CN115169406B - Instantaneous phase fingerprint feature enhancement method based on empirical mode decomposition - Google Patents
Instantaneous phase fingerprint feature enhancement method based on empirical mode decomposition Download PDFInfo
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Abstract
The invention belongs to the technical field of radiation source fingerprint identification, and provides an instantaneous phase fingerprint feature enhancement method based on empirical mode decomposition. Public standard phase fingerprint characteristics are obtained through calculation, correlation operation is carried out on the instantaneous phase fingerprint characteristics of each signal, the difference parts between the instantaneous phase fingerprint characteristics and the instantaneous phase fingerprint characteristics are amplified, and then non-fingerprint characteristic components are removed, so that the slight difference of carried individual information is enhanced. The invention has the following technical effects: the amplification of the instantaneous phase characteristic difference between the individual radiation sources is realized, and non-fingerprint characteristic components are eliminated, so that the accuracy and the efficiency of radiation source fingerprint identification are improved; obtaining more stable instantaneous phase characteristics with main trend removed through sliding window average and curve fitting in instantaneous phase characteristic calculation; the elimination of the field values in the fingerprint characteristics is realized, and the common standard phase of the radiation source fingerprint characteristic commonality is conveniently and accurately extracted.
Description
Technical Field
The invention belongs to the technical field of radiation source fingerprint identification, and particularly relates to an instantaneous phase fingerprint characteristic enhancement method based on empirical mode decomposition, which specifically comprises the steps of calculating an actually received electromagnetic signal to obtain instantaneous phase fingerprint characteristics, iteratively eliminating outliers according to Pearson correlation coefficients to obtain a common standard phase of multiple radiation sources, and realizing enhancement of fingerprint difference through correlation calculation, so that the performance of a radiation source individual identification system is improved.
Background
When a radiation source device emits electromagnetic signals, it unintentionally modulates information from its device hardware onto all the radiated signals. This information, like a person's fingerprint, i.e. radiation source fingerprint information, can be used to identify the radiation source. The related art is called radiation source fingerprinting technology, also called Specific Emitter Identification (SEI), and specifically refers to extracting features that can characterize hardware differences of a radiation source transmitter from a received electromagnetic signal, so as to identify a Specific radiation source device.
It should be noted that the difference in the signal caused by the transmitter hardware is independent of the modulation pattern and modulation parameter of the transmission signal, independent of the transmission information, and is not forged or avoided, and is relatively stable for a certain time. This fingerprint difference is also called unintentional modulation information. Compared with the intentional modulation of the signal, the unintentional modulation energy is lower, so that the practical application difficulty of the radiation source fingerprint identification technology is higher.
The core problem of SEI is to acquire unintentional modulation information embedded in the signal. To date, existing research has defined a variety of radiation source fingerprint features to characterize unintentional modulation information, where feature extraction based on the instantaneous phase of an electromagnetic signal is an important method to achieve high-precision characterization of radiation source fingerprint information: the first document (Ru, X. -H., et al., correlation analysis of elementary phases and matters transformed defects for radio estimation. IET Radar, sonar & Navigation,2016.10 (5): p.945-952.), document two (Ye, H., Z.Liu, and W.Jiang, composition of elementary frequencies and phase modulation defects for specific estimation. Electronics Letters,2012.48 (14)) derived and demonstrated that the transient phase based characterization method is more effective than the frequency based characterization method; the third document (Liu, z.m., multi-feature fusion for specific electronic identification device deep learning-scientific direct. Digital Signal Processing, 2020.) proposes a radiation source identification method based on deep learning of instantaneous phase features, which achieves good identification results and also proves the effectiveness of the instantaneous phase features. However, the instantaneous phase calculation process of the method is too simple, and the recognition performance is more dependent on the design and training of the neural network.
The fingerprint information of the radiation source carried on the instantaneous phase mainly comes from the change of the injection voltage or injection current of the amplifier caused by the envelope distortion of the modulation pulse, and the parasitic modulation of the phase caused by factors such as the non-ideality and the non-linearity of the amplifier. Furthermore, variations in the energy of the excitation signal also affect the amplitude transfer characteristics of the amplifier and thus the phase characteristics.
Although the instantaneous phase characteristics of the individual signals of different radiation sources have differences, the differences are lower than the intentional modulation energy of the signals, the intentional modulation and the unintentional modulation are mixed together to carry out radiation source fingerprint identification, the automatic classification identification is not facilitated, the requirement on the over-parameter setting of classifiers comprising thresholds, tolerances and the like is high, and the practical application difficulty is high. Therefore, it is desirable to amplify this difference as much as possible, and to eliminate the effect of the unintended modulation components as much as possible.
In terms of process flow, the existing SEI mainly comprises two processes, data training and target recognition. And in the stage of target recognition, the new data is subjected to feature extraction and is compared with the known features to determine the corresponding radiation source target. In fact, not only the individual difference of the unintentional modulation exists between the signals of different radiation sources, especially between the signals with the same intentional modulation, but the characteristics of the signals affected by the same intentional modulation have more similar main trends, so that the main trend caused by the correlation of the intentional modulation can be eliminated in a targeted manner in the training stage by fully utilizing the known data, and the unintentional modulation can be enhanced.
Empirical Mode Decomposition (EMD) [ four: huang N E, shen Z, long S R, et al, the empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis [ J ]. Proceedings of the Royal Society of London series A: physical, physical and engineering sciences,1998,454 (1971): 903-995 ] is a novel adaptive signal processing method proposed by Huang E (N.E. Huang) in the United states space agency of 1998 for signal decomposition according to the time scale characteristics of the data itself. The method does not need to preset a basis function, and is suitable for analyzing nonlinear and non-stationary signal sequences. Thus, EMD can be used to decompose different components of a radiation source fingerprint to obtain its main trending components.
Disclosure of Invention
The invention provides an instantaneous phase fingerprint characteristic enhancement method based on empirical mode decomposition, aiming at the problems that the instantaneous phase characteristic difference between different radiation source individuals in the radiation source fingerprint identification technology is small and identification is difficult. Public standard phase fingerprint characteristics (namely main trends) are obtained through calculation, the instantaneous phase fingerprint characteristics of each signal are subjected to correlation operation, the difference parts between the instantaneous phase fingerprint characteristics of each signal are amplified, and then non-fingerprint characteristic components are removed, so that the slight difference carrying individual information is enhanced.
The invention adopts the technical scheme that an instantaneous phase fingerprint feature enhancement method based on empirical mode decomposition comprises the following steps:
s1 data preprocessing and instantaneous phase fingerprint feature extraction
S1.1, data preprocessing
After receiving a radiation source signal, a receiver carries out pretreatment on the radiation source signal, including pulse detection, frequency domain filtering, signal noise reduction and the like, and obtains a signal sample x (t) to be treated;
s1.2, instantaneous phase characteristic calculation
S1.2.1 calculating instantaneous frequency of signal sample x (t) to be processed based on Kay method
The detailed calculation process is referenced to Kay S.A fast and acid single frequency estimator [ J].IEEE Transactions on Acoustics,Speech,and Signal Processing,1989,37(12):1987-1990；
S1.2.2 at instantaneous frequency based on maximum likelihood estimation method
On the basis of which the instantaneous phase x (t) of the signal sample x (t) to be processed is found>
For a detailed calculation process, see library SUN, xiang W, huang Z. Unintentational modulation evaluation in time domain and frequency domain [ J ]].Chinese Journal of Aeronautics,2022,35(4):376-389；
Here, instantaneous phase
Is the intentional modulation information of the signal. The following is the elimination of intentional modulation information.
S1.3, eliminating intentionally modulated information
S1.3.1 pairs of instantaneous phases
Performing a moving average operation to reduce the effect of random noise and obtaining the instantaneous phase which removes the effect of noise>
Wherein, N w Denotes the width of the sliding window, the index value K = 1.., K denotes the instantaneous phase dimension, and i denotes the index value of the element within the sliding window. Assuming an instantaneous phase
Is T, in performing a sliding window averaging operation>
Finally, data with less than one window width is ignored, namely, K = T-N is satisfied w Therefore, the characteristic dimension of the instantaneous phase changes, denoted by k.
S1.3.2 based on polynomial curve fitting pair
Fitting of order N, NRepresenting the polynomial order, the resulting fit being used as an approximation of intentional modulation, and then ÷ combining ÷ into a corresponding reference>
And subtracting the fitting result, and keeping a residual error as an instantaneous phase characteristic f (k) to eliminate the intentional modulation. The detailed calculation process is referenced to the library SUN, xiang W, huang Z. Unintentational modulation evaluation in time domain and frequency domain [ J ]].Chinese Journal of Aeronautics,2022,35(4):376-389。
The polynomial fitting is generally a low-order polynomial, with the order N generally being 2 or 3, to obtain
I.e. intentional modulation, without affecting its unintentional modulation details.
S2 data training
Assuming a total of M individual radiation sources, the M (M =1,. Multidot.m) individual radiation sources have N m A radiation source signal. Through S1, the corresponding instantaneous phase characteristic result f (k) of the radiation source signal can be obtained. For clarity of reference, denote by f i m (k),i＝1,...,N m M = 1.., M denotes the instantaneous phase characteristic of the i-th radiation source signal of the M-th radiation source obtained by step S1. In the data training stage, it is necessary to obtain the common component of the radiation source characteristics based on all the characteristic results.
S2.1, iteratively eliminating characteristic outliers based on the Person correlation coefficient
For any variable X, Y, person correlation coefficient is defined as
Wherein, the first and the second end of the pipe are connected with each other,
representing an averaging calculation.
In the process of rejecting the characteristic outlier, each radiation source needs to be processed independently and identically, and here, the mth radiation source is taken as an example for explanation. The method mainly comprises the following steps:
s2.1.1 calculates the center quantity of the mth radiation source
Also known as feature mean:
s2.1.2 calculating the instantaneous phase characteristic f of the i-th radiation source signal of the m-th radiation source according to equation (2) i m (k) Central to the m radiation source
In conjunction with->
Signal samples greater than a threshold η are retained, samples less than the threshold are deleted:
correlation coefficient
Capable of characterizing the instantaneous phase characteristic f of each radiation source signal i m (k) And central quantity
To a similar degree. />
Values between 0 and 1, with closer to 1 indicating more similarity. An appropriate threshold η may be set according to the requirement for the degree of similarity, and may be generally set to be between 0.85 and 0.95.
S2.1.3, after S2.1.2, the instantaneous phase characteristic less than threshold ηThe central value of the residual instantaneous phase characteristics can be changed after being removed, and the central value needs to be updated according to a formula (3)
S2.1.4, repeat S2.1.1-S2.1.3 until termination conditions are met.
The termination condition is typically set to the number of iterations reaching k or to the specified number of outliers having been eliminated. The number of iterations κ is usually set according to the dispersion of features, which requires more iterations as the features are more dispersed. In general, κ may be set to an integer within 20.
After iteration is stopped, the residual features after the outliers are deleted are combined into a set { f i m (k)}。
S2.2, obtaining public standard phase by characteristic accumulation
Set { f) obtained according to step S2.1 i m (k) And the central volume of the radiation source
Calculating common standard phase
Wherein alpha is m Is the weight value of the mth radiation source, satisfies
Weight value alpha of mth radiation source m Should be determined in combination with the number of samples and the characteristic distribution of the respective radiation sources. If the feature distribution is relatively concentrated, anAnd the characteristic distribution characteristics of different individuals are approximately the same, and if the number of samples of each radiation source is relatively balanced, the method leads the sample to be distributed to the target object
S2.3, calculating the autocorrelation characteristic of the common standard phase
Calculating common standard phase
The autocorrelation characteristics of (a):
wherein the content of the first and second substances,
representing a cross-correlation operation between two variables, representing an auto-correlation operation when the two variables are identical, and being->
Represents; n denotes an index value of the correlation operation. Result Y obtained after correlation 0 The dimension of (n) changes, being the sum of the dimensions of its inputs minus 1, i.e. n =1 0 The characteristic dimension of (n) is 2K-1.
S2.4, performing empirical mode decomposition on the autocorrelation characteristics
For the autocorrelation characteristics Y 0 (n) performing empirical mode decomposition. The specific calculation process is described in Huang N E, shen Z, long S R, et al, the empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis [ J].Proceedings of the Royal Society of London.Series A:mathematical,physical and engineering sciences,1998,454(1971):903-995。
After empirical Mode decomposition, L Intrinsic Mode Function (IMF) components and a residual component are obtained and expressed as
Where r (n) represents the residual component of the empirical mode decomposition, IMF l And (n) represents the I < th > intrinsic mode function component obtained by empirical mode decomposition.
S2.5, calculating non-fingerprint characteristic components
S2.5.1 calculates energy values of all eigenmode function components obtained after empirical mode decomposition, and sorts the eigenmode function components according to the sequence of the energy values and the frequency values from high to low.
S2.5.2 selects eigenmode function components with the highest energy and the lowest frequency from the L eigenmode function components obtained by decomposition, and forms a set L by indexes L corresponding to the components.
S2.5.3 derives a non-fingerprint feature component h (n) based on the set l and the residual component r (n):
h(n)＝Σ l∈l IMF l (n)+r(n) (8)
through the steps S2.1-S2.5, the public standard phase is obtained
And a non-fingerprint feature component h (n). The two quantities are obtained based on the instantaneous phase characteristics of all radiation sources, can represent the commonality of different radiation sources, and can be used commonly for all radiation sources. Therefore, step S2 only needs to be performed once and once ^ is determined>
And h (n), the existing ^ can be utilized directly in the subsequent processing>
And h (n).
S3 target recognition
In the target identification stage, the extraction and enhancement of instantaneous phase characteristics are mainly carried out aiming at new data which are received by a receiver and have no radiation source label information, so that the completion of the target is supportedAnd (5) identifying. Wherein, the calculation of the instantaneous feature is completed according to the step S1, and the enhancement of the feature needs to utilize the common standard phase
And a non-fingerprint feature component h (n). It is assumed here that a ^ is reached by step S2>
And h (n), it is no longer necessary to repeat step S2.
Therefore, before performing S3 object recognition, step S1 is repeated for each signal, and signal preprocessing and instantaneous phase feature extraction are performed as a preliminary stage of step S3. Then, the instantaneous phase characteristic of the obtained signal and the public standard phase are subjected to cross-correlation operation, and non-fingerprint characteristic components are eliminated, so that characteristic enhancement is realized.
S3.1, feature Cross-correlation computation
Calculating the ith instantaneous phase characteristic f of the mth radiation source according to the formula (9) i m (k) With common reference phase
Cross correlation of (Y) i m (n)：
Wherein the content of the first and second substances,
are different, here denotes a cross-correlation operation, and Y i m Dimension n =1, 1.
S3.2, enhanced feature calculation
Removing the cross-correlation Y according to equation (10) i m In the step (n), the non-fingerprint characteristic component h (n) obtained by the formula (8) is used for obtaining the instantaneous phase characteristic after the fingerprint difference of the radiation source is enhanced
The invention provides a method for decomposing instantaneous phase characteristic enhancement based on empirical mode, aiming at the problems that the difference of extracted fingerprint characteristics among different radiation source individuals in a radiation source fingerprint identification technology is small, and compared with the problems that the intentional modulation energy is lower and the identification is difficult. Calculating to obtain instantaneous phase characteristics, eliminating characteristic field values through Person correlation, obtaining a public standard phase (namely a main trend), carrying out correlation operation on the instantaneous phase characteristics of each signal and the instantaneous phase characteristics, amplifying the difference part between the instantaneous phase characteristics and the main trend, and then removing non-fingerprint characteristic components obtained through empirical mode decomposition, so that the slight difference carrying individual information is enhanced, and a foundation is laid for accurate identification of subsequent radiation source individuals.
The invention has the following technical effects:
1. the amplification of the instantaneous phase characteristic difference between the individual radiation sources is realized, and the non-fingerprint characteristic components are eliminated, so that the accuracy and the efficiency of the radiation source fingerprint identification are improved;
2. obtaining more stable instantaneous phase characteristics with main trend removed through sliding window average and curve fitting in instantaneous phase characteristic calculation;
3. the elimination of the field values in the fingerprint characteristics is realized, and the common standard phase of the radiation source fingerprint characteristic commonality is conveniently and accurately extracted.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a schematic diagram of an iterative feature outlier rejection algorithm based on the Person correlation coefficient;
fig. 3 is a common standard phase image;
FIG. 4 is a standard phase autocorrelation image;
FIG. 5 is a result of an adaptive decomposition of a common standard phase autocorrelation;
FIG. 6 is a preliminary instantaneous phase signature image;
FIG. 7 is an instantaneous phase signature image after removal of intentional modulations and culling outliers;
FIG. 8 is a resulting image of cross-correlation of instantaneous phase features with standard phase;
fig. 9 is an enhanced instantaneous phase signature image.
Detailed Description
The following further describes embodiments of the present invention with reference to the accompanying drawings.
Fig. 1 is a flow chart of the implementation of the present invention, and the present invention provides a method for decomposing instantaneous phase characteristic enhancement based on empirical mode, which is divided into the following three major steps:
s1, data preprocessing and instantaneous phase characteristic extraction;
s2, training data;
and S3, identifying the target.
The method comprises the following specific steps:
firstly, processing received data by S1.1-S1.3 to obtain a primary instantaneous phase characteristic;
then, whether the public standard phase is needed to exist is judged, if so, S2.1-S2.5 are carried out to obtain the public standard phase
And a non-fingerprint feature component h (n). Since the calculation of S2.1-S2.5 is based on a plurality of sample data of a plurality of radiation sources by cumulative weighting, therefore->
And h (n) are considered to be a common component common to all radiation sources. If the common standard phase has been calculated, as shown in fig. 1, step S3 can be performed directly without having to perform steps S2.1-S2.5 again. Therefore, in the practical application process, the steps S2.1-S2.5 are only required to be performed once, and the steps S2.1-S2.5 are not required to be repeated after the corresponding public standard phase and the corresponding non-fingerprint characteristic component are obtained, so that the calculation efficiency is improved.
Finally, for the new signal received subsequently, it is only necessary to extract the instantaneous phase characteristics through steps S1.1-S1.3, and perform steps S3.1 and S3.2 to obtain the enhanced instantaneous phase characteristics.
Fig. 2 is an iterative feature outlier rejection algorithm based on the Person correlation coefficient. This part of the operation is performed independently for each radiation source. Taking the mth radiation source as an example, first, the central value, i.e., the characteristic mean value, is calculated according to the formula (3)
Then all samples and->
Deleting samples smaller than a threshold η; then, the center amount is updated, and whether or not a termination condition is satisfied is determined. And if so, stopping. If not, the above process is repeated based on the data from which the sample was deleted.
The threshold may be set to 0.85-0.95 in general, and the termination condition may be set to delete a specified number of samples or reach a specified number of iterations.
FIG. 3 shows the common reference phase obtained after steps S2.1 and S2.2
The image of (2). The horizontal axis represents the characteristic dimension k, and the vertical axis represents the corresponding characteristic value. The radiation source takes a secondary response radar signal of a civil aircraft as an example, the sampling rate is 250MHz, and the number of signal samples is 120. Here based on a common portion of three radiation sources each for 100 samples. In the outlier rejection link, setting a termination condition to reject 10 outliers for each radiation source. The characteristic dimension of the common standard phase is K =100. Weight coefficient->
FIG. 4 is a common standard phase autocorrelation Y 0 (n) an image. The horizontal axis represents the feature dimension, and the vertical axis represents the corresponding feature value. Y is 0 (n) ofThe dimension is 199.
FIG. 5 is a common standard phase autocorrelation Y 0 (n) adaptively decomposing the image using empirical mode decomposition. The number of layers for empirical mode decomposition is L =4, resulting in 4 IMFs. It can be seen that the IMF1, IMF2 have stronger energy, the frequency of IMF1 is the lowest, and the frequency of IMF4 is the highest.
FIG. 6 shows the instantaneous phase obtained after step S1.2
Wherein different colors represent different radiation source individuals, and the specific label information is marked in the figure. As can be seen from the figure, the characteristic distributions of different radiation sources are relatively concentrated, and three obvious clusters are formed and respectively represent different radiation source individuals. In the graph, a part of stray curves are distributed outside the cluster in a disorderly way, the aggregation ratio is poor, the stray curves are regarded as outliers, and the outliers need to be eliminated. In addition, although three different individual radiation sources can be distinguished, the main shapes of the three groups of curves are the same, most of the curves are overlapped, and the difference between clusters is not very obvious. This substantially similar body shape is considered to be intentionally modulated and is intended to be eliminated by the present invention; whereas cluster-to-cluster differences can be used for individual identification of the radiation source, it is the unintentional modulation that the present invention aims to amplify.
Fig. 7 is an instantaneous phase characteristic image of three radiation sources after removing the intentional modulation through step S1.3 and rejecting outliers through step S2.1 on the basis of fig. 6. Here the fitting order is set to 2, the threshold of the correlation coefficient is η =0.92, and the number of reject outliers is 10 per radiation source. Compared with fig. 6, the stray-out curves of the three clusters are significantly reduced, and the distribution is more concentrated. After the intentional modulation and elimination, the curve shape changes to a certain extent, and the fluctuation becomes more obvious. The variability between different targets is increased, especially between dimensions 30-40. But the main body shapes of the three-cluster curves still have higher similarity.
Figure 8 is the resulting image of cross-correlation amplification (step S3.1) of the instantaneous phase characteristics of the three radiation sources with the standard phase. I.e. the result of cross-correlating the instantaneous phase characteristics of the three radiation sources of figure 7 with the common standard phase of figure 3. In practical application, the cross-correlation operation (step S3.1) belongs to a target identification stage, the radiation source label corresponding to the processed signal is unknown, and here, to prove the effectiveness of the present invention, the data result of the known labels of the three radiation sources is used for displaying, and the corresponding radiation source label is marked in the figure.
FIG. 9 is a graph showing the enhanced instantaneous phase characteristics of the three sources
The image of (2). Compared with the preliminary instantaneous phase characteristic in fig. 6, the difference between the three radiation sources after the treatment of the invention is obviously enhanced, the characteristic curves of different radiation sources are in different shapes, and the discrimination is greatly increased. />
Claims (10)
1. An instantaneous phase fingerprint feature enhancement method based on empirical mode decomposition is characterized by comprising the following steps:
s1 data preprocessing and instantaneous phase fingerprint feature extraction
S1.1, data preprocessing
After receiving a radiation source signal, a receiver carries out pretreatment on the radiation source signal, including pulse detection, frequency domain filtering and signal noise reduction, and obtains a signal sample x (t) to be treated;
s1.2, instantaneous phase characteristic calculation
S1.2.1 calculating the instantaneous frequency of the signal sample x (t) to be processed
S1.2.2 at instantaneous frequency
On the basis of which the instantaneous phase x (t) of the signal sample x (t) to be processed is found>
S1.3, eliminating intentionally modulated information
S1.3.1 pairs of instantaneous phases
Performing a moving average operation to reduce the effect of random noise and obtaining the instantaneous phase which removes the effect of noise>
Wherein, N w Denotes the width of the sliding window, the index value K = 1.., K denotes the instantaneous phase dimension, i denotes the index value of the element within the sliding window; default instantaneous phase
Is T, in performing a sliding window averaging operation, is based on>
Finally, the data with less than one window width is ignored, namely K = T-N is satisfied w Therefore, the characteristic dimension of the instantaneous phase changes, denoted by k;
s1.3.2 based on polynomial curve fitting pair
Fitting of order N, N representing the polynomial order, the result of the fitting being obtained as an approximation of the intentional modulation, and then->
Subtracting the fitting result, and reserving a residual error as an instantaneous phase characteristic f (k) to eliminate intentional modulation;
s2 data training
Assuming a total of M individual radiation sources, the mth individual radiation source has N m A radiation source signal, M =1, ·, M; through S1, an instantaneous phase characteristic result f (k) corresponding to the radiation source signal can be obtained; for clarity of reference, denote by f i m (k),i＝1,...,N m M = 1.., M denotes an instantaneous phase characteristic of the i-th radiation source signal of the M-th radiation source obtained by step S1; in the data training stage, the common components of the radiation source characteristics are obtained based on all characteristic results;
s2.1, iteratively eliminating characteristic outliers based on Person correlation coefficient
For any variable X, Y, person correlation coefficient is defined as
Wherein the content of the first and second substances,
representing the calculation of an average value;
in the process of rejecting the characteristic outlier, each radiation source needs to be independently and identically processed, and here, the mth radiation source is taken as an example for explanation, and the method mainly comprises the following steps:
s2.1.1 calculates the center quantity of the mth radiation source
Also known as feature mean:
s2.1.2, the instantaneous phase characteristic f of the i-th radiation source signal of the m-th radiation source is calculated according to equation (2) i m (k) Central to the m radiation source
Is greater than or equal to>
Retaining signal samples greater than a threshold η, and deleting samples less than the threshold: />
Correlation coefficient
Capable of characterizing the instantaneous phase characteristic f of each radiation source signal i m (k) And a central quantity->
To a similar extent, <' > based on>
Values between 0 and 1 are taken, and the closer to 1, the more similar the values are;
s2.1.3, after the step S2.1.2, the instantaneous phase feature smaller than the threshold η is removed, the center value of the remaining instantaneous phase feature changes, and the center value needs to be updated according to the formula (3)
S2.1.4, repeating S2.1.1-S2.1.3 until termination conditions are met;
after iteration is stopped, the residual features after the outliers are deleted are combined into a set { f i m (k)}；
S2.2, feature accumulation to obtain public standard phase
Set { f) obtained according to step S2.1 i m (k) And central volume of the radiation source
Calculating a common standard phase +>
Wherein alpha is m The weight value of the mth radiation source is satisfied
S2.3, calculating the autocorrelation characteristic of the common standard phase
Calculating common standard phase
The autocorrelation characteristics of (a):
wherein the content of the first and second substances,
representing a cross-correlation between two variables, an auto-correlation when the two variables are identical, by
Representing; n represents an index value of the correlation operation; result Y obtained after correlation 0 The dimension of (n) will change, being the sum of the dimensions of its inputs minus 1, i.e. n =11, i.e. autocorrelation characteristic Y 0 (n) has a characteristic dimension of 2K-1;
s2.4, performing empirical mode decomposition on the autocorrelation characteristics
For the autocorrelation characteristics Y 0 (n) performing empirical mode decomposition;
after empirical mode decomposition, L intrinsic mode function components and a residual component are obtained and expressed as
Where r (n) represents the residual component of the empirical mode decomposition, IMF l (n) the first intrinsic mode function component obtained by empirical mode decomposition is expressed;
s2.5, calculating non-fingerprint characteristic components
S2.5.1 calculates energy values of all intrinsic mode function components obtained after empirical mode decomposition, and sorts the intrinsic mode function components according to the sequence of the energy values and the frequency values from high to low;
s2.5.2 the eigenmode function components with the highest energy and the lowest frequency are selected from the L eigenmode function components obtained by decomposition, and the indexes L corresponding to these components are combined into a set
S2.5.3 is based on aggregation
And the residual component r (n) to obtain a non-fingerprint characteristic component h (n):
through the steps S2.1-S2.5, the public standard phase is obtained
And a non-fingerprint feature component h (n); these two quantities are obtained on the basis of the instantaneous phase characteristics of all the radiation sources, which represent the commonality of the different radiation sources and which can be common to all the radiation sources, so that step S2 only has to be carried out once and once the->
And h (n), the existing ones can be directly utilized in the subsequent processing
And h (n);
s3 object recognition
Before the target identification of S3, firstly, repeating the step S1 for each signal, and performing signal preprocessing and instantaneous phase characteristic extraction as a preparation stage of the step S3; then, performing cross-correlation operation on the instantaneous phase characteristics of the obtained signal and a public standard phase, and eliminating non-fingerprint characteristic components to realize characteristic enhancement;
s3.1, feature Cross-correlation computation
Calculating the ith instantaneous phase characteristic f of the mth radiation source according to the formula (9) i m (k) With common standard phase
Cross correlation Y of i m (n)：
Wherein the content of the first and second substances,
is different, here denotes a cross-correlation operation, and Y i m (n) has a dimension n =1,.., 2K-1;
s3.2, enhanced feature calculation
Removing the cross-correlation Y according to equation (10) i m In (n) is composed ofObtaining the non-fingerprint characteristic component h (n) obtained by the formula (8) to obtain the instantaneous phase characteristic after the fingerprint difference of the radiation source is enhanced
2. An instantaneous phase fingerprint feature enhancement method based on empirical mode decomposition according to claim 1, characterized in that: s1.2.1, calculating the instantaneous frequency of the signal sample x (t) to be processed
The method of (1) is the Kay method.
3. An instantaneous phase fingerprint feature enhancement method based on empirical mode decomposition according to claim 1, characterized in that: s1.2.2, at instantaneous frequency
On the basis of which the instantaneous phase x (t) of the signal sample x (t) to be processed is found>
The method of (4) is a maximum likelihood estimation method.
4. The method for enhancing instantaneous phase fingerprint features based on Empirical Mode Decomposition (EMD) according to claim 1, wherein: s1.3.2, the polynomial fitting generally uses a low-order polynomial, and the order N generally takes 2 or 3.
5. An instantaneous phase fingerprint feature enhancement method based on empirical mode decomposition according to claim 1, characterized in that: s2.1.2, the threshold η may be set between 0.85 and 0.95.
6. An instantaneous phase fingerprint feature enhancement method based on empirical mode decomposition according to claim 1, characterized in that: s2.1.4, the termination condition is typically set to the number of iterations to k or to the specified number of outliers that have been removed.
7. An instantaneous phase fingerprint feature enhancement method based on empirical mode decomposition according to claim 6, characterized in that: the number of iterations κ is usually set according to the dispersion of features, which requires more iterations as the features are more dispersed.
8. An instantaneous phase fingerprint feature enhancement method based on empirical mode decomposition according to claim 7, characterized in that: the number of iterations κ is set to an integer within 20.
9. An instantaneous phase fingerprint feature enhancement method based on empirical mode decomposition according to claim 1, characterized in that: weight value alpha of mth radiation source m Should be determined in combination with the number of samples and the characteristic distribution of the respective radiation sources.
10. An instantaneous phase fingerprint feature enhancement method based on empirical mode decomposition according to claim 9, characterized in that: if the feature distribution is relatively concentrated, the characteristics of the feature distributions of different individuals are approximately the same, and the numbers of samples of the respective radiation sources are relatively balanced, then
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| CN101271516A (en) * | 2008-04-02 | 2008-09-24 | 范九伦 | Direction filtering reinforcement method of fingerprint image |
| CN101996321A (en) * | 2009-08-24 | 2011-03-30 | 北京易创科技有限公司 | Fingerprint recognition pretreatment method and device |
| CN108375747A (en) * | 2018-03-22 | 2018-08-07 | 复旦大学 | A kind of Dynamic Contrast-enhanced Magnetic Resonance Imaging method based on magnetic resonance fingerprint |
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| CN101271516A (en) * | 2008-04-02 | 2008-09-24 | 范九伦 | Direction filtering reinforcement method of fingerprint image |
| CN101996321A (en) * | 2009-08-24 | 2011-03-30 | 北京易创科技有限公司 | Fingerprint recognition pretreatment method and device |
| CN108375747A (en) * | 2018-03-22 | 2018-08-07 | 复旦大学 | A kind of Dynamic Contrast-enhanced Magnetic Resonance Imaging method based on magnetic resonance fingerprint |
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