CN114781512A - Electromagnetic target track fitting method based on multi-source heterogeneous data fusion - Google Patents

Electromagnetic target track fitting method based on multi-source heterogeneous data fusion Download PDF

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CN114781512A
CN114781512A CN202210427449.0A CN202210427449A CN114781512A CN 114781512 A CN114781512 A CN 114781512A CN 202210427449 A CN202210427449 A CN 202210427449A CN 114781512 A CN114781512 A CN 114781512A
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严牧
杨健
解凯
马钰
邢伟宁
肖德政
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32802 Troops Of People's Liberation Army Of China
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Abstract

The invention discloses an electromagnetic target track fitting method based on multi-source heterogeneous data fusion, which is realized by an observation platform and a track fitting processing center server, and comprises the following steps: each observation platform sends the acquired data to a track fitting processing center server; the flight path fitting processing center server performs fusion processing on electromagnetic target data of each observation platform, classifies the electromagnetic targets, and performs flight path fusion on the classified electromagnetic targets; and the track fitting processing center server distributes the class label information and the data matched with the electromagnetic targets to corresponding observation platforms, and each observation platform finishes the classification and track fusion of the electromagnetic targets in the platform. According to the invention, under the condition that a large amount of missing or invalid data exist in the total observed data of the electromagnetic target characteristics, the fusion of multi-source heterogeneous data of the electromagnetic target characteristics is realized by recovering and complementing the low-rank observed data matrix.

Description

Electromagnetic target track fitting method based on multi-source heterogeneous data fusion
Technical Field
The invention relates to the field of target tracking, in particular to an electromagnetic target track fitting method based on multi-source heterogeneous data fusion.
Background
At present, the track fitting of an airborne electromagnetic target is one of key problems to be solved in air detection and target tracking, and the method aims to acquire electromagnetic and azimuth characteristics of a plurality of electromagnetic targets in an airspace through an observation platform on the ground, distinguish the plurality of unmarked electromagnetic targets in the airspace and complete the track fitting of each target.
The traditional track fitting mainly adopts a least square method, a spline interpolation method and the like to fit the track. Taking a spline interpolation method as an example, the method constructs an interpolation polynomial in a certain form, and solves a smooth curve passing through the point trace set by using the acquired discrete square locus trace information so as to approximate the real flight path of the target.
The technical scheme of the flight path fitting based on the least square method has the following defects:
firstly, the technical scheme can only fit a specified interpolation function curve, and cannot realize accurate fitting for a target track with high complexity, strong maneuverability and high randomness.
Secondly, the technical scheme needs a large amount of intensive track data to realize accurate target track fitting. If the observation frequency of the observation platform is relatively low, the real track cannot be accurately fitted.
Thirdly, the technical scheme only carries out the track fusion aiming at the azimuth information of the same target, and when the observation platform observes a plurality of targets simultaneously, if the observation platform does not contain the label information of different targets, the greater error of the track fitting is possibly caused by the confusion and the error separation of the target information.
The technical scheme of the flight path fitting based on the spline interpolation method enables a flight path fitting algorithm to have higher accuracy and rationality through deep learning of a neural network, and reduces the error between the flight path fitting algorithm and a real flight path. The scheme uses a large amount of electromagnetic and coordinate data to carry out model training on the neural network, and realizes the detection and track fitting of a plurality of targets, but the scheme has the following defects:
firstly, the training cost of the technical scheme is large. For new or unknown types of electromagnetic targets, effective target detection and track fitting cannot be achieved.
Secondly, the technical scheme has strict requirements on the input format of data. If the observation data of the observation platform does not meet the input data format during training, or missing data and abnormal data exist, the influence on target detection is large, and even effective track fitting cannot be performed.
Thirdly, the technical scheme belongs to a 'black box' model, target data are input into the model, an improved spline interpolation function curve is output, and the model does not have clear mathematical and physical significance. The flight path fitting result has poor interpretability for non-experts, and the reliability is difficult to evaluate. In practical applications, there may be an untrusted user of the model.
Disclosure of Invention
The invention discloses an electromagnetic target track fitting method based on multisource heterogeneous data fusion, which aims at solving the problem of how to realize track fitting of multisource heterogeneous data of an aerial electromagnetic target under the conditions that a plurality of observation platforms exist and the formats of collected target characteristic data are different, and is realized by the observation platforms and a track fitting processing center server, wherein the ground observation platforms are used for collecting data of the electromagnetic target in an aerial domain, and the track fitting processing center server is used for receiving the data of the electromagnetic target collected by the observation platforms and summarizing and processing the data, and the method comprises the following steps:
s1, the observation platform acquires data of the electromagnetic target in the airspace;
and S2, each observation platform sends the collected data to a track fitting processing center server.
And S3, the track fitting processing center server performs fusion processing on the electromagnetic target data of each observation platform, classifies the electromagnetic targets based on the fused data, and performs track fusion on the classified electromagnetic targets.
And S4, the track fitting processing center server distributes the class label information and the data matched with the electromagnetic target to the corresponding observation platform.
And S5, completing the electromagnetic target classification and track fusion in the platform by each observation platform according to the received data from the track fitting processing center server.
The step S1 includes:
through a plurality of observation platforms, a plurality of electromagnetic targets in the airspace are observed and data are collected, and the collected data comprise electromagnetic characteristic data such as wavelength, frequency spectrum and power of electromagnetic target radiation signals and position characteristic data such as position longitude and latitude, height and pitch angle of the electromagnetic targets.
And the electromagnetic target data are sparsely sampled at mutually spaced sampling moments among the observation platforms. Therefore, the workload of a single platform is reduced, and the trace points of different moments in the target navigation are acquired to the maximum extent. The electromagnetic characteristics of the same target have stability when observed at different moments, but the observation moments of a single platform are sparse, and the observation data volume is small, so that the electromagnetic characteristics of different electromagnetic targets cannot be distinguished in the platform.
In step S2, the data collected by each observation platform is heterogeneous data, and the track fitting center server summarizes the heterogeneous data into matrix data with a partial missing value to obtain a multi-source heterogeneous data set.
The data collected by the observation platform comprises two parts of electromagnetic characteristics and azimuth characteristics of the target. The orientation features are the basic data that all platforms can observe. Due to the limitation of the functions of each observation platform and the difference between different platforms, for the complex electromagnetic characteristics of the target, each platform can only observe and collect part of the characteristic information, and the formats of the characteristic data are different. Therefore, the heterogeneous data of each observation platform is sent to the track fitting center server and is summarized into a matrix form with partial missing values.
The step S3 includes:
s31, performing fusion processing on the multi-source heterogeneous data set to obtain a complete observation data matrix;
the electromagnetic characteristic vectors observed for the same electromagnetic target have high correlation at different platforms and different moments. Therefore, the rank of the multi-source heterogeneous data matrix is far smaller than the number of rows of the matrix. For the sparse low-rank matrix, missing data in the matrix can be complemented through a low-rank matrix recovery algorithm, so that a complete observation data matrix of a plurality of electromagnetic targets is recovered and obtained.
Firstly, a matrix D composed of all electromagnetic characteristic data is extracted from a multi-source heterogeneous data set. Matrix D contains partial missing values. The matrix D contains electromagnetic characteristic data of k electromagnetic targets, and a matrix recovery and completion method is used for solving the matrix D to obtain a complete observation data matrix A*。
The matrix D is solved by using a matrix recovery and completion method to obtain a complete observation data matrix A*The method comprises the following steps:
an observation data matrix A is constructed by utilizing a matrix D, and the matrix A is decomposed into two low-dimensional matrixes U and V with the same rank by utilizing a matrix decomposition method, wherein U belongs to Rm×k，V∈Rk×nSolving the optimal solution of the matrix A by constructing an observation optimization function, wherein the expression of the observation optimization function is as follows:
Figure BDA0003608933610000041
wherein beta represents a penalty parameter, and Lambda epsilon Rm×n，Rm×nRepresenting a matrix of m rows and n columns with real numbers, a is a lagrange multiplier matrix,<.，.>representing matrix inner product operation, | | | | non-conducting1(| | | purple hair)FRespectively representing a 1 norm and an F norm. Under the condition that the first-order gradient of the observation optimization function is 0, the observation optimization function obtains the value of the matrix A with the minimum value, namely the optimal solution A of the matrix A*。
Adopting a successive iteration method for the observation optimization function to solve the optimal solution A of the matrix A*Initializing the integral observation data matrix A to obtain an estimated value A thereof when the number of initialization iterations j is equal to 00To the matrix A0Performing maximum rank decomposition to obtain a matrix V0，V0∈Rk×nInitializing the Lagrange multiplier matrix to obtain Lambda0，Λ0∈Rm×nIn each iteration, calculating U+，V+The calculation formula is as follows:
Figure BDA0003608933610000042
in the formula of U+，V+Respectively representing corresponding matrixes obtained after carrying out one-time iterative optimization on the matrixes U and V,
Figure BDA0003608933610000043
respectively represent U+Moore-penes generalized Inverse matrix of V (Moore-Penrose Pseudo-Inverse); in each iteration, calculate A+The calculation formula is as follows:
Figure BDA0003608933610000044
wherein, A+The matrix value obtained after one-time iterative optimization is carried out on the matrix A is represented, and the expression of the function S () is S (x, tau): sign (x) max (| x | - τ, 0). In each iteration, a is calculatedj+1The calculation formula is as follows:
Λj+1＝Λj+β(Uj+1Vj+1-Aj+1).
wherein, Vj，Uj，Aj，ΛjRepresents the values of the matrix V, U, A, Λ after the jth iteration, Vj+1，Uj+1，Aj+1，Aj+1Representing the values of the matrix V, U, A and Λ after the j +1 th iteration;
by a jth iterationThe matrix value V obtained by the generationj，Uj，Aj，ΛjCalculating the matrix value V of the j +1 th iterationj +1，Uj+1，Aj+1，Aj+1Judging whether the calculated matrix value is converged, if not, continuing to perform the next iteration, if so, terminating the iteration, and at the moment, determining the calculated value of the matrix A as the optimal solution A of the matrix A*And taking the optimal solution as a complete observation data matrix.
The matrix A is decomposed by a matrix decomposition method, and the matrix decomposition method is a maximum matrix rank decomposition method.
S32, classifying the electromagnetic targets by a clustering method according to the correlation of the electromagnetic characteristic data of the electromagnetic targets;
in a complete observation data matrix, the similarity between the electromagnetic characteristic data vectors corresponding to each electromagnetic target is calculated, and the electromagnetic targets are clustered according to the numerical value of the similarity, so that the classification of all the electromagnetic targets is realized.
S33, matching the electromagnetic characteristic data of the electromagnetic targets in each category with the position characteristic data of the electromagnetic targets, extracting a square locus information set of each electromagnetic target in a certain period of time, and fitting the tracks of the corresponding electromagnetic targets by using the square locus information set.
The method for fitting the flight path of the corresponding electromagnetic target by utilizing the azimuth trajectory information set comprises the following steps: fitting the flight path by using a polynomial curve, and determining the coefficient of the polynomial curve by using a minimum error criterion;
the determining the coefficients of the polynomial curve by using the error minimum criterion comprises:
the expression of the polynomial curve for track fitting is:
y＝a0+a1x+a2x2+…+akxk，
wherein, [ x, y]Is the independent variable and dependent variable of the polynomial curve, [ a ]0，a1，a2，…，ak]Is the coefficient of the polynomial curve, k is the order of the polynomial curve;
the sum of the distances from each discrete square locus trace of the electromagnetic target to the polynomial curve is expressed as the sum of squared deviations R2：
Figure BDA0003608933610000051
Wherein n is the number of square loci, yiAnd taking the value of the dependent variable of the ith position locus of the electromagnetic target when the x is taken out from the independent variable. Solving a minimum value point of the deviation square sum, and constructing a non-homogeneous linear equation system related to the coefficient matrix when the first derivative of the deviation square sum to each coefficient of the polynomial curve is 0:
Figure BDA0003608933610000052
and solving the non-homogeneous linear equation system related to the coefficient matrix to obtain the coefficient of the polynomial curve.
The step S4 includes:
and matching the classified class label information of the electromagnetic targets with the data information of the corresponding electromagnetic targets by the track fitting processing center server, and sending the matched data to an observation platform for acquiring the data of the electromagnetic targets.
The step S5 includes:
and each observation platform divides the data belonging to different electromagnetic targets in the platform according to the category label information acquired from the track fitting processing center server, so that the track fitting of each electromagnetic target in a single observation platform is realized.
The beneficial effects of the invention are as follows:
under the condition that a large amount of missing or invalid data exists in the total observation data of the electromagnetic target characteristics, the fusion of multi-source heterogeneous data of the electromagnetic target characteristics is realized by restoring and complementing the low-rank observation data matrix.
Under the condition that a plurality of aerial electromagnetic targets are observed, the invention realizes the efficient and accurate detection and classification of the label-free mixed target group by carrying out cluster analysis on the correlation coefficient of the target characteristics.
The invention can realize the fitting of each target track with high precision by utilizing the observation data after the fusion processing and the target detection under the framework of the track fitting processing center server. And a single platform can realize simple and effective target track fitting only based on small amount of self observation data by using target label information issued by the server.
Under the conditions that a plurality of observation platforms exist and the collected target characteristic data formats are different, the fusion of multi-source heterogeneous data is effectively realized; under the condition that a large amount of missing or invalid data exists in the observed data, the recovery and completion of the observed data are realized, so that the track fitting can be better carried out. According to the invention, under the condition that a plurality of targets are observed simultaneously and the collected target point trace set is sparse, the detection classification and track fitting of the targets are realized.
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FIG. 1 is a process flow diagram of the method of the present invention;
FIG. 2 is a flow chart of the specific processing of the server of the track fitting processing center according to the method of the present invention.
Detailed Description
For a better understanding of the present disclosure, an example is given here.
FIG. 1 is a process flow diagram of the method of the present invention; FIG. 2 is a flow chart of the specific processing of the server of the track fitting processing center according to the method of the present invention. The invention discloses an electromagnetic target track fitting method based on multi-source heterogeneous data fusion, which is realized by a ground observation platform and a track fitting processing center server, wherein the ground observation platform is used for acquiring data of an electromagnetic target in an airspace, and the track fitting processing center server is used for receiving the data of the electromagnetic target acquired by the ground observation platform, summarizing and processing the data, and the method comprises the following steps:
s1, the ground observation platform acquires data of the electromagnetic target in the airspace;
and S2, each observation platform sends the collected data to a track fitting processing center server.
And S3, the track fitting processing center server performs fusion processing on the electromagnetic target data of each observation platform, classifies the electromagnetic targets based on the fused data, and performs track fusion on the classified electromagnetic targets.
And S4, the track fitting processing center server distributes the class label information and the data matched with the electromagnetic target to the corresponding observation platform.
And S5, completing the electromagnetic target classification and track fusion in the platform by each observation platform according to the received data from the track fitting processing center server.
The step S1 includes:
through a plurality of ground observation platforms, a plurality of electromagnetic targets in the airspace are observed and data are collected, and the collected data comprise electromagnetic characteristic data such as wavelength, frequency spectrum and power of electromagnetic target radiation signals and position characteristic data such as position longitude and latitude, height and pitch angle of the electromagnetic targets.
And the electromagnetic target data are sparsely sampled at mutually spaced sampling moments among the ground observation platforms. Therefore, the workload of a single platform is reduced, and the trace points at different moments in the target navigation are acquired to the maximum extent. The electromagnetic characteristics of the same target have stability when observed at different moments, but the observation moments of a single platform are sparse, the observation data volume is small, and the platform is not enough for distinguishing different electromagnetic targets.
In step S2, the data collected by each observation platform is heterogeneous data, and the track fitting center server summarizes the heterogeneous data into matrix data with a partial missing value to obtain a multi-source heterogeneous data set.
The data collected by the observation platform comprises two parts of electromagnetic characteristics and orientation characteristics of the target. The orientation features are the basic data that all platforms can observe. Due to the limitation of the functions of each observation platform and the difference between different platforms, for the complex electromagnetic characteristics of the target, each platform can only observe and collect part of the characteristic information, and the formats of the characteristic data are different. Therefore, the heterogeneous data of each observation platform is sent to the track fitting center server, and is summarized into a matrix form with partial missing values, as shown in the following table.
TABLE 1 aggregated examples of multi-source heterogeneous data matrices
(where X represents the corresponding electromagnetic signature of the line of data not observing the target)
Figure BDA0003608933610000081
The step S3 includes:
s31, performing fusion processing on the multi-source heterogeneous data set to obtain a complete observation data matrix;
the electromagnetic characteristic vectors observed for the same electromagnetic target have high correlation at different platforms and different moments. Therefore, the rank of the multi-source heterogeneous data matrix is much smaller than the number of rows of the matrix. For the sparse low-rank matrix, missing data in the matrix can be complemented through a low-rank matrix recovery algorithm, so that a complete observation data matrix of a plurality of electromagnetic targets is recovered and obtained.
First, from the multi-source heterogeneous data set, a matrix D composed of all electromagnetic characteristic data is extracted. Matrix D contains partial missing values. The matrix D contains electromagnetic characteristic data of k electromagnetic targets, and a matrix recovery and completion method is used for solving the matrix D to obtain a complete observation data matrix A*。
The matrix D is solved by using a matrix recovery and completion method to obtain a complete observation data matrix A*The method comprises the following steps:
an observation data matrix A is constructed by utilizing a matrix D, and the matrix A is decomposed into two low-dimensional matrixes U and V with the same rank by utilizing a matrix decomposition method, wherein U belongs to Rm×k，V∈Rk×nBy constructing observationsAnd (3) solving an optimal solution of the matrix A by using an optimization function, wherein the expression of the observation optimization function is as follows:
Figure BDA0003608933610000091
wherein, beta represents a penalty parameter, and Lambda epsilon Rm×n，Rm×nRepresenting a matrix of m rows and n columns with real numbers, a is a lagrange multiplier matrix,<.，.>representing matrix inner product operation, | | | | non-conducting1(| | | purple hair)FRespectively representing a 1-norm and an F-norm. Under the condition that the first-order gradient of the observation optimization function is 0, the observation optimization function obtains the value of the matrix A with the minimum value, namely the optimal solution A of the matrix A*。
Adopting a successive iteration method for the observation optimization function to solve the optimal solution A of the matrix A*Initializing the integral observation data matrix A to obtain an estimated value A thereof when the number of initialization iterations j is equal to 00To the matrix A0Performing maximum rank decomposition to obtain a matrix V0，V0∈Rk×nInitializing the Lagrange multiplier matrix to obtain Lambda0，Λ0∈Rm×nIn each iteration, calculating U+，V+The calculation formula is as follows:
Figure BDA0003608933610000092
in the formula of U+，V+Respectively representing corresponding matrixes obtained after one-time iterative optimization is carried out on the matrixes U and V,
Figure BDA0003608933610000093
respectively represent U+Moore-penes generalized Inverse matrix of V (Moore-Penrose Pseudo-Inverse); in each iteration, calculate A+The calculation formula is as follows:
Figure BDA0003608933610000094
wherein, A+The matrix value obtained after one-time iterative optimization is carried out on the matrix A is represented, and the expression of the function S () is S (x, tau): sign (x) max (| x | - τ, 0). In each iteration, a is calculatedj+1The calculation formula is as follows:
Λj+1＝Λj+β(Uj+1Vj+1-Aj+1)，
wherein, Vj，Uj，Aj，ΛjRepresents the values of the matrix V, U, A, Λ after the jth iteration, Vj+1，Uj+1，Aj+1，Aj+１Representing the values of the matrix V, U, A and Λ after the j +1 th iteration;
matrix value V obtained by jth iterationj，Uj，Aj，ΛjCalculating the matrix value V of the j +1 th iterationj +1，Uj+1，Aj+1，Λj+1Judging whether the calculated matrix value is converged, if not, continuing to perform the next iteration, if so, terminating the iteration, and the calculated value of the matrix A is the optimal solution A of the matrix A*And taking the optimal solution as a complete observation data matrix.
The matrix A is decomposed by a matrix decomposition method, and the matrix decomposition method is a maximum matrix rank decomposition method.
Matrix A*The method is solved and recovered by an observation matrix D containing partial missing values, and the matrix comprises a plurality of electromagnetic target complete observation data.
S32, classifying the electromagnetic targets by a clustering method according to the correlation of the electromagnetic characteristic data of the electromagnetic targets;
in a complete observation data matrix, the similarity between the electromagnetic characteristic data vectors corresponding to each electromagnetic target is calculated, and the electromagnetic targets are clustered according to the numerical value of the similarity, so that the classification of all the electromagnetic targets is realized.
Matrix A*Completes all the targets under multi-platform observationThe electromagnetic characteristic data, however, is from a plurality of different platforms, and there is no classification label information of targets in the observed data, the arrangement of the target characteristic vectors in the matrix rows has no regularity, and the track information belonging to different targets are mixed together, so that effective characteristic analysis and track fitting cannot be performed on each target. Thus, for matrix A*K-Means clustering analysis was performed.
For a matrix A containing k target electromagnetic characteristic data*，rank(A*) K. For a single target, the observed electromagnetic eigenvectors have a high degree of correlation,
Figure BDA0003608933610000101
using correlation coefficient as neighbor measure, and applying matrix A*Performing K-means cluster analysis. In the clustering result, the electromagnetic feature vectors contained in each class have high correlation, and the electromagnetic feature vectors between different classes are linearly independent. Therefore, each category represents all electromagnetic characteristic data of one electromagnetic target under the multi-observation platform. In the observation data without labels and multiple targets, the detection and classification of the targets are realized.
S33, matching the electromagnetic characteristic data of the electromagnetic targets in each category with the position characteristic data of the electromagnetic targets, extracting a square locus information set of each electromagnetic target in a certain period of time, and fitting the flight path of the corresponding electromagnetic target by using the square locus information set.
The method for fitting the flight path of the corresponding electromagnetic target by utilizing the azimuth trajectory information set comprises the following steps: fitting the flight path by using a polynomial curve, and determining the coefficient of the polynomial curve by using a minimum error criterion;
the determining the coefficients of the polynomial curve by using the error minimum criterion comprises:
the expression of the polynomial curve for the track fit is:
y＝a0+a1x+a2x2+…+akxk，
wherein, [ x, y [ ]]Is thatIndependent and dependent variables of polynomial curves, [ a ]0，a1，a2，…，ak]Is the coefficient of the polynomial curve, k is the order of the polynomial curve;
the sum of the distances from each discrete square locus trace of the electromagnetic target to the polynomial curve is expressed as the sum of squared deviations R2：
Figure BDA0003608933610000111
Wherein n is the number of square loci, yiAnd taking the value of the dependent variable of the ith azimuth locus trace of the electromagnetic target when the independent variable is taken as x. Solving a minimum value point of the deviation square sum, and constructing a non-homogeneous linear equation system related to the coefficient matrix when the first derivative of the deviation square sum to each coefficient of the polynomial curve is 0:
Figure BDA0003608933610000112
and solving the non-homogeneous linear equation system related to the coefficient matrix to obtain the coefficient of the polynomial curve.
Because the observation data of all the observation platforms to the electromagnetic targets at different moments are summarized in the track fitting central server, the target square position track information set contained in the total track fitting is very dense, the error between the track fitting result and the real track is very small, and the accuracy of the track fitting is very high.
The step S4 includes:
and the track fitting processing center server matches the classified class label information of the electromagnetic targets with the corresponding data information of the electromagnetic targets, and sends the matched data to an observation platform for acquiring the electromagnetic target data.
The step S5 includes:
and each observation platform divides the data belonging to different electromagnetic targets in the platform according to the category label information acquired from the track fitting processing center server, so that the track fitting of each electromagnetic target in a single observation platform is realized.
The specific flow of the track fitting processing is the same as the total track fitting processing flow in the track fitting central server. Because a single observation platform does not have the capabilities of large-scale data acquisition, data summarization and data processing, classification of an observation target into track fitting cannot be realized. In contrast, in the scheme, the track fitting of each electromagnetic target can be realized without acquiring additional observation data of other observation platforms on the basis of a small amount of own observation data of a single observation platform through corresponding target label information issued by the track fitting central server.
The above description is only an example of the present application and is not intended to limit the present application. Various modifications and changes may occur to those skilled in the art to which the present application pertains. Any modification, equivalent replacement, improvement or the like made within the spirit and principle of the present application shall be included in the scope of the claims of the present application.

Claims (10)

1. The method is characterized by being realized through an observation platform and a track fitting processing center server, wherein the observation platform is used for acquiring data of the electromagnetic target in an airspace, and the track fitting processing center server is used for receiving the data of the electromagnetic target acquired by the observation platform, summarizing and processing the data, and comprises the following steps:
s1, the observation platform acquires data of the electromagnetic target in the airspace;
s2, each observation platform sends the collected data to a track fitting processing center server;
s3, the track fitting processing center server performs fusion processing on the electromagnetic target data of each observation platform, classifies the electromagnetic targets based on the fused data, and performs track fusion on the classified electromagnetic targets;
s4, the track fitting processing center server distributes the class label information and data matched with the electromagnetic target to the corresponding observation platform;
and S5, completing electromagnetic target classification and track fusion inside each observation platform according to the received data from the track fitting processing center server.
2. The method for electromagnetic target track fitting based on multi-source heterogeneous data fusion according to claim 1, wherein the step S1 includes:
through a plurality of observation platforms, a plurality of electromagnetic targets in the airspace are observed and data are collected, and the collected data comprise electromagnetic characteristic data such as wavelength, frequency spectrum and power of electromagnetic target radiation signals and position characteristic data such as position longitude and latitude, height and pitch angle of the electromagnetic targets.
3. The method for electromagnetic target track fitting based on multi-source heterogeneous data fusion of claim 1, wherein the electromagnetic target data are sparsely sampled at mutually spaced sampling moments between each observation platform.
4. The electromagnetic target track fitting method based on multi-source heterogeneous data fusion of claim 1, wherein in step S2, the data collected by each observation platform is heterogeneous data, and the track fitting center server summarizes the heterogeneous data into matrix-form data with partial missing values to obtain a multi-source heterogeneous data set.
5. The method according to claim 1, wherein the step S3 includes:
s31, performing fusion processing on the multi-source heterogeneous data set to obtain a complete observation data matrix;
s32, classifying the electromagnetic targets by a clustering method according to the correlation of the electromagnetic characteristic data of the electromagnetic targets;
s33, matching the electromagnetic characteristic data of the electromagnetic targets in each category with the position characteristic data of the electromagnetic targets, extracting a square locus information set of each electromagnetic target in a certain period of time, and fitting the tracks of the corresponding electromagnetic targets by using the square locus information set.
6. The method of claim 5, wherein the electromagnetic target trajectory fitting method based on multi-source heterogeneous data fusion,
the step S31 includes:
extracting a matrix D formed by all electromagnetic characteristic data from the multi-source heterogeneous data set; the matrix D contains electromagnetic characteristic data of k electromagnetic targets, and a matrix recovery and completion method is used for solving the matrix D to obtain a complete observation data matrix A*；
The matrix D is solved by using a matrix recovery and completion method to obtain a complete observation data matrix A*The method comprises the following steps:
the method comprises the following steps of constructing an observation data matrix A by using a matrix D, decomposing the matrix A into two low-dimensional same-rank matrices U and V by using a matrix decomposition method for the observation data matrix A, and solving an optimal solution of the matrix A by constructing an observation optimization function, wherein the expression of the observation optimization function is as follows:
Figure FDA0003608933600000021
wherein beta represents a penalty parameter, and Lambda epsilon Rm×n，Rm×nRepresenting a matrix of m rows and n columns with real numbers, a is a lagrange multiplier matrix,<.,.>representing matrix inner product operation, | | | non-calculation1(| | | purple hair)FRespectively represent 1 norm and F norm; under the condition that the first-order gradient of the observation optimization function is 0, the observation optimization function obtains the value of the matrix A with the minimum value, namely the optimal solution A of the matrix A*；
Adopting a successive iteration method for the observation optimization function to solve the optimal solution A of the matrix A*Initializing the complete observation data matrix A to obtain the estimation, where the number of initialization iterations j is equal to 0Value A0To the matrix A0Carrying out maximum rank decomposition to obtain a matrix V0Initializing the Lagrange multiplier matrix to obtain Lambda0In each iteration, calculating U+,V+The calculation formula is as follows:
Figure FDA0003608933600000022
in the formula of U+,V+Respectively representing corresponding matrixes obtained after one-time iterative optimization is carried out on the matrixes U and V,
Figure FDA0003608933600000031
respectively represent U+Moore-penes generalized inverse matrix of V; in each iteration, calculate A+The calculation formula is as follows:
Figure FDA0003608933600000032
wherein A is+Representing a matrix value obtained after one-time iterative optimization is performed on the matrix A, wherein the expression of the function S () is S (x, tau): sign (x) max (| x | -tau, 0); in each iteration, a is calculatedj+1The calculation formula is as follows:
Λj+1＝Λj+β(Uj+1Vj+1-Aj+1)，
wherein, Vj,Uj,Aj,ΛjRepresents the values of the matrix V, U, A, Λ after the jth iteration, Vj+1,Uj+1,Aj+1,Λj+1Representing the values of the matrix V, U, A and Λ after the j +1 th iteration;
matrix value V obtained by jth iterationj,Uj,Aj,ΛjCalculating the matrix value V of the j +1 th iterationj+1,Uj+1,Aj+1,Λj+1Judging whether the calculated matrix value is converged, if not, continuing to perform the next iteration,if convergence and iteration are terminated, the value of the matrix A obtained by calculation at the moment is the optimal solution A of the matrix A*And taking the optimal solution as a complete observation data matrix.
7. The method of claim 5, wherein the electromagnetic target trajectory fitting method based on multi-source heterogeneous data fusion,
in the step S32, in the complete observation data matrix, the similarity between the electromagnetic feature data vectors corresponding to each electromagnetic target is calculated, and the electromagnetic targets are clustered according to the numerical value of the similarity, so as to classify all the electromagnetic targets.
8. The method of claim 5, wherein the electromagnetic target trajectory fitting method based on multi-source heterogeneous data fusion,
the method for fitting the flight path of the corresponding electromagnetic target by using the azimuth trajectory information set comprises the steps of fitting the flight path by using a polynomial curve and determining the coefficient of the polynomial curve by using an error minimum criterion.
9. The method for electromagnetic target track fitting based on multi-source heterogeneous data fusion according to claim 1,
the step S4 includes:
and the track fitting processing center server matches the classified class label information of the electromagnetic targets with the corresponding data information of the electromagnetic targets, and sends the matched data to an observation platform for acquiring the electromagnetic target data.
10. The method for electromagnetic target track fitting based on multi-source heterogeneous data fusion of claim 1,
the step S5 includes:
and each observation platform divides the data belonging to different electromagnetic targets in the platform according to the category label information acquired from the track fitting processing center server, so that the track fitting of each electromagnetic target in a single observation platform is realized.
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