CN111487612A - CPD-based allopatric configuration radar/ESM track robust correlation method - Google Patents
CPD-based allopatric configuration radar/ESM track robust correlation method Download PDFInfo
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- G—PHYSICS
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- 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
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Abstract
The invention belongs to a track correlation technology in the field of target tracking, and provides a track robust correlation method based on Coherent Point Drift (CPD) aiming at the problem of track correlation of a radar and an ESM (automatic position sensing) sensor which are configured in different places under the condition of system deviation. And considering the influence of system deviation on the radar and ESM parameter tracks, describing the mapping relation between homologous track points of the radar and the ESM by using a nonlinear transformation function, and modeling the mapping relation as a non-rigid registration problem. And carrying out batch normalization processing on the target point sets of the radar and the ESM under the modified polar coordinates, and then estimating a displacement function in the nonlinear transformation function by using a CPD (compact peripheral component interconnect) method to obtain a point set after registration. And finally, obtaining a radar/ESM track robust correlation result by using global optimization and hypothesis testing, wherein the radar/ESM track robust correlation result is suitable for the condition that the distance between a radar and an ESM is long, and the correlation effect on a dense target is good.
Description
Technical Field
The invention belongs to a flight path correlation technology in the field of target tracking, and provides a flight path robust correlation method based on Coherent Point Drift (CPD) aiming at the problem of flight path correlation of a radar and an ESM sensor configured in different places under the condition of system deviation.
Background
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 it is necessary to research a track association algorithm of a radar and an EMS.
The invention aims to realize radar/ESM track robust association under remote configuration by using a CPD algorithm, is suitable for the condition of long distance between a radar and an ESM and has good association effect on dense targets.
Disclosure of Invention
The invention aims to provide a track robust correlation method based on coherent point drift aiming at the problem of track correlation of a radar/ESM configured in different places under the condition of system deviation. And considering the influence of system deviation on the radar and ESM parameter tracks, describing the mapping relation between homologous track points of the radar and the ESM by using a nonlinear transformation function, and modeling the mapping relation as a non-rigid registration problem. And (3) carrying out batch normalization processing on target point sets of the radar and the ESM under a Modified Polar Coordinate (MPC), and then estimating a displacement function in a nonlinear transformation function by using a CPD algorithm to obtain a point set after registration. And finally, obtaining a final radar/ESM track robust correlation result by using global optimization and hypothesis testing.
The method is suitable for the problem of track correlation of the radar/ESM sensor configured in different places. The invention comprises the following steps:
1 description of the problems
Two platforms configured in different places are arranged in a two-dimensional scene at a certain moment, and a radar and an ESM are respectively carried to observe a target. Radar and ESM are located at pr＝[xryr]TAnd pe＝[xeye]TAt a speed of respectively
And
the position and velocity of the nth object is ptn＝[xtnytn]TAnd
taking into account systematic and random errors, radar measurements can be modeled as
Wherein,
indicating the radial distance of the nth target to the radar,
representing the nth target true azimuth measurement, Δ ρ and Δ θrRepresenting the systematic errors, rho and theta, of the radar radial and azimuth measurements, respectivelyrIndicating the random error of the measurement. Similarly, ESM metrics can be modeled as
Wherein,
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 utilizes the conventional Extended Kalman Filter (EKF) to estimate the target state, and the filtering result and the self motion state p of each target are obtainedrAnd vrSent to a fusion center, where { Xrn,P′rnThe radar filters the target under the local coordinate system
The ESM adopts an MPCEKF filtering algorithm on the target, and the result is expressed as { Yen,PenAnd (c) the step of (c) in which,
theta is the azimuth angle and theta is the azimuth angle,
the ratio of the rate of change in distance To the distance (Inverse-Time-To-Go, ITTG),
as a result of the rate of change of the azimuth angle,
the inverse of the radial distance.
2 Effect of systematic biases on track correlation
Assuming the filtering results have been time aligned, the ESM is used as the fusion center to establish the coordinate system, the radar and the ESM are moving in formation at L intervals, the scene diagram at a certain moment is shown in FIG. 1rn,P′rnConverting to local MPC of ESM to obtain { Y }rn,PrnSince the first three variables under MPC are decoupled from the fourth and the fourth variable is not observable at some point in time, only the first three variables are considered, where
Wherein,
representing state vectors
N is 1,2, …, N.
Neglecting the influence of the estimation error after filtering, the filtering result X exists under the condition of system errorrnIs composed of
By bringing formula (7) into formula (4)
Consider a set of points Y in MPC parameter spacer＝{YrnN is 1,2, …, N and Ye＝{YemM is 1,2, …, M, where the number of radiation sources M may be more than the number of radar targets N. By observing formula (8), Y is knownrIs about YeAnd the transformation parameters are different for different targets. For homologous data points, the transformation relationship can be modeled as the sum of the set of origins and their displacement functions.
Yr＝(Ye)＝Ye+v(Ye) (9)
3 non-rigid point set registration method
Will YeAs a center of Gaussian Mixture Model (GMM), consider YrData samples generated for the GMMThen the probability density function of GMM is
Wherein D is the dimension of the data points in the point set, sigma2In order to be an isotropic covariance,
i | · | | represents the euclidean distance. The difference of the azimuth angles is in the range of-pi < + ><θr-θe>Not more than pi, using cosine value to calculate angle difference
<θr-θe>＝arccos(cosθrcosθe+sinθrsinθe) (12)
In fact, the dimensions of the different parameter dimensions are different for the filtering results in the parameter space, such as
And
because of the differential term, the scale of the differential term in the parameter space is far smaller than theta. Therefore, the use of the euclidean distance metric directly tends to overwhelm the dimension with a small scale in the euclidean distance, and the difference of the data points in the dimension cannot be effectively characterized. In the correlation algorithm, mahalanobis distance is usually used to replace euclidean distance, but due to the system deviation and the problem of remote configuration, the filtering result of the homologous target has a large deviation in the parameter space, so that mahalanobis distance is large, the probability density of the GMM is extremely small, and calculation cannot be performed, and therefore Batch Normalization (BN) is used to preprocess each dimension of data points in the parameter space:
wherein, XnormIn order to be the normalized data, the data,
and
mean and standard deviation in different dimensions, respectively. By normalization, the capability of measuring the data point correlation when Euclidean distance is used can be improved on one hand, and the convergence speed and the registration accuracy can be improved on the other hand.
Assuming independent co-distribution between state estimates of the targets, the unknown parameters v and σ can be estimated by minimizing the negative logarithm of the likelihood function2
Where φ (v) is a regularization term and λ represents a trade-off factor between likelihood function fitness and regularization term. The CPD method provides an optimal displacement function, and solves unknown variables by using a maximum expectation method, thereby realizing non-rigid registration. Then, the registered point set Z is usede＝{Zen＝(Yen) And calculating posterior probability for representing the association relation among the point sets. However, directly selecting the associated point pair with the maximum a posteriori probability ignores the constraint in the flight path association problem for the association result, that is, a single radar target may carry multiple radiation source targets, and a single ESM target corresponds to only one radar target. Furthermore, the posterior probability utilizes only dataThe position relation of the points does not consider each data point as an estimated value of the filter in the parameter space, and certain estimation errors exist. In summary, registered point set Z can be utilizedeAnd a set of points Y of the radar in the parameter spacerConstructing a statistical quantity munm
Wherein, PemAnd PrnFor the normalized estimated covariance matrix
Wherein, P(i,j)Represents the (i, j) th element in the covariance matrix,
representing the elements in the normalized matrix, note that the set of points Z is due to the non-rigid transformation defined as a translation on the original data pointseThe covariance matrix and Y of the data points in (1)eThe same is true.
The hypothesis testing problem is constructed 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.
Is easy to know munmObeying chi-square distribution with degree of freedom d, gamma being a suitable threshold, preferably
α is significance level, making α ═ 0.9.
Finally, based on the global optimal association judgment method, solving the primary association result of the radar/ESM flight path, and constructing a global optimization objective function as
Wherein s isnmBeing binary variables, s nm1 indicates that the nth track of the radar and the mth track of the ESM are from the same target, otherwise snm0. And processing the preliminary correlation result by using hypothesis testing to obtain a final 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, is suitable for the radar and the ESM sensor configured in different places, and has better effect under the condition of dense targets.
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 Coherent Point Drift (CPD) based flight path robust association method aiming at the flight path association problem of a radar and an ESM sensor which are configured in different places under the condition of system deviation. Firstly, under a modified polar coordinate system taking an ESM as a coordinate origin, the influence of system deviation on the radar and ESM parameter tracks is analyzed, a nonlinear transformation function is used for describing the mapping relation between homologous track points of the radar and the ESM, and the mapping relation is modeled as a non-rigid registration problem. Secondly, normalization processing is carried out on the target point set of the radar and the ESM under the modified polar coordinates, and then a CPD algorithm is used for estimating a displacement function in the nonlinear transformation function to obtain a point set after registration. And finally, obtaining a final radar/ESM track robust correlation result by using global optimization and hypothesis testing.
The algorithm flow is as follows:
step 1: the radar and the ESM sensor respectively utilize EKF and MPCEKF to carry out filtering tracking on the target, and the target state estimation results are respectively { X }rn,P′rn1,2, …, N, and Yem,Pem(M-1, 2, …, M), the radar estimation result is converted to { Y in a modified polar coordinate system with ESM as the originrn,PrnN and M are the number of targets observed by the radar and ESM, respectively;
step 2.1: set of point pairs Yr＝{{Yrn,P rn1,2, …, N and a set of points Ye＝{{Yem,PemDifferent dimensions of 1,2, …, M are batch normalized:
wherein, X and XnormRespectively representing data before and after normalization, the superscript (i) representing the ith dimension, P(i,j)Is the (i, j) th element in the original covariance matrix,
representing the (i, j) th element in the normalized matrix,
and
respectively representing the mean value and the standard deviation of the point set on the ith dimension;
step 2.2: set points YeAs the center of the Gaussian mixture model, set the points YrTaking the data samples as the data samples generated by the Gaussian mixture model, and realizing non-rigid registration by using a CPD (continuous phase detection) method to obtain a registered point set Ze＝{{Zem,P em1,2, …, M }, wherein Z isem＝(Yem) Is a set of points YeArrival set YrIs performed by a non-linear transformation.
And step 3: according to { Zem,PemAnd { Y }rn,PrnCalculating statistics
μnm＝(Yrn-Zem)T(Prn+Pem)-1(Yrn-Zem)， (25)
And obtaining a final association result by using a method based on the global optimal association judgment and the hypothesis test method.
Claims (2)
1. The CPD-based allopatric configuration radar/ESM track robust correlation method is characterized by comprising the following steps of:
step 1: the radar tracks and filters the state of the target by utilizing EKF (extended Kalman Filter), and the state estimation of the target and the covariance matrix of the target are obtained as { X }rn,P′rnAnd (N is 1,2, …, N), the ESM sensor tracks and filters the state of the radiation source target by using MPCEKF to obtain a target state estimation and a covariance matrix of the target state estimation and the covariance matrix of the target state estimation, wherein the target state estimation is Yem,Pem(M-1, 2, …, M), the radar estimation result is converted to { Y in a modified polar coordinate system with ESM as the originrn,PrnN and M are the number of targets observed by the radar and ESM, respectively;
step 2: set of point pairs Yr＝{{Yrn,Prn1,2, …, N and a set of points Ye＝{{Yem,PemCarrying out non-rigid registration on M-1, 2, …, M to obtain a non-rigid transformation result Ze＝{{Zem,Pem},m＝1,2,…,M}；
And step 3: according to { Zem,PemAnd { Y }rn,PrnCalculating statistics
μnm＝(Yrn-Zem)T(Prn+Pem)-1(Yrn-Zem)，
And obtaining a final association result by using a method based on the global optimal association judgment and the hypothesis test method.
2. The track robust correlation method according to claim 1, wherein the non-rigid registration in step 2 is specifically:
step 2.1, point set YrSum point set YeEach state vector and its covariance matrix in (a) are preprocessed using batch normalization
Wherein, X and XnormRespectively representing data before and after normalization, the superscript (i) representing the ith dimension, P(i,j)Is the (i, j) th element in the original covariance matrix,
representing the (i, j) th element in the normalized matrix,
and
respectively representing the mean value and the standard deviation of the point set on the ith dimension;
step 2.2, set points YeAs the center of the Gaussian mixture model, set the points YrTaking the data samples as the data samples generated by the Gaussian mixture model, and realizing non-rigid registration by using a CPD (continuous phase detection) method to obtain a registered point set Ze＝{{Zem,Pem1,2, …, M }, wherein Z isem＝(Yem) Is a set of points YeArrival set YrIs performed by a non-linear transformation.
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