CN109901153B - Target track optimization method based on information entropy weight and nearest neighbor data association - Google Patents
Target track optimization method based on information entropy weight and nearest neighbor data association Download PDFInfo
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Abstract
The invention discloses a target track optimization method based on information entropy weight and nearest neighbor data association, which comprises the following steps of: measuring vectors of measuring points at the first two moments after the track is started are obtained, and an initial state vector of a target is calculated; initializing the Kalman filter; calculating a state estimation vector, an estimation error covariance matrix, a prediction vector, an innovation covariance matrix and a Kalman gain of a target at the moment k by adopting an iterative method; acquiring candidate measuring points falling into the center of a wave gate at the moment k; and when the number of the candidate measuring points at the moment k is more than 1, optimizing and updating the target track at the moment k by adopting an entropy weight method. The method fully utilizes the information carried by the target measurement by deeply mining the known measurement information on the basis of not changing the prior information, and has lower modification cost and better applicability; meanwhile, the accuracy of tracking the track by the radar is improved.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a target track optimization method based on information entropy weight and nearest neighbor data association.
Background
At present, with the continuous emergence of various radars of new systems, the available characteristics in the field of multi-target tracking are more and more diversified, a data association technology is still a key technology in the field of multi-target tracking, data association is a mapping relation established between a target and measurement thereof according to a specific data association algorithm, and data association can be used for judging which measurement the target is specifically associated with. Therefore, the accuracy of data association seriously affects the target tracking performance of the radar.
Typical data-associated target tracking algorithms include Nearest Neighbor (NN) algorithm, probabilitY Data Association (PDA), joint ProbabilitY Data Association (JPDA), and Multiple HYpothesis Tracking (MHT) algorithm. The working principle of the nearest neighbor algorithm is that a tracking gate is firstly arranged, and echoes obtained by primary screening of the tracking gate become candidate echoes so as to limit the number of targets participating in relevant judgment. Because the method has the characteristics of simple principle, low calculation complexity and easy engineering realization, in engineering application, the nearest neighbor algorithm is widely applied to single target tracking in a low signal-to-noise ratio environment or multi-target tracking in a high signal-to-noise ratio environment.
However, the existing nearest neighbor algorithm still has the problems that the data association accuracy is not high, the filtering result is not accurate enough and the error association is easy to generate during multi-target tracking; meanwhile, since all attributes are equally involved in the calculation in the data association process, the importance degree of the attributes is not highlighted, and the result is susceptible to the influence of a single attribute.
The existing various different types of improving methods aiming at the problems are limited in improving the accuracy of data association by adopting a method of estimating the actual distance between the position and the measured position at the next moment instead of counting the distance, introducing a method of radial Doppler velocity information, introducing a method of associating probability between a measured value and a map feature and the like, and the methods are all used for improving the nearest neighbor algorithm by introducing various new feature information, so that the introduction of the new feature information can increase the engineering realization difficulty and the modification cost, and limit the popularization and application range of the improving method.
Disclosure of Invention
In order to solve the above problems, the present invention aims to provide a target track optimization method (IEWNN) based on information entropY weight and nearest neighbor data association, which utilizes the information carried by target measurement points more fully without changing prior information by deep mining known measurement information, and has lower modification cost and better applicability; meanwhile, the accuracy of radar track tracking is improved by using the information entropy of the target measuring points.
According to the basic principle of information theory, information is a measure of the degree of system order, and entropy is a measure of the degree of system disorder. The average uncertainty of the source, which is a random quantity in the information theory, can be measured by probability distribution. If the information entropy of the index is smaller, the larger the information amount provided by the index is, the greater the role played in the comprehensive evaluation is, i.e., the higher the weight is.
If the information source symbol has n values: u shape1，U2，…，UnThe corresponding probability is: p is1，P2，…，PnAnd the various symbols appear independently of one another. In this case, the average uncertainty of the source should be a single symbol uncertainty — logPiThe statistical mean (E) of (A) may be called the entropy of the information
The entropy weight method introduced by the information entropy can realize comprehensive evaluation of multiple objects and multiple indexes, and accurately empowers the attributes of the data objects by using the information entropy value, so that the accuracy of radar target track tracking is improved.
In order to achieve the above object, the present invention is achieved by the following means.
The target track optimization method based on the association of the information entropy weight and the nearest neighbor data comprises the following steps:
Setting measuring points obtained by the radar tracking system at the first two moments after the track is started as unique real measuring points; measuring vector Z of measuring points at two moments before and after track start acquired by radar tracking system0，Z1Calculating an initial state vector of the target
Wherein, Xk+1Is the state vector, X, of the radar tracking system at time k +1kFor the state vector of the radar tracking system at time k, WkMeasuring a noise sequence at the k moment; f is a state transition matrix of the radar tracking system, and H is a measurement matrix of the radar tracking system; x is a radical of a fluorine atom0Is the position of the target in the X direction, y, under a two-dimensional rectangular coordinate system at the initial moment0Is two-dimensional at the initial momentThe position of the target Y direction in the angular coordinate system,
is the speed of the target in the X direction under the two-dimensional rectangular coordinate system at the initial moment,
the speed of the target in the Y direction under the two-dimensional rectangular coordinate system at the initial moment is obtained.
And when the number of the candidate measuring points at the moment k is 1, using the measuring vector of the candidate measuring points at the moment k for track updating.
And when the number of the candidate measuring points at the moment k is more than 1, optimizing and updating the target track at the moment k by adopting an entropy weight method.
The optimization updating of the target track at the time k by adopting the entropy weight method comprises the following substeps:
substep 5.1, according to the l (l =1,2, \ 8230;, n, n ≧ 1) measuring index a of the j (j =1,2, \ 8230;, m, m > 1) candidate measuring point at the time kjlAnd the prediction vector of the target at the k time
Calculating the jth measurement index a of the jth candidate measurement point at the time kjlFirst measurement index a of a predicted measurement point i tracking the center of the wave gateilError value delta therebetweenjl：
Δjl＝|ajl-ail|。
Step 5.2, according to the error value delta between the jth candidate measuring point at the moment k and the measuring index corresponding to the pre-measuring point i at the center of the tracking wave gatejlAnd the number m of candidate measuring points at the moment k to obtain the uncertainty S of the first measuring index at the moment kl(ii) a Uncertainty S of the first measurement indicator at time klNormalization processing is carried out to obtain the weight coefficient alpha of the first measuring index at the k momentl。
Step 5.3, according to the weighting coefficient alpha of the first measuring index at the moment klTo adoptWeighting the statistical distance between the k moment pre-measurement measuring point i and the candidate measuring point by using a statistical distance correlation criterion to obtain a weighted statistical distance IEWd at the k momentij，k(ii) a Selecting weighted statistical distance IEWd of k timeij，kAnd taking the candidate measuring point corresponding to the minimum as the optimal target measuring point at the time k, and optimally updating the target track at the time k.
Using the measurement vector z of the target measurement point preferred at time kk' calculating the optimized state estimation vector of the target at the k moment
Sum estimation error covariance matrix Pk：
Pk＝Pk/k-1-KkHPk/k-1；
Estimating a vector according to the state of the optimized k-time target
Sum target estimation error covariance matrix PkEstimating the vector for the state of the target at time k +1
Sum estimation error covariance matrix Pk+1/kPredicting to obtain a prediction vector of the target at the k +1 moment
Innovation covariance matrix Sk+1And Kalman gain Kk+1And repeating the step 3 to the step 5, and iterating to obtain the optimized tracking track of the target.
Compared with the prior art, the invention has the following beneficial effects:
(1) The invention further deeply excavates the known measurement information, more fully utilizes the information carried by the target measurement point on the basis of not changing the prior information, has lower modification cost and better applicability, and is more easily used for modification and upgrading of related equipment.
(2) The invention determines the weight coefficient of each attribute by analyzing and calculating the information entropy of the known measurement information and adopting an entropy weight method, and weights the statistical distance association criterion, so that each index of the target measurement point can be weighted according to the size of the information carried by the index, and the defect that the tracking result is easily influenced by a single attribute is avoided.
(3) The method is not limited to the improvement and optimization under two-dimensional measurement, but also is suitable for the radar tracking track optimization under multi-dimensional measurement information, and the more diversified the measurement information is, the richer the mined information is, and the track tracking accuracy is improved.
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The invention is described in further detail below with reference to the figures and the specific embodiments.
FIG. 1 is a schematic flow chart of a target track optimization method based on information entropy weight and nearest neighbor data association according to the present invention.
FIG. 2 is a flowchart illustrating the operation of the target track optimization method based on the association between the information entropy weight and the nearest neighbor data according to the present invention.
Fig. 3 is a target track graph obtained in the embodiment of the present invention, wherein the icon tube represents a real track, NN represents a conventional nearest neighbor track, and IEWNN represents a track obtained by the method of the present invention.
FIG. 4 is a graph of a target tracking comparison using a conventional Nearest Neighbor (NN) and an Information Entropy Weight Nearest Neighbor (IEWNN) of the present invention in an embodiment of the present invention; wherein, fig. 4 (a) is a comparison graph of X-direction distances, an icon X-true represents the X-direction distance of the real track, NN represents the X-direction distance tracking result obtained based on the conventional nearest neighbor, IEWNN represents the X-direction distance tracking result obtained by the method of the present invention; FIG. 4 (b) is a diagram comparing the X-direction velocity, where the X-true represents the X-direction velocity of the real track, NN represents the X-direction velocity tracking result based on the conventional nearest neighbor, and IEWNN represents the X-direction velocity distance tracking result obtained by the method of the present invention; FIG. 4 (c) is a Y-direction distance comparison graph, where the Y-future is the Y-direction distance of the real track, NN is the Y-direction distance tracking result based on the conventional nearest neighbor, and IEWNN is the Y-direction distance tracking result obtained by the method of the present invention; fig. 4 (d) is a Y-direction velocity comparison graph, Y-true represents the Y-direction distance of the real track, NN represents the Y-direction distance tracking result based on the conventional nearest neighbor, and IEWNN represents the Y-direction distance tracking result obtained by the method of the present invention.
FIG. 5 is a graph of a comparison of target tracking errors using a conventional Nearest Neighbor (NN) and an Information Entropy Weight Nearest Neighbor (IEWNN) of the present invention in an embodiment of the present invention; FIG. 5 (a) is a graph showing a distance error in the X direction; FIG. 5 (b) is a graph of X-direction velocity error comparison; FIG. 5 (c) is a Y-direction distance error comparison chart; fig. 5 (d) is a Y-direction velocity error map.
FIG. 6 is a comparison graph of the root mean square error of the target tracking Monte Carlo experiment using the conventional Nearest Neighbor (NN) and the Information Entropy Weight Nearest Neighbor (IEWNN) of the present invention in an embodiment of the present invention; FIG. 6 (a) is a plot of X-direction distance root mean square error; FIG. 6 (b) is a plot of root mean square error versus velocity in the X direction; FIG. 6 (c) is a plot of the Y-direction distance root mean square error comparison; FIG. 6 (d) is a plot of the root mean square error of the velocity in the Y direction.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to examples, but it will be understood by those skilled in the art that the following examples are only illustrative of the present invention and should not be construed as limiting the scope of the present invention.
Referring to fig. 1 and 2, the present invention includes the steps of:
Setting measuring points obtained by the radar tracking system at the first two moments after the track is started as unique real measuring points; a radar tracking system is adopted to obtain a measurement vector Z of measurement points at two moments before and after the track is started0，Z1Calculating an initial state vector of the target
Wherein, Xk+1Is the state vector, X, of the radar tracking system at time k +1kFor the state vector of the radar tracking system at time k, WkMeasuring a noise sequence at the k moment; f is a state transition matrix of the radar tracking system, and H is a measurement matrix of the radar tracking system; x is the number of0Is the position of the target in the X direction, y, under a two-dimensional rectangular coordinate system at the initial moment0Is the position of the target in the Y direction under the two-dimensional rectangular coordinate system at the initial moment,
is the speed of the target X direction under the two-dimensional rectangular coordinate system at the initial moment,
the speed of the target in the Y direction under the two-dimensional rectangular coordinate system at the initial moment is obtained.
Specifically, in step 1, a state transition matrix F of the radar tracking system, a measurement matrix H of the radar tracking system, and a measurement vector Z of the target at the time k are set in two-dimensional motionkAnd the measuring vector Z of the measuring points at the first two moments after the track start0，Z1Are respectively:
Zk＝[Zx，kZy，k]T，Z0＝[Zx，0Zy，0]T，Z1＝[Zx，1Zy，1]T；
in the above formula [ ·]TIs the transposition of the matrix, and t is the sampling interval; zx，kIs k atCarving the distance of the target in the X direction under a two-dimensional rectangular coordinate system; zy，kThe distance of the target Y direction under the two-dimensional rectangular coordinate system at the moment k is obtained; zx，1X-direction position measurement value, Z, obtained for target at 1 st moment in two-dimensional rectangular coordinate systemx，0X-direction position measurement value, Z, in a two-dimensional rectangular coordinate system obtained at the 0 th moment for the targety，1The measured value of the position in the Y direction, Z, in the two-dimensional rectangular coordinate system obtained at the 1 st moment for the targety，0The Y-direction position measurement value in the two-dimensional rectangular coordinate system obtained at the 0 th time point is taken as the target.
The specific calculation for initializing the kalman filter by the two-point difference method is as follows:
Z0＝[Zx，0Zy，0]T，Z1＝[Zx，1Zy，1]T；
wherein r is the measurement noise W0The variance of (a) is determined,
is an X-direction position estimated value of the Kalman filter in the initial state under a two-dimensional rectangular coordinate system,
is an estimated value of the speed in the X direction in the initial state of the Kalman filter under a two-dimensional rectangular coordinate system,
is an estimated value of the Y-direction position of the Kalman filter in the initial state under a two-dimensional rectangular coordinate system,
is an estimated value of the velocity in the Y direction at the initial state of a Kalman filter in a two-dimensional rectangular coordinate system, Zx，1X-direction position measurement value, Z, in a two-dimensional rectangular coordinate system obtained at the 1 st moment for the targetx，0X-direction position measurement value, Z, in a two-dimensional rectangular coordinate system obtained at the 0 th moment for the targety，1The measured value of the position in the Y direction, Z, in the two-dimensional rectangular coordinate system obtained at the 1 st moment for the targety，0And measuring the position value in the Y direction under the two-dimensional rectangular coordinate system obtained at the 0 th moment for the target.
Pk/k-1＝FPk-1FT
Sk＝HPk/k-1HT+Rk
Wherein the content of the first and second substances,
estimating a vector, P, for the state of the target at time k-1k-1Estimation error covariance matrix, R, for the target at time k-1kMeasure the noise covariance matrix for time k ·TIs a transposition of a matrix, ·-1Is the inverse of the matrix.
When k =1, the number of the bits is set to k =1,
is that
Pk-1Is namely P0And carrying out iterative computation according to the formula to obtain the state estimation vector, the estimation error covariance matrix, the prediction vector, the innovation covariance matrix and the Kalman gain of the target at any time except the initial time.
Specifically, the set of measurement points WkIncluding real measuring points and false measuring points generated randomly, and the target at the k moment obtained in the step 3Prediction vector
And the position is used as the center of the tracking wave gate, and the tracking wave gate of the nearest neighbor algorithm is set to be selected according to the elliptic wave gate rule under a two-dimensional rectangular coordinate system. Taking the predicted position of the tracking target as the center of a wave gate, designing the size of the wave gate to ensure that a correct echo can be received with a certain probability, and determining the area of the tracking wave gate as A under a two-dimensional rectangular coordinate system if the measurement vector is two-dimensionalv＝πγ|S(k)|1/2And tracking the wave gate gamma =16, and then judging whether the candidate measuring points meet the following conditions:
wherein z iskIs the measurement vector of the measurement point at the time k,
the parameter gamma is determined by the chi under the tracking wave gate rule for the prediction vector of the target obtained by predicting the k time at the k-1 time2And obtaining a distribution table.
And taking the measuring points which fall into the wave gate and satisfy the condition of the formula as candidate measuring points at the k moment.
And when the number of the candidate measuring points at the moment k is 1, using the measuring vector of the candidate measuring points at the moment k for track updating.
And when the number of the candidate measuring points at the moment k is more than 1, optimizing and updating the target track at the moment k by adopting an entropy weight method.
The method for optimizing and updating the target track at the k moment by adopting the entropy weight method comprises the following substeps:
substep 5.1, according to the l (l =1,2, \8230;, n, n ≧ 1) measuring index a of the j (j =1,2, \8230;, m, m > 1) candidate measuring point at the time kjlAnd the prediction vector of the target at the k time
Calculating the jth measurement index a of the jth candidate measurement point at the time kjlThe first measurement index a of the predicted measurement point i tracking the center of the wave gateilCalculated error value Δ therebetweenjl：
Δjl＝|ajl-ail|；
The method comprises the following specific steps:
as shown in fig. 1, when no measurement point falls within the correlation gate, the state estimation vector of the target at time k calculated in step 3
Sum estimation error covariance matrix Pk/k-1And directly used for track extrapolation.
If only 1 measurement point falls into the relevant wave gate, the measurement point can be directly used for track updating.
If more than one measuring point falls in the correlated wave gate of the tracked target, forming an information matrix A for the candidate measuring points at the time k according to respective measuring indexes l (l =1,2, \8230;, n, n is more than or equal to 1), and if a radar tracking system has m candidate measuring points, and each candidate measuring point has n measuring indexes, the information matrix A is as follows:
wherein each column in A is n measuring indexes of one candidate measuring point, each row in A is the same measuring index of m candidate measuring points, ajlIs the l-th measurement indicator for the j-th candidate measurement point.
A measurement index of each candidate measurement point in the information matrix A is corresponding to the center of the tracking wave gateThe matrix formed by the absolute values of the differences between the corresponding measurement indices of the measurement points is recorded as the information error matrix deltaA：
Wherein, deltaAThe absolute value of the difference between the n measuring indexes of each column of the candidate measuring points and the corresponding measuring index predicted value; deltajlThe l measurement index a of the j candidate measurement pointjlThe first measuring index a of the pre-measuring point iilThe absolute value of the difference between, i.e. deltajl＝|ajl-ail|。
Substep 5.2, according to the error value delta between the jth candidate measuring point at the moment k and the measuring index corresponding to the pre-measuring point i of the tracking wave gate centerjlAnd the number m of candidate measuring points at the moment k to obtain the uncertainty S of the first measuring index at the moment kl(ii) a Uncertainty S of the first measurement index at time klNormalization processing is carried out to obtain the weight coefficient alpha of the first measuring index at the k momentl。
Substep 5.2 comprises the following substeps:
substep 5.2.1, based on the first measurement indicator a of the jth candidate measurement point at time kjlThe first measuring index a of the pre-measuring point iilError value delta therebetweenjlCalculating the ratio p of the jth measurement index of the jth candidate measurement point at the time k in the m candidate measurement pointsjl：
Substep 5.2.2, based on the proportion p of the first measurement indicator of the jth candidate measurement point at time k in the m candidate measurement pointsjlCalculating the information entropy H of the first measurement index at the time kl：
Substep 5.2.3, according to the number m of jth candidate measuring points at the moment k, calculating the maximum information entropy H of the ith measuring index at the moment klmax。
Specifically, the larger the information entropy of a measurement indicator, the closer the error value between the measurement and the predicted measurement is; conversely, the further away the error between the measurement and the predicted measurement. When p isjlIf the measurement index is not less than 1/m, that is, if the probability of each candidate measurement point occupying the specific gravity under the measurement index is the same, the maximum information entropy of the l-th measurement index at the time k is calculated to be Hlmax＝log2m。
Substep 5.2.4, entropy H of the information of the first measurement indicator at time klMaximum information entropy H of the first measurement index at the time klmaxCalculating the uncertainty S of the first measurement index at time kl：
Substep 5.2.5, using the uncertainty S of the first measurement index at time klCalculating the weight coefficient alpha of the first measurement index at the time kl：
By using the method for visualizing the distribution of the measurement information by using the information entropy, if the information entropy of the measurement index is smaller, the larger the information quantity provided by the measurement index is, the larger the information quantity plays a role in the comprehensive evaluation is.
Substep 5.3, based on the weighting factor α of the first measurement indicator at time klWeighting the statistical distance between the k moment pre-measurement measuring point i and the candidate measurement point by adopting a statistical distance association rule to obtain a weighted statistical distance IEWd at the k momentij，k(ii) a Selecting weighted statistical distance IEWd of k timeij，kAnd taking the candidate measuring point corresponding to the minimum as the optimal target measuring point at the k moment, and optimally updating the target track at the k moment.
Step 5.3 comprises the following substeps:
substep 5.3.1, residual e from Kalman filter at time kij，kObtaining the statistical distance d between the k moment pre-measurement measuring point i and the jth candidate measurement pointij，k(ii) a Comprising the following substeps:
substep 5.3.1.1, setting m candidate measuring points in a wave gate, wherein each candidate measuring point comprises n measuring indexes, and then the Kalman filter residual e at the moment kij，kComprises the following steps:
wherein z isj，kThe measurement vector of the jth candidate measurement point at time k,
a vector is estimated for the state of the predicted measurement point i at time k-1 versus time k.
Substep 5.3.1.2, residual e from Kalman filter at time kij，kCalculating the statistical distance d between the predicted measurement point i at the moment k and the jth candidate measurement pointij，kComprises the following steps:
eij，k＝[Δ1，…，Δl，…，Δn]T；
wherein S isij，kPredicting an innovation covariance matrix, Δ, for the measurement point i and the jth candidate measurement point at time k1Is the absolute value, Δ, of the difference between the 1 st measurement indicator of the jth candidate measurement point and the corresponding measurement indicator of the predicted measurement point ilThe absolute value, Δ, of the difference between the l (l =1,2, \8230;, n) th measurement indicator of the jth candidate measurement point and the corresponding measurement indicator of the predicted measurement point inThe absolute value of the difference between the nth measuring index of the jth candidate measuring point and the corresponding measuring index of the predicted measuring point i
The innovation variance of the first measurement indicator at time k.
In the above statistical distance calculation formula, the weighting values of the measurement indexes in the statistical distance are the same, that is, the weighting coefficients are the same, and the information of the measurement indexes is not fully utilized, so that a larger deviation occurs in the nearest neighbor algorithm under the statistical distance.
5.3.2, using the weighting factor α of the first measurement indicator at time klWeighting the statistical distance between the k-time pre-measurement measuring point i and the jth candidate measurement point to obtain the weighted statistical distance IEWdij，k：
Wherein alpha islThe weighting factor, Δ, of the l (l =1,2, \8230;, n) th measurement index at time klIs the absolute value of the difference between the measurement index l (l =1,2, \8230;, n) of the jth candidate measurement point and the corresponding measurement index of the predicted measurement point,
is the innovation variance of the first measurement indicator at time k.
The smaller the entropy value of a certain measurement index is, the larger the variation level of the measurement index is. The radar tracking system can obtain more information amount from the measurement indexes, and in combination with all the measurement indexes, the measurement indexes with small entropy values have larger effect in the system, so that larger weight should be given. Conversely, the larger the entropy of the measurement indicator is, the smaller the variation level of the measurement indicator is, the less information the system will obtain, and the smaller the weight should be given.
5.3.3 statistical distance IEWd weighted according to time kij，kSelecting weighted statistical distance IEWd at time kij，kAnd taking the candidate measuring point corresponding to the minimum as the optimal target measuring point at the k moment, and optimally updating the target track at the k moment.
IEWdij，kFor calculating the distance between the candidate measurement point and the predicted measurement point based on the statistical distance of the entropy weight, taking IEWdij，kAnd taking the candidate measuring point corresponding to the minimum as the optimal target measuring point at the k moment, and optimally updating the target track at the k moment.
By utilizing the entropy of the measurement index information and introducing the entropy weight method into the statistical distance method, the tracking error can be further reduced.
In the invention, according to the obtained measurement vector z of the optimized target measurement point with the minimum statistical distance based on the information entropy weightk' calculating the state estimation vector of the optimized k-time target
Sum estimation error covariance matrix Pk。
Pk＝Pk/k-1-KkH Pk/k-1
Estimating a vector according to the state of the optimized k-time target
Sum estimation error covariance matrix PkEstimating the vector for the state of the target at time k +1
Sum estimation error covariance matrix Pk+1/kPredicting to obtain a state prediction vector of the target at the k +1 moment
Innovation covariance matrix Sk+1And Kalman gain Kk+1Then, repeating the steps 3 to 5, optimally updating the target track at the moment k +1, and deducing the state estimation vector of the target at the moment k +1
Sum estimation error covariance matrix Pk+1And repeating the steps to obtain the optimal tracking track information of the target.
Simulation experiment:
two target tracking algorithms are commonly adopted in the set simulation process, and the nearest neighbor algorithm (NN) and the algorithm of the Invention (IEWNN) are used for tracking the targets of the single target in the clutter environment. Assuming a target tracking scene under a clutter environment, simulating in a two-dimensional plane coordinate system, and if the measurement vector of a measurement point is two-dimensional, determining the area of a tracking gate to be Av＝πγ|S(k)|1/2Wherein the tracking wave gate is set to γ =16,SkThe false measurement in unit area is 0.0089 and the false measurement number in unit time is 50 for the innovation covariance matrix. The target makes a uniform linear (CV) motion, the system state equation is shown as step 1, and the initial state vector of the target is x0＝[200 0 10000 -35]TMeasuring noise W by using the measurement equation of the radar tracking system as shown in step 1kIs variance r =200m2With an initial covariance matrix of R0And R is11＝R22＝200m2，R12＝R21＝0m2And the sampling interval is t =1s, no false measurement is added in the first 10s during the target motion process, and false measurement is added from 10s to 200 s.
The radar continuously scans for 200 times to obtain a target tracking track graph based on a nearest neighbor algorithm and associated tracking based on the method, as shown in fig. 3, as can be seen from fig. 3, the tracking track of the method is closer to the real situation, which shows that the method reduces the data association error.
Fig. 4 is a target tracking comparison graph of the nearest neighbor algorithm (NN) and the nearest neighbor algorithm (IEWNN) based on the entropy weight, and as can be seen from fig. 4 (a), 4 (b), 4 (c), and 4 (d), compared with the nearest neighbor algorithm, the method of the present invention has the advantages of faster convergence speed of the estimated values of the distance and the speed in the X and Y directions after tracking, better convergence effect, and closer actual tracking condition to the true value. Fig. 5 is a comparison graph of target tracking errors using a nearest neighbor algorithm (NN) and a nearest neighbor algorithm (IEWNN) based on information entropy weight, and it can be seen from fig. 5 (a), 5 (b), 5 (c), and 5 (d) that the error convergence speed of the distance and speed in the X and Y directions after tracking by the method of the present invention is faster and closer to the true distance and speed in the X and Y directions compared with the nearest neighbor algorithm. Fig. 6 is a comparison graph of the root mean square error of 100 monte carlo experiments respectively performed by using a nearest neighbor algorithm (NN) and a nearest neighbor algorithm (IEWNN) based on information entropy weight, and it can be seen from fig. 6 (a), 6 (b), 6 (c), and 6 (d) that the root mean square error of the X-direction distance, the Y-direction distance, and the direction velocity at each time of the method of the present invention is better than that of the NN algorithm.
From the above, it can be seen that the radar tracking result obtained by the method of the present invention is closer to the real situation, which shows that the method of the present invention determines the weight coefficient of each measurement index by analyzing and calculating the information entropy of the known measurement information and adopting the entropy weight method, and weights the statistical distance association criterion, thereby solving the disadvantages that the statistical distance criterion is not emphasized in the important degree of the attributes because all attributes are equal to participate in the calculation, and the result is easily influenced by a single attribute. Compared with other improved algorithms, the method has lower modification cost and better applicability, and is easier to be used for modification and upgrading of related equipment. The method is theoretically not limited to the nearest neighbor algorithm improvement optimization under two-dimensional measurement, but is also suitable for the nearest neighbor algorithm under multi-dimensional measurement information, and along with the diversification of the measurement information, the mined information is richer, and the algorithm improvement effect is more ideal.
The first measuring index in the embodiment of the invention is information such as distance, speed, azimuth angle, amplitude and the like in X and Y directions under a two-dimensional rectangular coordinate system corresponding to the track prediction measuring point at the corresponding moment. The fact in the drawings of the present specification is the real case of the object.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the method embodiments may be implemented by hardware related to program instructions, and the program may be stored in a computer readable storage medium, and when executed, the program performs the steps including the method embodiments; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily think of the changes or substitutions within the technical scope of the present invention, and shall cover the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the appended claims.
Claims (10)
1. The target track optimization method based on information entropy weight and nearest neighbor data association is characterized by comprising the following steps of:
step 1, setting a state equation of a radar tracking system to be Xk+1＝FXkAnd the measurement equation of the radar tracking system is Zk＝HXk+Wk；
Setting measuring points obtained by the radar tracking system at the first two moments after the track is started as unique real measuring points; measuring vector Z of measuring points at two moments before and after track start acquired by radar tracking system0，Z1Calculating an initial state vector of the target
Wherein Xk+1Is the state vector, X, of the radar tracking system at time k +1kFor the state vector of the radar tracking system at time k, WkIs a set of measurement points at time k; f is a state transition matrix of the radar tracking system, and H is a measurement matrix of the radar tracking system; x is a radical of a fluorine atom0Is the position of the target in the X direction, y, under a two-dimensional rectangular coordinate system at the initial moment0Is the position of the target in the Y direction under the two-dimensional rectangular coordinate system at the initial moment,
is the speed of the target X direction under the two-dimensional rectangular coordinate system at the initial moment,
is the speed of the target in the Y direction under a two-dimensional rectangular coordinate system at the initial moment [ ·]TIs the transposition of the matrix;
step 2, measuring vectors Z of measuring points at two moments before and after the track start are obtained according to the radar tracking system0，Z1Initializing the Kalman filter by a two-point difference method, and calculating the initial state estimation vector of the Kalman filter
And initial estimation error covariance matrix P0；
Step 3, estimating a vector according to the initial state of the Kalman filter
And initial estimation error covariance matrix P0Calculating the state estimation vector of the target at the k moment by adopting an iterative method
Covariance matrix P of estimation error of target at k timek/k-1Prediction vector of target at time k
Innovation covariance matrix S of k time targetskAnd k isKalman gain K of the target of engravingkWherein k =1,2.. N, N ∈ N+；
Step 4, obtaining a measurement point set W obtained by radar scanning at the moment kkThe prediction vector of the target at the k moment
The position of the point is used as the center of a tracking wave gate, a threshold value of the tracking wave gate is selected, and a measurement point set W at the moment k is measuredkCarrying out primary screening to obtain candidate measuring points at the moment k;
step 5, when the number of candidate measuring points at the time k is 0, then the state estimation vector of the target at the time k is obtained
And the covariance matrix P of the estimated error of the target at the k timek/k-1For track extrapolation;
when the number of the candidate measuring points at the moment k is 1, the measuring vector of the candidate measuring points at the moment k is used for track updating;
and when the number of the candidate measuring points at the moment k is more than 1, optimizing and updating the target track at the moment k by adopting an entropy weight method.
2. The method for optimizing the target track based on the information entropy weight and the nearest neighbor data association as claimed in claim 1, wherein in step 1, a state transition matrix F of the radar tracking system, a measurement matrix H of the radar tracking system, and a measurement vector Z of the target at the time k are set under two-dimensional motionkAnd the measuring vector Z of the measuring points at the first two moments after the track is started0，Z1Are respectively:
Zk＝[Zx，k Zy，k]T，Z0＝[Zx，0 Zy，0]T，Z1＝[Zx，1 Zy，1]T；
wherein [ ·]TIs the transposition of the matrix, and t is the sampling interval; zx，kThe distance of the target X direction under the two-dimensional rectangular coordinate system at the moment k is obtained; z is a linear or branched membery，kThe distance of the target Y direction under the two-dimensional rectangular coordinate system at the moment k is obtained; zx，1X-direction position measurement value, Z, obtained for target at 1 st moment in two-dimensional rectangular coordinate systemx，0X-direction position measurement value, Z, in a two-dimensional rectangular coordinate system obtained at the 0 th moment for the targety，1The measured value of the position in the Y direction, Z, in the two-dimensional rectangular coordinate system obtained at the 1 st moment for the targety，0And measuring the position value in the Y direction under the two-dimensional rectangular coordinate system obtained at the 0 th moment for the target.
3. The method for optimizing target track based on information entropy weight and nearest neighbor data association as claimed in claim 2, wherein in step 2, the calculation formula for initializing the kalman filter by the two-point difference method is:
wherein r is the measurement noise sequence W at the initial time0The variance of (a) is calculated,
is an estimated value of the position in the X direction of the Kalman filter in the initial state under a two-dimensional rectangular coordinate system,
is an estimated value of the speed in the X direction in the initial state of the Kalman filter under a two-dimensional rectangular coordinate system,
is an estimated value of the Y-direction position of the Kalman filter in the initial state under a two-dimensional rectangular coordinate system,
the estimated value of the Y-direction speed of the Kalman filter in the initial state under the two-dimensional rectangular coordinate system is obtained.
4. The target track optimization method based on information entropy weight and nearest neighbor data association as claimed in claim 3, wherein in step 3, the formula adopted by the iterative method is:
Pk/k-1＝FPk-1FT
Sk＝HPk/k-1HT+Rk
wherein, the first and the second end of the pipe are connected with each other,
estimating a vector, P, for the state of the target at time k-1k-1Estimation error covariance matrix, R, for the target at time k-1kMeasuring noise for time kCovariance matrix,Tis a transposition of the matrix,. 1-1Is the inverse of the matrix.
5. The method for optimizing target track based on information entropy weight and nearest neighbor data association as claimed in claim 1, wherein in step 4, the preliminary screening comprises the following sub-steps:
and a substep 4.1 of setting a two-dimensional rectangular coordinate system, selecting a tracking wave gate according to an elliptic wave gate rule, determining the measurement vector of the target to be two-dimensional, and determining the area of the tracking wave gate to be Av＝πγ|Sk|1/2；
And substep 4.2, judging whether the candidate measuring points meet the tracking wave gate threshold value condition or not according to the tracking wave gate area:
taking the measuring points meeting the conditions as candidate measuring points at the k moment;
wherein z iskIs the measurement vector of the measurement point at the time k,
a target prediction vector is obtained by predicting the k moment at the k-1 moment; gamma is a parameter and is defined by chi under the rule of elliptic wave gate2And obtaining a distribution table.
6. The method for optimizing the target track based on the association of the information entropy weight and the nearest neighbor data according to claim 1, wherein in the step 5, the optimizing and updating the target track at the time k by using the entropy weight method comprises the following substeps:
substep 5.1, according to the l (l =1,2, \ 8230;, n, n ≧ 1) measuring index a of the j (j =1,2, \ 8230;, m, m > 1) candidate measuring point at the time kjlAnd the prediction vector of the target at the k time
Calculating the first measuring index a of the jth candidate measuring point at the moment kjlFirst measurement index a of a predicted measurement point i tracking the center of the wave gateilError value Δ therebetweenjl：
△jl＝|ajl-ail|；
Step 5.2, according to the first measuring index a of the jth candidate measuring point at the moment kjlFirst measurement index a of a predicted measurement point i tracking the center of the wave gateilError value Δ therebetweenjlAnd the number m of candidate measuring points at the moment k to obtain the uncertainty S of the first measuring index at the moment kl(ii) a Uncertainty S of the first measurement indicator at time klNormalization processing is carried out to obtain the weight coefficient alpha of the first measuring index at the k momentl；
Step 5.3, according to the weighting coefficient alpha of the first measurement index at the time klWeighting the statistical distance between the k moment pre-measurement measuring point i and the candidate measurement point by adopting a statistical distance association rule to obtain a weighted statistical distance IEWd at the k momentij，k(ii) a Selecting weighted statistical distance IEWd of k timeij，kAnd taking the candidate measuring point corresponding to the minimum as the optimal target measuring point at the time k, and optimally updating the target track at the time k.
7. The method for optimizing a target track based on the association of the information entropy weight and the nearest neighbor data according to claim 6, wherein the substep 5.2 comprises the substeps of:
substep 5.2.1, based on the first measurement index a of the jth candidate measurement point at time kjlFirst measurement index a of a predicted measurement point i tracking the center of the wave gateilError value Δ therebetweenjlCalculating the ratio p of the jth measurement index of the jth candidate measurement point at the time k in the m candidate measurement pointsjl：
Substep 5.2.2, based on the proportion p of the first measurement indicator of the jth candidate measurement point at time k in the m candidate measurement pointsjlCalculating the information entropy H of the first measurement index at the time kl：
Substep 5.2.3, according to the number m of jth candidate measuring points at the moment k, calculating the maximum information entropy H of the ith measuring index at the moment klmax：
Hlmax＝log2m；
Substep 5.2.4, entropy H of the information of the first measurement indicator at time klMaximum information entropy H of the first measurement index at time klmaxCalculating the uncertainty S of the first measurement index at the time kl：
Substep 5.2.5, using the uncertainty S of the first measurement indicator at time klCalculating the weight coefficient alpha of the first measurement index at the time kl：
8. The method for optimizing target track based on information entropy weight and nearest neighbor data association as claimed in claim 7, wherein the step 5.3 comprises the following sub-steps:
substep 5.3.1, residual e from Kalman filter at time kij，kObtaining the statistical distance d between the k moment pre-measurement measuring point i and the jth candidate measurement pointij，k；
Substep 5.3.2, using the weight of the first measurement indicator at time kCoefficient of gravity alphalWeighting the statistical distance between the k-time pre-measurement measuring point i and the jth candidate measurement point to obtain the weighted statistical distance IEWd of the k-timeij，k；
Substep 5.3.3, accounting for the distance IEWd according to the empowerment at time kij，kSelecting weighted statistical distance IEWd at time kij，kAnd taking the candidate measuring point corresponding to the minimum as the optimal target measuring point at the k moment, and optimally updating the target track at the k moment.
9. The method for optimizing a target track based on the association of the information entropy weight and the nearest neighbor data according to claim 8, wherein the substep 5.3.1 comprises the substeps of:
substep 5.3.1.1, setting m candidate measuring points in the tracking wave gate, wherein each candidate measuring point comprises n measuring indexes, and then the Kalman filter residual e at the moment kij，kComprises the following steps:
wherein z isj，kThe measurement vector of the jth candidate measurement point at time k,
estimating a vector for the state of the predicted metrology point i at time k-1 to time k;
substep 5.3.1.2, residual e from Kalman filter at time kij，kCalculating the statistical distance d between the predicted measurement point i at the moment k and the jth candidate measurement pointij，kComprises the following steps:
eij，k＝[△1，…，△l，…，△n]T；
wherein s isij，kPredicting an innovation covariance matrix, Δ, for the measurement point i and the jth candidate measurement point at time klIs the absolute value of the difference between the first measuring index of the jth candidate measuring point at the moment k and the corresponding measuring index of the predicted measuring point i,
the innovation variance of the first measurement index at the moment k is l =1,2, \8230, and n is more than or equal to 1.
10. The method for optimizing the target track based on the information entropy weight and the nearest neighbor data association as claimed in claim 9, wherein in sub-step 5.3.2, the weighting process is:
wherein, IEWdij，kWeighted statistical distance, alpha, for time klIs the weighting factor of the first measurement indicator at time k.
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