CN110849372B - Underwater multi-target track association method based on EM clustering - Google Patents
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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
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 estimation algorithm aspect; 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 fewer conditions than Bayes reasoning, the combination condition of 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 have researched the D-S evidence theory problem based on 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 by the method,
2.1 grading the Pre-treatment uncertainty level α j (k) Level 1 track set X B The locus set X of other levels is regarded as the centroid of Gaussian model in GMM A A set of sample points considered to be GMM;
2.2 mixing different data points by Gaussian distribution, calculating the mean vector, covariance matrix and mixing weight in GMM model, obtaining model probability density expression, carrying out vector estimation on sensor deviation, and carrying out vector estimation according to bias vector eta k Predicting 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 higher the association degree between the tracks is, and after the optimal matching relation is obtained in a certain mode, the matching association relation between the track sets is obtained by utilizing posterior probability.
3. In the second step, a Gaussian radial basis function is obtained:
X A a track sample point set is obtained, and K is a dimension; delta 2 Introducing a uniform distribution for the covariance in the Gaussian model
Then, a probability density function is obtained:
where ω is a uniformly distributed weight coefficient.
4. In the second step, the sensor deviation is estimated by vector, and the offset vector of the sensor is represented by eta k Is expressed as eta k Different for each sensor, the offset vector η is for the time-varying case k Following the following dynamic model η k ＝F k-1,η η k-1 +w k-1,η In the formula F k-1,η Is a transition matrix, and w k-1,η Is a zero mean; an initial bias estimate and corresponding covariance are
For
Obtaining an optimal corresponding bias estimate using maximum likelihood rules
WhereinU is a correspondence matrix.
5. The maximum likelihood is evaluated in the third step, the solution is realized by a linear binary distribution problem and a least square continuous optimization problem, and the estimation is based on the current deviation
Determining a correspondence matrix
i, j are track points and are based on passing current
Calculating a deviation estimate
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,
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
In the formula:
is to carry out the judgment threshold of the track association and simultaneously to carry out
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. according to the method, by a preprocessing method of the track grading condition, the characteristic information representing the track quality is used for establishing the entropy grade, so that the entropy weight is obtained for track association, the track fusion accuracy is effectively improved, the risk that the track quality is reduced after fusion, the track fusion robustness is enhanced, and the fusion precision is improved. 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 H A {H A1 The track status is scanned and changed, H A2 The scanning condition of the track is unchanged }, H B {H B1 Track is within extrapolation time, H B2 Track outside of maximum extrapolation time }, H C {H C1 Trajectory state estimation is stable, H C2 Trajectory state estimation jitter, H D {H D1 Stable track, H D2 Track 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
In the formula C nn Normalized weight for the nth event; m nn The 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 the k time has O tracks in common, the mass entropy E (k) { E) is obtained 1 (k),E 2 (k),...,E U (k) And normalizing the obtained product, namely:
in the formula E j (k) For the tracking quality entropy of the trace j at time k, j ∈ {1,2, \8230;,O}。
k time trajectory j uncertainty level alpha j (k) The method is divided into the following steps: e is not less than 0 j (k) 1 when the content is less than or equal to 0.2; e is more than 0.2 j (k) 2 when the content is less than or equal to 0.5; e is more than 0.5 j (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 carry out track association matching.
(2) Construction of GMM model
Ranking the pre-processing to a level of uncertainty α j (k) Level 1 track set X B The locus set X of other levels is regarded as the centroid of Gaussian model in GMM A Considering the sample point set of the GMM, their gaussian radial basis functions are given by:
in the formula: k is dimension; delta 2 Is 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:
thus obtaining the track
The GMM probability density function of (a) is:
in the formula: ω is a uniformly distributed weight coefficient. Since the smaller the difference of the neighborhood topology of the trajectory, the higher the probability that they are from the same target, the higher the corresponding weight ratio in the GMM, and the probability of the proportional weight of each gaussian component is described as:
in the formula:
the resulting GMM probability density function is therefore:
(3) Evaluating maximum likelihood function and performing MINLP modeling recursion
(1) Vector estimation of sensor bias
The offset vector of the sensor can be represented by eta k Is expressed as eta k May be different for each sensor. For time-varying cases, the offset vector η k Following the following dynamic model
η k ＝F k-1,η η k-1 +w k-1,η
In the formula F k-1,η Is a transition matrix, and w k-1,η Is a zero mean; the initial bias estimate and corresponding covariance are
(2) Evaluating a 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 separately k,η |U k ,η k ) And P (Z) k ,z k,η |U k ,η k ) And (4) evaluating.
1) Evaluation of P (z) k,η |U k ,η k )
For
Under the Gaussian assumption, the likelihood function z k,η Can be represented by the following formula
In the formula n η Denotes a deviation parameter, P (z) k,η |U k ,η k ) And matrix U k Are independent of each other.
2) Evaluation of P (Z) k ,z k,η |U k ,η k ),
A target density over the monitored volume defined by the target number per unit volume is beta t The monitoring probability of the sensor is
β t Can be regarded as beta t ＝1/4D 2 Where D represents the average target distance from its nearest target point. The likelihood function relating the two local orbits can be evaluated, and the local orbit estimate can be obtained as
Maximizing the likelihood function P (Z) k ,z k,η |U k ,η k ) Corresponding to minimizing its negative logarithm. Bonding with
Comprises the following steps:
while removing constants not related to parameter estimation to obtain the following optimization model
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) Recursive MINLP
Estimation of bias based on current
Determining a correspondence matrix
And (3) eliminating the influence of invariant parameters to obtain an optimization model as follows:
by the current time
Calculating a deviation estimate
Obtaining a corresponding covariance:
the MINLP model can be recursive, the pseudo-code is as follows:
inputting the deviation estimated value of the current time k
1) By the present deviation estimation
Calculating a correspondence matrix
2) In view of the current matrix
Updating bias estimates
3) Repeating (1) and (2) until the corresponding matrix is not changed any more.
4) Outputting a final deviation estimate
And a corresponding matrix
The transformation relationship between sets of point sets may be expressed as follows:
X A ＝X B +v(X B )
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
Obtain an expectation of a set of parameters and a set of sample points as
In the formula:
{ω，δ 2 v is the unknown parameter set;
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
Wherein: omega j Is a weight coefficient matrix W = [ omega ] 1 ,ω 2 ,...,ω m ] T An element of (1);
is a Gaussian kernel matrix; beta is a smoothness coefficient. Thus, the matching incidence relation among the target track point set is obtained and is X A ＝X B + GW, while substituting into the above formula
In the formula: g j,n Is a row vector of a gaussian kernel matrix.
(4) Performing EM clustering to perform underwater target track association
At the expected step, the posterior probability is known as follows according to Bayesian theorem:
in the formula: j =1,2. If a posterior probability
Higher, this means that the probability that the object trajectories i and j are from the same object is higher, while the matrix
Is the associated probability matrix of the set of trajectories. Therefore, the probability that non-homologous trajectories can be obtained is:
in the maximization step, in order to maximize Q, the unknown parameter sets are respectively extremized. Solution (II)
So as to obtain the composite material,
W＝[diag(P1)G+λδ 2 I] -1 (PX A -diag(P1)X B )
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:
in the formula:
is the judgment threshold for performing 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
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 correlation deviation through MINLP modeling recursion, can better perform track correlation and simultaneously has excellent tolerance and can keep a relatively stable correlation rate under the condition of increasing system errors in an underwater environment with multiple noise points and a high false alarm environment.
FIG. 5 is a comparison graph of performance 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)
As can be seen from the running time of the algorithms in table 1, the average running time of each algorithm gradually becomes higher 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 (5)
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: grading according to the track quality entropy;
step two: establishing a GMM model;
2.1 grading the preprocessing into a trajectory set X with uncertainty level 1 B The locus set X of other levels is regarded as the centroid of Gaussian model in GMM A A set of sample points considered to be GMM; obtaining a gaussian radial basis function:
X A a track sample point set is obtained, and K is a dimension; delta. For the preparation of a coating 2 Introducing a uniform distribution for covariance in Gaussian model
Then, a probability density function is obtained:
wherein ω is a uniformly distributed weight coefficient;
2.2 mixing different data points by Gaussian distribution, calculating the mean vector, covariance matrix and mixing weight in GMM model, obtaining model probability density expression, carrying out vector estimation on sensor deviation, and carrying out vector estimation according to bias vector eta k Predicting 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;
for two parts of maximum likelihood P (z) k,η |U k ,η k ) And P (Z) k ,z k,η |U k ,η k ) Evaluating, converting the optimized dynamic model into an MINLP problem, and recursion is carried out on the MINLP: estimation of bias based on current
Determining a correspondence matrix
To trace points, based on passing current
Calculating a deviation estimate
Recursion is continued until the matrix and the bias estimate no longer change; adding regularization function in regeneration kernel Hilbert space
Enabling the track set to move integrally;
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 processing the idea of introducing weights into the four event sets according to the track scanning state, the fact that whether the collection is within extrapolation time, the track state estimation stability condition and the track stability condition, and grading the obtained track quality entropy.
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 higher the association degree between the tracks is, and after the optimal matching relation is obtained, the matching association relation between the track sets is obtained by utilizing posterior probability.
4. The underwater multi-target track association method based on EM clustering as claimed in claim 3, wherein: in step two, the sensor deviation is subjected to vector estimation, and the offset vector of the sensor uses eta k Is expressed as eta k Different for each sensor, the offset vector eta for the time-varying case k Following the following dynamic model η k ＝F k-1,η η k-1 +w k-1,η In the formula F k-1,η Is a transition matrix, w k-1,η Is a zero mean; an initial bias estimate and corresponding covariance are
For
Obtaining an optimal corresponding bias estimate using maximum likelihood rules
Wherein U is k Is a correspondence matrix.
5. The underwater multi-target track association method based on EM clustering as claimed in claim 4, wherein: the correlation method in the fourth step is that the EM clustering algorithm completes correlation matching of underwater target tracks, 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,
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
In the formula:
is to carry out the judgment threshold of the track association and simultaneously to carry out the judgment of the track association
The largest corresponding trajectory matches.
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