CN113095175A - Low altitude unmanned machine identification method based on radio frequency characteristics of data transmission radio station - Google Patents

Low altitude unmanned machine identification method based on radio frequency characteristics of data transmission radio station Download PDF

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CN113095175A
CN113095175A CN202110339185.9A CN202110339185A CN113095175A CN 113095175 A CN113095175 A CN 113095175A CN 202110339185 A CN202110339185 A CN 202110339185A CN 113095175 A CN113095175 A CN 113095175A
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transient signal
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aerial vehicle
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田园
王思源
唐斌
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Chengdu Aeronautic Polytechnic
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
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    • G06F2218/12Classification; Matching
    • G06F2218/16Classification; Matching by matching signal segments
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00Pattern recognition
    • G06F18/20Analysing
    • G06F18/22Matching criteria, e.g. proximity measures
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00Pattern recognition
    • G06F18/20Analysing
    • G06F18/24Classification techniques
    • G06F18/241Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches
    • G06F18/2413Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches based on distances to training or reference patterns
    • G06F18/24147Distances to closest patterns, e.g. nearest neighbour classification
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00Pattern recognition
    • G06F18/20Analysing
    • G06F18/24Classification techniques
    • G06F18/241Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches
    • G06F18/2415Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches based on parametric or probabilistic models, e.g. based on likelihood ratio or false acceptance rate versus a false rejection rate
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/02Preprocessing
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/08Feature extraction

Abstract

The invention discloses a low-altitude unmanned aerial vehicle identification method based on radio frequency characteristics of a data transmission radio station, which comprises the steps of S1, collecting signals of data transmission radio station equipment of an unmanned aerial vehicle, carrying out digital representation on the collected signals, and converting the signals into L-dimensional signals; s2, extracting transient signals of the L-dimensional signals; s3, performing statistical analysis on the transient signal in a time domain, and extracting the characteristics of the transient signal; and S4, identifying the transient signal characteristics based on the K-nearest neighbor algorithm. According to the invention, the classification weight is comprehensively calculated by combining the characteristic distance and the contribution degree of the characteristics to the identification performance based on the weighted KNN optimization algorithm of the characteristic contribution degree, so that the influence of the imbalance of the data set and the difference between the characteristics on the accuracy of the radio frequency fingerprint identification of the unmanned aerial vehicle is avoided, and the accuracy of the radio frequency fingerprint identification of the unmanned aerial vehicle is improved.

Description

Low altitude unmanned machine identification method based on radio frequency characteristics of data transmission radio station
Technical Field
The invention belongs to the technical field of unmanned aerial vehicle radio frequency signal detection and identification, and particularly relates to a low-altitude unmanned aerial vehicle identification method based on radio frequency characteristics of a data transmission radio station.
Background
In recent years, the unmanned aerial vehicle technology is rapidly developed and is increasingly widely applied in the civil field. However, the existing civil unmanned aerial vehicle lacks of uniform industrial standards and specifications, and the admission threshold is low, so that the problems of 'black flight' of the unmanned aerial vehicle and the like exist, and a series of safety events are caused. In order to cope with the current situation, research on the detection technology of the low-altitude unmanned aerial vehicle is strengthened in various countries. From the perspective of safety and protection, the control, detection and disposal of the low-altitude unmanned aerial vehicle are a worldwide problem, and the potential safety hazard brought by the low-altitude unmanned aerial vehicle is more and more prominent. With the popularization of the application of the unmanned aerial vehicle and the gradual opening of a low-altitude airspace, how to deal with the threat brought by the illegal flight of the unmanned aerial vehicle is very urgent for social public safety and aviation flight safety.
For the technical problem of low altitude unmanned accurate detection and identification, scholars at home and abroad also develop related researches. The existing detection and identification method of the unmanned aerial vehicle comprises a detection technology based on image identification, a detection technology based on radar, a detection technology based on sound waves and a detection technology based on infrared thermal imaging, but still has the problems of low detection and identification rate, large influence of environment, insufficient detection distance and the like.
Disclosure of Invention
The invention aims to provide a low-altitude unmanned aerial vehicle identification method based on radio frequency characteristics of a data transmission radio station, aiming at overcoming the defects in the prior art, and solving the problems of low detection identification rate, large influence of environment and insufficient detection distance in the prior art.
In order to achieve the purpose, the invention adopts the technical scheme that:
a low altitude unmanned aerial vehicle identification method based on radio frequency characteristics of a data transmission radio station comprises the following steps:
s1, collecting signals of the data transmission radio station equipment of the unmanned aerial vehicle, carrying out digital representation on the collected signals, and converting the signals into L-dimensional signals;
s2, extracting transient signals of the L-dimensional signals;
s3, performing statistical analysis on the transient signal in a time domain, and extracting the characteristics of the transient signal;
and S4, identifying the transient signal characteristics based on the K-nearest neighbor algorithm.
Preferably, in S1, signal acquisition is performed on the unmanned aerial vehicle data transmission radio station device through the USRP X310 software radio device and the UBX-160 radio frequency daughter board, the acquired signal is digitally represented, and the signal is converted into an L-dimensional signal X ═ X1,x2,…,xL]Wherein x isLIs the sampled signal.
Preferably, extracting the transient signal of the L-dimensional signal in S2 includes coarse positioning and fine alignment of the transient signal.
Preferably, the transient signal coarse positioning comprises:
a2.1, read L dimension unmanned aerial vehicle number transmission radio station signal X ═ X of collection1,x2,…,xL];
A2.2, setting an energy detection threshold coefficient alpha, wherein alpha belongs to (0, 1);
a2.3, dividing the signal X into n window intervals, wherein the width of each window interval is w sampling points, and the energy E (n) of each window interval is as follows:
Figure BDA0002998613410000021
wherein k is the sampling point number in each window;
a2.4, calculating the energy difference E of two adjacent windowsdiff(j);
Ediff(j)=E(j+1)-E(j)j=1,2,…,n-1
Wherein, E (j +1) and E (j) are respectively the energy values of the j +1 th window and the j th window;
a2.5, checking the jth energy difference, if Ediff(j)≥αEmax,j=1,2,…,n-1,EmaxThe searched coarse positioning transient signal is X 'as the maximum value of all window energies'i=[x(j-1)w,x(j-1)w+1,…,xjw]i is 1,2, … N and the extracted coarse positioning transient signal is saved.
Preferably, the transient signal fine alignment comprises:
b2.1, reading a set X' ═ X of the roughly positioned transient signal samples1';X2';…;XN'],XN' is the localized transient signal sample;
b2.2, setting an amplitude detection coefficient beta of a sampling point, and coarsely positioning an initial sequence number i of the transient signal sample to be 1;
B23, from the coarsely positioned set of transient signal samples X' ═ X1';X2';…;XN']Obtaining a single sample yi=X'i
B2.4, search yiMaximum amplitude A of sampling point in samplemax(i)=max(yi);
B2.5, setting the size of the sliding window to be k, and setting the sliding window to be yiBeginning at the first sample point in the sample, yi(j) j is 0 which is the starting point of the current window;
b2.6, calculation
Figure BDA0002998613410000031
Wherein A iswThe amplitude value of the continuous k sampling points is the average value;
b2.7, if Aw≥βAmax(i) Then the first sample point x of the current windowi(s)=yi(j) (ii) a Otherwise, the current window moves backwards by one sampling point, the starting point position j is updated to be j +1, and B2.6 is returned;
b2.8: sample point xi(s) is X'iAt a starting point of xi(s) extracting the transient signal Y with dimension d as a starting pointi
B2.9: updating the serial number i of the sample of the coarse positioning transient signal to i + 1;
b2.10: if i > N, returning the extracted transient signal sample set Y ═ Y1;Y2;…;YN](ii) a Otherwise, B2.3 is returned.
Preferably, the transient signal characteristics in S3 include:
variance Va, peak factor C, pulse factor I, and margin factor C of transient signaleKurtosis factor K, form factor SfAnd a skewness factor S.
Preferably, the identifying the transient signal features in S4 based on the K-nearest neighbor algorithm includes:
s4.1, reading a transient signal characteristic training sample set X ═ X1;X2;…;XN]And testing the transient signal sample data set Y ═ Y1;Y2…;YJ]Each sample is m-dimensional data;
s4.2, carrying out zero equalization on each column of the transient signal characteristic training sample set X;
s4.3, calculating covariance matrix
Figure BDA0002998613410000041
S4.4, calculating the eigenvalue lambda of the covariance matrix Ci
S4.5, calculating the identification contribution rate of each feature
Figure BDA0002998613410000042
S4.6, calculating test sample data YjAnd X in the training sample setiIs a distance of
Figure BDA0002998613410000043
Wherein, thetakFor the recognition contribution, x, of the k-dimensional feature in the training samplekFor training sample XiThe k-dimension feature of (1), ykTo test sample data YjThe k-dimensional feature of (1);
s4.7, sorting the training samples from small to large according to the distance, and selecting the first K training samples X' with the minimum distance from the training sample set as [ X ═ X1';X2';…;XK']And the corresponding D' ═ D1';D2';…;DK']D' is the number of test samples YjSet of distances from each sample in the set X', DK' is the number of test samples YjDistance from the kth sample in the set of X';
s4.8, calculating the weight
Figure BDA0002998613410000044
S4.9, calculating test sample data YjProbability of belonging to class label (x):
Figure BDA0002998613410000045
wherein, WkIs' WiThe weight in (1) belonging to class (label (x));
S4.10、Yjthe category corresponding to the maximum probability value is YjThe category to which it belongs.
The low-altitude unmanned aerial vehicle identification method based on the radio frequency characteristics of the data transmission radio station has the following beneficial effects:
according to the invention, the classification weight is comprehensively calculated by combining the characteristic distance and the contribution degree of the characteristics to the identification performance based on the weighted KNN optimization algorithm of the characteristic contribution degree, so that the influence of the imbalance of the data set and the difference between the characteristics on the accuracy of the radio frequency fingerprint identification of the unmanned aerial vehicle is avoided, and the accuracy of the radio frequency fingerprint identification of the unmanned aerial vehicle is improved.
Drawings
Fig. 1 is a GNU Radio signal flow chart.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
According to an embodiment of the application, referring to fig. 1, the method for identifying a low altitude and unmanned aerial vehicle based on radio frequency characteristics of a data transmission radio station according to the present scheme includes:
s1, collecting signals of the data transmission radio station equipment of the unmanned aerial vehicle, carrying out digital representation on the collected signals, and converting the signals into L-dimensional signals;
s2, extracting transient signals of the L-dimensional signals;
s3, performing statistical analysis on the transient signal in a time domain, and extracting the characteristics of the transient signal;
and S4, identifying the transient signal characteristics based on the K-nearest neighbor algorithm.
The above steps will be described in detail below;
s1, collecting unmanned aerial vehicle data transmission radio station equipment signals, digitally representing the collected signals, and converting the collected signals into L-dimensional signals, specifically comprising the following steps:
through USRP X310 software radio equipment and UBX-160 radio frequency daughter board, carry out signal acquisition to unmanned aerial vehicle data transmission radio station equipment, carry out digital representation with the signal of gathering, convert into L dimension signal X ═ X1,x2,…,xL]。
S2, extracting transient signals of the L-dimensional signals;
after the data transmission signal sampling of the unmanned aerial vehicle is completed, a transient signal needs to be extracted from the sampling data for subsequent processing and analysis. The unmanned aerial vehicle data transmission signal start of collection is channel noise etc. and its short-time energy value is less. The energy value begins to fluctuate shortly after the start of the transient signal. Transient signal extraction is divided into two steps of transient signal coarse positioning and fine alignment.
The transient signal rough positioning detects the abrupt change interval of the signal energy by a short-time window energy difference based method. The fine alignment of the transient signal needs to ensure the alignment of the position of the starting point of each extracted transient signal, so as to facilitate the subsequent feature processing analysis of the transient signal sample.
The transient signal coarse positioning method comprises the following steps:
a2.1, read L dimension unmanned aerial vehicle number transmission radio station signal X ═ X that USRP equipment gathered1,x2,…,xL];
A2.2, setting an energy detection threshold coefficient alpha, wherein alpha belongs to (0, 1);
a2.3, dividing X into n window intervals, where the width of each window interval is w sampling points, and the energy of each window interval can be represented as:
Figure BDA0002998613410000061
wherein E ismaxThe maximum value of all window energies;
a2.4, calculating the energy difference E of two adjacent windowsdiff(j)
Ediff(j)=E(j+1)-E(j)j=1,2,…,n-1
A2.5, checking the jth energy difference, if Ediff(j)≥αEmaxAnd j is 1,2, …, n-1, the searched coarse positioning transient signal is represented as X'i=[x(j-1)w,x(j-1)w+1,…,xjw]i is 1,2, … N and the extracted coarse positioning transient signal is saved.
Because the size of the energy detection window is w, the position of the initial point of the roughly positioned transient signal in the sample is not precisely aligned, and the precise alignment of the transient signal mainly comprises the following steps:
b2.1, reading a set X' ═ X of the roughly positioned transient signal samples1';X2';…;XN'];
B2.2, setting an amplitude detection coefficient beta of a sampling point, and coarsely positioning an initial sequence number i of the transient signal sample to be 1;
b2.3. from the coarsely positioned set of transient signal samples X ═ X1';X2';…;XN']Obtaining a single sample yi=X'i
B2.4, search yiMaximum amplitude A of sampling point in samplemax(i)=max(yi);
B2.5, setting the size of the sliding window to be k, and setting the sliding window to be yiBeginning at the first sample point in the sample, yi(j) j is 0 which is the starting point of the current window;
b2.6, calculation
Figure BDA0002998613410000071
AwThe amplitude value of the continuous k sampling points is the average value;
b2.7 if Aw≥βAmax(i) Then the first sample point x of the current windowi(s)=yi(j) (ii) a Otherwise, the current window moves backwards by one sampling point, the starting point position j is updated to be j +1, and B2.6 is returned;
b2.8, sample point xi(s) is X'iAt a starting point of xi(s) extracting the transient signal Y with dimension d as a starting pointi
B2.9, updating the serial number i of the coarse positioning transient signal sample to be i + 1;
b2.10, if i > N, returning the extracted transient signal sample set Y ═ Y1;Y2;…;YN]The processing procedure is ended; otherwise, B2.3 is returned.
S3, performing statistical analysis on the transient signal in a time domain, and extracting the characteristics of the transient signal;
the transient signal characteristics are that the transient signal is subjected to statistical analysis in a time domain, and characteristic parameters such as a maximum value, a minimum value, a peak value, a mean value, a variance, a peak factor, a pulse factor, a margin factor, a kurtosis factor, a wave form factor, skewness and the like of the signal are calculated.
In this embodiment, the variance Va, the crest factor C, the pulse factor I, and the margin factor C of the transient signal are selectedeKurtosis factor K, form factor SfAnd the skewness factor S forms a 7-dimensional feature vector FeatureVector [ V ]a C I Ce K Sf S]. The calculation method of each characteristic parameter is shown in Table 1, where xiAnd transmitting the radio station transient signal sample for the extracted unmanned aerial vehicle.
TABLE 1 time domain characteristic parameter description and calculation method
Figure BDA0002998613410000072
Figure BDA0002998613410000081
S4, identifying transient signal characteristics based on a K-nearest neighbor algorithm;
the K-nearest Neighbor (KNN) algorithm is to classify by measuring the distance between different characteristic values, compare the characteristics of the test sample with the characteristics corresponding to the training samples, and find the first K samples most similar to the characteristics in the training set, so that the classification corresponding to the test sample is the classification with the largest occurrence frequency in the K samples. KNN makes decisions by basing the decision on the dominant class among K objects, typically using Euclidean distancesThe distance between the sample feature values is calculated. n-dimensional spatial point A (x)1,x2,…,xn) And B (y)1,y2,…,yn) The euclidean distance between them.
Figure BDA0002998613410000082
On the basis of the weighted KNN algorithm, the weighted KNN optimization algorithm based on the characteristic contribution degree is provided, and the identification accuracy of the data transmission signals of the unmanned aerial vehicle is improved.
The method comprises the following steps:
s4.1, reading a transient signal characteristic training sample set X ═ X1;X2;…;XN]And testing the transient signal sample data set Y ═ Y1;Y2…;YJ]Each sample is m-dimensional data;
s4.2, carrying out zero averaging on each column (representing a characteristic attribute field) of the X;
s4.3, calculating covariance matrix
Figure BDA0002998613410000091
S4.4, calculating the eigenvalue lambda of the covariance matrix Ci
S4.5, calculating the identification contribution rate of each feature
Figure BDA0002998613410000092
S4.6, calculating test sample data YjAnd X in the training sample setiIs a distance of
Figure BDA0002998613410000093
S4.7, sorting the training samples from small to large according to the distance, and selecting the first K training samples X' with the minimum distance from the training sample set as [ X ═ X1';X2';…;XK']And the corresponding D' ═ D1';D2';…;DK'];
S4.8, calculating the weight
Figure BDA0002998613410000094
S4.9, calculating test sample data YjProbability of belonging to class label (x):
Figure BDA0002998613410000095
wherein WkIs' WiThe weight in (1) belonging to class (label (x));
S4.10、Yjthe category corresponding to the maximum probability value is YjThe category to which it belongs.
The classification weight is comprehensively calculated by combining the characteristic distance and the contribution degree of the characteristics to the identification performance, the influence of the imbalance of the data set and the difference between the characteristics on the accuracy of the radio frequency fingerprint identification of the unmanned aerial vehicle is avoided, and the defect of the existing detection modes of radar, visible light, infrared and the like on the low-altitude unmanned aerial vehicle detection can be overcome.
In the selection of the transient signal characteristics, the variance Va, the peak factor C, the pulse factor I and the margin factor C of the transient signal of the data transmission radio station of the unmanned aerial vehicle are utilizedeKurtosis factor K, form factor SfAnd 7-dimensional feature vectors formed by the skewness factors S reduce the signal feature dimension while ensuring the feature identification accuracy.
While the embodiments of the invention have been described in detail in connection with the accompanying drawings, it is not intended to limit the scope of the invention. Various modifications and changes may be made by those skilled in the art without inventive step within the scope of the appended claims.

Claims (7)

1. A low altitude unmanned aerial vehicle identification method based on radio frequency characteristics of a data transmission radio station is characterized by comprising the following steps:
s1, collecting signals of the data transmission radio station equipment of the unmanned aerial vehicle, carrying out digital representation on the collected signals, and converting the signals into L-dimensional signals;
s2, extracting transient signals of the L-dimensional signals;
s3, performing statistical analysis on the transient signal in a time domain, and extracting the characteristics of the transient signal;
and S4, identifying the transient signal characteristics based on the K-nearest neighbor algorithm.
2. The low altitude unmanned aerial vehicle identification method based on radio frequency characteristics of data transmission radio station according to claim 1, characterized in that: in the S1, signal acquisition is carried out on the data transmission radio station equipment of the unmanned aerial vehicle through the USRP X310 software radio equipment and the UBX-160 radio frequency daughter board, the acquired signals are digitally represented and converted into L-dimensional signals X ═ X1,x2,…,xL]Wherein x isLIs the sampled signal.
3. The method for identifying the low altitude unmanned aerial vehicle based on radio frequency characteristics of data transmission station as claimed in claim 1, wherein the extracting the transient signal of the L-dimensional signal in S2 comprises coarse positioning and fine alignment of the transient signal.
4. The method for identifying the low altitude unmanned aerial vehicle based on the radio frequency characteristics of the data transmission station as claimed in claim 3, wherein the rough positioning of the transient signal comprises:
a2.1, read L dimension unmanned aerial vehicle number transmission radio station signal X ═ X of collection1,x2,…,xL];
A2.2, setting an energy detection threshold coefficient alpha, wherein alpha belongs to (0, 1);
a2.3, dividing the signal X into n window intervals, wherein the width of each window interval is w sampling points, and the energy E (n) of each window interval is as follows:
Figure FDA0002998613400000011
wherein k is the sampling point number in each window;
a2.4, calculating the energy difference E of two adjacent windowsdiff(j);
Ediff(j)=E(j+1)-E(j)j=1,2,…,n-1
Wherein, E (j +1) and E (j) are respectively the energy values of the j +1 th window and the j th window;
a2.5, checking the jth energy difference, if Ediff(j)≥αEmax,j=1,2,…,n-1,EmaxThe searched coarse positioning transient signal is X 'as the maximum value of all window energies'i=[x(j-1)w,x(j-1)w+1,…,xjw]i is 1,2, … N and the extracted coarse positioning transient signal is saved.
5. The method for identifying the low altitude unmanned aerial vehicle based on the radio frequency characteristics of the data transmission station as claimed in claim 4, wherein the transient signal fine alignment comprises:
b2.1, reading a set X' ═ X of the roughly positioned transient signal samples1';X2';…;XN'],XN' is the localized transient signal sample;
b2.2, setting an amplitude detection coefficient beta of a sampling point, and coarsely positioning an initial sequence number i of the transient signal sample to be 1;
b2.3. from the coarsely positioned set of transient signal samples X ═ X1';X2';…;XN']Obtaining a single sample yi=X'i
B2.4, search yiMaximum amplitude A of sampling point in samplemax(i)=max(yi);
B2.5, setting the size of the sliding window to be k, and setting the sliding window to be yiBeginning at the first sample point in the sample, yi(j) j is 0 which is the starting point of the current window;
b2.6, calculation
Figure FDA0002998613400000021
Wherein A iswThe amplitude value of the continuous k sampling points is the average value;
b2.7, if Aw≥βAmax(i) Then the first sample point x of the current windowi(s)=yi(j) (ii) a Otherwise, the current window moves backwards by one sampling point, and the position j of the initial point is updated to be j +1Returning to B2.6;
b2.8: sample point xi(s) is X'iAt a starting point of xi(s) extracting the transient signal Y with dimension d as a starting pointi
B2.9: updating the serial number i of the sample of the coarse positioning transient signal to i + 1;
b2.10: if i > N, returning the extracted transient signal sample set Y ═ Y1;Y2;…;YN](ii) a Otherwise, B2.3 is returned.
6. The method for identifying the low altitude unmanned aerial vehicle based on radio frequency characteristics of the data transmission station as claimed in claim 1, wherein the transient signal characteristics in S3 include:
variance Va, peak factor C, pulse factor I, and margin factor C of transient signaleKurtosis factor K, form factor SfAnd a skewness factor S.
7. The method for identifying a low altitude unmanned aerial vehicle based on radio frequency characteristics of a data transmission station according to claim 1, wherein the identifying transient signal characteristics in S4 based on a K-nearest neighbor algorithm comprises:
s4.1, reading a transient signal characteristic training sample set X ═ X1;X2;…;XN]And testing the transient signal sample data set Y ═ Y1;Y2…;YJ]Each sample is m-dimensional data;
s4.2, carrying out zero equalization on each column of the transient signal characteristic training sample set X;
s4.3, calculating covariance matrix
Figure FDA0002998613400000031
S4.4, calculating the eigenvalue lambda of the covariance matrix Ci
S4.5, calculating the identification contribution rate of each feature
Figure FDA0002998613400000032
S4.6, calculating test sample data YjAnd X in the training sample setiIs a distance of
Figure FDA0002998613400000033
Wherein, thetakFor the recognition contribution, x, of the k-dimensional feature in the training samplekFor training sample XiThe k-dimension feature of (1), ykTo test sample data YjThe k-dimensional feature of (1);
s4.7, sorting the training samples from small to large according to the distance, and selecting the first K training samples X' with the minimum distance from the training sample set as [ X ═ X1';X2';…;XK']And the corresponding D' ═ D1';D2';…;DK']D' is the number of test samples YjSet of distances from each sample in the set X', DK' is the number of test samples YjDistance from the kth sample in the set of X';
s4.8, calculating the weight
Figure FDA0002998613400000034
S4.9, calculating test sample data YjProbability of belonging to class label (x):
Figure FDA0002998613400000041
wherein, WkIs' WiThe weight in (1) belonging to class (label (x));
S4.10、Yjthe category corresponding to the maximum probability value is YjThe category to which it belongs.
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