CN109343043B - Radar HRRP target identification method based on selected principal component analysis - Google Patents
Radar HRRP target identification method based on selected principal component analysis Download PDFInfo
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Abstract
The invention discloses a radar HRRP target identification method based on selected principal component analysis, which is characterized in that the selection of principal components with the maximum separability among different targets is realized by utilizing a Fisher criterion, then the fast reconstruction of an original HRRP signal is realized by utilizing the selected principal components with the maximum separability among the different targets, and finally the identification of the radar HRRP target is realized by utilizing the reconstruction error between the original HRRP signal and the reconstructed HRRP signal. The invention reduces the reconstruction time and the computer operation resource, and simultaneously achieves the effect of further improving the target recognition rate; the complex calculation of a kernel method is avoided, and the identification effect equivalent to that of the complex calculation method is kept on the premise of effectively reducing the complexity of the algorithm and improving the real-time performance of the algorithm by using the simple Fisher selection criterion.
Description
Technical Field
The invention relates to a radar HRRP target recognition method based on selected principal component analysis, which is used for radar automatic target recognition of a high-resolution range profile.
Background
The radar automatic target identification technology is a hot research 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 relatively small data volume, and has the advantages of convenience in acquisition and simplicity in processing. In an actual radar automatic target recognition system, the algorithm complexity and the real-time performance of the system are two mutually restricted factors. The higher the complexity of the algorithm, the worse the real-time performance of the system. Therefore, how to ensure the identification rate of the target while reducing the complexity of the algorithm is an urgent problem to be solved in order to ensure the real-time performance of the radar automatic target identification system based on the high-resolution range profile.
In recent years, a kernel method has been widely applied to a radar automatic target recognition method based on principal component analysis, and a series of kernel algorithms represented by a radar automatic target recognition algorithm based on kernel principal component analysis have been proposed in succession. Compared with the radar HRRP target recognition algorithm based on principal component analysis, although the recognition rate of the kernel algorithms can be greatly improved, the real-time performance of the kernel algorithms is relatively poor.
Disclosure of Invention
The invention aims to: aiming at the problem that algorithm complexity and algorithm instantaneity are mutually restricted in the radar HRRP target recognition algorithm, the invention is inspired by the idea that for radar automatic target recognition, only maximum separability between reconstruction signals of different targets is ensured without ensuring that the reconstruction signals have extremely high reconstruction precision, and provides a radar HRRP target recognition algorithm based on principal component analysis on the basis of the radar HRRP target recognition algorithm based on principal component analysis. The method comprises the steps of utilizing a Fisher criterion to realize selection of a main component with the maximum separability among different targets, then utilizing the selected main component with the maximum separability among the different targets to realize rapid reconstruction of an original HRRP signal, and finally utilizing a reconstruction error between the original HRRP signal and a reconstructed HRRP signal to realize radar HRRP target identification. Compared with a radar HRRP target recognition algorithm based on kernel principal component analysis, the method provided by the invention has the advantages that the algorithm complexity is obviously reduced, the algorithm real-time performance is obviously improved, and meanwhile, the recognition rate is quite high.
The technical scheme is as follows: a radar HRRP target identification method based on selected principal component analysis utilizes a Fisher criterion to realize the selection of principal components with maximum separability among different targets, then utilizes the selected principal components with maximum separability among the different targets to realize the rapid reconstruction of an original HRRP signal, and finally utilizes the reconstruction error between the original HRRP signal and a reconstructed HRRP signal to realize the radar HRRP target identification. The radar HRRP target recognition algorithm based on the selected principal component analysis has the following flow:
step 1: framing the omnibearing training HRRP signals of different targets by adopting an average framing method so as to eliminate the azimuth sensitivity of the HRRP;
step 2: adopting a 2 norm normalization method to normalize the training HRRP signals of different targets so as to eliminate the strength sensitivity of the HRRP;
and 3, step 3: performing Fourier transform on the normalized training HRRP signal to obtain a frequency spectrum of the normalized training HRRP signal so as to eliminate the translational sensitivity of the HRRP;
and 4, step 4: performing principal component analysis on the frequency spectrums of the normalized HRRP of different frames to obtain a characteristic value matrix L, a characteristic value contribution matrix E and a characteristic vector matrix W of the frequency spectrums of the normalized HRRP corresponding to the frames;
and 5: selecting principal components with maximum separability among different targets by utilizing a Fisher criterion based on a characteristic value matrix L, a characteristic value contribution matrix E and a characteristic vector matrix W of different frames of different targets respectively to form a new selected characteristic vector matrix SW with maximum separability among different targets;
and 6: sequentially carrying out 2 norm normalization and Fourier transform on the test HRRP signal to obtain a frequency spectrum of the normalized test HRRP signal, and realizing rapid reconstruction of the frequency spectrum of the normalized test HRRP signal by using a selected feature vector matrix SW of different targets and different frames;
and 7: calculating a reconstruction error err between an original spectrum and a reconstructed spectrum of the normalized test HRRP signal i ；
And step 8: find the minimum reconstruction error e min The target class to which the corresponding training HRRP signal belongs is the target class to which the testing HRRP signal belongs. Therefore, radar HRRP target identification based on the selected principal component analysis is realized.
Has the beneficial effects that: compared with the prior art, the technical scheme adopted by the invention has the following beneficial effects:
1. compared with the radar HRRP target identification method based on principal component analysis, the radar target identification method based on principal component analysis only utilizes the selected eigenvector matrix formed by eigenvectors with the maximum separability among different targets to reconstruct, so that the reconstruction time and computer operation resources are reduced, and the effect of further improving the target identification rate is achieved;
2. compared with a radar HRRP target identification method based on kernel principal component analysis, the radar HRRP target identification method based on principal component analysis selection avoids complex calculation of a kernel method, and maintains the identification effect equivalent to the complex calculation method based on the simple Fisher selection criterion on the premise of effectively reducing algorithm complexity and improving algorithm instantaneity.
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FIG. 1 is a schematic flow chart of a radar HRRP target identification method based on selected principal component analysis;
fig. 2 is a schematic diagram of HRRP signals of three different types of ship targets V1, V2 and V3, in which the reference numbers are (a), (b) and (c), respectively.
Detailed Description
The present invention is further illustrated by the following examples, which are intended to be purely exemplary and are not intended to limit the scope of the invention, which is to be given the full breadth of the claims appended hereto.
The general flow chart of the radar HRRP target identification method based on the selected principal component analysis is shown in figure 1. The high-resolution range image signals of three types of ship targets V1, V2 and V3 are shown in fig. 2(a), fig. 2(b) and fig. 2(c), respectively. Taking actually measured HRRP signals of three types of ship targets as an example, a radar HRRP target identification method based on selected principal component analysis is specifically introduced, and compared with the identification effect of the radar HRRP target identification method based on principal component analysis and nuclear principal component analysis, the effectiveness and superiority of the radar HRRP target identification method based on selected principal component analysis are verified.
Step 1: carrying out average framing on the HRRP signals of different targets according to the maximum azimuth angle of the unit which does not move with distance, and eliminating the azimuth sensitivity of the HRRP signals;
and 2, step: normalizing all the training and testing HRRP signals y (N), N is 1,2, N, N according to the formula (1) by 2 norms to obtain a normalized HRRP signal
Thereby eliminating the strength sensitivity of HRRP;
and 3, step 3: obtaining a normalized HRRP signal according to equation (2)
N ═ 1,2, …, N, thereby eliminating translational sensitivity of the HRRP signal;
in the formula, FFT represents discrete fourier transform.
And 4, step 4: forming a spectrum matrix S by the spectrum of each frame of normalized training HRRP signal in a column vector mode, and performing principal component analysis on the S according to a formula (3) to obtain a characteristic value matrix L, a characteristic value contribution matrix E and a characteristic vector matrix W of the frame of spectrum matrix;
[L,E,W,Mean]＝pca(S) (3)
in the formula, pca represents principal component analysis transformation; mean represents the Mean vector of the spectrum of the HRRP signal of the frame.
And 5: suppose that three different types of ship targets are respectively divided into Q 1 、Q 2 And Q 3 The HRRP data of the frame, ship V1, V2 and V3 respectively can obtain Q by using the step 4 1 、Q 2 And Q 3 An eigenvalue matrix L, which can be constructed for different targets using equation (4) i ,i＝1,2,3；
In the formula I i Each column of (a) represents a column vector formed by sorting eigenvalues in each eigenvalue matrix of the ship target i according to the magnitude of the eigenvalues.
And 6: using eigenvalue matrices l of different targets i The i is 1,2 and 3, and the separability size between different characteristic values of different targets based on the Fisher criterion can be obtained through the formula (5);
wherein p represents the order of eigenvalues in the eigenvalue matrix;
representing the p-th characteristic value in the characteristic value matrix after the Kth frame HRRP data of the q-th ship target is subjected to principal component analysis;
representing the mean value of the p-th characteristic value in the characteristic value matrix after the HRRP data of all frames of the q-th ship target are subjected to principal component analysis;
representing the mean value of the p-th characteristic value in the characteristic value matrix after the HRRP data of all frames of the i-th and j-th ship targets are subjected to principal component analysis;
and representing the variance of the p-th eigenvalue in the eigenvalue matrix after the HRRP data of all frames of the q-th ship target are subjected to principal component analysis.
And 7: the step 6 can obtain HRRP data of the three types of ship targets as main component analysis, and the separability size m of the three types of targets is obtained according to different characteristic values obtained after the HRRP data of the three types of ship targets are used as main component analysis p (i, j), i, j ═ 1,2, 3; i ≠ j, and respectively finding out corresponding positions pos of the eigenvalues with the maximum dividable rows of the other two types of targets in the eigenvalue matrix L according to a formula (6) for different targets i ,i＝1,2,3；
And 8: the separability of the characteristic values of the HRRP data of different ship targets to different targets indirectly reflects the characteristic vectors of the HRRP data of different ship targets, namely the separability of different principal components to different targets, and the characteristic vector with the largest separability between different targets is selected from the characteristic vector matrixes W of different ship targets according to a formula (7) to form a selected characteristic vector matrix SW;
SW＝W[pos] (7)
and step 9: the spectrum P (n) of the HRRP (normalized test) can be reconstructed according to a formula (8) by utilizing the selected eigenvector matrix SW corresponding to the different frames of the different targets obtained in the step (8), so as to obtain a series of reconstructed samples of the HRRP spectrum corresponding to the different frames of the different targets
Step 10: calculating a reconstruction error err between the reconstructed spectrum of the series of HRRP testing signals obtained in the step 9 and the original spectrum of the HRRP testing signals according to a formula (9) i ；
Step 11: the ship target class corresponding to the frame where the minimum reconstruction error is located is the class of the ship target to which the HRRP test signal belongs.
The radar HRRP target identification method based on the L-based selected principal component analysis is mainly introduced, and the radar HRRP target identification method based on the E-based selected principal component analysis and the W-based selected principal component analysis is similar to the method, and mainly differs in that the separability between different targets is calculated for the E and the W by using the Fisher criterion, which is not described herein again.
Based on the detailed method introduction, the invention utilizes the actually measured HRRP signals of the three types of ship targets to carry out radar HRRP target identification based on principal component selection analysis. The measured HRRP signals of the three ship targets V1, V2 and V3 respectively have 2400 samples, 1800 samples and 1600 samples. And totally dividing the frame into 29 frames by a uniform frame dividing method, taking 90% HRRP signals of each frame as training samples to perform main component selection analysis to obtain a feature vector selection matrix of the HRRP of each frame, and taking other 10% HRRP signals of each frame as test samples to verify the effectiveness of the radar HRRP target identification method based on the main component selection analysis.
TABLE 1 identification rates of HRRP targets of three types of ships under different methods
The radar HRRP target recognition rates of the three types of ship targets based on the selected principal component analysis, the principal component analysis and the nuclear principal component analysis are shown in the table 1. As can be seen from table 1, no matter whether the Fisher criterion is applied to L or E, W in the main component analysis to select the main component with the maximum separability between different targets, the average recognition rate of the three types of ship targets under the radar HRRP target recognition method based on the main component analysis is over 94%, which is far higher than the highest average recognition rate 83.45% of the three types of ship targets under the same experimental conditions. Although the radar HRRP target recognition rate based on the kernel principal component analysis is about two percent higher than that based on the selection principal component analysis, the algorithm complexity of the kernel principal component analysis is far higher than that of the selection principal component analysis, and the real-time performance of the kernel principal component analysis is obviously inferior to that of the selection principal component analysis. Therefore, a 2% recognition rate penalty is acceptable with reduced algorithm complexity and significantly improved algorithm real-time.
Claims (4)
1. A radar HRRP target identification method based on selected principal component analysis is characterized by comprising the following steps:
step 1: framing the omnibearing training HRRP signals of different targets by adopting an average framing method so as to eliminate the azimuth sensitivity of the HRRP;
step 2: performing normalization processing on training HRRP signals of different targets by adopting a 2 norm normalization method so as to eliminate the strength sensitivity of the HRRP;
and step 3: performing Fourier transform on the normalized training HRRP signal to obtain a frequency spectrum of the normalized training HRRP signal so as to eliminate the translational sensitivity of the HRRP;
and 4, step 4: performing principal component analysis on the frequency spectrums of the normalized HRRP of different frames to obtain a characteristic value matrix L, a characteristic value contribution matrix E and a characteristic vector matrix W of the frequency spectrums of the normalized HRRP corresponding to the frames;
and 5: selecting principal components with maximum separability among different targets by utilizing a Fisher criterion based on a characteristic value matrix L, a characteristic value contribution matrix E and a characteristic vector matrix W of different frames of different targets respectively to form a new selected characteristic vector matrix SW with maximum separability among different targets;
let three different ship targets respectively be divided into Q 1 、Q 2 And Q 3 HRRP data utilization of the frame, ship V1, V2 and V3 results in Q 1 、Q 2 And Q 3 An eigenvalue matrix L is constructed for different targets by using a formula (4) i ,i＝1,2,3；
In the formula I i Each column of (a) represents a column vector formed by sorting eigenvalues in each eigenvalue matrix of the ship target i according to the magnitude of the eigenvalue;
using a matrix of eigenvalues l of different targets i The i is 1,2 and 3, and the separability size between different characteristic values of different targets based on the Fisher criterion can be obtained through the formula (5);
wherein p represents the order of eigenvalues in the eigenvalue matrix;
representPerforming principal component analysis on the Kth frame HRRP data of the qth ship target to obtain the pth eigenvalue in the eigenvalue matrix;
representing the mean value of the p-th characteristic value in the characteristic value matrix after the HRRP data of all frames of the q-th ship target are subjected to principal component analysis;
representing the mean value of the p-th characteristic value in the characteristic value matrix after the HRRP data of all frames of the i-th and j-th ship targets are subjected to principal component analysis;
representing the variance of the p-th eigenvalue in an eigenvalue matrix after the HRRP data of all frames of the q-th ship target are subjected to principal component analysis;
the separability size m of different characteristic values obtained by taking HRRP data of three types of ship targets as main components for analysis on the three types of targets p (i, j), i, j ═ 1,2, 3; i is not equal to j, and corresponding positions pos of the eigenvalue with the maximum dividable row with other two types of targets in the eigenvalue matrix L are respectively found for different targets according to a formula (6) i ,i＝1,2,3；
The separability of the characteristic values of the HRRP data of different ship targets to different targets indirectly reflects the characteristic vectors of the HRRP data of different ship targets, namely the separability of different principal components to different targets, and the characteristic vector with the largest separability between different targets is selected from the characteristic vector matrixes W of different ship targets according to a formula (7) to form a selected characteristic vector matrix SW;
SW＝W[pos] (7)
step 6: sequentially carrying out 2 norm normalization and Fourier transform on the test HRRP signal to obtain a frequency spectrum of the normalized test HRRP signal, and realizing rapid reconstruction of the frequency spectrum of the normalized test HRRP signal by using a selected feature vector matrix SW of different targets and different frames;
the spectrum P (n) of the normalized HRRP can be reconstructed by using the selected eigenvector matrix SW corresponding to different frames of different targets according to the formula (8), and a series of reconstructed samples of the tested HRRP spectrum corresponding to different frames of different targets are obtained
And 7: computing a reconstruction error err between an original spectrum and a reconstructed spectrum of a normalized test HRRP signal i (ii) a Calculating a reconstruction error err between a reconstructed spectrum of the test HRRP signal and an original spectrum of the test HRRP signal according to formula (9) i ；
And step 8: find the minimum reconstruction error e min The corresponding target category to which the training HRRP signal belongs is the target category to which the testing HRRP signal belongs; the ship target class corresponding to the frame where the minimum reconstruction error is located is the class of the ship target to which the HRRP test signal belongs;
2. the method as claimed in claim 1, wherein training and testing HRRP signal y (N), N is 1,2, …, N is normalized by 2 norm according to formula (1) to obtain normalized HRRP signal
3. The method of claim 1, wherein the HRRP target identification method is based on a selective principal component analysis (SPC-RARE) radar, and is characterized in that a normalized HRRP signal is obtained according to the formula (2)
N-1, 2, …, N, thereby eliminating translational sensitivity of the HRRP signal;
in the equation, FFT represents discrete fourier transform.
4. The HRRP-target recognition method for radars based on PCA as claimed in claim 1, wherein in step 4, the spectrum matrix S is formed by the spectrum of each frame of normalized training HRRP signal in the form of column vector, and the eigenvalue matrix L, the eigenvalue contribution matrix E and the eigenvector matrix W of the frame spectrum matrix are obtained by principal component analysis of S according to the formula (3);
[L,E,W,Mean]＝pca(S) (3)
in the formula, pca represents principal component analysis transformation; mean represents the Mean vector of the spectrum of the frame HRRP signal.
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