CN106529478A - Radar radiation source signal identification method according to three-dimensional entropy characteristic - Google Patents

Abstract

The invention discloses a radar radiation source signal identification method according to a three-dimensional entropy characteristic. The method of the invention is a novel identification method for settling defects in radiation source signal identification based on an in-pulse characteristic. According to the radar radiation source signal identification method, sample entropy, fuzzy entropy and normalized energy entropy are used as a three-dimensional characteristic vector of a signal. The sample entropy is used for describing complexity of a radiation source signal. The fuzzy entropy is used for measuring uncertainty of the signal. Furthermore the normalized energy entropy is utilized for describing distribution condition of the signal energy. According to the radar radiation source signal identification method, characteristic extraction is performed on six typical radar radiation source signals, and furthermore a support vector machine is used for performing classification testing. A testing result proves a fact that the extracted characteristic vector can well realize classification and identification on the radar radiation source signal in a relatively large signal-to-noise range, thereby preventing high effectiveness of the radar radiation source signal identification method.

Description

A kind of radar emitter signal recognition methodss of joint three-dimensional entropy feature

Technical field

The invention belongs to blipology field, specifically, is related to a kind of radar emission of the three-dimensional entropy feature of joint Source signal recognition methodss.

Background technology

Radar emitter signal identification is the weight in electronic intelligence reconnaissance system (ELINT) and electronic support system (ESM) Ingredient is wanted, the performance of electronic reconnaissance equipment performance is directly affected and is related to follow-up warfare decision.Tional identification side Method depends on conventional five parameters (RF, PA, PW, DOA and TOA), but this method is appropriate only for conventional thunder under certain condition It is up to the identification of signal, not good for the recognition effect of intensive radar signal under complex electromagnetic environment.Therefore, current research direction becomes To in by being analyzed to data in Radar Signal In-Pulse Characteristics, modulation signature and unintentionally modulation signature intentionally in research arteries and veins, extension are joined Number space, reduces the crossover probability of multi-parameter spatial, fast and accurately to recognize signal.In this sense, it is many new Intrapulse feature extractive technique is suggested in succession, for example Wavelet Transform, time-frequency distributions method, atom decomposition, high-order statistical analysis Method etc..But, all there is certain deficiency in these methods, the feature that the small wave converting method that some technologies are adopted is extracted only is fitted Minority signal is closed, application limitation is big, while the number of features extracted is more, causes time overhead larger；Use Choi- Williams distributions extract the characteristic vector processed of emitter Signals, and the characteristic vector taken out are entered with neural network classifier Row classification, can obtain preferable classifying quality.Although but the friendship beyond the distribution can suppress in fuzzy field horizontally and vertically Fork item, but still the cross term for horizontally and vertically going up is remained, signal modulate is still had an impact；Lost using quantum is improved Propagation algorithm carries out match tracing to realize the Rapid matching of optimal atom, and author's thought is mainly reflected in time-frequency atom and matches, But characteristic atomic number is more, although 30 Gabor atoms can fully represent the principal character information of original signal, directly When being identified using these atoms, its dimension is at a relatively high, and the amount of calculation for causing is also huge.

And compensate for the deficiency of said method based on the emitter Signals Recognition method of entropy feature to a certain extent, have Technology carries out Classification and Identification by approximate entropy and norm entropy constitutive characteristic vector and using neural network classifier, achieves preferably Recognition effect.

At present, also there is no a kind of radar emitter signal recognition methodss of the three-dimensional entropy feature of joint in prior art.

The content of the invention

It is an object of the invention to defect present in emitter Signals Recognition based on intrapulse feature, there is provided a kind of joint The radar emitter signal recognition methodss of three-dimensional entropy feature, by Sample Entropy, fuzzy entropy and normalized energy entropy are used as letter for the method Number three-dimensional feature vector, the complexity of emitter Signals is described with Sample Entropy, using fuzzy entropy come the uncertain of gauge signal Degree, while using the distribution situation of normalized energy entropy metric signal energy.Article enters to six kinds of typical radar emitter Signals Row feature extraction, and Classification and Identification test is carried out using support vector machine, as a result showing, the characteristic vector of extraction is in larger noise The Classification and Identification to radar emitter signal can be preferably realized than in the range of, it was demonstrated that the method is effective.

Its concrete technical scheme is：

A kind of radar emitter signal recognition methodss of joint three-dimensional entropy feature, comprise the following steps：

Step 1, Signal Pretreatment

Pulse data is transformed to frequency domain by 1.1, and intercepts the central point of symmetrical amplitude-frequency spectrum with right half, is designated as f (i), i= 1,2 ..., M, M for pulse data length 1/2；

1.2 according to formula (1) by signal f (i) energy normalized：

1.3 obtain the mid frequency of signal f ' (i) and effective bandwidth after energy normalized, and are normalized place to bandwidth Reason；

In the case that 1.4 sample frequencys are certain, pulse data its signal lengths of distinct pulse widths be it is different, in order to avoid Impact of this different length signal to extracting feature hereinafter, carries out resampling to the signal after all bandwidth normalizeds, And the signal after resampling is remembered for x (n), n=1,2 ..., N, N attach most importance to sampled signal length；

Step 2, feature extraction

2.1 Sample Entropy feature extractions

N points signal sequence after note resampling is x (n)=[x₁x₂…x_N], then SampEn algorithm for estimating is as described below：

2.1.1 m n dimensional vector ns are constructed to sequence x (n) according to formula (2)：

X (i)=[x_i x_i+1…x_i+m-1], i=1,2 ..., N-m+1 (2)

2.1.2 according to formula (3) calculate vector to the distance between：

2.1.3 calculate the number of similar vectors pair：

(1) make n_m=0, if d_m[x (i), x (j)]≤r, i ≠ j, then n_m=n_m+1；

(2) make n_m+1=0, if d_m+1[x (i), x (j)]≤r, i ≠ j, then n_m+1=n_m+1+1；

2.1.4 all similar vectors are calculated to Similar measure according to formula (4)：

2.1.5 similar vectors are calculated to average Similar measure according to formula (5)：

2.1.6 sample entropy estimate is calculated according to formula (6)：

Wherein, the present invention adopts scale parameter m=2 and tolerance parameterUsed as the parameter of estimation Sample Entropy, σ is The standard deviation of x (n)；

2.2 fuzzy entropy feature extractions

Entropy represents the average uncertainty of information source in theory of information, can be used to measure one and obscure in fuzzy subset's opinion The size of the contained ambiguity of set, therefore with fuzzy entropy representing the uncertainty of fuzzy set；The fuzzy entropy of fuzzy set A is fixed Justice is：

Wherein, f (t)=- tlnt- (1-t) ln (1-t), k>0 is normal number, μ_A(x_i) represent fuzzy set A membership function；

Prove, f (t) is a symmetric function with regard to t=0.5, in interval [0,0.5] interior strictly monotone increasing, in area Between [0.5,1] interior strictly monotone decreasing, as t=0.5 obtain maximum ln2；By (7) if formula can be seen that μ_A(x)∈ { 0,1 }, then F_e(A)=0；If μ_A(x) ∈ { 1 }, then F_e(A) maximum Nln2 is obtained, takes k^-1=Nln2 as normalization because Son；

Jing test of many times, using such as the S type functions of (8) formula^[9]As membership function：

Wherein, b=(a+c)/2；A and c obscures the scope of window width in determining S function, and with the difference of taken fuzzy window And change, as a transit point of function, the parameter of optimum can be obtained by trying to achieve the entropy maximum of fuzzy set The value of a, b, c, i.e., required parameter should meet (9) formula；

max{F_e(A), a, b, c ∈ x (n) ＆a ＜ b ＜ c } (9)

Certain uncertainty is contained in view of emitter Signals, therefore can be with fuzzy entropy come the not true of gauge signal It is qualitative；N points signal sequence after note resampling is x (n)=[x₁x₂…x_N], A is the corresponding fuzzy subset of the sequence, it is determined that After the value of optimized parameter a, b, c, can be by the mould of (7) formula single sequence according to the degree of membership of (8) formula single sequence Paste entropy；

2.3 normalized energy entropy feature extractions

2.3.1 i=1, j=1 are made；

2.3.2 connect the local maximum and minimum value sequence of signal s (t) with cubic spline function respectively, form signal Upper lower envelope；

2.3.3 calculate average m of upper lower envelope_ijT (), while remember h_ij(t)=s (t)-m_ij(t)；

If 2.3.4 h_ijT () meets IMF conditions, then go to step 5, otherwise with h_ijT () substitutes s (t), and make j=j+ 1, go to step 2；

2.3.5 remember c_iT () is that EMD decomposes the i-th IMF component for obtaining, then c_i(t)=h_ijT (), makes r_i(t)=s (t)- c_iT (), if r_iT () is a monotonic function, then catabolic process terminates, and now claims r_iT () is trend remainder, otherwise with r_i(t) S (t) is substituted, and makes i=i+1, go to step 2；

By above step as can be seen that original signal s (t) Jing EMD be decomposed into k IMF component and trend remainder and, i.e.,：

Wherein, k is to decompose altogether number of times；

After obtaining the IMF components of pulse data sequence s (t), you can obtain the IMF component normalization of signal by formula (11) Energy-Entropy：

In formula (11),

Wherein, p_iNormalization IMF energy is represented, N represents the length of signal sequence s (t)；Obvious ∑ p_i=1, i=1,2 ... K, number of times k is relevant with the complexity of signal for decomposition, should determine that by decomposition algorithm is adaptive；From entropy theory, if radiation source The Energy distribution of each IMF components of signal is uniform, then normalized energy entropy is maximum；If energy is concentrated at minority IMF component, return One change Energy-Entropy is less；

Step 3, emitter Signals Recognition method

3.1 pairs of emitter Signals carry out pretreatment, obtain signal x (n) after resampling, n=1,2 ..., N, calculating normalizing When changing Energy-Entropy, sequence s (t) is obtained by individual pulse data resampling directly, t=1,2 ..., N, N are the signal after resampling Length；

3.2 Sample Entropies S for trying to achieve signal sequence x (n) according to SampEn algorithm for estimating_e；

The 3.3 fuzzy entropy F for trying to achieve sequence x (n) according to (7) formula_e；

The 3.4 normalized energy entropy P for trying to achieve sequence s (t) according to (11) formula_e；

3.5 by characteristic vector T=[S_e, F_e, P_e] input SVM classifier Classification and Identification is carried out to signal.

Compared with prior art, beneficial effects of the present invention：

The present invention by Sample Entropy, retouched with Sample Entropy as the three-dimensional feature vector of signal by fuzzy entropy and normalized energy entropy The complexity of emitter Signals is stated, using fuzzy entropy come the uncertainty of gauge signal, while measuring using normalized energy entropy The distribution situation of signal energy.Article carries out feature extraction to six kinds of typical radar emitter Signals, and utilizes support vector machine Classification and Identification test is carried out, is as a result shown, the characteristic vector of extraction preferably can be realized to thunder in larger SNR ranges Up to the Classification and Identification of emitter Signals, it was demonstrated that the method is effective.

Description of the drawings

Fig. 1 is emitter Signals characteristic profile, wherein, (a) is Sample Entropy, fuzzy entropy and normalized energy entropy feature point Cloth, (b) Sample Entropy and fuzzy entropy feature distribution are (c) Sample Entropy and normalized energy entropy feature distribution, (d) for fuzzy entropy and Normalized energy entropy feature distribution.

Specific embodiment

Technical scheme is described in more detail with specific embodiment below in conjunction with the accompanying drawings.

1 emitter Signals Recognition based on entropy feature

1.1 Signal Pretreatment

It is in order to avoid the feature extracted is affected by emitter Signals carrier frequency and noise etc., individual after needing to segmentation Body pulse data carries out further pretreatment, mainly including following step^[5]：

Pulse data is transformed to frequency domain by step 1, and intercepts the central point of symmetrical amplitude-frequency spectrum with right half, is designated as f (i), i =1,2 ..., M, M for pulse data length 1/2；

Step 2 is according to formula (1) by signal f (i) energy normalized：

Step 3 obtains the mid frequency of signal f ' (i) and effective bandwidth after energy normalized, and bandwidth is normalized Process；

In the case that step 4 sample frequency is certain, pulse data its signal length of distinct pulse widths is different, in order to keep away Exempt from impact of this different length signal to extracting feature hereinafter, the signal after all bandwidth normalizeds is adopted again Sample, and remember the signal after resampling for x (n), n=1,2 ..., N, N are attached most importance to sampled signal length.

Sample Entropy and fuzzy entropy feature extraction algorithm hereinafter is both for what signal x (n) after resampling was carried out.

1.2 feature extracting method

Entropy represents the average uncertainty of information source in theory of information, due to noise jamming and the shadow of different modulating mode Ring, emitter Signals contain certain uncertainty, and this uncertainty is mainly shown as the difference of time domain plethysmographic signal, frequency Difference of difference and Energy distribution of spectral shape etc., these uncertain or ambiguities can be weighed with entropy.The present invention Extract Sample Entropy from emitter Signals respectively, three kinds of parameter group of fuzzy entropy and normalized energy entropy into characteristic vector be used for into The Classification and Identification of row emitter Signals.

1.2.1 Sample Entropy feature extraction

Approximate entropy is a kind of statistics parameter of measure time sequence complexity, it only need compared with short data just it is mensurable go out The probability of new model is produced in signal, and capacity of resisting disturbance is preferable^[6]But, the estimation that the method has signal Self Matching and brings Offset issue.Document [7] proposes that using Sample Entropy (SampEn) as seasonal effect in time series statistical parameter the parameter has and approximate entropy Identical physical significance and advantage, solve estimated bias and change insensitive problem to small complexity.Therefore, this It is bright using Sample Entropy as emitter Signals a characteristic parameter, while effectively can suppressing noise using this feature, Avoid impact of the estimated bias problem to emitter Signals Classification and Identification.

N points signal sequence after note resampling is x (n)=[x₁x₂…x_N], then SampEn algorithm for estimating is as described below：

Step 1 constructs m n dimensional vector ns according to formula (2) to sequence x (n)：

X (i)=[x_i x_i+1…x_i+m-1], i=1,2 ..., N-m+1 (2)

Step 2 according to formula (3) calculate vector to the distance between：

Step 3 calculates the number of similar vectors pair：

(1) make n_m=0, if d_m[x (i), x (j)]≤r, i ≠ j, then n_m=n_m+1；

(2) make n_m+1=0, if d_m+1[x (i), x (j)]≤r, i ≠ j, then n_m+1=n_m+1+1；

Step 4 calculates all similar vectors to Similar measure according to formula (4)：

Step 5 calculates similar vectors to average Similar measure according to formula (5)：

Step 6 calculates sample entropy estimate according to formula (6)：

Wherein, the present invention adopts scale parameter m=2 and tolerance parameterUsed as the parameter of estimation Sample Entropy, σ is The standard deviation of x (n).

1.2.2 fuzzy entropy feature extraction

Entropy represents the average uncertainty of information source in theory of information, can be used to measure one and obscure in fuzzy subset's opinion The size of the contained ambiguity of set, therefore with fuzzy entropy representing the uncertainty of fuzzy set.The fuzzy entropy of fuzzy set A is fixed Justice is^[8]：

Wherein, f (t)=- tlnt- (1-t) ln (1-t), k>0 is normal number, μ_A(x_i) represent fuzzy set A membership function.

Easily prove, f (t) is a symmetric function with regard to t=0.5, in interval [0,0.5] interior strictly monotone increasing, In interval [0.5,1] interior strictly monotone decreasing, maximum ln2 is obtained as t=0.5.By (7) if formula can be seen that μ_A(x) ∈ { 0,1 }, then F_e(A)=0；If μ_A(x) ∈ { 1 }, then F_e(A) maximum Nln2 is obtained, therefore, the present invention takes k^-1=Nln2 As normalization factor.

Jing test of many times, the present invention is using such as the S type functions of (8) formula^[9]As membership function：

Wherein, b=(a+c)/2.A and c obscures the scope of window width in determining S function, and with the difference of taken fuzzy window And change, as a transit point of function, the parameter of optimum can be obtained by trying to achieve the entropy maximum of fuzzy set The value of a, b, c, i.e., required parameter should meet (9) formula.

max{F_e(A), a, b, c ∈ x (n) ＆a ＜ b ＜ c } (9)

Certain uncertainty is contained in view of emitter Signals, therefore can be with fuzzy entropy come the not true of gauge signal It is qualitative.N points signal sequence after note resampling is x (n)=[x₁x₂…x_N], A is the corresponding fuzzy subset of the sequence, it is determined that After the value of optimized parameter a, b, c, can be by the mould of (7) formula single sequence according to the degree of membership of (8) formula single sequence Paste entropy.

1.2.3 normalized energy entropy feature extraction

Empirical mode decomposition (empirical mode decomposition, EMD) refers to difference in decomposed signal step by step The fluctuation of yardstick or trend, produce a series of data sequence with different characteristic yardstick, are called intrinsic mode component function (intrinsic mode function,IMF)^[10,11].The essence of EMD methods be exactly by signal decomposition be some different IMF it With the composition of different IMF representation signal different frequency ranges, the frequency content included by each frequency range are differed.IMF is defined For meeting the component of signal of following two conditions：(1) the number difference of extreme point and zero cross point is less than 1；(2) by local It is 0 that maximum and local minizing point constitute the average of envelope.

For radar emitter signal, the signal energy distribution in different frequency bands changes with the different of modulation system Become, therefore may determine that the type of emitter Signals by calculating the IMF component normalized energy entropys of different emitter Signals.If It is s (t) Jing after step 4 resampling in Signal Pretreatment that the pulse data sequence that obtains is direct, then decompose s's (t) using EMD Process is as described below：

Step 1 makes i=1, j=1；

Step 2 connects the local maximum and minimum value sequence of signal s (t) respectively with cubic spline function, forms signal Upper lower envelope；

Step 3 calculates average m of upper lower envelope_ijT (), while remember h_ij(t)=s (t)-m_ij(t)；

If step 4 h_ijT () meets IMF conditions, then go to step 5, otherwise with h_ijT () substitutes s (t), and make j=j+ 1, go to step 2；

Step 5 remembers c_iT () is that EMD decomposes the i-th IMF component for obtaining, then c_i(t)=h_ijT (), makes r_i(t)=s (t)- c_iT (), if r_iT () is a monotonic function, then catabolic process terminates, and now claims r_iT () is trend remainder, otherwise with r_i(t) S (t) is substituted, and makes i=i+1, go to step 2；

By above step as can be seen that original signal s (t) Jing EMD be decomposed into k IMF component and trend remainder and, i.e.,：

Wherein, k is to decompose altogether number of times.

After obtaining the IMF components of pulse data sequence s (t), you can obtain the IMF component normalization of signal by formula (11) Energy-Entropy：

In formula (11),

Wherein, p_iNormalization IMF energy is represented, N represents the length of signal sequence s (t).Obvious ∑ p_i=1, i=1,2 ... K, number of times k is relevant with the complexity of signal for decomposition, should determine that by decomposition algorithm is adaptive.From entropy theory, if radiation source The Energy distribution of each IMF components of signal is uniform, then normalized energy entropy is maximum；If energy is concentrated at minority IMF component, return One change Energy-Entropy is less.

1.3 emitter Signals Recognition methods

It is generally not the application problem of very complete and actual battlefield surroundings in view of radiation source tranining database, needs choosing Select a kind of suitable for less training sample, and train fast with classification speed, it is not easy to be absorbed in the grader of local minimum, and SVM has these advantages just, therefore the present invention selects SVM as the learning algorithm of Classification and Identification.

SVM is that method not only preferably resolves small sample present in conventional machine learning method, non-linear, excessively The practical problems such as habit, high dimension, local minizing point, and calculate with the neural network learning based on empirical risk minimization principle Method is compared, and SVM has higher theoretical basiss and more preferable generalization ability^[12].SVM by kernel function by input feature vector vector by Low-dimensional feature space is mapped to high-dimensional feature space, and the Nonlinear separability problem of original input space is converted into higher dimensional space Linear separability problem, so that reach the purpose of Classification and Identification emitter Signals.

In view of Sample Entropy and fuzzy entropy can effectively describe the complexity and uncertainty of emitter Signals, the present invention is proposed The characteristic vector constituted using Sample Entropy and fuzzy entropy is carrying out the svm classifier recognition methodss of emitter Signals, concrete steps It is as follows：

Step 1 carries out pretreatment to emitter Signals, obtains signal x (n) after resampling, and n=1,2 ..., N, calculating return During one change Energy-Entropy, sequence s (t) is obtained by individual pulse data resampling directly, t=1,2 ..., N, N are the letter after resampling Number length；

Step 2 tries to achieve Sample Entropy S of signal sequence x (n) according to SampEn algorithm for estimating_e；

Step 3 tries to achieve the fuzzy entropy F of sequence x (n) according to (7) formula_e；

Step 4 tries to achieve the normalized energy entropy P of sequence s (t) according to (11) formula_e；

Step 5 is by characteristic vector T=[S_e, F_e, P_e] input SVM classifier Classification and Identification is carried out to signal.

2 experimental results and analysis

The present invention selects 6 kinds of typical radar emitter Signals to carry out emulation experiment^[13], this 6 kinds of signals are respectively：Conventional thunder Up to signal (CW), linear frequency modulated radar signal (LFM), nonlinear frequency modulation radar signal (NLFM), binary phasecoded radar signal (BPSK), four phases code radar signal (QPSK) and frequeney-wavenumber domain signal (FSK).Signal carrier frequency is 850MHz, and sampling is frequently Rate is 2.4GHz, and pulsewidth is 10.8us, and the frequency deviation of LFM is 45MHz, and, using sinusoidal frequency modulation, BPSK is pseudo- using 31 for NLFM Random code, QPSK adopt Huffman codes, FSK to adopt Barker code.To each radar signal 0～20dB signal to noise ratio model 120 samples are produced every 5dB in enclosing, 600 samples are total up to, wherein 200 are used for classifier training, remaining 400 use Make the test set of Modulation recognition identification.Before training grader and test signal Classification and Identification effect, all samples be entered The extraction of row Sample Entropy and fuzzy entropy feature.In order to intuitively reflect the feature distribution situation of each emitter Signals, the present invention is from carrying 60 stack features samples of each signal difference signal to noise ratio are chosen in the characteristic vector got, and 300 stack features samples are done such as Fig. 1 institutes altogether The characteristic profile for showing.

By in Fig. 1 (a) as can be seen that in the three-dimensional feature class of tri- kinds of signals of CW, LFM and NLFM aggregation preferably, and The feature of tri- kinds of signals of FSK, BPSK and QPSK relatively dissipates；By the Sample Entropy and the mould that can be seen that BPSK and QPSK in Fig. 1 (b) Paste entropy feature overlaps；In Fig. 1 (c), FSK and NFLM overlap, while QPSK and LFM overlaps are more serious, it is several Can not differentiate；In Fig. 1 (d), NLFM and QPSK overlap.Therefore only rely on two-dimensional entropy feature always to obtain Classification and Identification result.In view of above-mentioned factor, present invention SVM is carried out to the emitter Signals that three-dimensional feature vector is characterized point Class identification, as a result as shown in table 1.

The situation of change of each signal correct recognition rata for obtaining using SVM with signal to noise ratio is listed in table 1, and wherein classification is known Rate does not refer to the average of 20 result of the tests, and average recognition rate refers to that each signal is classified in 0～20dB SNR ranges and knows Rate is not average.

Situation of change of the 1 emitter Signals correct recognition rata of table with signal to noise ratio

As can be seen from Table 1, in certain SNR range, vector is characterized with the three kinds of entropys for extracting, and uses SVM classifier When carrying out Classification and Identification to emitter Signals, every kind of radar emitter signal can obtain higher correct recognition rata.Signal is known The height of rate and the complexity of signal be not relevant, for relatively simple signal form, such as CW and LFM modulated signals, its Average correct recognition rata can reach 98.74% and 96.97%, the preferable feature class of both signals in this result and Fig. 1 (a) Interior aggregation is consistent；For complex signal form, such as BPSK and fsk modulated signal, its average correct identification Rate is 90.21% and 88.21%, the result is not good with the aggregation extent of three-dimensional feature and feature partly overlap it is relevant, but This result can be acceptance in engineer applied.In addition, the average correct recognition rata of 6 kinds of emitter Signals reaches 94.02%, recognition effect is preferable.

The above, preferably specific embodiment only of the invention, protection scope of the present invention not limited to this are any ripe Those skilled in the art are known in the technical scope of present disclosure, the letter of the technical scheme that can be become apparent to Altered or equivalence replacement are each fallen within protection scope of the present invention.

Claims (1)

1. the radar emitter signal recognition methodss of the three-dimensional entropy feature of a kind of joint, it is characterised in that comprise the following steps：

Step 1, Signal Pretreatment

Pulse data is transformed to frequency domain by 1.1, and intercepts the central point of symmetrical amplitude-frequency spectrum with right half, is designated as f (i), i=1, 2 ..., M, M for pulse data length 1/2；

1.2 according to formula (1) by signal f (i) energy normalized：

$f^{\′}\left(i\right)=\frac{f\left(i\right)}{\sqrt{\left({\mathrm{\Σ}}_{i=1}^M{f}^{*}\right(i)\·f(i\left)\right)/M}}---\left(1\right)$

1.3 obtain the mid frequency of signal f ' (i) and effective bandwidth after energy normalized, and bandwidth is normalized；

In the case that 1.4 sample frequencys are certain, pulse data its signal length of distinct pulse widths is different, in order to avoid this Impact of the different length signal to extracting feature hereinafter, carries out resampling to the signal after all bandwidth normalizeds, and remembers Signal after resampling is x (n), n=1,2 ..., and N, N attach most importance to sampled signal length；

Step 2, feature extraction

2.1 Sample Entropy feature extractions

N points signal sequence after note resampling is x (n)=[x₁x₂…x_N], then SampEn algorithm for estimating is as described below：

2.1.1 m n dimensional vector ns are constructed to sequence x (n) according to formula (2)：

X (i)=[x_ix_i+1…x_i+m-1], i=1,2 ..., N-m+1 (2)

2.1.2 according to formula (3) calculate vector to the distance between：

$d_m\[x\left(i\right),x\left(j\right)\]=\underset{k=0,...,m-1}{\max }\[|x_{i+k}-x_{j+k}|\]---\left(3\right)$

2.1.3 calculate the number of similar vectors pair：

(1) make n_m=0, if d_m[x (i), x (j)]≤r, i ≠ j, then n_m=n_m+1；

(2) make n_m+1=0, if d_m+1[x (i), x (j)]≤r, i ≠ j, then n_m+1=n_m+1+1；

2.1.4 all similar vectors are calculated to Similar measure according to formula (4)：

$\begin{array}{c}{B}_i^m(r,N)=\frac{1}{N-m-1}{n}_m,\\ A_i^m(r,N)=\frac{1}{N-m-1}{n}_{m+1},i=1,2,\mathrm{...},N-m\end{array}---\left(4\right)$

2.1.5 similar vectors are calculated to average Similar measure according to formula (5)：

$\begin{array}{c}{B}^m(r,N)=\frac{1}{N-m}{\mathrm{\Σ}}_{i=1}^{N-m}{B}_i^m\left(r,N\right)\\ A^m(r,N)=\frac{1}{N-m}{\mathrm{\Σ}}_{i=1}^{N-m}{A}_i^m\left(r,N\right)\end{array}---\left(5\right)$

2.1.6 sample entropy estimate is calculated according to formula (6)：

$S_e(m,r)=-ln\frac{A^m(r,N)}{B^m(r,N)}---\left(6\right)$

Wherein, the present invention adopts scale parameter m=2 and tolerance parameterUsed as the parameter of estimation Sample Entropy, σ is x (n) Standard deviation；

2.2 fuzzy entropy feature extractions

Entropy represents the average uncertainty of information source in theory of information, is used for measuring contained by a fuzzy set in fuzzy subset's opinion The size of some ambiguities, therefore with fuzzy entropy representing the uncertainty of fuzzy set；The fuzzy entropy of fuzzy set A is defined as：

$F_e\left(A\right)=k\underset{i=1}{\overset{N}{\Σ}}\[f\left({\mathrm{\μ}}_A\right(x_i)\]---\left(7\right)$

Wherein, f (t)=- t ln t- (1-t) ln (1-t), k>0 is normal number, μ_A(x_i) represent fuzzy set A membership function；

Prove, f (t) is a symmetric function with regard to t=0.5, in interval [0,0.5] interior strictly monotone increasing, in interval [0.5,1] interior strictly monotone decreasing, obtains maximum ln2 as t=0.5；Found out by (7) formula, if μ_A(x) ∈ { 0,1 }, then F_e(A)=0；If μ_A(x) ∈ { 1 }, then F_e(A) maximum Nln2 is obtained, takes k^-1=Nln2 is used as normalization factor；

Jing test of many times, using such as the S type functions of (8) formula^[9]As membership function：

${\mathrm{\μ}}_A\left(x_i\right)=\left\{\begin{array}{c}0,x_i\≤a;\\ {(x_i-a)}^2/(b-a)(c-a),a\≤x_i\≤b;\\ 1-{(x_i-c)}^2/(c-b)(c-a),b\≤x_i\≤c;\\ 1,x_i\≥c\end{array}\right.---\left(8\right)$

Wherein, b=(a+c)/2；A and c obscures the scope of window width in determining S function, and sends out with the different of taken fuzzy window Changing, as a transit point of function, obtains parameter a of optimum by trying to achieve the entropy maximum of fuzzy set, b, c's Value, i.e., required parameter should meet (9) formula；

max{F_e(A), a, b, c ∈ x (n) ＆a ＜ b ＜ c } (9)

Certain uncertainty is contained in view of emitter Signals, with fuzzy entropy come the uncertainty of gauge signal；Note is adopted again N points signal sequence after sample is x (n)=[x₁ x₂ … x_N], A is the corresponding fuzzy subset of the sequence, it is determined that optimized parameter After the value of a, b, c, according to the degree of membership of (8) formula single sequence, by the fuzzy entropy of (7) formula single sequence；

2.3 normalized energy entropy feature extractions

2.3.1 i=1, j=1 are made；

2.3.2 connect the local maximum and minimum value sequence of signal s (t) with cubic spline function respectively, form the upper of signal Lower envelope；

2.3.3 calculate average m of upper lower envelope_ijT (), while remember h_ij(t)=s (t)-m_ij(t)；

If 2.3.4 h_ijT () meets IMF conditions, then go to step 5, otherwise with h_ijT () substitutes s (t), and make j=j+1, goes to Step 2；

2.3.5 remember c_iT () is that EMD decomposes the i-th IMF component for obtaining, then c_i(t)=h_ijT (), makes r_i(t)=s (t)-c_i T (), if r_iT () is a monotonic function, then catabolic process terminates, and now claims r_iT () is trend remainder, otherwise with r_iT () replaces For s (t), and i=i+1 is made, go to step 2；

Found out by above step, original signal s (t) Jing EMD be decomposed into k IMF component and trend remainder and, i.e.,：

$s\left(t\right)={\mathrm{\Σ}}_{i=1}^k{c}_i\left(t\right)+r_k\left(t\right)---\left(10\right)$

Wherein, k is to decompose altogether number of times；

After obtaining the IMF components of pulse data sequence s (t), the IMF component normalized energy entropys of signal are obtained by formula (11)：

$P_e=-{\mathrm{\Σ}}_{i=1}^k{p}_i\ln p_i---\left(11\right)$

In formula (11),

$p_i=\frac{\sqrt{{\mathrm{\Σ}}_{j=1}^N|c_i\left(j\right){|}^2}}{{\mathrm{\Σ}}_{i=1}^k\sqrt{{\mathrm{\Σ}}_{j=1}^N|c_i\left(j\right){|}^2}}---\left(12\right)$

Wherein, p_iNormalization IMF energy is represented, N represents the length of signal sequence s (t)；Obvious ∑ p_i=1, i=1,2 ... k, point Number of times k is relevant with the complexity of signal for solution, should determine that by decomposition algorithm is adaptive；Obtained by entropy theory, if emitter Signals The Energy distribution of each IMF components is uniform, then normalized energy entropy is maximum；If energy is concentrated at minority IMF component, normalization Energy-Entropy is less；

Step 3, emitter Signals Recognition method

3.1 pairs of emitter Signals carry out pretreatment, obtain signal x (n) after resampling, n=1,2 ..., N, calculating normalization energy During amount entropy, sequence s (t) is obtained by individual pulse data resampling directly, t=1,2 ..., N, N are the Chief Signal Boatswain after resampling Degree；

3.2 Sample Entropies S for trying to achieve signal sequence x (n) according to SampEn algorithm for estimating_e；

The 3.3 fuzzy entropy F for trying to achieve sequence x (n) according to (7) formula_e；

The 3.4 normalized energy entropy P for trying to achieve sequence s (t) according to (11) formula_e；

3.5 by characteristic vector T=[S_e, F_e, P_e] input SVM classifier Classification and Identification is carried out to signal.