CN110849372A - Underwater multi-target track association method based on EM clustering - Google Patents

Underwater multi-target track association method based on EM clustering Download PDF

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CN110849372A
CN110849372A CN201911188834.9A CN201911188834A CN110849372A CN 110849372 A CN110849372 A CN 110849372A CN 201911188834 A CN201911188834 A CN 201911188834A CN 110849372 A CN110849372 A CN 110849372A
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初妍
王科智
宁慧
王丽娜
于海涛
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Harbin Engineering University
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Abstract

The invention provides an underwater multi-target track association method based on EM clustering. Preprocessing the data; constructing and constructing a track quality grading model by introducing an information entropy, and preferentially performing track association matching by taking a point with good quality as a center when a track is associated; establishing a Gaussian mixture model through the topological information among the tracks, and simultaneously taking the points with good quality as the mass center to obtain a Gaussian probability density function; establishing a mixed integer nonlinear programming model, and reducing association deviation by using a recursive idea; and solving an extreme value of the unknown parameters through EM clustering to set a correlation judgment threshold, simultaneously carrying out uniqueness processing on the result, solving to obtain a corresponding relation of the underwater target track, and finally matching the track of the underwater target. Under the conditions of different target numbers, different sensor angle and distance measurement errors, different sensor detection probabilities and the like, the method has good positive correlation rate and has certain superiority and robustness.

Description

Underwater multi-target track association method based on EM clustering
Technical Field
The invention relates to an underwater multi-target track association method.
Background
The ocean resources of the earth are very abundant, and the ocean area accounts for about seventy percent of the total surface area of the earth. However, as the development of the method is slower in the exploration and utilization link of the ocean, a large development space is left for ocean resources. The development of the ocean is undoubtedly the most important in the development of each country in the world nowadays, but before the ocean resources are developed and utilized, the ocean needs to be relatively comprehensively understood through a large amount of ocean data, and the process needs a series of ocean development support technologies including track correlation technology. Meanwhile, the detection and tracking technology of underwater targets is greatly improved and the space is improved, the targets can be detected in time and accurately tracked, the development and utilization of the ocean are very important, meanwhile, in the field of multi-sensor information fusion, track association is a premise and a basis of multi-sensor information fusion, the purpose is to judge whether tracks reported by different sensors originate from the same target, when the sensors have monitoring areas, missed detection and random false alarms which are not identical, the reported targets of the sensors are not identical, so that a corresponding track does not exist in a track set reported by another sensor, and the difficulty of the original complex track association problem is increased. In addition, system errors generally exist in the detection process of the sensor and are influenced by various factors, so that deviation exists between the position state estimation of the target and the real target position, and the performance of the traditional track correlation algorithm is seriously deteriorated. If the target tracks can be accurately correlated under the complex environment with multiple noise points under water, the method is a premise and a basis for target tracking under high level water. If the high-resolution track association can be carried out in the multi-target track association, the subsequent link influence caused by noise and false alarm can be reduced, a new target can be perceived by finding a new track, and the influence caused by track omission is reduced.
Common algorithms adopted by the multi-sensor track association include Bayes (Bayes) estimation, least square estimation and evidence combination theory (Dempster-Shafer, D-S) in the aspect of estimation algorithm; BP neural network series in the aspect of artificial intelligence algorithm, GA genetic algorithm optimization algorithm, weighted fusion algorithm and the like. The Bayesian estimation is the earliest algorithm, and has great limitation because the prior measurement variance of the sensor is needed, so that the algorithm is difficult to be widely applied. Although the D-S evidence theory does not need prior information and needs less conditions than Bayes reasoning, the combination condition of the evidence is very strict and cannot be applied to the premise background of evidence conflict and evidence basic probability determination, and a plurality of scholars study the D-S evidence theory problem based on the evidence conflict at present. Although the information fusion algorithm based on the neural network type has good parallel processing capability and stability, when the number of layers of the network is large, the convergence cannot be fast, and the global optimal solution is difficult to obtain. The information fusion method for optimizing by using the genetic algorithm has the advantages of implicit parallel capability, strong robustness and the like, but the time complexity of the algorithm is high. Meanwhile, for the conditions of high noise and more false alarms of the underwater environment, an algorithm which can still accurately and effectively solve the problem of track association of underwater multiple targets when a certain system error exists in the sensor is needed.
Disclosure of Invention
The invention aims to provide an underwater multi-target track association method based on EM clustering, which has better precision and tolerance.
The purpose of the invention is realized as follows:
the method comprises the following steps: carrying out classification pretreatment on the track, and simultaneously carrying out classification according to the track quality entropy;
step two: the GMM model is established, and the GMM model is established,
2.1 ranking Pre-processing post uncertainty level αj(k) Level 1 set of traces XBThe locus set X of other levels is regarded as the centroid of Gaussian model in GMMAA set of sample points considered to be GMM;
2.2 mixing different data points with Gaussian distribution, calculating the mean vector, covariance matrix and mixing weight in GMM model, and obtaining model probability density expressionWhere the sensor bias is vector estimated from the offset vector ηkPredicting the covariance of the deviation vector by the followed dynamic model to obtain the optimal corresponding deviation estimation;
step three: evaluating the maximum likelihood and establishing an MINLP model for recursion;
step four: and performing EM clustering, and finally realizing accurate target classification and identification.
The present invention may further comprise:
1. in step one, the set of quality exclusion events for the tracked trace is: and (4) according to the track scanning state, whether the collection is in the extrapolation time, the track state estimation stable condition and the track stable condition, processing the idea of introducing weights into the four event sets to obtain track quality entropy for grading.
2. In the second step, a GMM model is established, corresponding movement is carried out on the center of mass of the GMM to the sample point set according to the neighborhood topological structure, if the distance between the final center of mass and the sample point is smaller, the association degree between the tracks is higher, and after the optimal matching relation is obtained in a certain mode, the matching association relation between the track sets is obtained by using posterior probability.
3. In the second step, a Gaussian radial basis function is obtained:
Figure BDA0002293062370000021
XAa track sample point set is obtained, and K is a dimension; delta2Introducing a uniform distribution for the covariance in the Gaussian model
Figure BDA0002293062370000022
Then, a probability density function is obtained:
Figure BDA0002293062370000023
where ω is a uniformly distributed weight coefficient.
4. In step two, the sensor bias is vector estimated, η for the sensor bias vectorkηkDifferent for each sensor, and for the time-varying case, the offset vector ηkThe following dynamic model η is followedk＝Fk-1,ηηk-1+wk-1,ηIn the formula Fk-1,ηIs a transition matrix, and wk-1,ηIs a zero mean; the initial bias estimate and corresponding covariance are
Figure BDA0002293062370000031
For theObtaining an optimal corresponding bias estimate using maximum likelihood rules
Figure BDA0002293062370000033
Where U is the correspondence matrix.
5. Evaluating the maximum likelihood in the third step, solving the problem by linear binary distribution and least square continuous optimization, and estimating the maximum likelihood based on the current deviation
Figure BDA0002293062370000034
Determining a correspondence matrix
Figure BDA0002293062370000035
j is a trace point based on passing the current
Figure BDA0002293062370000036
Calculating a deviation estimate
Figure BDA0002293062370000037
Recursion is continued until the matrix and bias estimates no longer change.
6. The correlation method in the fourth step is that the EM clustering algorithm completes the correlation matching of the underwater target track, wherein the EM algorithm comprises the step E and the step M,
e, calculating the posterior probability of the feature vector to the GMM model on the basis of the initial parameters,
Figure BDA0002293062370000038
the M step is the posterior probability obtained by the E step,respectively solving extreme values of the unknown parameter sets, if the target track i monitored on the sensor A and the target track j monitored on the sensor B come from the same underwater target, then the target track i and the target track j have
Figure BDA0002293062370000039
In the formula:
Figure BDA00022930623700000310
is to carry out the judgment threshold of the track association and simultaneously to carry out the judgment of the track association
Figure BDA00022930623700000311
The largest corresponding trajectory matches.
The invention relates to the technical field of underwater multi-target track association, in particular to a multi-sensor underwater multi-target track association method based on EM clustering application recursion idea modeling. Compared with the prior art, the invention has the advantages that: a. the underwater environment is complex and changeable, the noise interference is serious, the accuracy of a single sensor is low, and in order to improve the probability and the accuracy of detection and tracking, the invention adopts multiple sensors for correlation; b. the method has important engineering significance c in the environment with more noise points under the condition that noise points are underwater, the GMM model is established for the distribution of the characteristic vectors, Gaussian distribution mixing is carried out on different data points, a probability density function in the GMM model is calculated, and difference resistance modeling is carried out. d. The method has the advantages that the MINLP is used for recursion, deviation estimation is reduced, and the tolerance can be effectively improved in the environment with multiple underwater noise points and high false alarm. The method can solve the problem of poor anti-noise capability of the traditional underwater target correlation, can effectively improve the underwater multi-target track correlation accuracy rate, and has certain applicability.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a simulation of a simulation experiment of the present method;
FIG. 3 is a graph comparing performance of an upper limit algorithm for sensor angle measurement error;
FIG. 4 is a graph comparing the performance of the sensor range error ceiling algorithm;
FIG. 5 is a graph comparing performance of different detection probability algorithms of a sensor;
FIG. 6 is a comparison graph of performance of an algorithm for detecting the number of different targets by a sensor;
FIG. 7 is a plot of root mean square error for different sensor goniometric system errors;
FIG. 8 is a plot of the root mean square error under different sensor ranging system errors.
Detailed Description
The invention is described in more detail below by way of example.
With reference to fig. 1, the specific steps of the present invention are as follows:
(1) track grading pretreatment for underwater target track
The set of quality exclusion events for the traced trajectory is: h is HA{HA1The track status is scanned and changed, HA2The scanning condition of the track is unchanged, HB{HB1Track is within extrapolation time, HB2Track outside of maximum extrapolation time }, HC{HC1Stable estimation of trajectory state, HC2Trajectory state estimation jitter, HD{HD1Stable track, HD2Track hunting }.
The event set H can reflect the track condition, i.e. the track quality, in a period of time, the above four event sets are all repulsive, and whether the track state detected by the sensor is stable and the deviation degree is known through the four event sets. The situation of the quality entropy is judged by the frequency of the occurrence of the above H event set. While preprocessing the data for trajectory correlation.
Entropy I of the quality classification of the trace points is
Figure BDA0002293062370000041
In the formula CnnNormalized weight for the nth event; mnnThe total number of sub-events for the nth event; p (m) represents the probability of the mth sub-event of the nth event. Assuming that O tracks are shared at time k, the mass entropy E (k) { E) is obtained1(k),E2(k),...,EU(k) And normalizing the obtained product, namely:
Figure BDA0002293062370000042
in the formula Ej(k) And j is the tracking quality entropy of the track j at the moment k, wherein j is equal to {1, 2, …, O }.
Uncertainty level α for time k trajectory jj(k) The method comprises the following steps: e is not less than 0j(k) 1 when the content is less than or equal to 0.2; e is more than 0.2j(k) 2 when the content is less than or equal to 0.5; e is more than 0.5j(k) When the content is less than or equal to 1, the content is 3. Therefore, data preprocessing is graded, the lower the grade number is, the better the tracking quality is, and the higher the grade number is, the worse the tracking quality is, so that in the process of track association, a point with good quality can be taken as a center to perform track association matching.
(2) Construction of GMM model
Ranking the pre-processing with uncertainty level αj(k) Level 1 set of traces XBThe locus set X of other levels is regarded as the centroid of Gaussian model in GMMAConsidering the sample point set of the GMM, their gaussian radial basis functions are given by:
in the formula: k is dimension; delta2Is the covariance in the gaussian model. Meanwhile, when the sensor is in a noisy state, a system error state and the like, the target of the two sensors is inconsistent, namely a non-homologous track appears in the track set, so that a uniform distribution is brought:
Figure BDA0002293062370000052
thus obtaining the track
Figure BDA0002293062370000053
The GMM probability density function of (a) is:
in the formula: ω is a uniformly distributed weight coefficient. Because the smaller the difference of the neighborhood topology of the tracks, the higher the probability that they are from the same target, the higher the corresponding weight proportion in the GMM, and the probability of the proportional weight of each gaussian component is described as:
in the formula:
Figure BDA0002293062370000056
the resulting GMM probability density function is therefore:
Figure BDA0002293062370000057
(3) evaluating maximum likelihood function and performing MINLP modeling recursion
① vector estimation of sensor bias
The offset vector of the sensor can be used as ηkηkFor time varying conditions, the offset vector ηkFollowing the following dynamic model
ηk＝Fk-1,ηηk-1+wk-1,η
In the formula Fk-1,ηIs a transition matrix, and wk-1,ηIs a zero mean; the initial bias estimate and corresponding covariance are
Figure BDA0002293062370000061
② evaluating the maximum likelihood function
If one wants to optimize the model, the first solution is the evaluation of the likelihood function, for which the two parts P (z) of the likelihood function are considered separatelyk,η|Uk,ηk) And P (Z)k,zk,η|Uk,ηk) Evaluation was performed.
1) Evaluation of P (z)k,η|Uk,ηk)
For the
Figure BDA0002293062370000062
Under the Gaussian assumption, the likelihood function zk,ηCan be represented by the following formula
Figure BDA0002293062370000063
In the formula nηDenotes a deviation parameter, P (z)k,η|Uk,ηk) And matrix UkAre independent of each other.
2) Evaluation of P (Z)k,zk,η|Uk,ηk),
Figure BDA0002293062370000064
Figure BDA0002293062370000065
Figure BDA0002293062370000066
For a single point distance, the distance between the points,
Figure BDA0002293062370000067
is deviation of track
The target density per unit volume defines a target density β over the monitored volumetThe monitoring probability of the sensor is
Figure BDA0002293062370000068
βtCan be regarded as βt＝1/4D2Where D represents the average target distance from its nearest target point. The likelihood function that relates two local orbits can be evaluated, the local orbit estimate can be calculated as
Figure BDA0002293062370000069
Maximizing the likelihood function P (Z)k,zk,η|Uk,ηk) Corresponding to minimizing its negative logarithm. Bonding of
Figure BDA00022930623700000610
Comprises the following steps:
Figure BDA00022930623700000611
while removing constants not related to parameter estimation to obtain the following optimization model
Figure BDA0002293062370000071
This problem then becomes the MINLP problem. It can be solved by a linear binary allocation problem and a least-squares continuous optimization problem.
③ recursion of MINLP
Estimation of bias based on current
Figure BDA0002293062370000072
Determining a correspondence matrix
Figure BDA0002293062370000073
Eliminating the influence of invariant parameters to obtain an optimization model as follows:
Figure BDA0002293062370000074
by the current time
Figure BDA0002293062370000075
Calculating a deviation estimate
Figure BDA0002293062370000076
Figure BDA0002293062370000077
The corresponding covariance is obtained:
Figure BDA0002293062370000078
the MINLP model can be recursive, the pseudo-code is as follows:
inputting the deviation estimated value of the current time k
Figure BDA0002293062370000079
1) By current deviation estimation
Figure BDA00022930623700000710
Calculating a correspondence matrix
2) In view of the current matrix
Figure BDA00022930623700000712
Updating bias estimates
3) Repeating (1) and (2) until the corresponding matrix is not changed any more.
4) Outputting a final deviation estimate
Figure BDA00022930623700000714
And a corresponding matrix
Figure BDA00022930623700000715
The transformation relationship between sets of point sets may be expressed as follows:
XA＝XB+v(XB)
in the formula v (X)n) For the offset function, a regularization term is added to allow the trajectory set to move as a whole. Therefore, a regularization function is added to the regenerated kernel Hilbert space
Figure BDA0002293062370000081
Obtain an expectation of a set of parameters and a set of sample points as
Figure BDA0002293062370000082
In the formula:
Figure BDA0002293062370000083
{ω，δ2v is the unknown parameter set;
Figure BDA0002293062370000084
is the posterior probability; λ is the weight coefficient of the regularization term. Describing the form of the v function by maximizing it according to the variational method
Figure BDA0002293062370000085
Wherein: omegajIs the weight coefficient matrix W ═ ω1,ω2,...,ωm]TAn element of (1);is a Gaussian kernel matrix, β is a smoothness coefficient, thus obtaining the matching incidence relation among the target track point set, which is XA＝XB+ GW, while substituting into the above formula
Figure BDA0002293062370000087
In the formula: gj,nIs a row vector of a gaussian kernel matrix.
(4) Performing EM clustering to perform underwater target track association
In the expectation step, the posterior probability is known as follows according to Bayesian theorem:
in the formula: j is 1, 2. If a posterior probability
Figure BDA0002293062370000089
Higher, this means that the probability that the object trajectories i and j are from the same object is higher, while the matrix
Figure BDA0002293062370000091
Is the associated probability matrix of the set of trajectories. Therefore, the probability that non-homologous trajectories can be obtained is:
Figure BDA0002293062370000092
in the maximization step, in order to maximize Q, the unknown parameter sets are respectively extremized. Solution (II)
Figure BDA0002293062370000093
So as to obtain the compound with the characteristics of,
W＝[diag(P1)G+λδ2I]-1(PXA-diag(P1)XB)
Figure BDA0002293062370000095
Figure BDA0002293062370000096
in the formula: 1 is a full 1 column vector; and I is an identity matrix.
From the above equation, if the target trajectory i monitored on sensor a and the target trajectory j monitored on sensor B are from the same underwater target, then there are:
Figure BDA0002293062370000097
in the formula:
Figure BDA0002293062370000098
is the decision threshold for making the track association. Meanwhile, because one-to-many error association conditions exist, in order to ensure the uniqueness of the association result, the method can be used for solving the problem that the error association between the two or more error association conditions exists
Figure BDA0002293062370000099
The largest corresponding trajectory matches.
In order to verify the effectiveness of the EM clustered underwater multi-target track association method, N underwater target track association problems are detected by using two sensors in a global rectangular coordinate system, and a simulation diagram is shown in FIG. 2.
The effectiveness of each algorithm under different angle measurement errors of a sensor is detected, and fig. 3 is an algorithm effectiveness comparison graph under different angle measurement system errors.
FIG. 4 is a comparison graph of performance of the proposed algorithm under different ranging system errors, and when the ranging system errors become large, the accuracy rate of the FFT and REP algorithms decreases significantly, and the non-homologous trajectory is wrongly associated. The algorithm reduces the association deviation through MINLP modeling recursion, can better perform track association and simultaneously has excellent tolerance to error under the environment of multiple noise points and high false alarm in an underwater environment, and can keep a relatively stable association rate under the condition of increasing system errors.
FIG. 5 is a performance comparison diagram of the proposed algorithm under different detection probabilities, and we only change the detection probability of the sensor under the condition that other conditions are not changed, so that the detection probability is changed at intervals of 0.5-1, and other parameters are not changed. As can be seen from the figure, when the detection probability of the sensor is small, the algorithm has obvious advantages in positive correlation rate and strong tolerance.
FIG. 6 is a positive correlation efficiency graph of an algorithm for the number of different underwater targets, and since the algorithm is adaptive to a threshold after passing through neighborhood topology information and an optimization model, when non-homologous tracks increase, the algorithm can still identify the correlation matching relationship of each target track, and the influence of the non-homologous tracks on a matching result is reduced.
It can be known from fig. 7 and 8 that the estimation accuracy of the algorithm of the present invention is more accurate than that of the other three algorithms in terms of the system error of the sensor, the average estimation deviation between the angle measurement and the distance measurement is small, and when the system error between the angle measurement and the distance measurement is fixed, the experimental result shows that the algorithm of the present invention has higher accuracy, because the algorithm of the present invention continuously performs model optimization on the deviation in the MINLP recursion, and reduces the influence caused by the sensor deviation, the accuracy of the algorithm of the present invention is higher than that of the other three algorithms in the continuous iteration process.
TABLE 1 Algorithm average run time Table(s)
Figure BDA0002293062370000101
As can be seen from the running times of the algorithms in table 1, the average running time of each algorithm gradually increases as the number of targets increases. The FFT algorithm continuously and alternately iterates the target track position, and the time consumption is shortest. The algorithm needs to be updated iteratively all the time in the clustering process of the EM algorithm when the track association is carried out, so the running time of the algorithm is relatively long. However, under the condition that the time is similar to the REP algorithm FCM algorithm, the tolerance of the algorithm is superior to the three algorithms, although the running time of the algorithm is greater than that of the FFT algorithm, under the condition that the underwater track correlation noise is high, certain requirements are required on the accuracy and the tolerance of the track correlation, and the tolerance of the FFT algorithm obviously does not meet the actual requirements, so that the algorithm has certain superiority in the track correlation for underwater targets.

Claims (7)

1. An underwater multi-target track association method based on EM clustering is characterized by comprising the following steps:
the method comprises the following steps: carrying out classification pretreatment on the track, and simultaneously carrying out classification according to the track quality entropy;
step two: the GMM model is established, and the GMM model is established,
2.1 ranking Pre-processing post uncertainty level αj(k) Level 1 set of traces XBThe locus set X of other levels is regarded as the centroid of Gaussian model in GMMAA set of sample points considered to be GMM;
2.2 mixing different data points with Gaussian distribution, calculating the mean vector, covariance matrix and mixing weight in GMM model, obtaining model probability density expression, carrying out vector estimation to sensor deviation, η according to bias vectorkPredicting the covariance of the deviation vector by the followed dynamic model to obtain the optimal corresponding deviation estimation;
step three: evaluating the maximum likelihood and establishing an MINLP model for recursion;
step four: and performing EM clustering, and finally realizing accurate target classification and identification.
2. The underwater multi-target track association method based on EM clustering as claimed in claim 1, wherein: in step one, the set of quality exclusion events for the tracked trace is: and (4) according to the track scanning state, whether the collection is in the extrapolation time, the track state estimation stable condition and the track stable condition, processing the idea of introducing weights into the four event sets to obtain track quality entropy for grading.
3. The underwater multi-target track association method based on EM clustering as claimed in claim 2, wherein: in the second step, a GMM model is established, corresponding movement is carried out on the center of mass of the GMM to the sample point set according to the neighborhood topological structure, if the distance between the final center of mass and the sample point is smaller, the association degree between the tracks is higher, and after the optimal matching relation is obtained in a certain mode, the matching association relation between the track sets is obtained by using posterior probability.
4. The underwater multi-target track association method based on EM clustering as claimed in claim 3, wherein: in the second step, a Gaussian radial basis function is obtained:XAa track sample point set is obtained, and K is a dimension; delta2Introducing a uniform distribution for the covariance in the Gaussian modelThen, a probability density function is obtained:
Figure FDA0002293062360000013
where ω is a uniformly distributed weight coefficient.
5. The method as claimed in claim 4, wherein the bias vector of the sensor is ηkηkDifferent for each sensor, and for the time-varying case, the offset vector ηkThe following dynamic model η is followedk＝Fk-1,ηηk-1+wk-1,ηIn the formula Fk-1,ηIs a transition matrix, and wk-1,ηIs a zero mean; the initial bias estimate and corresponding covariance are
Figure FDA0002293062360000021
For the
Figure FDA0002293062360000022
Obtaining an optimal corresponding bias estimate using maximum likelihood rules
Figure FDA0002293062360000023
Where U is the correspondence matrix.
6. The underwater multi-target track association method based on EM clustering as claimed in claim 5, wherein: evaluating the maximum likelihood in the third step, solving the problem by linear binary distribution and least square continuous optimization, and estimating the maximum likelihood based on the current deviation
Figure FDA0002293062360000024
Determining a correspondence matrixj is a trace point based on passing the current
Figure FDA0002293062360000026
Calculating a deviation estimate
Figure FDA0002293062360000027
Recursion is continued until the matrix and bias estimates no longer change.
7. The underwater multi-target track association method based on EM clustering as claimed in claim 6, wherein: the correlation method in the fourth step is that the EM clustering algorithm completes the correlation matching of the underwater target track, wherein the EM algorithm comprises the step E and the step M,
e, calculating the posterior probability of the feature vector to the GMM model on the basis of the initial parameters,
Figure FDA0002293062360000028
m is that the posterior probability obtained by E is used to respectively calculate the extreme value of the unknown parameter set, if the target track i monitored on the sensor A and the target track j monitored on the sensor B come from the same underwater target, then there is a target
Figure FDA0002293062360000029
In the formula:
Figure FDA00022930623600000210
is to carry out the judgment threshold of the track association and simultaneously to carry out the judgment of the track association
Figure FDA00022930623600000211
The largest corresponding trajectory matches.
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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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CN113793327A (en) * 2021-09-18 2021-12-14 北京中科智眼科技有限公司 High-speed rail foreign matter detection method based on token
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Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102724631A (en) * 2012-06-28 2012-10-10 上海交通大学 Position information updating method for position-based routing of vehicular ad hoc network
US20150338515A1 (en) * 2014-05-20 2015-11-26 Bae Systems Information And Electronic Systems Integration Inc. Automated Track Projection Bias Removal Using Frechet Distance and Road Networks
CN106959618A (en) * 2017-05-05 2017-07-18 国网山东省电力公司电力科学研究院 A kind of voltage control method for coordinating for optimizing weight based on ladder
CN107066806A (en) * 2017-02-15 2017-08-18 中国人民解放军海军航空工程学院 Data Association and device
CN108286971A (en) * 2017-10-18 2018-07-17 北京航空航天大学 A kind of forecast Control Algorithm that the Inspector satellite based on the optimization of MIXED INTEGER second order cone is evaded
CN109858526A (en) * 2019-01-08 2019-06-07 沈阳理工大学 Sensor-based multi-target track fusion method in a kind of target following
CN110188951A (en) * 2019-05-30 2019-08-30 重庆大学 A kind of method for building up of the optimizing scheduling of the brick field ferry bus based on least energy consumption
CN110361744A (en) * 2019-07-09 2019-10-22 哈尔滨工程大学 RBMCDA underwater multi-target tracking based on Density Clustering

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102724631A (en) * 2012-06-28 2012-10-10 上海交通大学 Position information updating method for position-based routing of vehicular ad hoc network
US20150338515A1 (en) * 2014-05-20 2015-11-26 Bae Systems Information And Electronic Systems Integration Inc. Automated Track Projection Bias Removal Using Frechet Distance and Road Networks
CN107066806A (en) * 2017-02-15 2017-08-18 中国人民解放军海军航空工程学院 Data Association and device
CN106959618A (en) * 2017-05-05 2017-07-18 国网山东省电力公司电力科学研究院 A kind of voltage control method for coordinating for optimizing weight based on ladder
CN108286971A (en) * 2017-10-18 2018-07-17 北京航空航天大学 A kind of forecast Control Algorithm that the Inspector satellite based on the optimization of MIXED INTEGER second order cone is evaded
CN109858526A (en) * 2019-01-08 2019-06-07 沈阳理工大学 Sensor-based multi-target track fusion method in a kind of target following
CN110188951A (en) * 2019-05-30 2019-08-30 重庆大学 A kind of method for building up of the optimizing scheduling of the brick field ferry bus based on least energy consumption
CN110361744A (en) * 2019-07-09 2019-10-22 哈尔滨工程大学 RBMCDA underwater multi-target tracking based on Density Clustering

Non-Patent Citations (16)

* Cited by examiner, † Cited by third party
Title
HAN-LIM CHOI等: "An outer-approximation algorithm for generalized maximum entropy sampling", 《2008 AMERICAN CONTROL CONFERENCE》 *
HONGYANZHU等: "joint track-to-track association and sensor registration at the track level", 《DIGITAL SIGNALPROCESSING41(2015)》 *
JÉRÉMY OMER等: "Hybridization of Nonlinear and Mixed-Integer Linear Programming for Aircraft Separation With Trajectory Recovery", 《IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS》 *
PRAMOD ABICHANDANI等: "Mixed Integer Nonlinear Programming Framework for Fixed Path Coordination of Multiple Underwater Vehicles Under Acoustic Communication Constraints", 《IEEE JOURNAL OF OCEANIC ENGINEERING》 *
WEISEN SHI等: "3D Multi-Drone-Cell Trajectory Design for Efficient IoT Data Collection", 《ICC 2019 - 2019 IEEE INTERNATIONAL CONFERENCE ON COMMUNICATIONS (ICC)》 *
丁婕: "复杂场景中运动目标的检测与跟踪", 《中国优秀硕士学位论文全文数据库 (信息科技辑)》 *
吴亮红: "差分进化算法及应用研究", 《中国优秀硕士学位论文全文数据库 (信息科技辑)》 *
孙少超等: "过失误差识别和数据校正的MILP模型的新视角", 《华东理工大学学报(自然科学版)》 *
崔亚奇等: "地空协同防空目标抗差跟踪算法", 《航空学报》 *
廖辉荣等: "多目标跟踪中联合概率数据关联优化算法", 《计算机仿真》 *
朱洪艳等: "基于松弛标号算法的多传感抗差航迹关联", 《控制与决策》 *
李伟: "复杂背景下多目标跟踪技术研究", 《中国优秀硕士学位论文全文数据库 (信息科技辑)》 *
李保珠等: "基于航迹矢量分级聚类的雷达与电子支援措施抗差关联算法", 《电子与信息学报》 *
李保珠等: "基于高斯混合模型的航迹抗差关联算法", 《航空学报》 *
谷晓琳等: "基于m-best数据关联和小轨迹关联多目标跟踪算法", 《系统工程与电子技术》 *
陈艳波等: "混合整数线性规划形式的抗差状态估计方法", 《电力自动化设备》 *

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112598061A (en) * 2020-12-23 2021-04-02 中铁工程装备集团有限公司 Tunnel surrounding rock clustering and grading method
CN112598061B (en) * 2020-12-23 2023-05-26 中铁工程装备集团有限公司 Clustering and grading method for tunnel surrounding rock
CN112906746A (en) * 2021-01-25 2021-06-04 北京工业大学 Multi-source track fusion evaluation method based on structural equation model
CN112906746B (en) * 2021-01-25 2024-04-02 北京工业大学 Multi-source track fusion evaluation method based on structural equation model
CN113793327A (en) * 2021-09-18 2021-12-14 北京中科智眼科技有限公司 High-speed rail foreign matter detection method based on token
CN113793327B (en) * 2021-09-18 2023-12-26 北京中科智眼科技有限公司 Token-based high-speed rail foreign matter detection method
CN116381607A (en) * 2023-04-11 2023-07-04 哈尔滨工程大学 Multi-target water-striking sound characteristic association method
CN116381607B (en) * 2023-04-11 2023-10-27 哈尔滨工程大学 Multi-target water-striking sound characteristic association method

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