CN111598163A - Stacking integrated learning mode-based radar HRRP target identification method - Google Patents

Stacking integrated learning mode-based radar HRRP target identification method Download PDF

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CN111598163A
CN111598163A CN202010408431.7A CN202010408431A CN111598163A CN 111598163 A CN111598163 A CN 111598163A CN 202010408431 A CN202010408431 A CN 202010408431A CN 111598163 A CN111598163 A CN 111598163A
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谢文科
刘凯
欧建平
彭一鸣
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Wuhan Eryuan Technology Co.,Ltd.
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Abstract

The invention discloses a Stacking integrated learning mode-based radar HRRP target identification method, and belongs to the field of radar target identification. The method comprises a training stage and an identification stage, wherein the training stage comprises the following steps: extracting various features from an original HRRP, then selecting the extracted features by utilizing a Relieff algorithm and an SVM _ RFE algorithm, training three base classifiers based on the selected feature subsets, and taking classification results of the base classifiers as training data of a meta classifier; and (3) identification: extracting a plurality of characteristics from the original HRRP, then multiplying the characteristics by a characteristic screening matrix obtained in a training stage to complete a characteristic selection process, importing the obtained characteristic subset into a trained base classifier for classification, taking a classification result as test data of a meta classifier, and taking the classification result of the meta classifier as a final classification recognition result. The radar HRRP target identification method provided by the invention has high-precision identification capability when the classification problem of multiple types of targets is solved, and is less in required samples and high in identification efficiency.

Description

Stacking integrated learning mode-based radar HRRP target identification method
Technical Field
The invention relates to a High Resolution Range Profile (HRRP) target identification method for a Stacking ensemble learning type radar, which is used for automatic target identification of a high resolution Range Profile radar and belongs to the field of automatic target identification of radars.
Background
The radar automatic target identification technology is a hot field of current radar signal processing. Compared with a synthetic aperture radar image and an inverse synthetic aperture radar image, the high-resolution range profile is a one-dimensional high-resolution radar signal which contains abundant target structure information and has a small data volume, and has the advantages of convenience in acquisition, simplicity in processing, low cost and the like. In an actual radar target identification system, the identification accuracy of a target and the complexity of the identification system are two mutually restricted factors. Therefore, how to increase the identification accuracy without greatly increasing the complexity of the identification system is an urgent problem to be solved.
In recent years, decision fusion and multi-feature fusion are widely applied to radar automatic target identification methods, and radar HRRP target identification algorithms based on feature fusion or decision fusion are successively deduced. But the method has the problems of low recognition accuracy, low recognition efficiency, no combination of feature fusion and decision fusion and the like.
Disclosure of Invention
The method aims at the problems that the conventional radar HRRP target recognition algorithm is low in recognition accuracy, and the combination of feature fusion and decision fusion is not realized. The invention provides a Stacking ensemble learning mode-based radar HRRP target identification method, which is inspired by that the identification efficiency and the identification accuracy are reduced due to useless redundancy characteristics, and different classifiers have different identification advantages. The method can effectively improve the identification accuracy, has low complexity of the identification algorithm, and has better identification efficiency.
The invention adopts the technical scheme that a Stacking integrated learning mode-based radar HRRP target identification method comprises the following steps:
s1, establishing a training set and a testing set according to the rule that the training set should contain data of each angle of the target as much as possible and the samples of the testing set and the training set do not repeatedly appear: the jth HRRP sample for the ith class of target in the training set can be expressed as
Figure BDA0002492194680000011
Figure BDA0002492194680000012
The jth HRRP sample for the ith class of target in the test set may be represented as
Figure BDA0002492194680000013
Figure BDA0002492194680000014
N denotes the nth sample point of the HRRP sample, and N denotes N total sample points of the HRRP sample.
In the S2 training stage, the mean distance image feature, the radial length feature and the PCA transformation feature are extracted from the HRRP training sample during training. Thirdly, connecting the three types of features in series to form combined features, then screening the features by using a Relieff algorithm, extracting an optimal feature subset from the screened features by using an SVM _ RFE algorithm, and finally obtaining a trained base classifier and a trained meta classifier by using a Stacking ensemble learning mode based on the optimal feature subset, wherein the method specifically comprises the following steps:
s2.1 HRRP training sample of j of i-th class target
Figure BDA0002492194680000015
2 norm normalization is carried out to obtain a normalized HRRP training sample signal
Figure BDA0002492194680000016
Figure BDA0002492194680000021
S2.2 training sample signals based on normalized HRRP
Figure BDA0002492194680000022
Carrying out feature extraction, and connecting the extracted three types of features in series to form combined features, wherein the method comprises the following specific steps:
s2.2.1 extracting normalized HRRP training sample signal
Figure BDA0002492194680000023
Mean range image feature of
Figure BDA0002492194680000024
Figure BDA0002492194680000025
The mean distance image characteristic corresponding to the whole training set is
Figure BDA0002492194680000026
Figure BDA0002492194680000027
Where z represents z training samples per class of targets.
S2.2.2 extracting normalized HRRP training sample signal
Figure BDA0002492194680000028
Characteristic of radial length of
Figure BDA0002492194680000029
The method comprises the following specific steps: computing
Figure BDA00024921946800000210
Amplitude mean of
Figure BDA00024921946800000211
Threshold value is set to
Figure BDA00024921946800000212
In turn will
Figure BDA00024921946800000213
1 st to 1 th
Figure BDA00024921946800000214
The amplitude of each sample point is compared with a threshold value from 1 st to the second
Figure BDA00024921946800000215
The coordinates of each sampling point are sequentially
Figure BDA00024921946800000216
The coordinate value of the first point larger than the threshold value is recorded as
Figure BDA00024921946800000217
Then sequentially make the above-mentioned materials pass through
Figure BDA00024921946800000218
N to n of
Figure BDA00024921946800000219
The amplitude of each sample point is compared with a threshold value from the n-th to the n-th
Figure BDA00024921946800000220
The coordinates of each sampling point are sequentially
Figure BDA00024921946800000221
The coordinate value of the first point larger than the threshold value is recorded as
Figure BDA00024921946800000222
The radial length feature corresponding to the jth HRRP training sample of the ith target can be expressed as
Figure BDA00024921946800000223
The radial length characteristic corresponding to the whole training set is
Figure BDA00024921946800000224
Figure BDA00024921946800000225
Where z represents z training samples per class of targets.
S2.2.3 extracting normalized HRRP training sample signal
Figure BDA00024921946800000226
Characteristic of PCA transformation of
Figure BDA00024921946800000227
For the features obtained after transformation, pca is a function in MATLAB. The whole training set pairThe desired PCA transformation is characterized by Fpca：
Figure BDA00024921946800000228
Where z represents z training samples per class of targets.
S2.2.4, connecting the three kinds of features in series to form a combined feature, and the jth HRRP sample of the ith target corresponds to the combined feature as
Figure BDA00024921946800000229
The combined features corresponding to the whole training set are
Figure BDA00024921946800000230
S2.3 weight calculation and sorting of F by RelifF algorithm [ Fr,sortr](ii) RelifF (F), wherein FrIs a feature that is ranked well from high to low in weight, sortrThe generated feature sorting matrix can be used for sorting sample feature weights in test data, and the reason for using the algorithm is to preliminarily screen out useless features and reduce the operating pressure of the SVM _ RFE algorithm.
S2.4 finding F by SVM _ RFE algorithmrOptimal feature subset of [ F ]s,sorts]＝SVM_RFE(Fr) Obtaining an optimal feature subset FsAnd an optimal feature subset extraction matrix sortsAnd preparing for extracting the optimal feature subset of the test data.
S2.5, training three classes of base classifiers and a meta classifier by means of a Stacking ensemble learning mode, wherein the first class of base classifier is a support vector machine classifier (SVM), the second class of base classifier is a k-nearest neighbor classifier (KNN), the third class of base classifier is a random forest classifier (RF), the meta classifier is a k-nearest neighbor classifier (KNN), and the operation is as follows:
s2.5.1 first, the optimal feature subset F obtained in S2.4 is obtainedsEqually dividing into 5 parts: fs 1,Fs 2,Fs 3,Fs 4,Fs 5Training the 1 st classifier SVM of the first class base classifier SVM1When usingFs 1As verification test data, with Fs 2,Fs 3,Fs 4,Fs 5Training classifier SVM for training data1And the verification test result is marked as Psvm 1Training the 2 nd classifier SVM in the SVM classifier SVM2When using Fs 2As verification test data, with Fs 1,Fs 3,Fs 4,Fs 5Training classifier SVM based on training data2And the verification test result is marked as Psvm 2… …, in turn, converting Fs 3,Fs 4,Fs 5Respectively as verification test data, and the rest four data as training data to obtain five trained first class base classifiers SVM1,SVM2,SVM3,SVM4,SVM5And five verification test results P can be obtained simultaneouslysvm＝[Psvm 1,Psvm 2,Psvm 3,Psvm 4,Psvm 5]T。
S2.5.2 training the second class KNN and the third class RF to verify the test according to S2.5.1 to obtain five trained second class KNN classifiers1,KNN2,KNN3,KNN4,KNN5And five trained third class base classifiers RF1,RF2,RF3,RF4,RF5And also can obtain verification test result Pf_knn＝[Pf_knn 1,Pf_knn 2,Pf_knn 3,Pf_knn 4,Pf_knn 5]TAnd Prf＝[Prf 1,Prf 2,Prf 3,Prf 4,Prf 5]T。
S2.5.3 splicing the above test results as the latest training data Flast＝[Psvm,Pf_knn,Prf]；
S2.6 treating Flast＝[Psvm,Pf_knn,Prf]And importing a meta classifier KNN for training to obtain a trained meta classifier.
S3 test phase: during testing, mean distance image characteristics, radial length characteristics and PCA conversion characteristics are extracted from HRRP training samples. And connecting the three types of features in series to form combined features, and sequentially multiplying the combined features by a feature sequencing matrix and an optimal feature subset extraction matrix obtained in training to obtain an optimal feature subset. And finally, classifying the latest test data set by using the trained meta classifier to obtain a final classification result, wherein the method specifically comprises the following steps:
s3.1 HRRP test sample of jth class i target
Figure BDA0002492194680000031
Normalization by 2 norms to obtain normalized HRRP test sample signal
Figure BDA0002492194680000032
Figure BDA0002492194680000033
S3.2 test sample signals based on normalized HRRP
Figure BDA0002492194680000034
Carrying out feature extraction, and connecting the extracted three types of features in series to form combined features, wherein the method comprises the following specific steps:
s3.2.1 extracting normalized HRRP test sample signal
Figure BDA0002492194680000035
Mean range image feature of
Figure BDA0002492194680000036
Figure BDA0002492194680000037
The mean range profile corresponding to the whole test set is characterized in that
Figure BDA0002492194680000038
Figure BDA0002492194680000039
Where y indicates that there are y test samples per class of target.
S3.2.2 extracting normalized HRRP test sample signal
Figure BDA0002492194680000041
Characteristic of radial length of
Figure BDA0002492194680000042
The specific process is as follows: find out
Figure BDA0002492194680000043
Amplitude mean of
Figure BDA0002492194680000044
Threshold value is set to
Figure BDA0002492194680000045
In turn will
Figure BDA0002492194680000046
1 st to 1 th of
Figure BDA0002492194680000047
The amplitude of each sample point is compared with a threshold value from 1 st to the second
Figure BDA0002492194680000048
The coordinates of each sampling point are sequentially
Figure BDA0002492194680000049
The coordinate value of the first point larger than the threshold value is recorded as
Figure BDA00024921946800000410
Then sequentially make the above-mentioned materials pass through
Figure BDA00024921946800000411
N to n of
Figure BDA00024921946800000412
The amplitude of each sample point is compared with a threshold value from the n-th to the n-th
Figure BDA00024921946800000413
The coordinates of each sampling point are sequentially
Figure BDA00024921946800000414
The coordinate value of the first point larger than the threshold value is recorded as
Figure BDA00024921946800000415
The radial length feature corresponding to the jth HRRP test sample of the ith target can be expressed as
Figure BDA00024921946800000416
The radial length corresponding to the whole test set is characterized by
Figure BDA00024921946800000417
Figure BDA00024921946800000418
Where y indicates that there are y test samples per class of target.
S3.2.3 extracting normalized HRRP test sample signal
Figure BDA00024921946800000419
Characteristic of PCA transformation of
Figure BDA00024921946800000420
For the features obtained after transformation, PCA is a function in MATLAB, and the PCA transformation feature corresponding to the whole test set is fpca：
Figure BDA00024921946800000421
Where y indicates that there are y test samples per class of target.
S3.2.4, connecting the three characteristics in series to form a combined characteristic, wherein the combined characteristic corresponding to the jth HRRP test sample of the ith target is
Figure BDA00024921946800000422
The corresponding combination characteristics of the whole test set are
Figure BDA00024921946800000423
S3.3 sort obtained by S2.3rMultiplying the obtained result by the combined characteristic f to carry out characteristic screening to obtain the screened characteristic fr＝f×sortr。
S3.4 sort obtained by S2.4sMultiplying by the filtered feature frObtaining the desired optimal feature subset fs＝fr×sorts。
S3.5 sub-set f of optimal featuressSequentially importing five trained first class base classifiers SVM obtained in training1,SVM2,SVM3,SVM4,SVM5In (1), five classification results R are obtainedsvm 1,Rsvm 2,Rsvm 3,Rsvm 4,Rsvm 5Averaging the five classification results to obtain RsvmAs a subset of the most recent test data.
According to the method, the optimal feature subset f is divided intosSequentially importing five trained second-class base classifiers KNN obtained in training1,KNN2,KNN3,KNN4,KNN5And five trained third class base classifiers RF1,RF2,RF3,RF4,RF5Respectively obtaining the latest subsets R of test dataf_knnAnd Rrf. Stitching the three test subsets into a total test data set Tlast＝[Rsvm,Rf_knn,Rrf]。
S4 is S2.6 trained Meta-classifier on the latest test data set Tlast＝[Rsvm,Rf_knn,Rrf]And (5) classifying to obtain a final classification result.
The invention has the following beneficial effects: the method can effectively improve the identification accuracy of the HRRP multi-classification targets of the radar, has low complexity and better identification efficiency, and has important engineering application value for automatic target identification of the radar.
Drawings
FIG. 1 is a schematic diagram of a training and testing stage of a Stacking ensemble learning mode-based radar HRRP target recognition method;
FIG. 2 is a schematic representation of optical images and HRRP of 10 classes of targets used in the experiments, from left to right, from top to bottom, for BMP2, BTR70, T72, BTR60,2S1, BRDM2, D7, T62, ZIL and ZSU, respectively;
fig. 3 is a schematic diagram of Stacking ensemble learning classification according to the present invention, in which Mode1, Mode2, and Mode3 represent three classes of basis classifiers SVM, KNN, and RF, respectively, and the meta classifier in the diagram is KNN.
Detailed Description
The present invention is further illustrated below by the following examples of implementation routines, it being understood that these implementations are merely illustrative of the present invention and are not intended to limit the scope of the present invention, which is to be read and modified by those skilled in the art in various equivalent forms within the scope of the present invention as defined in the appended claims.
The invention provides a radar HRRP target identification method based on a Stacking integrated learning mode, a general flow chart is shown in figure 1, and the method comprises the following steps:
s1, establishing a training set and a testing set according to the rule that the training set should contain data of each angle of the target as much as possible and the samples of the testing set and the training set do not appear repeatedly;
in the S2 training stage, the mean distance image feature, the radial length feature and the PCA transformation feature are extracted from the HRRP training sample during training. Thirdly, connecting the three types of features in series to form combined features, screening the features by using a Relieff algorithm, extracting an optimal feature subset from the screened features by using an SVM _ RFE algorithm, and finally obtaining a trained base classifier and a trained meta classifier by using a Stacking ensemble learning mode based on the optimal feature subset;
s3 test phase: during testing, mean distance image characteristics, radial length characteristics and PCA conversion characteristics are extracted from HRRP training samples. And connecting the three types of features in series to form combined features, and sequentially multiplying the combined features by a feature sequencing matrix and an optimal feature subset extraction matrix obtained in training to obtain an optimal feature subset. Then, the optimal feature subset is led into a trained base classifier to obtain a latest test data set, and finally, the latest test data set is classified by using the trained meta classifier to obtain a final classification result;
s4 test the latest test data set T by using the meta classifier trained in S2.6last＝[Rsvm,Rf_knn,Rrf]And (5) classifying to obtain a final classification result.
The effect of the invention can be further verified and explained by the following simulation experiment:
(I) Experimental conditions
1. Experimental data
The data used in the experiment are measured data of high resolution range profiles of 10 types of ground targets, optical images of 10 types of targets and HRRP, as shown in fig. 2, from left to right and from top to bottom, BMP2, BTR70, T72, BTR60,2S1, BRDM2, D7, T62, ZIL and ZSU, respectively. Each type of target contains omnidirectional angle data at 15 degrees and 17 degrees pitch angle. Data at 17 degrees pitch angle were used for training in the experiment, and data at 15 degrees pitch angle were used for testing. The number of training samples is 2747 and the number of testing samples is 2425.
2. Experimental Environment
Software environment of simulation experiment: an operating system windows 10; the processor is Intel (R) core (TM) i7-8700k, and the main frequency of the processor is 3.70 GHz; the software platform is as follows: MATLAB 2019 b.
3. Experimental parameters
In the training stage, when the useless features are screened out by utilizing the RelifF algorithm, the threshold value is set to be 0, the features with the weight higher than 0 are reserved, and the features with the weight lower than 0 are screened out.
In the training stage, when the SVM _ RFE algorithm is used for solving the optimal feature subset, through a plurality of experiments, when the feature number of the feature subset is set to be 125, the classification effect is good.
The kernel function of the first class of base classifier SVM is a polynomial kernel function polynomial, and the polynomial order is set to be 2;
the second type base classifier is a K neighbor classifier KNN, the number of neighbor elements is 1, and the distance weights are set to be equal;
the third class of base classifier is a random forest classifier RF, using the fitsensing function in MATLAB, where the parameter Method is set to bag and the parameter NumLearningCycle is set to 30.
(II) contents and results of the experiment
Compared with other existing radar target identification methods, the method of the invention has the following results in Table 1:
TABLE 1
Classification method Recognition rate
Single classifier Support Vector Machine (SVM) 83.3％
Single classifier K mean value near neighbor (KNN) 84.5％
Single classifier Random Forest (RF) 85.1％
Multi-classifier voting 87.4％
Bayes Compressed Sensing (BCS) 86.2％
Joint dynamic sparse form classification (JDSRC) 86.5％
Multitask compressed sensing (MtCS) 86.7％
Methods of the invention 89.1％
As can be seen from Table 1, compared with other radar HRRP target identification methods, the method has high identification accuracy which reaches 89.1 percent and is obviously superior to other methods.

Claims (3)

1. A method for identifying HRRP (high resolution redundancy protocol) targets based on a Stacking integrated learning mode radar is characterized by comprising the following steps of:
s1, establishing a training set and a testing set according to the rule that the training set should contain data of each angle of the target as much as possible and the samples of the testing set and the training set do not repeatedly appear: the jth HRRP sample for the ith class of target in the training set can be expressed as
Figure FDA0002492194670000016
Figure FDA0002492194670000013
The jth HRRP sample for the ith class of target in the test set may be represented as
Figure FDA0002492194670000014
Figure FDA0002492194670000015
n represents HThe nth sampling point of the RRP sample, wherein N represents N sampling points in the HRRP sample;
s2 training stage: during training, firstly extracting mean distance image features, radial length features and PCA conversion features from HRRP training samples, then connecting three types of features in series to form combined features, then screening the features by using a Relieff algorithm, extracting an optimal feature subset from the screened features by using an SVM _ RFE algorithm, and finally obtaining a trained base classifier and a trained meta classifier by using a Stacking ensemble learning mode based on the optimal feature subset, wherein the method comprises the following specific steps:
s2.1 HRRP training sample of j of i-th class target
Figure FDA0002492194670000017
2 norm normalization is carried out to obtain a normalized HRRP training sample signal
Figure FDA0002492194670000018
Figure FDA0002492194670000011
S2.2 training sample signals based on normalized HRRP
Figure FDA0002492194670000019
Carrying out feature extraction, and connecting the extracted three types of features in series to form combined features, wherein the method comprises the following specific steps:
s2.2.1 extracting normalized HRRP training sample signal
Figure FDA00024921946700000110
Mean range image feature of
Figure FDA00024921946700000111
Figure FDA0002492194670000012
The whole training set corresponds toIs characterized by a mean range profile of
Figure FDA00024921946700000112
Figure FDA00024921946700000113
Figure FDA00024921946700000114
Wherein z represents z training samples per class of targets;
s2.2.2 extracting normalized HRRP training sample signal
Figure FDA00024921946700000115
Characteristic of radial length of
Figure FDA00024921946700000116
The method comprises the following specific steps: computing
Figure FDA00024921946700000117
Amplitude mean of
Figure FDA00024921946700000118
In turn will
Figure FDA00024921946700000119
1 st to 1 th
Figure FDA00024921946700000120
The amplitude of each sample point is compared with a threshold value from 1 st to the second
Figure FDA00024921946700000121
The coordinates of each sampling point are sequentially
Figure FDA00024921946700000122
The coordinate value of the first point larger than the threshold value is recorded as
Figure FDA00024921946700000123
Then sequentially make the above-mentioned materials pass through
Figure FDA00024921946700000124
N to n of
Figure FDA00024921946700000125
The amplitude of each sample point is compared with a threshold value from the n-th to the n-th
Figure FDA00024921946700000126
The coordinates of each sampling point are sequentially
Figure FDA00024921946700000127
The coordinate value of the first point larger than the threshold value is recorded as
Figure FDA00024921946700000128
The radial length feature corresponding to the jth HRRP training sample of the ith target can be expressed as
Figure FDA00024921946700000129
Figure FDA00024921946700000130
The corresponding radial length characteristic of the whole training set is Fl：
Figure FDA00024921946700000131
Figure FDA00024921946700000132
Wherein z represents z training samples per class of targets;
s2.2.3 extracting normalized HRRP training sample signal
Figure FDA0002492194670000021
Characteristic of PCA transformation of
Figure FDA0002492194670000022
Figure FDA0002492194670000023
For features obtained after transformation, pca is a function in MATLAB; the PCA conversion characteristic corresponding to the whole training set is Fpca：
Figure FDA0002492194670000024
Wherein z represents z training samples per class of targets;
s2.2.4, connecting the three kinds of features in series to form a combined feature, and the jth HRRP sample of the ith target corresponds to the combined feature as
Figure FDA0002492194670000025
The combined features corresponding to the whole training set are
Figure FDA0002492194670000026
S2.3 weight calculation and sorting of F by RelifF algorithm [ Fr,sortr](ii) RelifF (F), wherein FrIs a feature that is ranked well from high to low in weight, sortrThe generated feature sorting matrix can be used for sorting sample feature weights in test data;
s2.4 finding F by SVM _ RFE algorithmrOptimal feature subset of [ F ]s,sorts]＝SVM_RFE(Fr) Obtaining an optimal feature subset FsAnd an optimal feature subset extraction matrix sortsPreparing for extracting the optimal feature subset of the test data;
s2.5, training three classes of base classifiers and a meta classifier by means of a Stacking integrated learning mode, wherein the first class of base classifier is a support vector machine classifier, the second class of base classifier is a k neighbor classifier, the third class of base classifier is a random forest classifier, and the meta classifier is a k neighbor classifier, and the method specifically comprises the following operations:
s2.5.1 first, the optimal feature subset F obtained in S2.4 is obtainedsEqually dividing into 5 parts: fs 1,Fs 2,Fs 3,Fs 4,Fs 5Training the 1 st classifier SVM of the first class base classifier SVM1When using Fs 1As verification test data, with Fs 2,Fs 3,Fs 4,Fs 5Training classifier SVM for training data1And the verification test result is marked as Psvm 1Training the 2 nd classifier SVM in the SVM classifier SVM2When using Fs 2As verification test data, with Fs 1,Fs 3,Fs 4,Fs 5Training classifier SVM based on training data2And the verification test result is marked as Psvm 2… …, in turn, converting Fs 3,Fs 4,Fs 5Respectively as verification test data, and the rest four data as training data to obtain five trained first class base classifiers SVM1,SVM2,SVM3,SVM4,SVM5And five verification test results P can be obtained simultaneouslysvm＝[Psvm 1,Psvm 2,Psvm 3,Psvm 4,Psvm 5]T；
S2.5.2 training the second class KNN and the third class RF to verify the test according to S2.5.1 to obtain five trained second class KNN classifiers1,KNN2,KNN3,KNN4,KNN5And five trained third class base classifiers RF1,RF2,RF3,RF4,RF5And also can obtain verification test result Pf_knn＝[Pf_knn 1,Pf_knn 2,Pf_knn 3,Pf_knn 4,Pf_knn 5]TAnd Prf＝[Prf 1,Prf 2,Prf 3,Prf 4,Prf 5]T；
S2.5.3 splicing the above test results as the latest training data Flast＝[Psvm,Pf_knn,Prf]；
S2.6 treating Flast＝[Psvm,Pf_knn,Prf]Importing a meta classifier KNN for training to obtain a trained meta classifier;
s3 test phase: during testing, firstly extracting mean distance image features, radial length features and PCA conversion features from HRRP training samples, connecting the three types of features in series to form combined features, sequentially multiplying the combined features by a feature sorting matrix and an optimal feature subset extraction matrix obtained during training to obtain an optimal feature subset, then introducing the optimal feature subset into a trained base classifier to obtain a latest test data set, and finally classifying the latest test data set by using the trained element classifier to obtain a final classification result, wherein the method specifically comprises the following steps:
s3.1 HRRP test sample of jth class i target
Figure FDA0002492194670000033
Normalization by 2 norms to obtain normalized HRRP test sample signal
Figure FDA0002492194670000034
Figure FDA0002492194670000031
S3.2 test sample signals based on normalized HRRP
Figure FDA0002492194670000035
Carrying out feature extraction, and connecting the extracted three types of features in series to form combined features, wherein the method comprises the following specific steps:
s3.2.1 extracting normalized HRRP test sample signal
Figure FDA0002492194670000036
Mean range image feature of
Figure FDA0002492194670000037
Figure FDA0002492194670000032
The mean range profile corresponding to the whole test set is characterized in that
Figure FDA0002492194670000038
Figure FDA0002492194670000039
Figure FDA00024921946700000310
Wherein y represents y test samples per class of target;
s3.2.2 extracting normalized HRRP test sample signal
Figure FDA00024921946700000311
Characteristic of radial length of
Figure FDA00024921946700000312
The specific process is as follows: find out
Figure FDA00024921946700000313
Amplitude mean of
Figure FDA00024921946700000314
In turn will
Figure FDA00024921946700000315
1 st to 1 th of
Figure FDA00024921946700000316
The amplitude of each sample point is compared with a threshold value from 1 st to the second
Figure FDA00024921946700000317
The coordinates of each sampling point are sequentially
Figure FDA00024921946700000318
The coordinate value of the first point larger than the threshold value is recorded as
Figure FDA00024921946700000319
Then sequentially make the above-mentioned materials pass through
Figure FDA00024921946700000320
N to n of
Figure FDA00024921946700000321
The amplitude of each sample point is compared with a threshold value from the n-th to the n-th
Figure FDA00024921946700000322
The coordinates of each sampling point are sequentially
Figure FDA00024921946700000323
The coordinate value of the first point larger than the threshold value is recorded as
Figure FDA00024921946700000324
The radial length feature corresponding to the jth HRRP test sample of the ith target can be expressed as
Figure FDA00024921946700000325
Figure FDA00024921946700000326
Figure FDA00024921946700000327
The radial length characteristic corresponding to the entire test set is fl：
Figure FDA00024921946700000328
Figure FDA00024921946700000329
Wherein y represents y test samples per class of target;
s3.2.3 extracting normalized HRRP test sample signal
Figure FDA00024921946700000330
Characteristic of PCA transformation of
Figure FDA00024921946700000331
Figure FDA00024921946700000332
For the features obtained after transformation, PCA is a function in MATLAB, and the PCA transformation feature corresponding to the whole test set is fpca：
Figure FDA00024921946700000333
Wherein y represents y test samples per class of target;
s3.2.4, connecting the three characteristics in series to form a combined characteristic, wherein the combined characteristic corresponding to the jth HRRP test sample of the ith target is
Figure FDA00024921946700000334
The corresponding combination characteristics of the whole test set are
Figure FDA00024921946700000335
S3.3 sort obtained by S2.3rMultiplying the obtained result by the combined characteristic f to carry out characteristic screening to obtain the screened characteristic fr＝f×sortr；
S3.4 sort obtained by S2.4sMultiplying by the filtered feature frObtaining the desired optimal feature subset fs＝fr×sorts；
S3.5 sub-set f of optimal featuressObtained when training is conducted in sequenceFive trained first class basis classifiers SVM1,SVM2,SVM3,SVM4,SVM5In (1), five classification results R are obtainedsvm 1,Rsvm 2,Rsvm 3,Rsvm 4,Rsvm 5Averaging the five classification results to obtain RsvmAs a subset of the most recent test data;
sub-set f of optimal featuressSequentially importing five trained second-class base classifiers KNN obtained in training1,KNN2,KNN3,KNN4,KNN5And five trained third class base classifiers RF1,RF2,RF3,RF4,RF5In the method, the five classification results are respectively averaged to obtain the latest subset R of the test dataf_knnAnd RrfThe three test subsets are spliced into a total test data set Tlast＝[Rsvm,Rf_knn,Rrf]；
S4 test the latest test data set T by using the meta classifier trained in S2.6last＝[Rsvm,Rf_knn,Rrf]And (5) classifying to obtain a final classification result.
2. The Stacking ensemble learning mode-based radar HRRP target identification method according to claim 1, characterized in that: s2.2.2, the threshold value is set to
Figure FDA0002492194670000042
3. The Stacking ensemble learning mode-based radar HRRP target identification method according to claim 1, characterized in that: s3.2.2, the threshold value is set to
Figure FDA0002492194670000041
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