CN108268837B - Radiation source fingerprint feature extraction method based on wavelet entropy and chaotic characteristics - Google Patents
Radiation source fingerprint feature extraction method based on wavelet entropy and chaotic characteristics Download PDFInfo
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Abstract
A radiation source fingerprint feature extraction method based on wavelet entropy and chaotic characteristics relates to the field of individual identification of radiation sources. The method comprises the following steps: 1) extracting wavelet entropy characteristics of the radiation source signals to obtain characteristic parameters; 2) chaotic feature analysis is carried out on the radiation source signals, chaotic feature parameters are extracted, wavelet entropy feature vectors and chaotic feature vectors are combined to obtain combined feature vectors, and the combined feature vectors are input into a feature classifier to realize identification of individual radiation sources. The method overcomes the defect that the non-linear nature of the radiation source signal is not considered in the conventional time-frequency analysis method, not only exerts the strong time-frequency resolution characteristic of wavelet packet transformation and extracts the multi-scale local characteristics of the signal, but also considers the overall non-linear condition of the signal through the non-linear analysis method of chaos analysis, thereby more accurately reflecting the characteristics of the radiation source signal and leading the extracted characteristic parameters to have stronger distinguishability.
Description
Technical Field
The invention relates to the field of individual identification of radiation sources, in particular to a radiation source fingerprint feature extraction method based on wavelet entropy and chaotic characteristics.
Background
The "fingerprint" of the communication signal refers to the representation of the fine characteristics of the individual communication radiation sources by using the signal as a carrier, and generally refers to the fact that the individual characteristics which can be distinguished from other radiation sources are added to the emitted signal due to the difference of hardware devices among the individual radiation sources. In modern sea wars, underwater target identification is the premise that an enemy finds out and effectively carries out underwater sound countermeasure on the enemy, and the enemy uses a weapon to attack the enemy first to overcome the defeat of the enemy. If the fingerprint characteristics of the radiation source can be effectively extracted in a complex underwater environment, different radiation source equipment can be distinguished, the judgment of communication structure and strategic deployment can be further realized through the analysis and identification of individuals, a key basis is provided for the corresponding battle plan deployment of the army, and the method has important practical significance.
The existing commonly used radiation source fingerprint feature extraction method mainly analyzes the time-frequency domain of a radiation source signal, and has the defects that the radiation source signal is processed by approximating the radiation source signal to a linear signal, the nonlinear nature of the signal is not considered, and therefore the nonlinear feature of the radiation source signal cannot be well reflected. Chaos is an important motion state of a nonlinear system, and can well represent a special rule in a nonlinear random process.
Wavelet transform is an effective time-frequency analysis method, can finely extract information of signals under different scales, and has stronger time-frequency resolution compared with wavelet transform. The information entropy is an important parameter for measuring the uncertainty of the signal, and combines wavelet packet transformation and information entropy analysis, so that the multi-scale local characteristics of the signal can be reflected, and the overall complexity of the signal can be reflected.
Disclosure of Invention
The invention aims to overcome the defect that a radiation source fingerprint feature extraction method based on time-frequency analysis does not reflect the nonlinear nature of a radiation source signal, and provides a radiation source fingerprint feature extraction method based on wavelet entropy and chaotic characteristics.
The invention comprises the following steps:
1) extracting wavelet entropy characteristics of the radiation source signals to obtain characteristic parameters;
2) chaotic feature analysis is carried out on the radiation source signals, chaotic feature parameters are extracted, wavelet entropy feature vectors and chaotic feature vectors are combined to obtain combined feature vectors, and the combined feature vectors are input into a feature classifier to realize identification of individual radiation sources.
In step 1), the specific method for extracting the wavelet entropy characteristics of the radiation source signal to obtain the characteristic parameters may be: firstly, n layers of wavelet packet decomposition are carried out on a radiation source signal to obtain 2nSub-bands, calculating the information entropy of each sub-band to obtain 2nA dimensional feature vector.
In step 2), the chaotic characteristic analysis of the radiation source signal includes four parts: forming 4-dimensional chaotic characteristic vectors by correlation dimension analysis, Kolmogorov entropy analysis, Lyapunov index analysis and Hurst index analysis; firstly, phase space reconstruction is carried out on a received one-dimensional radiation source signal time sequence, correlation dimension, Kolmogorov entropy and Lyapunov index are calculated on the basis of reconstruction phase space analysis, and the Hurst index is obtained by adopting a re-standard pole difference method on the radiation source signal time sequence.
The invention overcomes the defect that the non-linear nature of the radiation source signal is not considered in the current common time-frequency analysis method, not only exerts the strong time-frequency resolution characteristic of wavelet packet transformation and extracts the multi-scale local characteristics of the signal, but also considers the overall non-linear condition of the signal through the non-linear analysis method of chaos analysis, thereby more accurately reflecting the characteristics of the radiation source signal and leading the extracted characteristic parameters to have stronger distinguishability.
Drawings
FIG. 1 is a block diagram of a radiation source fingerprint feature extraction method based on wavelet entropy and chaotic characteristics provided by the invention.
FIG. 2 is a flow chart of the operation of wavelet entropy feature extraction provided by the present invention.
Fig. 3 is a characteristic curve diagram of a radiation source signal after correlation dimension analysis according to an embodiment of the invention.
FIG. 4 is a characteristic graph of a radiation source signal after Kolmogorov entropy analysis according to an embodiment of the invention.
FIG. 5 is a characteristic curve diagram of a radiation source signal after Lyapunov exponential analysis according to an embodiment of the present invention.
FIG. 6 is a characteristic graph of a radiation source signal after Hurst index analysis according to an embodiment of the invention.
Detailed Description
In order to make the objects, aspects and advantages of the present invention more apparent, the following embodiments will be further described with reference to the accompanying drawings.
Fig. 1 is a block diagram illustrating an implementation of a radiation source fingerprint feature extraction method based on wavelet entropy and chaotic characteristics according to an embodiment of the present invention. Wavelet entropy characteristics and chaotic characteristic parameters are respectively extracted from the radiation source signals. The wavelet entropy characteristics are extracted by the following steps: carrying out n layers of wavelet packet decomposition on the radiation source signal to obtain 2nSub-bands, calculating the information entropy of each sub-band to obtain 2nA dimensional feature vector. The chaotic characteristic analysis comprises correlation dimension analysis, Lyapunov index analysis, Kolmogorov entropy analysis and Hurst index analysis, and 4-dimensional chaotic characteristic vectors are extracted. Finally, combining the wavelet entropy characteristic parameters and the chaos characteristic parameters to form 2nAnd inputting the + 4-dimensional feature vector into a classifier for individual identification.
Fig. 2 is a flowchart of wavelet entropy feature extraction operation. Firstly, N layers of wavelet packet decomposition are carried out on a radiation source signal sequence X (k) (k is 1, 2.., N), and 2 is obtainednSubband reconstructed signal xi(t)(i＝0,1,2,...,2n1, t 1, 2.. times.m), calculating the energy E of each discrete point of the reconstruction signali(t)＝|xi(t)|2Further, the total energy of each sub-band reconstruction signal is calculated
Each sonThe frequency band information entropy is calculated by the following formula:
pi(t) is the proportion of the energy of each discrete point of the sub-band signal to the total energy, SiI.e. the information entropy of the ith subband. The entropy of information of each sub-band is obtained by the above method, i.e. constitution 2nAnd (5) dimension wavelet entropy characteristic vector.
Before chaotic characteristic analysis is carried out on a radiation source signal, firstly, phase space reconstruction is carried out on the signal, and the reconstructed high-dimensional space signal contains rich nonlinear information. Reconstructing the original radiation source signal sequence X (k) (k is 1,2,.. multidot.N) into a high-dimensional space sequence X by selecting a proper delay time tau and an embedding dimension mi＝[x(i),x(i+1),...,x(i+(m-1)×τ)],i＝1,2,...,N-(m-1)×τ。
The method is realized by performing correlation dimension analysis and Kolmogorov entropy analysis on a radiation source signal, calculating correlation integral and drawing a correlation integral curve, and comprises the following steps of:
(1) after reconstructing the m-dimensional phase space of the signal, setting a critical distance r, and calculating any two points (X) in the phase spacei,Xj) Distance | | X betweeni,XjIf less than r, the phase point pair is retained. Repeating the step, counting the number of phase pairs with the distance less than r, and calculating the ratio of the number to the total number of the phase pairs to further obtain a correlation integral function:
where m is the embedding dimension; m ═ N- (M-1) τ, representing the total number of phase points; theta is a Heaviside function and is expressed as
(2) The correlation dimension function d (m) is obtained by the following formula:
and taking different embedding dimensions m to perform phase space reconstruction on the signal, taking different critical distances r under each embedding dimension, calculating corresponding associated integrals C (r, m), and drawing an ln [ C (r, m) ] -lnr curve. As shown in fig. 3, the curve in the figure sequentially represents the associated integral curve of which the embedding dimension m increases from 1 to 10 from top to bottom, and the slope of the curve gradually becomes stable as m increases, and the corresponding slope is equal to the associated dimension D.
(3) The Kolmogorov entropy, denoted as K, was calculated using the following formula:
first, the embedding dimension m is set to 1, and the initial critical distance r is setijCalculating the correlation integral C (r) according to the step (1)ijM) continuously decreasing the critical distance rijUntil C (r)ijM) does not follow rijWhen the change is made by reduction, the C (r) at that time is determinedijM) is denoted as C (r, m). And increasing the value of m, repeating the steps to calculate C (r, m +1), and calculating the value of K according to the formula (5), wherein the value of K is the value of Kolmogorov entropy when the value of K does not change along with the increase of m, as shown in FIG. 4.
The calculation of the maximum Lyapunov index is realized by a small data volume method, and the steps are as follows:
(1) performing FFT (fast Fourier transform) on a one-dimensional radiation source signal sequence X (k) (k is 1, 2.. N), and calculating an average period P;
(2) carrying out m-dimensional reconstruction on each point X in phase space of an original signal sequenceiFind its nearest neighbors
Distance of nearest neighbor point pair
Is marked as di(0) It satisfies the following conditions:
di(0)＝min(||Xi-Xv||),(i,v＝1,2,...,M；|i-v|＞P) (6)
(3) for each nearest neighbor point pair XiAnd
calculate its distance after j discrete time steps:
(4) for each discrete time step j, calculating the j step distance d of all nearest neighbor point pairsi(j) Taking the average value y (j) after logarithm:
wherein q is non-zero di(j) Is the sampling interval of the original radiation source signal sequence.
(5) And (4) selecting different embedding dimensions m, repeating the steps (2) to (4), and drawing y (j) -j curves under the conditions of different embedding dimensions. FIG. 5 shows a cluster of y (j) -j curves with embedding dimensions from 1 to 5, each curve having an approximately parallel portion for which a regression line is constructed by least squares, the slope of the line being the maximum Lyapunov index and being denoted as λ1。
The calculation of the Hurst index adopts a re-standard pole difference method, and comprises the following steps:
(1) a one-dimensional radiation source signal sequence x (k) (1, 2., N) is equally divided into s adjacent subintervals y of length li( i 1, 2.., s), N ═ l · s; the u term of the ith subinterval is denoted as yi,u(u＝1,2,...,l)。
(2) Calculating each subinterval yiMean value ofiCumulative dispersion ZiExtremely poor RiSum variance Si：
Ri＝max{Zi}-min{Zi} (11)
(3) Calculating R of all subintervalsi/SiIs recorded as (R/S)lThe method comprises the following steps:
(4) taking different subinterval lengths l to obtain different (R/S)lDrawing lnl-ln (R/S)lAnd fitting the slope of the curve by using a least square method to obtain a value H of the Hurst index, wherein the value H is shown in figure 6.
The above description is a detailed description of the present invention, and it should not be construed that the present invention is limited to the specific embodiments.
Claims (4)
1. The radiation source fingerprint feature extraction method based on the wavelet entropy and the chaotic characteristic is characterized by comprising the following steps of:
1) wavelet entropy feature extraction is carried out on the radiation source signals to obtain feature parameters, and the specific method comprises the following steps: firstly, n layers of wavelet packet decomposition are carried out on a radiation source signal to obtain 2nSub-bands, calculating the information entropy of each sub-band to obtain 2nA dimensional feature vector;
2) performing chaotic characteristic analysis on a radiation source signal, extracting chaotic characteristic parameters, combining a wavelet entropy characteristic vector with a chaotic characteristic vector to obtain a combined characteristic vector, and inputting the combined characteristic vector into a characteristic classifier to realize identification of individual radiation sources; the chaotic characteristic analysis of the radiation source signal comprises four parts: forming 4-dimensional chaotic characteristic vectors by correlation dimension analysis, Kolmogorov entropy analysis, Lyapunov index analysis and Hurst index analysis; firstly, carrying out phase space reconstruction on a received one-dimensional radiation source signal time sequence, calculating a correlation dimension, a Kolmogorov entropy and a Lyapunov index on the basis of analysis on reconstruction phase space, and solving the Hurst index by adopting a re-standard pole difference method on the radiation source signal time sequence;
performing chaotic characteristic analysis on a radiation source signal, firstly performing phase space reconstruction on the signal, wherein the reconstructed high-dimensional space signal contains abundant nonlinear information; the original radiation source signal sequence x (k) (k 1, 2.. and N) is reconstructed into a high-dimensional space sequence by selecting an appropriate delay time τ and an embedding dimension m:
Xi＝[x(i),x(i+1),...,x(i+(m-1)×τ)],i＝1,2,...,N-(m-1)×τ；
the method for performing correlation dimension analysis and Kolmogorov entropy analysis on the radiation source signal and drawing a correlation integral curve by calculating the correlation integral comprises the following steps of:
(1) after reconstructing the m-dimensional phase space of the signal, setting a critical distance r, and calculating any two points (X) in the phase spacei,Xj) Distance | | X betweeni,XjIf the distance is less than r, the phase point pair is reserved, the step is repeated, the number of the phase point pairs with the distance less than r is counted, the ratio of the phase point pairs to the total number of the phase point pairs is calculated, and then a correlation integral function is obtained:
where m is the embedding dimension; m ═ N- (M-1) τ, representing the total number of phase points; theta is a Heaviside function and is expressed as
(2) The correlation dimension function d (m) is obtained by the following formula:
taking different embedding dimensions m to carry out phase space reconstruction on signals, taking different critical distances r under each embedding dimension, calculating corresponding associated integrals C (r, m), drawing an ln [ C (r, m) ] -lnr curve, wherein the curve sequentially represents the associated integral curves of the embedding dimensions m from 1 to 10 from top to bottom, and the slope of the curve gradually tends to be stable along with the increase of m, and at the moment, the corresponding slope is equal to the associated dimension D;
(3) the Kolmogorov entropy, denoted as K, was calculated using the following formula:
first, the embedding dimension m is set to 1, and the initial critical distance r is setijCalculating the correlation integral C (r) according to the step (1)ijM) continuously decreasing the critical distance rijUntil C (r)ijM) does not follow rijWhen the change is made by reduction, the C (r) at that time is determinedijM) the value is denoted as C (r, m); and increasing the value of m, repeating the steps, calculating to obtain C (r, m +1), and calculating the value of K according to the value of K, wherein the value of K is the value of Kolmogorov entropy when the value of K does not change along with the increase of m.
2. The method for extracting fingerprint features of a radiation source based on wavelet entropy and chaotic characteristics as claimed in claim 1, wherein the operation flow of the wavelet entropy feature extraction is as follows: firstly, N layers of wavelet packet decomposition are carried out on a radiation source signal sequence X (k) (k is 1, 2.., N), and 2 is obtainednSubband reconstructed signal xi(t)(i＝0,1,2,...,2n1, t 1, 2.. times.m), calculating the energy E of each discrete point of the reconstruction signali(t)＝|xi(t)|2Further, the total energy of each sub-band reconstruction signal is calculated
The information entropy of each sub-band is calculated by the following formula:
pi(t) is the proportion of the energy of each discrete point of the sub-band signal to the total energy, SiThe information entropy of the ith sub-band is obtained; the entropy of information of each sub-band is obtained by the above method, i.e. constitution 2nAnd (5) dimension wavelet entropy characteristic vector.
3. The method for extracting the fingerprint features of the radiation source based on the wavelet entropy and the chaotic characteristics as claimed in claim 1, wherein the maximum Lyapunov index is calculated by a small data volume method, and the steps are as follows:
(1) performing FFT (fast Fourier transform) on a one-dimensional radiation source signal sequence X (k) (k is 1, 2.. N), and calculating an average period P;
(2) carrying out m-dimensional reconstruction on each point X in phase space of an original signal sequenceiFind its nearest neighbors
Distance of nearest neighbor point pair
Is marked as di(0) It satisfies the following conditions:
di(0)＝min(||Xi-Xv||),(i,v＝1,2,...,M；|i-v|＞P)
(3) for each nearest neighbor point pair XiAnd
calculate its distance after j discrete time steps:
(4) for each discrete time step j, calculating the j step distance d of all nearest neighbor point pairsi(j) Taking the average value y (j) after logarithm:
wherein q is non-zero di(j) Δ t is the sampling interval of the original radiation source signal sequence;
(5) selecting different embedding dimensions m, repeating the steps (2) to (4), drawing y (j) -j curves under the conditions of different embedding dimensions, embedding a cluster of y (j) -j curves when the embedding dimensions are from 1 to 5, wherein each curve has a section of approximately parallel part, and making a regression line for the part of curve by using a least square method, wherein the slope of the line is the maximum Lyapunov index and is marked as lambda1。
4. The method for extracting the fingerprint features of the radiation source based on the wavelet entropy and the chaotic characteristics as claimed in claim 1, wherein the calculation of the Hurst index adopts a re-scaling polar difference method, and the steps are as follows:
(1) a one-dimensional radiation source signal sequence x (k) (1, 2., N) is equally divided into s adjacent subintervals y of length li(i 1, 2.., s), N ═ l · s; the u term of the ith subinterval is denoted as yi,u(u＝1,2,...,l)；
(2) Calculating each subinterval yiMean value ofiCumulative dispersion ZiExtremely poor RiSum variance Si：
Ri＝max{Zi}-min{Zi}
(3) Calculating R of all subintervalsi/SiIs recorded as (R/S)lThe method comprises the following steps:
(4) taking different subinterval lengths l to obtain different (R/S)lDrawing lnl-ln (R/S)lAnd fitting the slope of the curve by using a least square method to obtain a value H of the Hurst index.
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| CN111695444B (en) * | 2020-05-21 | 2023-06-23 | 哈尔滨工业大学 | Wave atom transformation-based radiation source individual feature extraction method |
| CN112711026B (en) * | 2020-12-19 | 2022-09-13 | 西北工业大学 | Target detection and signal frequency estimation method based on variable differential step length relative change entropy |
| CN113255545B (en) * | 2021-06-03 | 2021-09-21 | 中国人民解放军国防科技大学 | Communication radiation source individual identification method combining artificial features and depth features |
| CN116257780A (en) * | 2023-02-22 | 2023-06-13 | 中国人民解放军国防科技大学 | Unsupervised feature extraction and self-adaptive DBSCAN clustering method based on blind signal separation |
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