all signals in the training set, wherein the value of N is equal to the total number P of samples in the training data set.
The steps of forming the N x 4 dimensional training sample feature matrix are as follows:
F1＝[p1；p2；...；pn；...；pN]
wherein, F1Representing a training sample feature matrix, pnFeature vector, p, representing the echo signal in the nth Doppler domain in the amplitude normalized training setn＝[MoTn,MoFn,En,δn]。
And normalizing the training sample feature matrix to obtain a training feature matrix.
The step of normalizing the training sample feature matrix is as follows:
first, calculating a training sample feature matrix F1The mean value and standard deviation of the 4 characteristics are obtained to obtain a characteristic mean value vector mu ═ mu1,μ2,μ3,μ4]Sum-feature standard deviation vector σ ═ σ [ σ ]1,σ2,σ3,σ4]。
Secondly, calculating a frequency domain second moment characteristic, a frequency domain fourth moment characteristic, a frequency domain waveform entropy characteristic and a frequency domain amplitude variance characteristic of the normalized training set Doppler domain echo signal by using the following formula:
Figure GDA0003426942820000101
wherein the content of the first and second substances,
Figure GDA0003426942820000102
respectively representing the frequency domain second moment characteristic, the frequency domain fourth moment characteristic, the frequency domain waveform entropy characteristic and the frequency domain amplitude variance characteristic of the nth Doppler domain echo signal in the normalized training set.
Thirdly, calculating a training feature matrix by using the following formula
Figure GDA0003426942820000103
Figure GDA0003426942820000104
Wherein the content of the first and second substances,
Figure GDA0003426942820000105
and 4, training the SVM classifier.
And selecting an SVM classifier, setting the kernel function of the SVM classifier as a Gaussian kernel function, and inputting the training sample feature matrix into the SVM classifier for training to obtain the trained SVM classifier.
And 5, preprocessing the test set.
And performing clutter suppression on each echo signal in the test set by using a regional clear method.
The method for area CLEAN comprises the following specific steps:
the method comprises the first step of estimating the ground clutter energy in radar echo according to radar working parameters.
And secondly, performing discrete Fourier transform on each echo signal to obtain a Doppler spectrum of the echo signal, and taking a region near zero frequency of the Doppler spectrum as a clutter region, wherein the region near zero frequency is determined by the type of clutter.
Thirdly, reconstructing a time domain signal corresponding to the maximum Doppler amplitude in the clutter region in each echo signal according to the following formula:
Figure GDA0003426942820000106
wherein, Ci(t) represents the signal amplitude of the reconstructed time domain signal corresponding to the maximum Doppler amplitude in the clutter region in the ith echo signal at the time t, YiRepresents the maximum Doppler amplitude of a clutter region of the Doppler spectrum of the ith echo signal, K represents the number of points of discrete Fourier transform, exp represents exponential operation with a natural constant e as the base, j represents an imaginary unit symbol, pi represents a circumferential ratio, ξiRepresents YiThe corresponding doppler frequency of the doppler frequency is,
Figure GDA0003426942820000111
represents YiThe corresponding phase.
And fourthly, subtracting the reconstructed time domain signal from each echo signal to obtain the echo processed signal.
And fifthly, calculating the energy of each processed echo signal in the clutter region.
Judging whether the energy of each processed echo signal in a clutter area is smaller than the energy of a ground clutter, if so, obtaining the echo signal after clutter suppression; otherwise, executing the second step of the step.
And removing the main component in each echo signal in the test set after clutter suppression by using a global CLEAN method.
The specific steps of the global CLEAN method are as follows:
firstly, estimating the energy of a main body component in a radar echo according to the radar working parameters.
And secondly, performing discrete Fourier transform on each echo signal to obtain the Doppler domain of the echo signal.
Thirdly, reconstructing a time domain signal corresponding to the main component in each echo signal according to the following formula:
Figure GDA0003426942820000112
wherein, Bodyi(t) represents the signal amplitude at time t of the main component echo signal reconstructed from the main component echo signal in the ith echo signal, RiIndicating the maximum Doppler amplitude, f, in the Doppler spectrum of the ith echo signaliRepresents RiCorresponding Doppler frequency, θiRepresents RiThe corresponding phase.
And fourthly, subtracting the reconstructed time domain signal from each echo signal subjected to clutter suppression to obtain an echo signal from which the main component is removed.
And carrying out the analog-to-two norm normalization processing on the amplitude of each echo signal in the test set after the main component is removed.
And performing echo enhancement processing on the echo signals in the normalized test set by using an orthogonal matching and tracking OMP (orthogonal matching and tracking) method.
The steps of the orthogonal matching tracking OMP method are as follows:
firstly, an unselected echo signal is selected from the noise-added data set as an observation signal, and the noise energy of the observation signal is estimated.
And secondly, selecting a Gaussian function corresponding to the waveform characteristics of the observation signal to construct a dictionary matrix phi.
Third, let r0Obtaining initialized residual signals r, r0Representing the residual signal without iteration, initializing a candidate support set Γ, and causing
Figure GDA0003426942820000121
Γ0Representing the set of candidate supports that have not been iterated,
Figure GDA0003426942820000122
and (5) representing an empty set, initializing the current iteration number iter, and making iter equal to 1.
Fourthly, calculating the atom index to be selected by using the following formula, and selecting the atom phi corresponding to the atom index from the dictionary matrix phiindex：
Figure GDA0003426942820000123
Wherein G represents the total number of atoms in the dictionary matrix,<·，·>it is shown that the vector inner product operation is solved,
Figure GDA0003426942820000124
the function represents the subscript operation corresponding to the output when the value in the parentheses is maximized, riter-1Representing the residual signal of the last iteration.
Fifthly, updating the support set by using the following formula:
Γiter＝Γiter-1∪Φindex
wherein, U represents and operation, ΓiterCandidate support set, Γ, representing the current iterationiter-1Representing the candidate support set for the last iteration.
Sixthly, using Schmidt orthogonalization method to process phiindexAnd performing orthogonalization processing.
And seventhly, decomposing the observation signals by using the following formula, and solving the signals on the support set gamma:
sigiter＝((Γiter)TΓiter)-1(Γiter)T
wherein, sigiterRepresenting the signal of the observed signal decomposition on the support set Γ in the current iteration, and the superscript T representing the transpose operation.
Eighth, the residual signal is updated using the following equation:
riter＝obs-Γitersigiter
where obs denotes the observed signal in the current iteration.
And ninthly, judging whether the energy of the updated residual signal is lower than the noise energy of the observation signal, if so, obtaining the observation signal after the echo enhancement, and executing the tenth step, otherwise, adding one to the current iteration number, and executing the fourth step of the step.
And step ten, judging whether all echo signals in the noise-added data set are selected completely, if so, obtaining all enhanced echo signals, and otherwise, executing the first step of the step.
And 6, generating a test feature matrix.
And carrying out fast Fourier transform on each echo signal in the test set to obtain each Doppler domain echo signal of the test set.
And performing amplitude normalization on the Doppler domain echo signals of each test set, wherein the formula for performing amplitude normalization on the Doppler domain echo signals of the test sets is as follows:
Figure GDA0003426942820000131
wherein S ism(k) Echo signal of nth Doppler domain in test set representing amplitude normalization, Vm(k) The M-th doppler domain echo signal in the test set is represented, and M is 1, 2.
And extracting the characteristics of frequency domain second moment, fourth moment, frequency domain waveform entropy and frequency domain amplitude variance of each Doppler domain echo signal after amplitude normalization.
The step of constructing the characteristic matrix of the test sample is as follows:
firstly, extracting the frequency domain second moment characteristics of echo signals of each Doppler domain in a test set after amplitude normalization according to the following formula:
Figure GDA0003426942820000132
wherein, CMoTmRepresenting the frequency domain second moment characteristics of the m-th Doppler domain echo signal of the test sample with normalized amplitude, BmDenotes Sm(k) The first moment characteristic of the frequency domain of (a),
Figure GDA0003426942820000133
k represents the total number of points of the fast fourier transform.
Secondly, extracting frequency domain fourth moment characteristics of echo signals of each Doppler domain in the test set after amplitude normalization according to the following formula:
Figure GDA0003426942820000141
wherein, CMoFmAnd representing the frequency domain fourth moment characteristic of the mth Doppler domain echo signal of the test set with normalized amplitude.
Thirdly, extracting the frequency domain waveform entropy characteristics of echo signals of each Doppler domain in the test set after the amplitude is normalized according to the following formula:
Figure GDA0003426942820000142
wherein, CEmRepresenting the frequency domain waveform entropy characteristics of the mth Doppler domain echo signal in the test set with normalized amplitude, | · | represents the operation of taking absolute value, log10A base 10 logarithmic operation is shown.
Fourthly, extracting the frequency domain amplitude variance characteristics of echo signals of each Doppler domain in the test set after amplitude normalization according to the following formula:
Figure GDA0003426942820000143
wherein, C ismRepresenting the frequency domain waveform entropy characteristic, mul, of the amplitude normalized test set mth Doppler domain echo signalmDenotes Sm(k) The average value of (a) of (b),
Figure GDA0003426942820000144
and (3) forming an M multiplied by 4-dimensional test sample characteristic matrix by using the frequency domain second moment, the fourth moment, the frequency domain waveform entropy and the frequency domain amplitude variance characteristics of all signals in the test set, wherein the value of M is equal to the total number F of samples in the test set.
The step of forming the characteristic matrix of the M multiplied by 4 dimensional test sample is as follows:
F2＝[q1；q2；...；qm；...；qM]
wherein q ismFeature vector representing the m-th Doppler domain echo signal in the amplitude normalized test set, qm＝[CMoTm,CMoFm,CEm,Cδm]，F2Representing a test sample feature matrix, M1, 2.
And normalizing the characteristic matrix of the test sample to obtain a test characteristic matrix.
The step of normalizing the characteristic matrix of the test sample is as follows:
firstly, calculating a characteristic matrix F of a test sample2And (5) obtaining a mean value vector mu ' of the feature of the test sample mu ' and a standard deviation of the mean value and the standard deviation of the 4 features '1,μ'2,μ'3,μ'4]And a characteristic standard deviation vector σ '═ σ'1,σ'2,σ'3,σ'4]。
Secondly, calculating the frequency domain second moment characteristic, the frequency domain fourth moment characteristic, the frequency domain waveform entropy characteristic and the frequency domain amplitude variance characteristic of the normalized test sample Doppler domain echo signal by using the following formula:
Figure GDA0003426942820000151
wherein the content of the first and second substances,
Figure GDA0003426942820000152
respectively representing the frequency domain second moment characteristic, the frequency domain fourth moment characteristic, the frequency domain waveform entropy characteristic and the frequency domain amplitude variance characteristic of the mth Doppler domain echo signal in the normalized test sample.
The third step is toUsing the following equation, a test feature matrix is obtained
Figure GDA0003426942820000153
Figure GDA0003426942820000154
Wherein the content of the first and second substances,
Figure GDA0003426942820000155
and 7, target identification: and inputting the test feature matrix into the trained SVM classifier to obtain a recognition result.
The effect of the present invention will be further described with reference to simulation experiments.
1. Simulation experiment conditions are as follows:
the hardware platform of the simulation experiment of the invention is as follows: the processor is Intel (R) core (TM) i7-7700 CPU @3.60GHZ 3.60GHZ, the main frequency is 2.00GHz, and the memory is 16 GB.
The software platform of the simulation experiment of the invention is as follows: windows 10 operating system and python 3.6.
The training samples and training samples used in the simulation experiment of the invention are radar target echo data of three types of airplanes generated by three-dimensional electromagnetic field simulation software CST. The parameters of the simulated radar are as follows: center frequency 3000MHz, pulse repetition frequency 5KHz, dwell time 110 ms. The structural parameters of the three simulated airplanes are randomly generated by simulation software, and the airplane structural parameters comprise the number of blades, the blade angle and the blade length. The simulation software randomly generates radar target echoes of three types of airplanes to form a training sample and a test sample, wherein the total number of echo signals of each type of airplane in the training sample is 200, and the total number of echo signals of each type of airplane in the test sample is 100.
Adding 30 Gaussian noises into each echo signal in a training sample to obtain 30 groups of noisy data sets, namely a first group of noisy data set X1With a signal-to-noise ratio of-9 dB, and a second set of noisy data set X2Has a signal-to-noise ratio of-8 dB, and so on, group thirtiethNoisy data set X30Has a signal-to-noise ratio of 20 dB.
Gaussian noise is added for 10 times in each echo signal in a test sample to obtain 10 groups of test data sets, namely the signal-to-noise ratio of the first group of test data sets is 0dB, the signal-to-noise ratio of the second group of test data sets is 2.5dB, the signal-to-noise ratio of the third group of test data sets is 5dB, and so on, the signal-to-noise ratio of the tenth group of test data sets is 20 dB.
2. Analysis of experimental content and results
The simulation experiment of the invention is to respectively carry out the simulation experiment on the echo data of the 3 types of airplane targets by adopting the invention and a traditional narrow-band radar target classification method based on the extraction of the stability time domain characteristics.
The narrow-band radar target classification method based on robust time domain feature extraction in the prior art is as follows: the patent document of the university of electronic technology in Xian "ground target classification method based on robustness time-frequency characteristics" (patent application No. CN201510475477.X, application publication No. CN105044701A) proposes a narrow-band radar target classification method.
30 groups of different training characteristic matrixes are respectively extracted from 30 groups of noisy data sets, and a first group of noisy data set X with the signal-to-noise ratio of-9 dB is utilized1Training a first SVM classifier by using the training feature matrix to obtain the trained first SVM classifier, and repeating the steps in the same way, wherein a thirty-th group of noisy data sets X with the signal-to-noise ratio of 20dB is used30Training a thirty-th SVM classifier by using the training feature matrix to obtain a thirty-th trained SVM classifier, and finally obtaining 30 trained SVM classifiers. Firstly, extracting a first group of test characteristic matrixes from a first group of test sets, inputting the first group of test characteristic matrixes into a trained tenth SVM classifier by utilizing a signal-to-noise ratio matching principle, obtaining the recognition accuracy rate of the first group of test sets with the signal-to-noise ratio of 0dB, analogizing in sequence, extracting a tenth group of test characteristic matrixes from a tenth group of test sets, wherein the signal-to-noise ratio of target echo signals in the tenth group of test sets is 20dB, and inputting the tenth group of test characteristic matrixes into the trained thirteenth SVM classifier by utilizing the signal-to-noise ratio matching principleAnd obtaining the identification accuracy of the tenth group of test sets with the signal-to-noise ratio of 20dB, and finally obtaining the identification accuracy of the ten groups of test data sets under different signal-to-noise ratios.
The method and the method for extracting the narrow-band radar target classification based on the time domain characteristics of robustness have the recognition accuracy results under different signal-to-noise ratios drawn into a curve as shown in figure 2. In fig. 2, the abscissa represents the signal-to-noise ratio of the echo sample in the test data set, which is 0dB and 2.5dB … … 25dB, respectively, and the ordinate represents the identification accuracy of the echo signal in the test data set. In fig. 2, a solid line marked by a plus sign represents a relationship curve between the identification accuracy and the signal-to-noise ratio of the test sample obtained by the method of the present invention, and a dotted line marked by a circle represents a relationship curve between the identification accuracy and the signal-to-noise ratio of the test sample obtained by the narrow-band radar target classification method based on the robust time domain feature extraction.
As can be seen from FIG. 2, under the condition of any signal-to-noise ratio of the test sample, the identification accuracy rate of the method is superior to that of the method for extracting the narrow-band radar target classification based on the robust time domain characteristics. When the signal-to-noise ratio of a test sample is 25dB, the recognition rate of the prior art is only 92.03%, the recognition rate of the invention is up to 93.52%, and the improvement is about 1.5%. At a test sample signal-to-noise ratio of 0dB, the recognition rate of the prior art is only 50%, whereas the recognition rate of the aspect of the present invention is as high as 70%. Therefore, it can be found that, as the signal-to-noise ratio is continuously reduced, the identification rate of the prior art is reduced obviously, and the anti-noise performance is poor, while the method of the present invention has good identification performance under the condition of low signal-to-noise ratio.
In conclusion, the radar target noise robust identification method based on signal-to-noise ratio matching and echo enhancement provided by the invention obviously reduces the influence of noise on the identification of a radar target, effectively improves the identification accuracy rate of the radar aircraft target under the condition of low signal-to-noise ratio, and has good noise robustness; meanwhile, the method can reduce the search range, reduce the operation amount and meet the requirement of real-time property. Therefore, the method of the present invention has good practicability.

Claims (12)

1. A radar target noise steady recognition method based on signal-to-noise ratio matching and echo enhancement is characterized in that the signal-to-noise ratio information of an echo signal of a target to be recognized is utilized for template matching, and an orthogonal matching and tracking OMP method is utilized for echo enhancement of the echo of the target to be recognized, and the method comprises the following steps:
(1) generating a noisy data set:
(1a) p radar echo signals of D category targets are extracted, D is larger than or equal to 3, and P is larger than or equal to 2400;
(1b) performing clutter suppression on each echo signal by using a regional clear method;
(1c) separating micro-motion component echo signals from each echo signal subjected to clutter suppression by using a global CLEAN method, and forming a micro-motion target data set by using all the micro-motion component echo signals;
(1d) independently adding 30 times of Gaussian noise to each echo signal in the micro-motion target data set to obtain 30 groups of noise-added data sets, wherein the signal-to-noise ratio of each echo signal in the ith group of noise-added data sets is-10 + i, and i is more than or equal to 1 and less than or equal to 30;
(2) and (3) carrying out template matching by utilizing signal-to-noise ratio information:
(2a) f target echo signals to be identified which are continuously received in real time form a test set, wherein F is more than or equal to 1, and the signal-to-noise ratio of each echo signal in the test set is estimated;
(2b) calculating the mode of the signal-to-noise ratio of all echo signals in the test set by using the following formula
Figure FDA0003426942810000011
Figure FDA0003426942810000012
Where Mode (. cndot.) denotes a Mode operation, round (. cndot.) denotes a rounding operation, SNRηRepresenting the signal-to-noise ratio of the eta echo signal in the test set, wherein eta is more than or equal to 1 and less than or equal to F;
(2c) selecting the signal-to-noise ratio of the echo signal in the 30 noisy data sets to be equal to
Figure FDA0003426942810000013
The noisy training data set; performing echo enhancement processing on each echo signal in the noise-added data set by using an orthogonal matching and tracking OMP (orthogonal matching and tracking) method to obtain a training set;
(3) generating a training feature matrix:
(3a) performing fast Fourier transform on each echo signal in the training set to obtain each Doppler domain echo signal of the training set;
(3b) carrying out amplitude normalization on each Doppler domain echo signal;
(3c) respectively extracting frequency domain second moment, fourth moment, frequency domain waveform entropy and frequency domain amplitude variance characteristics of each Doppler domain echo signal with the normalized amplitude;
(3d) forming an N multiplied by 4 dimensional training sample characteristic matrix by the frequency domain second moment, the fourth moment, the frequency domain waveform entropy and the frequency domain amplitude variance characteristics of all signals in the training set, wherein the value of N is equal to the total number P of samples in the training data set;
(3e) normalizing the training sample feature matrix to obtain a training feature matrix;
(4) training an SVM classifier:
selecting an SVM classifier and setting a kernel function of the SVM classifier as a Gaussian kernel function, inputting a training sample feature matrix into the SVM classifier for training, and obtaining a trained SVM classifier;
(5) preprocessing a test set:
(5a) performing clutter suppression on each echo signal in the test set by using a regional CLEAN method;
(5b) removing a main component in each echo signal in the test set after clutter suppression by using a global CLEAN method;
(5c) carrying out analog-to-two norm normalization processing on the amplitude of each echo signal in the test set after the main component is removed;
(5d) carrying out echo enhancement processing on the echo signals in the normalized test set by using an orthogonal matching and tracking OMP (orthogonal matching and tracking) method;
(6) generating a test feature matrix:
(6a) performing fast Fourier transform on each echo signal in the test set to obtain each Doppler domain echo signal of the test set;
(6b) carrying out amplitude normalization on each Doppler domain echo signal;
(6c) respectively extracting frequency domain second moment, fourth moment, frequency domain waveform entropy and frequency domain amplitude variance characteristics of each Doppler domain echo signal with the normalized amplitude;
(6d) forming an M multiplied by 4 dimensional test sample characteristic matrix by the frequency domain second moment, the fourth moment, the frequency domain waveform entropy and the frequency domain amplitude variance characteristics of all signals in the test set, wherein the value of M is equal to the total number F of samples in the test set;
(6e) normalizing the characteristic matrix of the test sample to obtain a test characteristic matrix;
(7) target identification:
and inputting the test feature matrix into the trained SVM classifier to obtain a recognition result.
2. The robust radar target noise identification method based on signal-to-noise ratio matching and echo enhancement according to claim 1, wherein the specific steps of the area CLEAN method in the steps (1b) and (5a) are as follows:
firstly, estimating ground clutter energy in radar echo according to radar working parameters;
secondly, performing discrete Fourier transform on each echo signal to obtain a Doppler spectrum of the echo signal, and taking a region near zero frequency of the Doppler spectrum as a clutter region, wherein the region near zero frequency is determined by the type of clutter;
thirdly, reconstructing a time domain signal corresponding to the maximum Doppler amplitude in the clutter region in each echo signal according to the following formula:
Figure FDA0003426942810000031
wherein, Ci(t) represents the time domain signal corresponding to the maximum Doppler amplitude in the clutter region in the ith echo signalSignal amplitude, Y, of the reconstructed time-domain signal at time tiRepresents the maximum Doppler amplitude of a clutter region of the Doppler spectrum of the ith echo signal, K represents the number of points of discrete Fourier transform, exp represents exponential operation with a natural constant e as the base, j represents an imaginary unit symbol, pi represents a circumferential ratio, ξiRepresents YiThe corresponding doppler frequency of the doppler frequency is,
Figure FDA0003426942810000032
represents YiA corresponding phase;
fourthly, subtracting the reconstructed time domain signal from each echo signal to obtain an echo processed signal;
fifthly, calculating the energy of each processed echo signal in the clutter area;
judging whether the energy of each processed echo signal in a clutter area is smaller than the energy of a ground clutter, if so, obtaining the echo signal after clutter suppression; otherwise, the second step is executed.
3. The robust radar target noise identification method based on snr matching and echo enhancement according to claim 2, wherein the global CLEAN method in the steps (1c) and (5b) comprises the following steps:
firstly, performing discrete Fourier transform on each echo signal to obtain a Doppler spectrum of the echo signal;
secondly, reconstructing a time domain signal corresponding to the main component in each echo signal according to the following formula:
Figure FDA0003426942810000033
wherein, Bodyi(t) represents the signal amplitude at time t of the main component echo signal reconstructed from the main component echo signal in the ith echo signal, RiIndicating the maximum Doppler amplitude, f, in the Doppler spectrum of the ith echo signaliRepresents RiCorresponding Doppler frequency, θiRepresents RiA corresponding phase;
and thirdly, subtracting the reconstructed time domain signal from each echo signal subjected to clutter suppression to obtain an echo signal from which the main component is removed.
4. The robust radar target noise identification method based on snr matching and echo enhancement according to claim 1, wherein the step of the orthogonal matching tracking OMP method in step (2c) is as follows:
firstly, selecting an unselected echo signal from a noise-added data set as an observation signal, and estimating the noise energy of the observation signal;
secondly, selecting a Gaussian function corresponding to the waveform characteristics of the observation signal, and constructing a dictionary matrix phi;
third, let r0Obtaining initialized residual signals r, r0Representing the residual signal without iteration, initializing a candidate support set Γ, and causing
Figure FDA0003426942810000041
Γ0Representing the set of candidate supports that have not been iterated,
Figure FDA0003426942810000042
representing an empty set, initializing the current iteration number iter, and making iter equal to 1;
fourthly, calculating the atom index to be selected by using the following formula, and selecting the atom phi corresponding to the atom index from the dictionary matrix phiindex：
Figure FDA0003426942810000043
Wherein G represents the total number of atoms in the dictionary matrix,<·，·>it is shown that the vector inner product operation is solved,
Figure FDA0003426942810000044
the function represents the subscript operation corresponding to the output when the value in the parentheses is maximized, riter-1Representing the residual signal of the last iteration;
fifthly, updating the support set by using the following formula:
Γiter＝Γiter-1∪Φindex
wherein, U represents and operation, ΓiterCandidate support set, Γ, representing the current iterationiter-1Representing a candidate support set of a last iteration;
sixthly, using Schmidt orthogonalization method to process phiindexCarrying out orthogonalization treatment;
and seventhly, decomposing the observation signals by using the following formula, and solving the signals on the support set gamma:
sigiter＝((Γiter)TΓiter)-1(Γiter)T
wherein, sigiterRepresenting the signals of the observed signal decomposition on the support set Γ in the current iteration, the superscript T representing the transpose operation;
eighth, the residual signal is updated using the following equation:
riter＝obs-Γitersigiter
wherein obs represents the observed signal in the current iteration;
ninth, judging whether the energy of the updated residual signal is lower than the noise energy of the observation signal, if so, obtaining the observation signal after echo enhancement, and executing the tenth step, otherwise, executing the fourth step after adding one to the current iteration times;
and step ten, judging whether all echo signals in the noise-added data set are selected completely, if so, obtaining all enhanced echo signals, and otherwise, executing the first step.
5. The robust radar target noise identification method based on snr matching and echo enhancement according to claim 1, wherein the amplitude normalization of the doppler domain echo signals in the training set in step (3b) is performed according to the following formula:
Figure FDA0003426942810000051
wherein, Xn(k) Indicating the n-th Doppler domain echo signal, U, in the training set after amplitude normalizationn(k) The amplitude normalization is represented by the nth Doppler domain echo signal of the training set before amplitude normalization, N is 1, 2.
6. The robust radar target noise identification method based on SNR matching and echo enhancement according to claim 5, wherein the step of extracting the features of frequency domain second moment, fourth moment, frequency domain waveform entropy and frequency domain amplitude variance in step (3c) comprises the following steps:
firstly, extracting the frequency domain second moment characteristics of each Doppler domain echo signal in a training set after amplitude normalization according to the following formula:
Figure FDA0003426942810000052
wherein, MoTnRepresenting the frequency domain second moment characteristics of the amplitude normalized training set nth Doppler domain echo signals, AnRepresents Xn(k) The first moment characteristic of the frequency domain of (a),
Figure FDA0003426942810000061
k1, 2, K representing the total number of points of the fast fourier transform;
secondly, extracting the frequency domain fourth moment characteristic of each Doppler domain echo signal in the training set after the amplitude normalization according to the following formula:
Figure FDA0003426942810000062
wherein, MoFnRepresenting the frequency domain fourth moment characteristic of the echo signal of the nth Doppler domain of the training set with normalized amplitude;
thirdly, extracting the frequency domain waveform entropy characteristics of echo signals of each Doppler domain in the training set after amplitude normalization according to the following formula:
Figure FDA0003426942810000063
wherein E isnRepresenting the frequency domain waveform entropy characteristic of the n-th Doppler domain echo signal of the amplitude normalized training set, | · | represents the operation of taking an absolute value, and log10Represents a base 10 logarithmic operation;
fourthly, extracting the frequency domain amplitude variance characteristics of echo signals of each Doppler domain in the training set after amplitude normalization according to the following formula:
Figure FDA0003426942810000064
wherein, deltanRepresenting the frequency domain amplitude variance characteristic, mu, of the amplitude normalized training set nth Doppler domain echo signalnRepresents Xn(k) The average value of (a) of (b),
Figure FDA0003426942810000065
7. the robust radar target noise identification method based on SNR matching and echo enhancement according to claim 6, wherein the step of forming the N x 4 dimensional training sample feature matrix in step (3d) comprises the following steps:
F1＝[p1；p2；...；pn；...；pN]
wherein, F1Representing a training sample feature matrix, pnFeature vector, p, representing the echo signal in the nth Doppler domain in the amplitude normalized training setn＝[MoTn,MoFn,En,δn]。
8. The robust radar target noise identification method based on SNR matching and echo enhancement according to claim 7, wherein the step of normalizing the training sample feature matrix in step (3e) is as follows:
first, calculating a training sample feature matrix F1The mean value and standard deviation of the 4 characteristics are obtained to obtain a characteristic mean value vector mu ═ mu1,μ2,μ3,μ4]Sum-feature standard deviation vector σ ═ σ [ σ ]1,σ2,σ3,σ4]；
Secondly, calculating a frequency domain second moment characteristic, a frequency domain fourth moment characteristic, a frequency domain waveform entropy characteristic and a frequency domain amplitude variance characteristic of the normalized training set Doppler domain echo signal by using the following formula:
Figure FDA0003426942810000071
wherein the content of the first and second substances,
Figure FDA0003426942810000072
respectively representing a frequency domain second moment feature, a frequency domain fourth moment feature, a frequency domain waveform entropy feature and a frequency domain amplitude variance feature of the nth Doppler domain echo signal in the normalized training set;
thirdly, calculating a training feature matrix by using the following formula
Figure FDA0003426942810000073
Figure FDA0003426942810000074
Wherein the content of the first and second substances,
Figure FDA0003426942810000075
9. the robust radar target noise identification method based on snr matching and echo enhancement according to claim 5, wherein the formula for amplitude normalization of the doppler domain echo signals of the test set in step (6b) is as follows:
Figure FDA0003426942810000076
wherein S ism(k) Echo signal of mth Doppler domain in test set, V, representing amplitude normalizationm(k) The M-th doppler domain echo signal in the test set is represented, and M is 1, 2.
10. The robust radar target noise identification method based on snr matching and echo enhancement according to claim 9, wherein the step (6c) of extracting the features of frequency domain second order moment, fourth order moment, frequency domain waveform entropy and frequency domain amplitude variance is as follows:
firstly, extracting the frequency domain second moment characteristics of echo signals of each Doppler domain in a test set after amplitude normalization according to the following formula:
Figure FDA0003426942810000081
wherein, CMoTmRepresenting the frequency domain second moment characteristics of the m-th Doppler domain echo signal of the test sample with normalized amplitude, BmDenotes Sm(k) The first moment characteristic of the frequency domain of (a),
Figure FDA0003426942810000082
secondly, extracting frequency domain fourth moment characteristics of echo signals of each Doppler domain in the test set after amplitude normalization according to the following formula:
Figure FDA0003426942810000083
wherein, CMoFmRepresenting the frequency domain fourth moment characteristic of the mth Doppler domain echo signal of the test set with normalized amplitude;
thirdly, extracting the frequency domain waveform entropy characteristics of echo signals of each Doppler domain in the test set after the amplitude is normalized according to the following formula:
Figure FDA0003426942810000084
wherein, CEmRepresenting the frequency domain waveform entropy characteristics of the mth Doppler domain echo signal in the test set with normalized amplitude, | · | represents the operation of taking absolute value, log10Represents a base 10 logarithmic operation;
fourthly, extracting the frequency domain amplitude variance characteristics of echo signals of each Doppler domain in the test set after amplitude normalization according to the following formula:
Figure FDA0003426942810000085
wherein, C ismRepresenting the frequency domain waveform entropy characteristic, mul, of the amplitude normalized test set mth Doppler domain echo signalmDenotes Sm(k) The average value of (a) of (b),
Figure FDA0003426942810000091
11. the robust radar target noise identification method based on snr matching and echo enhancement according to claim 10, wherein the step (6d) of forming the test sample feature matrix comprises the following steps:
F2＝[q1；q2；...；qm；...；qM]
wherein q ismRepresenting amplitudeFeature vector q of the mth Doppler domain echo signal in the normalized test setm＝[CMoTm,CMoFm,CEm,Cδm]，F2Representing a test sample feature matrix, M1, 2.
12. The robust radar target noise identification method based on snr matching and echo enhancement according to claim 11, wherein the step of normalizing the feature matrix of the test sample in step (6e) is as follows:
firstly, calculating a characteristic matrix F of a test sample2And (5) obtaining a mean value vector mu ' of the feature of the test sample mu ' and a standard deviation of the mean value and the standard deviation of the 4 features '1,μ'2,μ'3,μ'4]And a characteristic standard deviation vector σ '═ σ'1,σ'2,σ'3,σ'4]；
Secondly, calculating the frequency domain second moment characteristic, the frequency domain fourth moment characteristic, the frequency domain waveform entropy characteristic and the frequency domain amplitude variance characteristic of the normalized test sample Doppler domain echo signal by using the following formula:
Figure FDA0003426942810000092
wherein the content of the first and second substances,
Figure FDA0003426942810000093
respectively representing the frequency domain second moment characteristic, the frequency domain fourth moment characteristic, the frequency domain waveform entropy characteristic and the frequency domain amplitude variance characteristic of the mth Doppler domain echo signal in the normalized test sample;
thirdly, obtaining a test feature matrix by using the following formula
Figure FDA0003426942810000094
Figure FDA0003426942810000095
Wherein the content of the first and second substances,
Figure FDA0003426942810000096
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