CN111487613A - Radar/ESM (electronic stability management) track robust association method based on hierarchical clustering - Google Patents

Radar/ESM (electronic stability management) track robust association method based on hierarchical clustering Download PDF

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CN111487613A
CN111487613A CN202010309021.7A CN202010309021A CN111487613A CN 111487613 A CN111487613 A CN 111487613A CN 202010309021 A CN202010309021 A CN 202010309021A CN 111487613 A CN111487613 A CN 111487613A
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distance
esm
radar
class
track
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孙顺
董凯
刘瑜
徐从安
郭晨
丁自然
谭大宁
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Naval Aeronautical University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/86—Combinations of radar systems with non-radar systems, e.g. sonar, direction finder
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/66—Radar-tracking systems; Analogous systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/23—Clustering techniques

Abstract

The invention belongs to a track correlation technology in the field of target tracking, and provides a track robust correlation method based on hierarchical clustering analysis, aiming at the problem of radar/ESM (electronic stability management) track correlation with system deviation. The influence of formation and system deviation on track association is considered, the distance vectors in the correction polar coordinates are clustered by using a hierarchical clustering method to obtain the estimation expectation of the relative azimuth deviation between the radar and the ESM, a radar/ESM track robust association result is obtained by using a method based on global optimal association judgment and hypothesis test, the radar/ESM track association accuracy under the condition of system deviation is effectively improved, and the method is suitable for the condition that the distance between the radar and the ESM is far smaller than the distance between a sensor and a target.

Description

Radar/ESM (electronic stability management) track robust association method based on hierarchical clustering
Technical Field
The invention belongs to a track association technology in the field of target tracking, and provides a track robust association method based on hierarchical clustering aiming at the problem of radar/ESM (electronic service management) track association with system deviation.
Background
The passive sensor can utilize signal information of direct waves or reflected waves and scattered waves generated by a radiation source target, can realize positioning and tracking of the radiation source target through data processing, and has the advantages of long detection distance, good concealment, strong target identification capability and the like. The ESM is a common passive sensor, can provide target attribute information and azimuth angle measurement, has the advantages of long detection distance, good concealment, strong target identification capability and the like, and has important significance for long-distance early warning and reconnaissance. However, for a multi-target scene, observability of all targets is difficult to guarantee by measurement of a single ESM, and a combined active sensor (such as a radar) system is usually required, so that advantages are complementary, and a more complete and clear battlefield situation is provided for battlefield command, so that a radar/EMS track association method is necessary to be researched.
The traditional radar/ESM track robust association method has limited estimation precision on non-central parameters, the method aims to estimate the relative azimuth deviation between the radar and the ESM by carrying out hierarchical clustering on distance vectors under a Modified Polar Coordinate (MPC), and realizes track robust association based on global optimal allocation and hypothesis test, so that the method is suitable for the condition that the distance between the radar and the ESM is far less than the distance between a sensor and a target.
Disclosure of Invention
The invention aims to provide a hierarchical clustering-based track robust association method aiming at the problem of radar/ESM track association with system deviation, which analyzes the influence of the system deviation on observable variables in an MPC, estimates the relative azimuth deviation by adopting a hierarchical clustering method in a parameter space, corrects hypothesis test statistics and finally determines the track robust association result of the radar and the ESM based on global optimal allocation and an association threshold.
The method is suitable for the track correlation problem of the radar/ESM sensor under the condition of system deviation. The invention comprises the following steps:
1 description of the problems
Considering that two observation platform formation motions respectively carrying radar and ESM and N unknown targets exist in a two-dimensional scene at a certain moment, and the position and the speed of the nth target are ptn＝[xtnytn]TAnd
Figure BDA0002456943400000011
assuming that radar and ESM can observe all radiation source targets and record their positions and motion states, the positions are p respectivelyr＝[xryr]TAnd pe＝[xeye]TAt a speed of respectively
Figure BDA0002456943400000012
And
Figure BDA0002456943400000013
taking into account systematic bias and Gaussian random errors, radar metrology can be modeled as
Figure BDA0002456943400000014
Figure BDA0002456943400000015
Wherein the content of the first and second substances,
Figure BDA0002456943400000016
and
Figure BDA0002456943400000017
respectively representing the radial distance and azimuth angle, Δ ρ, of the nth target to the radarrAnd Δ θrSystem deviation, p, representing radar radial and azimuth measurements, respectivelyrAnd thetarThe random errors, which represent the radar radial distance and azimuth measurements, follow a gaussian distribution that is expected to be zero.
Similarly, the ESM metric can be modeled as
θen＝θen+Δθe+θe(3)
Wherein the content of the first and second substances,
Figure BDA0002456943400000021
represents the azimuthal measurement, Δ θ, of the nth target to the ESMeAnd thetaeRespectively, the systematic deviation and random error of the azimuth measurement.
The radar estimates the target state by using an Extended Kalman Filter (EKF), and the filtering result of each target is obtained
Figure BDA0002456943400000022
And the target motion state p acquired by the radar under the global coordinate systemrAnd vrIs sent to a fusion center, wherein
Figure BDA0002456943400000023
As a result of filtering the target in the radar local Cartesian coordinate system, Pr′nTo represent
Figure BDA0002456943400000024
A random error covariance matrix of (a); the ESM adopts an EKF filtering algorithm under Modified Polar Coordinate (MPC) on the nth target, and the result is expressed as
Figure BDA0002456943400000025
Wherein the content of the first and second substances,
Figure BDA0002456943400000026
is a state vector for the MPC,
Figure BDA0002456943400000027
is the ratio of the rate of change of distance To the distance, abbreviated as ITTG (Inverse-Time-To-Go),
Figure BDA0002456943400000028
as a result of the rate of change of the azimuth angle,
Figure BDA0002456943400000029
the inverse of the radial distance.
2 Effect of systematic biases on track correlation
Establishing a coordinate system by taking the ESM as a fusion center, and assuming that the filtering result is time-aligned, the radar and the ESM are moved in a formation by L distance, as shown in FIG. 1
Figure BDA00024569434000000210
Conversion to local MPC in ESM
Figure BDA00024569434000000211
Since the first three variables under MPC are decoupled from the fourth variable, and the fourth variable is not observable at some point in time, only the first three variables are considered, where
Figure BDA00024569434000000212
Figure BDA00024569434000000213
Figure BDA00024569434000000214
Wherein the content of the first and second substances,
Figure BDA00024569434000000215
representing state vectors
Figure BDA00024569434000000216
N is 1,2, …, N.
Under the existing system deviation condition, neglecting the influence of random noise, and obtaining the result after the filter process is converged and stabilized
Figure BDA00024569434000000217
Is composed of
Figure BDA00024569434000000218
By bringing formula (7) into formula (4)
Figure BDA0002456943400000031
When formation flying, the formation distance is usually far less than the distance between the radar and the target, the relative speed between the target and the sensor is small, and the system deviation is small, i.e.
Figure BDA0002456943400000032
Figure BDA0002456943400000033
Then (8) can be simplified to
Figure BDA0002456943400000034
Filtering MPCEKF ignoring random errors
Figure BDA0002456943400000035
Influence of the results obtained
Figure BDA0002456943400000036
For homologous targets, regardless of systematic variation and formation distance
Figure BDA0002456943400000037
And after the process of approximation has been carried out,
Figure BDA0002456943400000038
and
Figure BDA0002456943400000039
still respectively equal to
Figure BDA00024569434000000310
And
Figure BDA00024569434000000311
but due to the reason of the systematic deviation,
Figure BDA00024569434000000312
and
Figure BDA00024569434000000313
there is a fixed error between them. For long-range targets, the formation distance has little effect on the above parameters. Because of the estimation error in the filtering result, there is
Figure BDA00024569434000000314
The fixed error is the difference between the system deviations measured at azimuth by the radar and the ESM, defined as the relative azimuth error, and therefore the radar/ESM track correlation problem can be constructed as a hypothesis testing problem as follows.
H0: the tracks of the radar and the ESM come from the same target;
H1: the tracks of the radar and the ESM come from different targets.
The above assumption can be expressed as a nearest neighbor method
Figure BDA00024569434000000315
Wherein the detection statistic μ is obtained from equation (11)ijNon-central chi-square distribution with the degree of freedom of 3 is taken as a non-central parameter, gamma is a proper threshold
Figure BDA00024569434000000316
α is the level of significance.
3 hierarchical clustering-based radar/ESM track robust association method
In MPC, the state vector bias of radar and ESM is defined as the distance vector
Figure BDA00024569434000000317
(i, j ═ 1,2, …, N), then
E(Uij|(i,j)∈Ω)＝B (13)
Where B is a fixed value and the first element in B represents the expectation of relative azimuth deviation, the second three elements are 0, Ω { (i, j) | H0Represents the set of tag pairs corresponding to the radar/ESM's homologous track. Due to the fact that
Figure BDA0002456943400000041
And
Figure BDA0002456943400000042
for the estimation results of different sensors, the error terms are independent of each other, and for the same source track, UijHas a covariance of
Figure BDA0002456943400000043
Ideally, the distance vector is a constant vector when the radar path i and the ESM path j originate from the same target. Therefore, hierarchical clustering is introduced to cluster the distance vectors corresponding to the homologous tracks together, and the distance vectors corresponding to the heterologous tracks are separated.
First, the range vectors of all radar and ESM state vectors under MPC are calculated. In the initial clustering, each distance vector is considered as a class, and the distance between different elements is defined by the square of the mahalanobis distance:
Figure BDA0002456943400000044
wherein the content of the first and second substances,
Vijpq＝Uij-Upq(i,j,p,q＝1,2,…,N,(i,j)≠(p,q)) (15)
Figure BDA0002456943400000045
wherein the inter-class distance in the hierarchical cluster is determined by a minimum criterion, noting that when radar track i and track p are compared to ESM track j and trackWhen q are all homologous tracks, ηijpqObeying a chi-square distribution with a degree of freedom of 3. Therefore, a threshold λ is introduced as a termination condition for the clustering algorithm, wherein
Figure BDA0002456943400000046
The significance level was set to α -0.9-finally, the relative azimuth deviation was estimated from the clustering results.
Using relative azimuth systematic deviation estimates
Figure BDA0002456943400000047
The statistic is corrected to obtain
Figure BDA0002456943400000048
Wherein the content of the first and second substances,
Figure BDA0002456943400000049
and finally, solving a track association result by utilizing the global optimal association judgment. The global optimization objective function and constraints are constructed as follows
Figure BDA00024569434000000410
Wherein s isijBeing binary variables, sij1 means that track i and track j come from the same target, sij0 means that track i and track j come from different targets. Obtaining a preliminary track correlation result through global optimization, and then utilizing a correlation threshold
Figure BDA00024569434000000411
And performing hypothesis test to obtain a final track correlation result.
The numerical simulation result shows that the method can effectively correlate the tracks of the radar and the ESM under the condition of system deviation, and is suitable for the condition that the distance between the radar and the ESM is far less than the distance between the sensor and the target.
Drawings
FIG. 1: typical robust track association scenarios;
FIG. 2: the flowchart is implemented.
Detailed Description
The present invention is further described in detail with reference to the flow chart of the implementation of the present invention illustrated in fig. 2.
The invention provides a hierarchical clustering-based track robust association method aiming at the problem of radar/ESM (electronic service management) track association with system deviation. And defining the state vector deviation of the radar and the ESM under the correction polar coordinate as a distance vector, obtaining the relative azimuth angle deviation estimation of the radar/the ESM by using hierarchical clustering, correcting test statistic, converting the track robust correlation problem into the traditional track correlation problem, and determining the final track correlation result by using global optimal correlation judgment and hypothesis test.
The method comprises the following specific implementation steps:
step 1: converting the state estimation results of the radar and the ESM to the target under a modified polar coordinate system with the ESM as the origin, respectively representing the state estimation results as
Figure BDA0002456943400000051
And
Figure BDA0002456943400000052
i, j is 1,2, …, N is the target number;
step 2: constructing a distance vector
Figure BDA0002456943400000053
And calculating a corresponding covariance matrix
Figure BDA0002456943400000054
i,j＝1,2,…,N；
And step 3: clustering the distance vectors using a hierarchical clustering method, wherein each distance vector is constructed as an initial class of the hierarchical clustering, and the distance between different elements is defined by the square of the mahalanobis distance:
Figure BDA0002456943400000055
Vijpq＝Uij-Upq(i,j,p,q＝1,2,…,N,(i,j)≠(p,q))， (20)
Figure BDA0002456943400000056
note that η is the case when radar track i and track p are the same source track pairs as ESM track j and track qijpqObeying a chi-square distribution with a degree of freedom of 3. Therefore, the threshold λ is introduced as the termination threshold of the clustering algorithm
Figure BDA0002456943400000057
The significance level was set at α -0.9.
The specific implementation steps of the relative azimuth angle deviation estimation method are as follows:
step 3.1: each distance vector UijConstructed as an initial class, i.e.
Figure BDA0002456943400000058
Initializing an iteration number parameter r as 0;
step 3.2: computing inter-class distances based on minimum criteria
Figure BDA0002456943400000059
Wherein
Figure BDA00024569434000000510
Figure BDA00024569434000000511
Obtaining an inter-class distance matrix
Figure BDA00024569434000000512
Step 3.3: merging the two classes with the minimum merging distance into a new class, and canceling the merged class to obtain N2-r-1 classes;
step 3.4: recalculation between new classes and classesThe distance between other classes is not changed, and a new inter-class distance matrix is obtained
Figure BDA00024569434000000513
Step 3.5: if the total number of classes is 1 or the minimum inter-class distance is greater than the threshold lambda, the clustering algorithm is ended, and the operation is continued in the step 3.6, otherwise, the operation is continued in the step 3.3 when r is r + 1;
step 3.6: selecting class C with most elements in classresAs a result of clustering of homologous tracks, the estimation result of the relative azimuth deviation is
Figure BDA0002456943400000061
Wherein N iscIs of class CresThe number of elements in the vector, and the superscript (1) represents the 1 st element in the vector.
And 4, step 4: using relative azimuth systematic deviation estimates
Figure BDA0002456943400000062
The statistic is corrected to obtain corrected statistic
Figure BDA0002456943400000063
Wherein
Figure BDA0002456943400000064
And 5: after a preliminary track association result is obtained by using a method based on global optimal association judgment, an association threshold is utilized
Figure BDA0002456943400000065
Hypothesis testing was performed to obtain the final radar/ESM track robust correlation results, with the significance level set at α -0.9.

Claims (3)

1. The radar/ESM track robust correlation algorithm based on hierarchical clustering is characterized by comprising the following steps:
step 1, converting the state estimation results of the radar and the ESM to the target under a modified polar coordinate system with the ESM as the origin, respectively representing the state estimation results as
Figure FDA0002456943390000011
And
Figure FDA0002456943390000012
i, j is 1,2, …, N is the target number;
step 2, constructing a distance vector Uij；
Step 3, obtaining a relative azimuth angle deviation estimation result by using a hierarchical clustering method
Figure FDA0002456943390000013
Step 4, correcting the statistic by using the estimation result of the relative azimuth angle deviation to obtain the corrected statistic as
Figure FDA0002456943390000014
Wherein
Figure FDA0002456943390000015
Figure FDA0002456943390000016
And
Figure FDA0002456943390000017
the state estimation of the target for radar and ESM respectively is converted to the state estimation result in the corrected polar coordinate system with the ESM as the origin, PrjAnd PejThe covariance matrices for the corresponding state estimates, i, j ═ 1,2, …, N, respectively;
and 5, obtaining a preliminary track correlation result by using a method based on global optimal correlation judgment, and then obtaining a final radar/ESM track robust correlation result by using a correlation threshold through hypothesis testing.
2. The track robust correlation algorithm of claim 1, wherein the distance vector in step 2 is constructed by
Figure FDA0002456943390000018
The corresponding covariance matrix is PUij＝Pri+Pej，i,j＝1,2,…,N。
3. The track robust correlation method of claim 1, wherein the specific method for estimating the relative azimuth deviation by using the hierarchical clustering method in the step 3 is as follows: each distance vector is constructed as an initial class of hierarchical clusters and the distance between different elements is defined by the square of the mahalanobis distance:
Figure FDA0002456943390000019
Vijpq＝Uij-Upq(i,j,p,q＝1,2,…,N,(i,j)≠(p,q))，
Figure FDA00024569433900000110
meanwhile, the inter-class distance in the hierarchical clustering is determined by the minimum criterion, and the termination threshold of the clustering algorithm is
Figure FDA00024569433900000111
α is equal to 0.9, the specific implementation steps of the relative azimuth angle deviation estimation method are as follows:
step 3.1, every distance vector UijConstructed as an initial class, i.e.
Figure FDA00024569433900000112
Initializing an iteration number parameter r as 0;
step 3.2, calculating the inter-class distance based on the minimum criterion
Figure FDA00024569433900000113
Wherein
Figure FDA00024569433900000114
Obtaining an inter-class distance matrix
Figure FDA00024569433900000115
Step 3.3, merging the two classes with the minimum distance into a new class, and canceling the merged class to obtain N2-r-1 classes;
step 3.4, recalculating the distance between the new class and each class, keeping the distance between other classes unchanged, and obtaining a new inter-class distance matrix
Figure FDA00024569433900000116
Step 3.5, if the total number of classes is 1 or the minimum inter-class distance is greater than the threshold lambda, ending the clustering algorithm, and jumping to step 3.6 to continue to operate, otherwise, jumping to step 3.3 to continue to operate;
step 3.6, selecting class C with most elements in classresAs a result of clustering of homologous tracks, the estimation result of the relative azimuth deviation is
Figure FDA0002456943390000021
Wherein N iscIs of class CresThe number of elements in the vector, and the superscript (1) represents the 1 st element in the vector.
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