CN111474539A - Radar and AIS track association method based on improved grey association - Google Patents
Radar and AIS track association method based on improved grey association Download PDFInfo
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Abstract
The invention discloses a radar and AIS track association method based on improved grey association, which comprises the following steps: acquiring AIS track data and radar track data, and performing wavelet threshold denoising processing on the AIS track data and the radar track data to obtain a track data set; obtaining n in the track dataset1First AIS track data and n2A grey correlation coefficient between the first radar track data; constructing a first track incidence matrix according to the grey incidence coefficient; concentrating the flight path data by n1First AIS track data and n2Correlating the first radar track data to obtain an assignment problem mathematical model; and carrying out global optimal track association judgment on the first track association matrix by adopting a Hungary algorithm according to the assignment problem mathematical model to obtain an optimal solution matrix. The invention can solve the problem of local optimum judgment of grey track association and does not need to set the association thresholdAnd the process of ambiguity processing, and the track association precision is also improved.
Description
Technical Field
The invention relates to the field of multi-sensor track association, in particular to a radar and AIS track association method based on improved grey association.
Background
The association of radar and AIS tracks is one of important core technologies for the integration of AIS and radar tracks, and the quality of the integration of the tracks is directly influenced by the quality of the association performance. The students of the flight path association problem propose a plurality of methods, such as common statistical methods, fuzzy mathematical methods, classical distribution methods, neural network methods and the like. A plurality of uncertainties exist in the radar and AIS track association process, gray association analysis has the advantages of low requirements on sample size and no need of a typical distribution rule during analysis, and the method has great advantages for solving the track association problem.
However, the grey track correlation algorithm also has the defects that the correlation judgment is locally optimal, and the correlation threshold needs a large amount of experiments to be selected.
Disclosure of Invention
The invention aims to provide a radar and AIS track association method based on improved grey correlation, and aims to solve the problems that a grey track association algorithm adopted in the existing radar and AIS track association process has the defects that association judgment is locally optimal, an association threshold needs a large amount of experiments to be selected, and the like.
In order to solve the above problems, the present invention is realized by the following technical scheme:
a radar and AIS track association method based on improved gray association is characterized by comprising the following steps: and S1, acquiring AIS track data and radar track data, and performing wavelet threshold denoising processing on the AIS track data and the radar track data to obtain a track data set. Step S2, acquiring n in the track data set1First AIS track data and n2The grey correlation coefficient between the first radar track data is set. And step S3, constructing a first track incidence matrix according to the grey incidence coefficients. Step S4, collecting the flight path data set n1First AIS track data and n2Correlating the first radar track data to obtain an assignment problem mathematical model; and carrying out global optimal track association judgment on the first track association matrix by adopting a Hungary algorithm according to the assignment problem mathematical model to obtain an optimal solution matrix.
Preferably, the step S1 includes: decomposing the AIS track data and the radar track data by adopting multi-resolution analysis characteristics and a Mallat algorithm to obtain a low-frequency part and a high-frequency part;
s1.1, performing 4-layer wavelet decomposition on the AIS track data and the radar track data by adopting a wave basis function to obtain 4-level wavelet coefficients with different scales and scale coefficients;
s1.2, performing thresholding treatment on the wavelet coefficient by adopting a Visusarink method to obtain a first high-frequency coefficient;
s1.3, comparing the first high-frequency coefficient with a threshold value, and reserving a part of the first high-frequency coefficient, which is higher than the threshold value, to obtain a second high-frequency coefficient, wherein the second high-frequency coefficient is used as the maneuvering characteristic of a flight path; filtering out a part of the first high-frequency coefficient which is lower than the threshold value;
the threshold is calculated by the following formula:
wherein T represents the threshold; n is the length of the high-frequency coefficient sequence and is the standard deviation of random noise in the flight path;
and S1.4, performing wavelet reconstruction on the second high-frequency coefficient and the scale coefficient to obtain the track data set.
Preferably, the step S2 includes:
s2.1, selecting n from the track data set1A first AIS track data, n1The ith first AIS track data in the first AIS track data is taken as a reference sequence and is recorded as:
Xi＝{Xi(k)|k＝0,1,2,...,N}，i＝1,2,...,n1
selecting n from the track dataset2A first radar track data, n2Taking the jth first radar track data in the first radar track data as a comparison sequence, and recording as:
Xj＝{Xj(k)|k＝0,1,2,...,N}，j＝1,2,...,n2
the track data set comprises: observing position, speed and course characteristic parameters of the target, wherein k is a characteristic parameter influencing a flight path;
s2.2, carrying out absolute difference processing on the reference sequence and the comparison sequence under the condition of the characteristic parameters, wherein the difference is calculated by adopting the following formula:
Δij(k)＝|Xi(k)-Xj(k)|
step S2.3, the gray correlation coefficient calculation is carried out on the reference sequence and the comparison sequence, and the gray correlation coefficient ξij(k) The calculation formula is as follows:
in the formula, lambda represents a resolution coefficient, wherein the value range of lambda is 0-1.
Preferably, the step S3 includes:
s3.1, calculating the grey correlation coefficient by adopting a weighted average method to obtain the n under the condition of the characteristic parameter1The ith first AIS track data and the n in the first AIS track data2Gray correlation degrees between jth first radar track data in the first radar track data are as follows: the grey correlation degree is expressed by the following formula:
wherein a is the ratio of the characteristic parameters, and is 0-1;
s3.2, constructing the gray correlation degree into a matrix to obtain a gray correlation matrix:
where ρ is γ-1And rho represents the first track correlation momentAnd (5) arraying.
Preferably, the step S4 includes:
step S4.1, converting the n1First AIS track data and n2Correlating the first radar track data, wherein n is1One first AIS track data in the first AIS track data can only correspond to the n2Obtaining optimal association by one piece of first radar track data in the pieces of first radar track data, converting the method into an assignment problem, and constructing an assignment problem mathematical model;
s4.2, taking the element in the first track incidence matrix as the n1The ith first AIS track data and the n in the first AIS track data2And performing optimal distribution on the first track incidence matrix to obtain an optimal solution matrix, wherein the incidence elements are associated with the jth first radar track data in the first radar track data.
Preferably, said step S4.1 comprises: the assignment problem is formulated as:
is provided with
The mathematical model of the assignment problem is:
wherein r represents the associated element sum.
Preferably, said step S4.2 comprises: the distribution principle of the optimal distribution is as follows: at most one element is allocated to each row in the first track incidence matrix; at most one element is allocated to each column in the first track correlation matrix; and the sum of all the distributed elements in the first track incidence matrix is minimum.
Preferably, said step S4.2 comprises: adopting Hungarian algorithm to judge the first track incidence matrix to obtain the optimal solution matrix, wherein in the optimal solution matrix, elements in each row or each column are in the optimal solution matrixOnly one element is 1, the rest are 0, if the row i and the column j of the element with the element being 1 are located, the n is1The ith item of the first AIS track data and the n item of the first AIS track data2The jth piece of the first radar track data in the pieces of first radar track data has relevance.
Preferably, the optimal solution matrix is solved by the following process:
step S4.2.1, if n is mentioned1≠n2Filling the first track incidence matrix with digital zero to obtain a second track incidence matrix with n x n elements, wherein n is max { n { (n) }1，n2}。
Step S4.2.2, transforming the second track incidence matrix; subtracting the numerical value of the minimum element of each row and each column of the second track incidence matrix respectively to obtain a third track incidence matrix, so that each row and each column of the third track incidence matrix have digital zeros, and each element in the third track incidence matrix is not less than zero; recording the third track incidence matrix as a square matrix;
step S4.2.3, finding out zero elements in different rows and columns in the square matrix; when the number of the zero elements is n, obtaining the optimal solution matrix, and completing the association; when the number of zero elements is not n, the process proceeds to step S4.2.4.
Step S4.2.4, finding out the minimum straight line set which can cover all the zero elements in the square matrix; taking the value of the minimum element which is not covered by the straight line in the square matrix as t, subtracting t from each element of the row in which the element which is not covered by the straight line is positioned, and adding t to each element in the column drawing the straight line to obtain a fourth track incidence matrix; recording the fourth track incidence matrix as the square matrix; return to step S4.2.3.
Preferably, said step S4.2.3 includes:
and S4.2.3.1, if a certain row or a certain column in the third track correlation matrix only has one zero element, circling the zero element, drawing × the rest zero elements in the same row or the same column with the circled zero element, and so on until all the zero elements in the third track correlation matrix are circled or drawn ×.
And S4.2.3.2, setting m as the number of the circled zero elements, obtaining the optimal solution matrix when m is equal to n, completing the association, setting the circled zero element value to be 1, drawing × the zero element value to be 0, and entering the step S4.2.4 when m is not equal to n.
The step of finding the minimum set of lines in the step S4.2.4 is as follows:
step S4.2.4.1, if the zero element that is not circled in a certain row of the third track correlation matrix, drawing √ the row where the zero element that is not circled is located for marking;
step S4.2.4.2, drawing V on the column where the zero element of drawing × is located in the row drawing V;
step S4.2.4.3, drawing V on the circled row where the zero element is located in the column drawing V;
step S4.2.4.4, repeating the above steps until there is no row or column that can draw V;
step S4.2.4.5, draw a horizontal line for the rows not drawn with V, draw a vertical line for the columns drawn with V, and the resulting set of straight lines is the minimum set of straight lines.
The invention has at least one of the following advantages:
firstly, the gray correlation degree is obtained by combining wavelet threshold denoising and gray correlation, the accuracy of track correlation is further improved, and the correct correlation rate is higher in the dense clutter environment.
Secondly, the Hungarian algorithm is used for carrying out track association judgment, an association threshold does not need to be selected when the track association is carried out, and the adopted association judgment criterion is globally optimal.
Drawings
Fig. 1 is a flowchart of a radar and AIS track association method based on improved gray association according to an embodiment of the present invention;
FIG. 2 is a flowchart of generating a first track correlation matrix according to an embodiment of the present invention;
FIG. 3 is a flowchart illustrating a global optimal association decision performed by the Hungarian algorithm according to an embodiment of the present invention;
FIG. 4 is a graph of a comparison simulation result of a correct correlation curve according to an embodiment of the present invention;
FIG. 5 is a graph of a comparison simulation result of an error correlation curve according to an embodiment of the present invention;
fig. 6 is a graph comparing simulation results of a leak correlation rate curve according to an embodiment of the present invention.
Detailed Description
The radar and AIS track association method based on improved grey correlation according to the present invention is further described in detail with reference to fig. 1 to 4 and the detailed description thereof. The advantages and features of the present invention will become more apparent from the following description. It is to be noted that the drawings are in a very simplified form and are all used in a non-precise scale for the purpose of facilitating and distinctly aiding in the description of the embodiments of the present invention. To make the objects, features and advantages of the present invention comprehensible, reference is made to the accompanying drawings. It should be understood that the structures, ratios, sizes, and the like shown in the drawings and described in the specification are only used for matching with the disclosure of the specification, so as to be understood and read by those skilled in the art, and are not used to limit the implementation conditions of the present invention, so that the present invention has no technical significance, and any structural modification, ratio relationship change or size adjustment should still fall within the scope of the present invention without affecting the efficacy and the achievable purpose of the present invention.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
As shown in fig. 1, the method for associating a radar with an AIS track based on improved gray association provided in this embodiment includes the following steps:
as shown in fig. 2:
and S1, acquiring AIS track data and radar track data, and performing wavelet threshold denoising processing on the AIS track data and the radar track data to obtain a track data set.
Specifically, the AIS track data and the radar track data are decomposed by adopting multi-resolution analysis characteristics and a Mallat algorithm to obtain a low-frequency part and a high-frequency part.
Step S1.1, performing 4-layer wavelet decomposition on the AIS track data and the radar track data by adopting a wave basis function to obtain 4-level wavelet coefficients with different scales and scale coefficients.
And S1.2, performing thresholding treatment on the wavelet coefficient by adopting a VisuShrink method to obtain a first high-frequency coefficient.
S1.3, comparing the first high-frequency coefficient with a threshold value, and reserving a part of the first high-frequency coefficient, which is higher than the threshold value, to obtain a second high-frequency coefficient, wherein the second high-frequency coefficient is used as the maneuvering characteristic of a flight path; and filtering out the part of the first high-frequency coefficient, which is lower than the threshold value.
The threshold is calculated by the following formula:
wherein T represents the threshold; and N is the length of the high-frequency coefficient sequence and is the standard deviation of random noise in the flight path.
And S1.4, performing wavelet reconstruction on the second high-frequency coefficient and the scale coefficient to obtain the track data set.
Considering the flight path data as a piece of signal, the flight path data sequence function f (x) representing the signal can be decomposed into a low frequency part and a high frequency part according to the multi-resolution analysis characteristic and the Mallat algorithm. Selecting a wave basis function as haar wavelet to carry out 4-layer wavelet decomposition on the signal to obtain a wavelet coefficient d under 4 levels of different scales4，d4-1，...,d1And a scale factor c4(ii) a And performing thresholding treatment on the wavelet coefficients of each level by adopting a VisuShrink method, reserving the parts higher than the threshold value as the maneuvering characteristics of the flight path, and filtering the parts lower than the threshold value as noise. The selected threshold is satisfied
Where N is the length of the high frequency coefficient sequence. And then performing wavelet reconstruction on the wavelet coefficient and the scale coefficient after threshold processing to obtain new track data, wherein the new track data is the track data set.
Step S2, acquiring n in the track data set1First AIS track data and n2The grey correlation coefficient between the first radar track data is set.
S2.1, selecting n from the track data set1A first AIS track data, n1The ith first AIS track data in the first AIS track data is taken as a reference sequence and is recorded as:
Xi＝{Xi(k)|k＝0,1,2,...,N}，i＝1,2,...,n1(2)
selecting n from the track dataset2A first radar track data, n2Taking the jth first radar track data in the first radar track data as a comparison sequence, and recording as:
Xj＝{Xj(k)|k＝0,1,2,...,N}，j＝1,2,...,n2(3)
the track data set comprises: observing position, speed and course characteristic parameters of the target, wherein k is a characteristic parameter influencing a flight path;
s2.2, carrying out absolute difference processing on the reference sequence and the comparison sequence under the condition of the characteristic parameters, wherein the difference is calculated by adopting the following formula:
Δij(k)＝|Xi(k)-Xj(k)| (4)
step S2.3, the gray correlation coefficient calculation is carried out on the reference sequence and the comparison sequence, and the gray correlation coefficient ξij(k) The calculation formula is as follows:
in the formula, lambda represents a resolution coefficient, wherein the value range of lambda is 0-1.
Step S3, constructing a first track incidence matrix according to the grey incidence coefficients;
s3.1, calculating the grey correlation coefficient by adopting a weighted average method to obtain the n under the condition of the characteristic parameter1The ith first AIS track data and the n in the first AIS track data2Gray correlation degrees between jth first radar track data in the first radar track data are as follows: the grey correlation degree is expressed by the following formula:
wherein a is the ratio of the characteristic parameters, and is 0-1;
s3.2, constructing the gray correlation degree into a matrix to obtain a gray correlation matrix:
where ρ is γ-1And rho represents the first track incidence matrix.
Step S4, collecting the flight path data set n1First AIS track data and n2Correlating the first radar track dataObtaining an assignment problem mathematical model; according to the assignment problem mathematical model, performing global optimal track association judgment on the first track association matrix by adopting Hungary algorithm to obtain an optimal solution matrix
Step S4.1, converting the n1First AIS track data and n2Correlating the first radar track data, wherein n is1One first AIS track data in the first AIS track data can only correspond to the n2And obtaining optimal association by one piece of first radar track data in the pieces of first radar track data, converting the method into an assignment problem, and constructing a mathematical model of the assignment problem.
The assignment problem is formulated as:
is provided with
The mathematical model of the assignment problem is:
wherein r represents the associated element sum.
S4.2, taking the element in the first track incidence matrix as the n1The ith first AIS track data and the n in the first AIS track data2And performing optimal distribution on the first track incidence matrix to obtain an optimal solution matrix, wherein the incidence elements are associated with the jth first radar track data in the first radar track data.
Relating elements rho in a flight path correlation matrixijAnd the cost is associated with the ith track data as the first AIS track data and the jth track data of the radar track data, and the cost is the associated element and is optimally distributed to the track association matrix.
The distribution principle of the optimal distribution is as follows: at most one element is allocated to each row in the first track incidence matrix; at most one element is allocated to each column in the first track correlation matrix; and the sum of all the distributed elements in the first track incidence matrix is minimum.
Judging the first track incidence matrix by adopting Hungarian algorithm to obtain the optimal solution matrix
In the optimal solution matrix, only one element in each row or each column is 1, the rest are 0, if the row i and the column j of the element with 1 are located, the n is1The ith item of the first AIS track data and the n item of the first AIS track data2The jth piece of the first radar track data in the pieces of first radar track data has relevance.
As shown in fig. 3, the optimal solution matrix is solved by the following process:
step S4.2.1, if n is mentioned1≠n2Filling the first track incidence matrix with digital zero to obtain a second track incidence matrix with n x n elements, and recording the second track incidence matrix as rhon×nAnd n is max { n ═ n1，n2}；
Step S4.2.2, transforming the second track correlation matrix rhon×n(ii) a Correlating the second track with a matrix rhon×nSubtracting the numerical value of the minimum element of the line and the column from each element of the line and the column to obtain a third track correlation matrix, and recording the third track correlation matrix as rho'n×nCorrelating the third track with a matrix ρ'n×nDigital zeros appear in each row and column, and the third track correlation matrix ρ'n×nAll elements in the composition are not less than zero; correlating the third track with a matrix rho'n×nRecording as a square matrix;
step S4.2.3, finding out zero elements in different rows and columns in the square matrix; when the number of the zero elements is n, obtaining the optimal solution matrix, and completing the association; if the number of zero elements is not n, go to step S4.2.4;
step S4.2.3.1, if the third track correlation matrix ρ'n×nHas only one zero element in a certain row or a certain column, the zero element is circled out, the rest zero elements in the same row or the same column as the circled zero element are drawn ×, and so on until the third track correlation matrix rho'n×nAll of the zero elements in (a) are circled or drawn ×;
step S4.2.3.2, setting m as the number of the circled zero elements, obtaining the optimal solution matrix when m is equal to n, completing the association, setting the circled zero element value as 1, and drawing × the zero element value as 0, and entering the step S4.2.4 when m is not equal to n;
step S4.2.4, finding out the minimum straight line set which can cover all the zero elements in the square matrix; taking the value of the minimum element which is not covered by the straight line in the square matrix as t, subtracting t from each element of the row in which the element which is not covered by the straight line is positioned, and adding t to each element in the column drawing the straight line to obtain a fourth track incidence matrix; recording the fourth track incidence matrix as the square matrix; return to step S4.2.3.
The step of finding the minimum set of lines in the step S4.2.4 is as follows:
step S4.2.4.1, if the third track correlation matrix ρ'n×nIf the zero element is not circled in a certain row, drawing the row where the zero element is not circled in a V shape for marking;
step S4.2.4.2, drawing V on the column where the zero element of drawing × is located in the row drawing V;
step S4.2.4.3, drawing V on the circled row where the zero element is located in the column drawing V;
step S4.2.4.4, repeating the above steps until there is no row or column that can draw V;
step S4.2.4.5, draw a horizontal line for the rows not drawn with V, draw a vertical line for the columns drawn with V, and the resulting set of straight lines is the minimum set of straight lines.
In one embodiment of the invention, a surveillance zone of the radar is assumedThere are 30 ships with speed changes, intentional and unintentional maneuvers on a two-dimensional plane, process noise that can be considered as varying in speed, target initial speed evenly distributed between 4-1200 m/s, initial heading evenly distributed between 0-2 pi, target initial position normally distributed at x 190km, y 135km, range and angle error of radar σ r2＝150m，σθ20.025. The AIS is arranged on 10 ships, and the error of distance measurement and angle measurement is sigma r1＝80m，σθ10.015, sample interval T of AIS11s, sampling interval T of radar2The duration N is 50s, and it is assumed that the track information of the radar and the AIS are all in a rectangular coordinate system with the VTS fusion center as the origin of coordinates. Fig. 4-6 are a comparison graph of a correct correlation rate curve, a comparison graph of an incorrect correlation rate curve, and a comparison graph of a missing correlation rate curve of the improved algorithm and the conventional gray correlation algorithm under the above-mentioned environment, respectively. As can be seen from the comparison graph, the track association correct rate of the improved gray association algorithm is superior to that of the traditional gray association algorithm, the track association correct rate is improved by about 0.1, meanwhile, the error association rate is reduced, and the existence of missing association is eliminated.
In conclusion, the gray correlation degree is obtained by combining wavelet threshold denoising and gray correlation, the accuracy of track correlation is further improved, and the correct correlation rate is higher in the dense clutter environment. And the Hungarian algorithm is used for carrying out the track association judgment, the association threshold does not need to be selected when the track association is carried out, and the adopted association judgment criterion is globally optimal.
While the present invention has been described in detail with reference to the preferred embodiments, it should be understood that the above description should not be taken as limiting the invention. Various modifications and alterations to this invention will become apparent to those skilled in the art upon reading the foregoing description. Accordingly, the scope of the invention should be determined from the following claims.
Claims (10)
1. A radar and AIS track association method based on improved gray association is characterized by comprising the following steps:
s1, acquiring AIS track data and radar track data, and performing wavelet threshold denoising processing on the AIS track data and the radar track data to obtain a track data set;
step S2, acquiring n in the track data set1First AIS track data and n2A grey correlation coefficient between the first radar track data;
step S3, constructing a first track incidence matrix according to the grey incidence coefficients;
step S4, collecting the flight path data set n1First AIS track data and n2Correlating the first radar track data to obtain an assignment problem mathematical model; and carrying out global optimal track association judgment on the first track association matrix by adopting a Hungary algorithm according to the assignment problem mathematical model to obtain an optimal solution matrix.
2. The improved gray association based radar and AIS track association method of claim 1 wherein said step S1 includes: decomposing the AIS track data and the radar track data by adopting multi-resolution analysis characteristics and a Mallat algorithm to obtain a low-frequency part and a high-frequency part;
s1.1, performing 4-layer wavelet decomposition on the AIS track data and the radar track data by adopting a wave basis function to obtain 4-level wavelet coefficients with different scales and scale coefficients;
s1.2, performing thresholding treatment on the wavelet coefficient by adopting a Visusarink method to obtain a first high-frequency coefficient;
s1.3, comparing the first high-frequency coefficient with a threshold value, and reserving a part of the first high-frequency coefficient, which is higher than the threshold value, to obtain a second high-frequency coefficient, wherein the second high-frequency coefficient is used as the maneuvering characteristic of a flight path; filtering out a part of the first high-frequency coefficient which is lower than the threshold value;
the threshold is calculated by the following formula:
wherein T represents the threshold; n is the length of the high-frequency coefficient sequence and is the standard deviation of random noise in the flight path;
and S1.4, performing wavelet reconstruction on the second high-frequency coefficient and the scale coefficient to obtain the track data set.
3. The improved gray association based radar and AIS track association method of claim 1 wherein said step S2 includes:
s2.1, selecting n from the track data set1A first AIS track data, n1The ith first AIS track data in the first AIS track data is taken as a reference sequence and is recorded as:
Xi＝{Xi(k)|k＝0,1,2,...,N}，i＝1,2,...,n1
selecting n from the track dataset2A first radar track data, n2Taking the jth first radar track data in the first radar track data as a comparison sequence, and recording as:
Xj＝{Xj(k)|k＝0,1,2,...,N}，j＝1,2,...,n2
the track data set comprises: observing position, speed and course characteristic parameters of the target, wherein k is a characteristic parameter influencing a flight path;
s2.2, carrying out absolute difference processing on the reference sequence and the comparison sequence under the condition of the characteristic parameters, wherein the difference is calculated by adopting the following formula:
Δij(k)＝|Xi(k)-Xj(k)|
step S2.3, the gray correlation coefficient calculation is carried out on the reference sequence and the comparison sequence, and the gray correlation coefficient ξij(k) The calculation formula is as follows:
in the formula, lambda represents a resolution coefficient, wherein the value range of lambda is 0-1.
4. The improved gray association based radar and AIS track association method of claim 1 wherein said step S3 includes:
s3.1, calculating the grey correlation coefficient by adopting a weighted average method to obtain the n under the condition of the characteristic parameter1The ith first AIS track data and the n in the first AIS track data2Gray correlation degrees between jth first radar track data in the first radar track data are as follows: the grey correlation degree is expressed by the following formula:
wherein a is the ratio of the characteristic parameters, and is 0-1;
s3.2, constructing the gray correlation degree into a matrix to obtain a gray correlation matrix:
where ρ is γ-1And rho represents the first track incidence matrix.
5. The improved gray association based radar and AIS track association method of claim 1 wherein said step S4 includes:
step S4.1, converting the n1First AIS track data and n2Correlating the first radar track data, wherein n is1One first AIS track data in the first AIS track data can only correspond to the n2Obtaining optimal association by one piece of first radar track data in the pieces of first radar track data, converting the method into an assignment problem, and constructing an assignment problem mathematical model;
step (ii) ofS4.2, taking the element in the first track incidence matrix as the n1The ith first AIS track data and the n in the first AIS track data2And performing optimal distribution on the first track incidence matrix to obtain an optimal solution matrix, wherein the incidence elements are associated with the jth first radar track data in the first radar track data.
6. The improved gray correlation based radar and AIS track association method of claim 5 wherein said step S4.1 comprises: the assignment problem is formulated as:
is provided with
The mathematical model of the assignment problem is:
wherein r represents the associated element sum.
7. The improved gray correlation based radar and AIS track association method of claim 6 wherein said step S4.2 comprises: the distribution principle of the optimal distribution is as follows: at most one element is allocated to each row in the first track incidence matrix; at most one element is allocated to each column in the first track correlation matrix; and the sum of all the distributed elements in the first track incidence matrix is minimum.
8. The improved gray association based radar and AIS track association method of claim 7 wherein said step S4.2 comprises: judging the first track incidence matrix by adopting a Hungarian algorithm to obtain the optimal solution matrix, wherein in the optimal solution matrix, only one element in each row or each column is 1, the rest elements are 0, and if the row i and the column j of the element with the element of 1 are respectively, the n is1Strip noThe ith item of the first AIS track data and the n item of the first AIS track data in AIS track data2The jth piece of the first radar track data in the pieces of first radar track data has relevance.
9. The improved gray correlation based radar and AIS track correlation method of claim 8 wherein the optimal solution matrix is solved by:
step S4.2.1, if n is mentioned1≠n2Then the first track correlation matrix is padded with a number zero to obtain a second track correlation matrix with n × n elements, where n is max { n {1，n2}；
Step S4.2.2, transforming the second track incidence matrix; subtracting the numerical value of the minimum element of each row and each column of the second track incidence matrix respectively to obtain a third track incidence matrix, so that each row and each column of the third track incidence matrix have digital zeros, and each element in the third track incidence matrix is not less than zero; recording the third track incidence matrix as a square matrix;
step S4.2.3, finding out zero elements in different rows and columns in the square matrix; when the number of the zero elements is n, obtaining the optimal solution matrix, and completing the association; if the number of zero elements is not n, go to step S4.2.4;
step S4.2.4, finding out the minimum straight line set which can cover all the zero elements in the square matrix; taking the value of the minimum element which is not covered by the straight line in the square matrix as t, subtracting t from each element of the row in which the element which is not covered by the straight line is positioned, and adding t to each element in the column drawing the straight line to obtain a fourth track incidence matrix; recording the fourth track incidence matrix as the square matrix; return to step S4.2.3.
10. The improved gray association based radar and AIS track association method of claim 9 wherein said step S4.2.3 comprises:
s4.2.3.1, if a certain row or a certain column in the third track correlation matrix has only one zero element, circling the zero element, and drawing × the rest zero elements in the same row or the same column as the circled zero element, and so on until all the zero elements in the third track correlation matrix are circled or drawn ×;
step S4.2.3.2, setting m as the number of the circled zero elements, obtaining the optimal solution matrix when m is equal to n, completing the association, setting the circled zero element value as 1, and drawing × the zero element value as 0, and entering the step S4.2.4 when m is not equal to n;
the step of finding the minimum set of lines in the step S4.2.4 is as follows:
step S4.2.4.1, if the zero element that is not circled in a certain row of the third track correlation matrix, drawing √ the row where the zero element that is not circled is located for marking;
step S4.2.4.2, drawing V on the column where the zero element of drawing × is located in the row drawing V;
step S4.2.4.3, drawing V on the circled row where the zero element is located in the column drawing V;
step S4.2.4.4, repeating the above steps until there is no row or column that can draw V;
step S4.2.4.5, draw a horizontal line for the rows not drawn with V, draw a vertical line for the columns drawn with V, and the resulting set of straight lines is the minimum set of straight lines.
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