CN113516760B - Electromagnetic spectrum data marking and complementing method - Google Patents

Electromagnetic spectrum data marking and complementing method Download PDF

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CN113516760B
CN113516760B CN202110858400.6A CN202110858400A CN113516760B CN 113516760 B CN113516760 B CN 113516760B CN 202110858400 A CN202110858400 A CN 202110858400A CN 113516760 B CN113516760 B CN 113516760B
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申坤雨
林静然
利强
潘晔
邵怀宗
胡全
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University of Electronic Science and Technology of China
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Abstract

The invention discloses an electromagnetic spectrum data labeling and complementing method, which comprises the steps of observing and collecting an electromagnetic environment through a sensor to obtain observed electromagnetic spectrum data, then establishing a three-dimensional tensor labeling model according to the observed electromagnetic spectrum data, then determining normal electromagnetic spectrum data according to the three-dimensional labeling model and completing the labeling and complementing, slicing the observed electromagnetic spectrum data, aligning and stacking each piece of observed electromagnetic spectrum data on a three-dimensional coordinate axis to establish a three-dimensional model, and labeling and filling observation values of sampling frequency points on all single sampling time slots to corresponding positions in the three-dimensional model to obtain the three-dimensional tensor labeling model.

Description

Electromagnetic spectrum data marking and complementing method
Technical Field
The invention belongs to the technical field of electromagnetic spectrum data, and particularly relates to an electromagnetic spectrum data labeling and complementing method.
Background
The electromagnetic spectrum observation can provide a data base for reasonably distributing working frequency bands for electronic equipment, can also provide an actual basis for resisting wireless eavesdropping, electromagnetic interference and interference, and is also widely applied to the fields of electronic equipment electromagnetic compatibility debugging, radio emission, received signal quality detection and the like.
With the electromagnetic space entering the big data era, various communication devices are increasing, the signal patterns are more complex, a large amount of noise and interference exist in the electromagnetic environment, so that the data volume observed by the electromagnetic spectrum is increased, but the value density is reduced, namely, the electromagnetic spectrum data is lost or abnormal due to the large amount of noise, interference and abnormal device, so that errors are generated between the observed electromagnetic spectrum data and the actually used normal electromagnetic spectrum data.
On one hand, in the prior art, the electromagnetic spectrum data observed is more accurate by demodulating an authorized signal or detecting a pilot frequency, on the basis of accurate priori knowledge, better performance can be obtained in an additive white gaussian noise channel, but the sensing performance is greatly reduced in an electromagnetic environment with high signal density and high complexity, and the problems of computational complexity, overlarge resource consumption, processing delay and the like in the existing environment are difficult to be loaded in the prior art.
Therefore, how to label and complement electromagnetic spectrum data in a complex electromagnetic environment, so as to reduce the error between the electromagnetic spectrum data and normal electromagnetic spectrum data, and reduce resource consumption and delay at the same time is a technical problem to be solved by those skilled in the art.
Disclosure of Invention
The invention aims to solve the technical problems that the prior art cannot label and complement electromagnetic spectrum data in a complex electromagnetic environment, and has high resource consumption and high delay, and provides an electromagnetic spectrum data labeling and complementing method.
The technical scheme of the invention is as follows: a method of electromagnetic spectrum data annotation completion, the method comprising the steps of:
s1, observing an electromagnetic environment through a sensor and acquiring observed electromagnetic spectrum data;
s2, establishing a three-dimensional tensor labeling model according to the observed electromagnetic spectrum data;
and S3, determining normal electromagnetic spectrum data according to the three-dimensional tensor annotation model and completing annotation completion.
Further, the observed electromagnetic spectrum data is electromagnetic spectrum data within a preset time range and a preset frequency band range, and the observed electromagnetic spectrum data includes normal electromagnetic spectrum data and abnormal electromagnetic spectrum data.
Further, the abnormal electromagnetic spectrum data is specifically spectrum data corresponding to environmental noise, electromagnetic interference, equipment abnormality and observation data incompleteness in an electromagnetic environment, and the normal electromagnetic spectrum data is specifically real electromagnetic spectrum data excluding the abnormal electromagnetic spectrum data in the electromagnetic environment.
Further, the step S2 specifically includes the following sub-steps:
s21, discretely dividing the observed electromagnetic spectrum data into a plurality of sampling time slots and a plurality of sampling frequency points, and labeling observed values of the sampling frequency points on all the single sampling time slots;
s21, slicing the observed electromagnetic spectrum data according to a preset time period;
s23, taking the preset time period, the sampling time slot and the sampling frequency point as three-dimensional coordinate axes;
and S24, aligning and stacking each piece of observed electromagnetic spectrum data on the three-dimensional coordinate axis to establish a three-dimensional model, and filling the observed value labels of the sampling frequency points on all the single sampling time slots to corresponding positions in the three-dimensional model to obtain a three-dimensional tensor label model.
Further, the step S3 specifically includes the following sub-steps:
s31, establishing an optimized objective function according to the relation among the observed electromagnetic spectrum data, the normal electromagnetic spectrum data and the abnormal electromagnetic spectrum data;
s32, determining an optimal solution of the optimized objective function through an augmented Lagrange function;
and S33, determining the normal electromagnetic spectrum data based on the optimal solution, and completing the labeling and completion of the normal electromagnetic spectrum data.
Further, the optimization objective function is specifically shown as follows:
Figure BDA0003184856990000021
in the formula (I), the compound is shown in the specification,
Figure BDA0003184856990000025
data expressed as a normal electromagnetic spectrum, and>
Figure BDA0003184856990000026
for a set of normal electromagnetic spectrum data samples, a->
Figure BDA0003184856990000022
For observing a sample set of electromagnetic spectrum data, a decision is made as to whether a sample set is present>
Figure BDA0003184856990000023
And &>
Figure BDA0003184856990000024
Is an auxiliary variable, s.t. is a constraint condition, lambda is a penalty factor, | | · |. Luminance * Expressing the trace norm of the matrix, | · | luminance 1 Representing the 1-norm, alpha, of the matrix n Is the weight of the norm of each partial matrix trace, M n(n) 、Q n(n) Respectively representing tensors M n And Q n The resulting matrix is expanded in dimension n.
Compared with the prior art, the method has the following beneficial effects:
(1) According to the invention, the electromagnetic environment is observed through the sensor and the observed electromagnetic spectrum data is acquired, then the three-dimensional tensor labeling model is established according to the observed electromagnetic spectrum data, the normal electromagnetic spectrum data is determined according to the three-dimensional labeling model and the labeling completion is completed, the observed electromagnetic spectrum data is sliced, each piece of observed electromagnetic spectrum data is aligned and stacked on the three-dimensional coordinate axis to establish the three-dimensional model, the observed values of the sampling frequency points on all the single sampling time slots are labeled and filled into the corresponding positions in the three-dimensional model to obtain the three-dimensional tensor labeling model, the electromagnetic spectrum data can be labeled and completed in the complex electromagnetic environment, and further the error between the electromagnetic spectrum data and the normal electromagnetic spectrum data is reduced.
(2) According to the invention, by setting an optimized objective function, the separation of normal electromagnetic spectrum data and abnormal electromagnetic spectrum data can be realized, and the problem of spectrum situation labeling and completion under the condition of abnormal observation data is solved.
Drawings
Fig. 1 is a schematic flow chart of an electromagnetic spectrum data annotation completion method according to an embodiment of the present invention;
fig. 2 is a schematic diagram illustrating a three-dimensional labeling model constructed by observing electromagnetic spectrum data according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
Aiming at the technical problems that the prior art cannot label and complement electromagnetic spectrum data in a complex electromagnetic environment, and has high resource consumption and high delay, the application provides an electromagnetic spectrum data labeling and complementing method, as shown in fig. 1, the method comprises the following steps:
s1, observing an electromagnetic environment through a sensor and acquiring observed electromagnetic spectrum data.
In this application embodiment, survey electromagnetic spectrum data for predetermineeing the electromagnetic spectrum data in time range and the predetermined frequency band range, survey electromagnetic spectrum data including normal electromagnetic spectrum data and unusual electromagnetic spectrum data, unusual electromagnetic spectrum data specifically are environmental noise, electromagnetic interference, equipment in the electromagnetic environment and survey the incomplete spectrum data that corresponds of data, normal electromagnetic spectrum data specifically are the true electromagnetic spectrum data of excluding unusual electromagnetic spectrum data in the electromagnetic environment.
And S2, establishing a three-dimensional tensor labeling model according to the observed electromagnetic spectrum data.
In the embodiment of the application, S21, discretely dividing the observed electromagnetic spectrum data into a plurality of sampling time slots and a plurality of sampling frequency points, and labeling observed values of the sampling frequency points on all the single sampling time slots;
s21, slicing the observed electromagnetic spectrum data according to a preset time period;
s23, taking the preset time period, the sampling time slot and the sampling frequency point as three-dimensional coordinate axes;
and S24, aligning and stacking each piece of observed electromagnetic spectrum data on the three-dimensional coordinate axis to establish a three-dimensional model, and filling the observed value labels of the sampling frequency points on all the single sampling time slots to corresponding positions in the three-dimensional model to obtain a three-dimensional tensor label model.
In a specific application scenario, an electromagnetic spectrum data set Ω in a certain time range and a certain frequency band range is acquired as a target, i.e., electromagnetic spectrum data is observed. Wherein the time range and the frequency band range are discretely divided into M sampling time slots (time points) t i i =1,2, \ 8230and M and N sampling frequency points f j j =1,2, \ 8230, N. The minimum data unit of the data set is the observation amplitude of the signal on a single sampling time slot and a sampling frequency point, and the observation value is marked as
Figure BDA0003184856990000031
The dataset Ω may be represented as:
Figure BDA0003184856990000041
the spectrum raw data is sliced in a unit of a longer time period (such as one day), and is aligned and stacked in time slots and frequency points. And (3) constructing a data model of the spectrum tensor label (asking what label the label here refers to) of the three-dimensional dimension of the time period (Z axis), the time slot (X axis) and the frequency point (Y axis). In this model, a two-dimensional matrix slice of spectral data satisfying z = k in the three-dimensional tensor can be determined by the k-th time period (day) of observation. And filling each observation data value in the original time slot-frequency point two-dimensional matrix as a data label in the three-dimensional tensor model to a corresponding position to obtain the three-dimensional tensor label model, wherein as shown in fig. 2, the frequency in fig. 2 is a sampling frequency point, and the time slot is a sampling time slot.
And S3, determining normal electromagnetic spectrum data according to the three-dimensional tensor annotation model and completing annotation completion.
In this embodiment, the step S3 specifically includes the following sub-steps:
s31, establishing an optimized objective function according to the relation among the observed electromagnetic spectrum data, the normal electromagnetic spectrum data and the abnormal electromagnetic spectrum data;
s32, determining an optimal solution of the optimized objective function through an augmented Lagrange function;
and S33, determining the normal electromagnetic spectrum data based on the optimal solution, and completing the labeling and completion of the normal electromagnetic spectrum data.
In the embodiment of the present application, the optimization objective function is specifically as follows:
Figure BDA0003184856990000042
in the formula (I), the compound is shown in the specification,
Figure BDA0003184856990000047
is represented as normal electromagnetic spectrum data, is greater than or equal to>
Figure BDA0003184856990000048
For a set of normal electromagnetic spectrum data samples, a->
Figure BDA0003184856990000043
For observing a sample set of electromagnetic spectrum data, a decision is made as to whether a sample set is present>
Figure BDA0003184856990000044
And &>
Figure BDA0003184856990000045
Is an auxiliary variable, s.t. is a constraint condition, lambda is a penalty factor, | | · |. Luminance * To representThe trace norm, | · | of the matrix non-woven phosphor 1 Representing the 1-norm, alpha, of the matrix n Is the weight of the trace norm of each portion of the matrix, M n(n) 、Q n(n) Respectively representing tensors M n And Q n The resulting matrix is expanded in dimension n.
In a specific application scene, errors inevitably exist between observed data and actual frequency spectrum use conditions, and the errors are used in the constructed three-dimensional tensor data model
Figure BDA0003184856990000049
Representing the ideal tensor of spectral data, i.e., the normal electromagnetic spectral data. Because problems of environmental noise, electromagnetic interference, equipment abnormality, observation data insufficiency and the like exist in an actual observation environment, some abnormalities in the spectrum data can be caused, and the data tensor of the part of abnormalities is represented by epsilon, namely the abnormal electromagnetic spectrum data, so that the observed spectrum data tensor is/is greater than or equal to>
Figure BDA0003184856990000046
Is based on the data in the actual spectrum usage>
Figure BDA00031848569900000410
And error abnormal data epsilon caused by interference, abnormality and deficiency, and can be represented by the following relation:
Figure BDA0003184856990000051
by utilizing the low-rank characteristic that ideal spectrum data is highly correlated in a time domain, namely that the used frequency points are close, the amplitudes of the frequency points are close and the sparsity of abnormal data in the integral observed data tensor is considered to be on a plurality of different time slots of the same electronic equipment within a period of working time, the optimal objective function for labeling and complementing the ideal spectrum data in a sample set is obtained:
Figure BDA00031848569900000510
Figure BDA0003184856990000052
wherein the content of the first and second substances,
Figure BDA00031848569900000511
representing a three-dimensional tensor pick>
Figure BDA00031848569900000512
As a major part of the objective function; | Epsilon | non-woven phosphor 0 And the number of elements which are not 0 in the abnormal data three-dimensional tensor is represented (the single element in the abnormal data three-dimensional tensor is 0, namely the time slot and the signal amplitude data on the frequency point are not influenced by interference, abnormality and deletion, and the observed data completely conform to the use condition of a real frequency spectrum), and the observed data is multiplied by a penalty factor lambda and is added into a target function as a penalty term. Is at>
Figure BDA0003184856990000053
Under the constraint condition of (3), solving the minimization problem of the objective function can meet the ideal spectrum data tensor/based on the target function>
Figure BDA00031848569900000513
And the sparsity of the data with anomalies to a very small proportion of the overall observed data.
Since the problem is non-convex, the defect norm | | · | | luminance is not woven with tensor * To approximate rank of tensor, | | of tensor |. The | | luminance 0 Norm approximation | · | non conducting phosphor 1 Norm, the best convex approximation of the above optimized objective function is obtained:
Figure BDA00031848569900000514
Figure BDA0003184856990000054
/>
for the three-dimensional tensor labeling model, the trace norm can be expressed as the weighted average of the matrix trace norms of the tensor developed under each modality. Therefore, solving for ideal spectral annotation data is ultimately represented by the following optimization objective function:
Figure BDA0003184856990000055
Figure BDA0003184856990000056
three-dimensional tensor of ideal spectrum data needing to be solved
Figure BDA00031848569900000515
Can be further decomposed into a plurality of two-dimensional matrix data slices satisfying Z-axis coordinates Z = k:
Figure BDA0003184856990000057
wherein, X k Representing a two-dimensional matrix slice of signal amplitude data with time slot-frequency as two observation dimensions of data in the k-th time period (day). { X 1 ；X 2 ；…；X D Constitute all historical spectral data in the previous D time period ranges,
Figure BDA0003184856990000058
it represents the spectral observation data that has not been processed by the label completion algorithm in the current time period (day). By X D+1 Representative needs to be resolved, over from->
Figure BDA0003184856990000059
And an abnormal part is separated, so that the influences of data loss, noise interference, equipment abnormality and the like in the actual environment are reduced, and the ideal spectrum data (in a two-dimensional matrix slice form) in the D +1 time period (day) after the completion of the labeling is realized.
For the optimized objective function designed in the previous section:
Figure BDA0003184856990000061
Figure BDA0003184856990000062
the three-dimensional tensor of the ideal spectrum data is realized by iteratively solving the augmented Lagrange function of the optimization problem
Figure BDA00031848569900000619
Middle and last two-dimensional matrix data slice X D+1 And performing label completion. And adding the frequency spectrum observation data in the current time period into the historical frequency spectrum data for storage after the frequency spectrum observation data in the current time period is labeled and supplemented. In the next observation period, then { X } may be based 1 ；X 2 ；…；X D ；X D+1 Before the time, all historical spectrum data in D +1 time period range are judged, and spectrum observation data which are not processed by a marking completion algorithm in the D +2 time period (day) are judged>
Figure BDA0003184856990000063
And (5) performing label completion, and sequentially processing along with the lapse of the observation time period. First, an auxiliary variable is introduced>
Figure BDA0003184856990000064
And &>
Figure BDA0003184856990000065
Where initialization of the auxiliary variable is described, the initialization policy is randomly generated within the scope of X), re-representing the optimization objective function as £ based on £ r>
Figure BDA0003184856990000066
In the formula (I), the compound is shown in the specification,
Figure BDA00031848569900000621
is represented as normal electromagnetic spectrum data, is greater than or equal to>
Figure BDA00031848569900000620
For a set of normal electromagnetic spectrum data samples, a->
Figure BDA0003184856990000067
For observing a sample set of electromagnetic spectrum data, a decision is made as to whether a sample set is present>
Figure BDA0003184856990000068
And &>
Figure BDA0003184856990000069
Is an auxiliary variable, s.t. is a constraint condition, lambda is a penalty factor, | | · |. Luminance * Represents the trace norm of the matrix, | ·| non-woven phosphor 1 Representing the 1-norm, alpha, of the matrix n Is the weight of the trace norm of each portion of the matrix, M n(n) 、Q n(n) Respectively representing tensors M n And Q n The resulting matrix is expanded in dimension n.
Write the augmented Lagrangian function of the objective function:
Figure BDA00031848569900000610
wherein μ is [ μ ] 1 ,μ 2 ,…,μ N ]A penalty parameter vector is formed by the combined penalty parameter vector,
Figure BDA00031848569900000611
for the tensor of the lagrange multiplier,
Figure BDA00031848569900000612
express tensor pick>
Figure BDA00031848569900000613
And tensor>
Figure BDA00031848569900000614
The inner product between. For the above augmented Lagrangian function, the update is iterated
Figure BDA00031848569900000615
And &>
Figure BDA00031848569900000616
The concrete steps of solving are as follows:
a) Tensor labeling of observed spectral data input in a sample set
Figure BDA00031848569900000617
Initialization penalty parameter vector>
Figure BDA00031848569900000618
And setting a penalty parameter change factor rho.
b) Number of initialization iterations k =0, initialization of auxiliary variables
Figure BDA0003184856990000071
And the Lagrangian multiplier>
Figure BDA0003184856990000072
c) Calculated according to the following equation,
Figure BDA0003184856990000073
Figure BDA0003184856990000074
Figure BDA0003184856990000075
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003184856990000076
tensor, S, representing the folding transformation of the annotated data matrix into the corresponding modality ε [x]The soft threshold shrinking operator is expressed and specifically defined as:
Figure BDA0003184856990000077
d) Obtaining the tensor in the k +1 iteration process under the condition that other variables are solved and fixed
Figure BDA00031848569900000718
Analytic solution of (2):
Figure BDA0003184856990000079
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00031848569900000719
can be further decomposed into->
Figure BDA00031848569900000711
Figure BDA00031848569900000712
And representing the ideal spectrum two-dimensional matrix data slice in the current time period solved by the (k + 1) th iteration.
e) X when solved each iteration D+1 Sequence of
Figure BDA00031848569900000713
And when not converging, updating a Lagrange multiplier and a penalty parameter: />
Figure BDA00031848569900000714
Accumulating the iteration times, wherein k = k +1, and then turning to the step c) to continue execution; otherwise, when the tensor sequence is converged, the iteration is terminated, and the solved tensor is obtained at the moment
Figure BDA00031848569900000720
Is the optimal solution of the original optimization problem.
Zhang Liang
Figure BDA00031848569900000721
The method is ideal spectrum data which is recovered by marking and complementing actual observed spectrum data. Wherein the content of the first and second substances,
Figure BDA00031848569900000717
and slicing the ideal spectrum two-dimensional matrix data in the current time period after the label completion.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (1)

1. An electromagnetic spectrum data annotation completion method is characterized by comprising the following steps:
s1, observing an electromagnetic environment through a sensor and acquiring observed electromagnetic spectrum data;
s2, establishing a three-dimensional tensor labeling model according to the observed electromagnetic spectrum data;
s3, determining normal electromagnetic spectrum data according to the three-dimensional tensor annotation model and completing annotation completion;
the observed electromagnetic spectrum data is electromagnetic spectrum data within a preset time range and a preset frequency band range, and the observed electromagnetic spectrum data comprises normal electromagnetic spectrum data and abnormal electromagnetic spectrum data;
the abnormal electromagnetic spectrum data are spectrum data corresponding to environmental noise, electromagnetic interference, equipment abnormality and observation data incompleteness in an electromagnetic environment, and the normal electromagnetic spectrum data are real electromagnetic spectrum data excluding the abnormal electromagnetic spectrum data in the electromagnetic environment;
the step S2 specifically includes the following sub-steps:
s21, discretely dividing the observed electromagnetic spectrum data into a plurality of sampling time slots and a plurality of sampling frequency points, and labeling observed values of the sampling frequency points on all the single sampling time slots;
s21, slicing the observed electromagnetic spectrum data according to a preset time period;
s23, taking the preset time period, the sampling time slot and the sampling frequency point as three-dimensional coordinate axes;
s24, aligning and stacking each piece of observed electromagnetic spectrum data on the three-dimensional coordinate axis to establish a three-dimensional model, and filling observed value labels of sampling frequency points on all single sampling time slots to corresponding positions in the three-dimensional model to obtain a three-dimensional tensor label model;
the step S3 specifically includes the following sub-steps:
s31, establishing an optimized objective function according to the relation among the observed electromagnetic spectrum data, the normal electromagnetic spectrum data and the abnormal electromagnetic spectrum data;
s32, determining an optimal solution of the optimized objective function through an augmented Lagrange function;
s33, determining the normal electromagnetic spectrum data based on the optimal solution, and completing labeling and completion on the normal electromagnetic spectrum data;
the optimization objective function is specifically shown as follows:
Figure FDA0004101271160000011
in the formula (I), the compound is shown in the specification,
Figure FDA0004101271160000012
data expressed as a normal electromagnetic spectrum, and>
Figure FDA0004101271160000013
for normal electromagnetic spectrum dataSample set,. Or>
Figure FDA0004101271160000014
For observing a sample set of electromagnetic spectrum data, a decision is made as to whether a sample set is present>
Figure FDA0004101271160000021
And &>
Figure FDA0004101271160000022
Is an auxiliary variable, s.t. is a constraint condition, lambda is a penalty factor, | | · |. Luminance * Represents the trace norm of the matrix, | ·| non-woven phosphor 1 Representing the 1-norm, alpha, of the matrix n Is the weight of the norm of each partial matrix trace, M n(n) 、Q n(n) Respectively representing tensors M n And Q n The resulting matrix is expanded in dimension n. />
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