CN110120066A - Robust multiple targets tracking and tracking system towards monitoring system - Google Patents
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Abstract
The present invention provides a kind of robust multiple targets tracking towards monitoring system, comprising the following steps: S1, the foundation for mixing observation model；The calculating of the complete data joint probability density of S2, each state variable of monitoring system and measurement；The calculating of S3, approximate posterior probability density；The calculating of clutter density parameter in S4, measurement；S5, the clutter density parameter according to the approximate posterior probability density of each state variable and in measuring, calculate the mathematic expectaion of each state variable to obtain the estimated value of each state variable, repeat step S2-S4 predetermined number of times, it is believed that tracking terminates；The tracking estimation of S6, multiple targets: according to the estimated value and clutter density parameter of finally obtained each state variable, the estimation of multiple targets motion state, shape and environment clutter density is realized.The present invention solves the problems, such as that the observation noise for obeying heavytailed distribution, environment clutter are brought, while being estimated when tracking to multiple targets clutter density.
Description
Technical field
The present invention relates to robust multiple targets tracking technical fields, and in particular, to a kind of Shandong towards monitoring system
Stick multiple targets tracking, especially a kind of robust multiple targets tracking based on stochastic matrix models.
Background technique
Multiple targets is defined as: under conditions of meeting certain target spacing, keep spatial relationship within the time of a fixed length
(such as position) is relatively fixed (or have similar state parameter), and at least two distinguishable or can not resolution target
The target cluster being mixed to form.Multiple targets tracking needs while solving the problems, such as the mass motion of group and the Combined estimator of shape.It is based on
The multiple targets tracking of stochastic matrix models, using symmetric positive definite matrix come the shape of phenon.I.e. in two-dimensional surface, group's
Shape is the ellipse with a certain size and orientation.
Existing literature search is found, although the multiple targets tracking based on stochastic matrix models is better than previous group
Method for tracking target, but the interference of sensor noise and environment clutter is often faced in true multiple targets tracking scene,
Some will receive based on the multiple targets tracking result of stochastic matrix models and seriously affect.Gaussian Profile is disobeyed when observation noise and
Certain heavytailed distribution is obeyed, sensor often returns to some outlier and state estimation variance is caused to become larger, in turn results in multiple targets and estimate
Count the decline of performance.Secondly, needing to consider the influence that clutter tracks multiple targets in environment, modeling to environment clutter can be mentioned
Height estimation performance.In fact, a kind of multiple targets tracking of robust is needed in application scenarios to solve to obey heavytailed distribution
Observation noise, environment clutter the problem of bringing, moreover it is possible to clutter density is estimated while being tracked to multiple targets.
Summary of the invention
For the defects in the prior art, the object of the present invention is to provide a kind of robust multiple targets towards monitoring system with
Track method and tracking system solve the problems, such as that the observation noise for obeying heavytailed distribution, environment clutter are brought, while to multiple targets
Clutter density is estimated when tracking, realizing has heavytailed distribution characteristic in sensor observation noise and generate
It is abnormal to measure, monitor that there are Combined estimator multiple targets shape, motion state and the environment clutters in the case of noise jamming in environment
Density.
A kind of robust multiple targets tracking towards monitoring system provided according to the present invention, comprising the following steps:
S1, the foundation for mixing observation model: the mixing observation model of monitoring system measurement, the mixing observation model are established
It is formed by being originated from the observation model of multiple targets with the observation model from environment clutter, according to mixing observation model building monitoring system
The likelihood function that system measures；
The calculating of S2, joint probability density: the likelihood function measured according to monitoring system calculates each state of monitoring system
The complete data joint probability density of variable and measurement；
The calculating of S3, approximate posterior probability density: based on conjugation distributional assumption, the approximate posteriority of each state variable is minimized
The Kullback-Leibler divergence of probability density is then based on the complete data of each state variable and measurement that step S2 is obtained
Joint probability density calculates the approximate posterior probability density of each state variable；
The calculating of clutter density parameter in S4, measurement: keep the approximate posterior probability density of each state variable constant, most
The likelihood function lower bound that bigization monitoring system measures calculates the clutter density parameter in measuring；
The estimated value calculating of S5, each state variable: according in the approximate posterior probability density of each state variable and measurement
Clutter density parameter calculates the mathematic expectaion of each state variable to obtain the estimated value of each state variable, repeats step
S2-S4 predetermined number of times, it is believed that tracking terminates；
The tracking estimation of S6, multiple targets: real according to the estimated value and clutter density parameter of finally obtained each state variable
The estimation of existing multiple targets motion state, shape and environment clutter density.
The robust multiple targets tracking system towards monitoring system that the present invention also provides a kind of, including,
Mix the building module of observation model: for constructing the mixing observation model of monitoring system measurement, the mixing is seen
It surveys model and is formed by being originated from the observation model of multiple targets with the observation model from environment clutter, according to mixing observation model building
The likelihood function that monitoring system measures；
The computing module of joint probability density: the likelihood function measured according to monitoring system calculates each shape of monitoring system
The complete data joint probability density of state variable and measurement；
The computing module of approximate posterior probability density: the approximate posterior probability density of each state variable is minimized
Kullback-Leibler divergence is then based on the complete of each state variable that joint probability density computing module obtains and measurement
Data aggregate probability density calculates the approximate posterior probability density of each state variable；
The computing module of clutter density parameter: keeping the approximate posterior probability density of each state variable constant, maximizes prison
The likelihood function lower bound that viewing system measures calculates the clutter density parameter in measuring；
The computing module of each state variable estimate: according in the approximate posterior probability density of each state variable and measurement
Clutter density parameter calculates the mathematic expectaion of each state variable to obtain the estimated value of each state variable, repeats calculating
Predetermined number of times, it is believed that tracking terminates；
The tracking estimation module of multiple targets: according to the estimated value and clutter density parameter of finally obtained each state variable,
Realize the estimation of multiple targets motion state, shape and environment clutter density.
In the building module of step S1 or mixing observation model, the measurement of the observation model from multiple targets is obeyed heavy-tailed
Student t distribution, mean value zero, variance are multiple targets shape Xt, freedom degree v.J-th of measurement z of moment ttjIt obeys following
Student distribution:
Wherein, xtFor t moment multiple targets motion state, XtFor the shape state of t moment multiple targets, ztjIt is the of moment t
J measurement, parameter v >=1 control student t and are distributed heavy-tailed degree, and C is the observing matrix of system, and T is expressed as matrix transposition, d
It is ztjDimension, can be 2 (two-dimensional surfaces) or 3 (three-dimensional space).Measure ztjGaussian Profile of equal value expression are as follows:
p(ztj|xt)=N (Cxt,Xt/wtj)
Wherein variableRepresent one group of ntA weight variable.When each weight variable corresponds
Carve a measurement of t, weight variable wtjValue indicate to measure contribution to Posterior estimator；
The measurement obedience of observation model from environment clutter is uniformly distributedAssuming that clutter measures in space
It is evenly distributed in monitor area Θ, i.e., clutter, which measures, obeys following distribution:
Wherein U () is uniform density distribution.The clutter of monitor area measures the Poisson that quantum hypothesis obeys known mean value
Distribution.It, can be using Finite mixture model come the multimodal of simulated environment noise point for obeying the environmental background of non-uniform Distribution
Cloth, typical mixed model such as gauss hybrid models.
To sum up, it measures and obeys following mixing generation model:
Wherein C is the observing matrix of monitoring system, and parameter v >=1 controls student t and is distributed heavy-tailed degree, in this application
In, recommend Selecting All Parameters v=4, Θ to represent monitor area, when measuring from clutter, clutter measurement equably divides in space
Cloth is in monitor area Θ, identifierIt is one group of ntThe two-valued variable of measurement, ctjTo measure class variable, value
It represents to measure for 1 and is generated by multiple targets and obeyed student distribution, value is 0 to represent measurement and generate and obey uniform as environment clutter
Distribution, ztjFor j-th of measurement of moment t.The probability density of identifier ct is as follows:
Wherein parameter θ be measure in clutter density, based on above-mentioned definition, measure likelihood function be one group be originated from multiple targets and
It obeys the measurement of heavy-tailed student t distribution and is originated from environment clutter and obedience is uniformly distributedMeasurement ask product to obtain, can
With expression are as follows:
WhereinBi-distribution is represented,It is the n that moment t is originated from multiple targets and environment cluttertA sight
It surveys, variableRepresent one group of nt weight variables, each weight variable wtjAll correspond the one of moment t
A measurement, weight variable wtjValue indicate to measure contribution to Posterior estimator j-th.
In step S2 or the computing module of joint probability density, each state variable of monitoring system and the perfect number of measurement
According to joint probability density p (xt,Xt,wt,ct,Zt|Zt-1) by the likelihood function p (Z of monitoring system measurementt|xt,Xt,wt,ct)、xtWith
XtJoint probability density p (xt,Xt|Zt-1), weight variable wtProbability density p (wt), the two-valued variable c of one group of measurementtIt is general
Rate density p (ct), multiplication obtains.Each state variable of monitoring system and the complete data joint probability density p (x of measurementt,Xt,
wt,ct,Zt|Zt-1) specific calculating process it is as follows:
N(xt；xt|t-1,Pt|t-1)IW(Xt；vt|t-1,Vt|t-1)
Wherein xtFor t moment multiple targets motion state, Gaussian distributed N (), xt|t-1It is multiple targets motion state t-1
The predicted state at moment, Pt|t-1It is the covariance matrix of the predicted state at multiple targets motion state t-1 moment.Gamma () is
Gamma distribution, B () are bi-distribution, XtFor the shape state of t moment multiple targets, the Shape Prediction state X of multiple targetst|t-1Clothes
Being distributed freedom degree from inverse Wishart distribution IW, IW is vt|t-1, covariance matrix Vt|t-1, Zt-1For from the beginning of time to moment t-
1 accumulation measures, and parameter v >=1 controls student t and is distributed heavy-tailed degree.
In step S3 or the computing module of approximate posterior probability density, the approximate posterior probability of each state variable is minimized
The Kullback-Leibler divergence of density is then based on the complete data joint of each state variable and measurement that step S2 is obtained
Probability density p (xt,Xt,wt,ct,Zt|Zt-1) the approximate posterior probability density q (x of each state variable is calculated by iterative solution methodt),
q(Xt), q (wt) and q (ct).Circular is, to the joint probability density p (x of each state variable of systemt,Xt,wt,ct|
Zt) progress Factorization, and assume the prior distribution for defining each state variable with after according to the conjugation of each state variable distribution
It tests distribution and belongs to same distribution, available:
Wherein q (xt), q (Xt), q (wt) and q (ct) it is state variable x respectivelyt, Xt, wtAnd ctApproximate posterior probability it is close
Degree.According to variational Bayesian method, the approximate posterior probability density of each state variable can be by minimizing approximation probability density q
(xt), q (Xt), q (wt) and q (ct) with the joint probability density p (x of each state variable of systemt,Xt,wt,ct|Zt) between
Kullback-Leibler divergence (KLD) acquires, it may be assumed that
q(xt),q(Xt),q(wt),q(ct)=argmin KLD (q (xt)q(Xt)q(wt)q(ct)||p(xt,Xt,wt,ct|
Zt)), argmin is to minimize symbol, and KLD is Kullback-Leibler divergence (Kullback-Leiblerdivergence)
Abbreviation, argmin KLD indicate minimize KL divergence.
The approximate posterior probability density iterative solution method that available each state variable is optimized to above formula, to wherein
One state variable probability density optimizes, and keeps each of the constant available monitoring system of other state variable probability density
The following analytic formula of the approximate posterior probability density of state variable:
Wherein E [] represents the expectation of stochastic variable.Const is relative to state variable xt, Xt, wtAnd ctConstant.It is false
If variable wtAnd ctIndependently of system mode xtAnd Xt, the complete data joint of each state variable and measurement in above-mentioned formula is general
Rate density p (xt,Xt,wt,ct,Zt|Zt-1) can be decomposed into
Logarithm logp (the x of the complete data joint probability density of each state variable and measurement is calculatedt,Xt,wt,ct,Zt
|Zt-1) be expressed as follows:
Q after (i+1) secondary iterationx(·)、qX(·)、qw() and qc() expression formula is respectively WithHereinafter, subscript (i) and (i+1) indicate i-th and i+1 time
Expression formula.By the complete data joint probability density logarithm logp (x for calculating each state variable and measurementt,Xt,wt,ct,Zt|
Zt-1) expectation, being expressed as follows for above each state probability density can be provided,
Based on measurement ztjWtjApproximate posterior probability density logarithm expression are as follows:
WhereinWithRespectively represent variable xt、And ctjExpectation, i.e., With It is the target covariance matrix of moment t i-th iteration, T is expressed as matrix transposition, tr
The mark of matrix is represented,For the shape state X of t moment multiple targetstInverse matrix.
To above formula both ends fetching number and it is normalized, probability densityIt obeys
Distribution.
State xtProbability density logarithm expression may be calculated:
Wherein
Wherein Pt|t-1For the target prediction covariance matrix of moment t i-th iteration,It is Pt|t-1Inverse matrix.
State XtProbability density logarithm expression may be calculated:
It is the target covariance matrix of moment t i-th iteration, T is expressed as matrix transposition, and tr represents the mark of matrix.
The last one equation of above formula is the logarithmic form of inverse Wishart distribution, and the coefficient addition in equation can be obtained
It arrives:
Configuration variable XtIt obeysDistribution, and IW distribution freedom degree isCovariance matrix
For
Wherein
Based on measurement ztjVariable ctjProbability density logarithm expression may be calculated:
Wherein, Q is intermediate variable,
In the derivation of above formula, it can be seen thatWithThere is no analytic solutions, therefore use one
Rank Taylor expansion carries out approximate evaluation, and then obtainsWith
According to available c on the right of the last one equation of above formulatjObey Bernoulli Jacob's distribution, q (ctj) and q (ct) table
It is as follows up to formula:
It can be right based on above-mentioned derivationIt is iterated solution.
In step S4 or the computing module of clutter density parameter, the approximate posterior probability density of each state variable is kept not
Become, the derivative of clutter density parameter θ is asked by the likelihood function lower bound measured to monitoring system and it is enabled to be equal to 0, solution obtains
The value of clutter density parameter θ: log-likelihood function lower bound may be expressed as:
Solution can obtain:
Wherein const is the constant relative to parameter θ,It is from the beginning of time to the cumulative observations of moment t
In step S5 or the computing module of each state variable estimate, multiple targets motion state x is calculated separatelyt, group's mesh
Target shape state Xt, one group of measurement weight variable wt, one group of measurement two-valued variable ctMathematic expectaion
To obtain the estimated value of each state variable,
Due to wtJ-th of variable wtjGamma distribution is obeyed, takes its mean value as state estimation, i.e., Due to xtGaussian distributed takes its mean value as state estimation, i.e.,Due to XtDistribution
Inverse Wishart distribution is obeyed, takes its mean value as state estimation, thenAccording to inverse Wishart distribution propertyDue to ctJ-th of variable obey bi-distribution, take its mean value as state estimation, i.e.,
Compared with prior art, the present invention have it is following the utility model has the advantages that
1, the invention proposes a kind of new robust multiple targets track algorithms based on stochastic matrix models.Using student t
The modeling to multiple targets shape not only may be implemented in distribution, but also the weight coefficient by defining each measurement can portray the amount
Survey the contribution estimated for multiple targets.Model is generated by the mixing that building measures, is integrated in multiple targets System State Model
The estimation of environment clutter density, the performance of multiple targets state estimation is improved using environment clutter density estimated result.In variation shellfish
Under the frame of this method of leaf, using the mathematical method of expectation maximization, by the side for estimating and maximizing the continuous iteration of two steps
Formula calculates the probability density and estimated value of each variable of system mode, in addition to this, clutter density parameter also can be obtained.It is proposed
Algorithm can using to measure iterative processing implementation so that computation complexity meets Practical Project demand.
2, it is an object of the invention to propose one kind to generate different in sensor observation noise with heavytailed distribution characteristic
Constant survey, monitor environment in there are in the case of noise jamming Combined estimator multiple targets shape, motion state and environment clutter it is close
The method of degree.This method is directed to multiple targets and measures foundation mixing generation model, is based on student t distribution and variational Bayesian method,
Obtain the desired calculation method of multiple targets tracking system complete data log-likelihood function is under maximum-likelihood criterion
The probability density and clutter density parameter for each state variable of uniting, can be achieved at the same time multiple targets motion state, shape and environment clutter
The estimation of density.
3, the present invention provides a kind of Shandong based on stochastic matrix models using student t distribution and variational Bayesian method
Stick multiple targets track algorithm, the algorithm can using to measure iterative processing implementation, and to multiple targets motion state,
Shape and environment clutter density are realized while being estimated.In addition, this algorithm frame is clearly conducive to realize, thus under complex environment
Multiple targets tracking system provides important technical support.
Detailed description of the invention
Upon reading the detailed description of non-limiting embodiments with reference to the following drawings, other feature of the invention,
Objects and advantages will become more apparent upon:
Fig. 1 is ideally multiple targets motion profile in the present invention；
Fig. 2 is that ideally multiple targets location estimation compares in the present invention；
Fig. 3 is that ideally the estimation of multiple targets shape is compared in the present invention；
Fig. 4 is that observation noise obeys multiple targets motion profile in the case of heavytailed distribution in the present invention；
Fig. 5 is that multiple targets location estimation compares in the case of observation noise obedience heavytailed distribution in the present invention；
Fig. 6 is that the estimation of multiple targets shape is compared in the case of observation noise obedience heavytailed distribution in the present invention；
Fig. 7 is multiple targets motion profile in the case of clutter in the present invention and heavytailed distribution；
Fig. 8 compares for multiple targets location estimation in the case of clutter in the present invention and heavytailed distribution；
Fig. 9 compares for multiple targets shape estimation in the case of clutter in the present invention and heavytailed distribution；
Figure 10 estimates for clutter density in the case of clutter in the present invention and heavytailed distribution.
Specific embodiment
The present invention is described in detail combined with specific embodiments below.Following embodiment will be helpful to the technology of this field
Personnel further understand the present invention, but the invention is not limited in any way.It should be pointed out that the ordinary skill of this field
For personnel, without departing from the inventive concept of the premise, several changes and improvements can also be made.These belong to the present invention
Protection scope.
The orientation of multiple targets changes therewith with the variation of motion profile as can be seen from Figure 1.
The ideal feelings influenced in the heavytailed distribution and environment clutter for not accounting for observation error are set forth in Fig. 2 and Fig. 3
The location estimation RMS and shape of the lower three kinds of algorithms of condition estimate RMS comparison result.Koch method has in ideal simulating scenes herein
There is the smallest evaluated error, our method is in close proximity to Feldmann method for location estimation, estimates me for shape
Method be better than Feldmann method.
Fig. 4 gives the multiple targets motion profile figure under the conditions of heavytailed distribution, and "+", which represents, to be measured.It weighs as can be seen from Figure 5
Tail is distributed the influence for measurement, and a small amount of measurement has very big error, this proposes very high requirement to track algorithm.
Traditional track algorithm is not due to accounting for such abnormal decline that certainly will will cause estimation performance.
The location estimation RMS and shape estimation RMS of three kinds of algorithms in heavytailed distribution is set forth in Fig. 5 and Fig. 6
Comparison result.Our method is due to having used student t distribution to estimate to be fitted measurement abnormal point to obtain best position
Meter and shape estimation, Koch method and Feldmann method are due to considering that insufficient therefore performance has greatly for the abnormal point in measuring
Decline, Koch method due to just for ideal situation thus evaluated error is maximum.
Fig. 7 gives the multiple targets motion profile figure under clutter conditions, measures use+number indicate, and clutter is indicated with putting.From
It is more extensive that Fig. 8 can be seen that the abnormal point in monitor area is more distributed.
The location estimation RMS and shape estimation RMS that three kinds of algorithms in clutter are set forth in Fig. 8 and Fig. 9 compare
As a result.Our method be fitted due to having used student t distribution measure abnormal point to obtain best location estimation and
Shape estimation estimates that Koch method and Feldmann method almost dissipate in particular for shape.This illustrates in true field
Influence of the very common clutter for Koch method and Feldmann is huge in scape.
Figure 10 gives clutter density estimation, our method it is very close for the estimated value of clutter density with it is true
Value.
Embodiment
In the present embodiment, the robust multiple targets tracking of the invention towards monitoring system is described below:
S1, the foundation for mixing observation model: the mixing observation model of monitoring system measurement, the mixing observation model are established
It is formed by being originated from the observation model of multiple targets with the observation model from environment clutter, according to mixing observation model building monitoring system
Unite the likelihood function p (Z measuredt|xt,Xt,wt,ct)；
The calculating of S2, joint probability density: the likelihood function measured according to monitoring system calculates each state of monitoring system
The complete data joint probability density p (x of variable and measurementt,Xt,wt,ct,Zt|Zt-1)；
The calculating of S3, approximate posterior probability density: based on conjugation distributional assumption, the approximate posteriority of each state variable is minimized
Probability density q (xt), q (Xt), q (wt) and q (ct) Kullback-Leibler divergence, be then based on step S2 obtain it is each
The complete data joint probability density p (x of state variable and measurementt,Xt,wt,ct,Zt|Zt-1) each state calculated by iterative solution method
The approximate posterior probability density q (x of variablet), q (Xt), q (wt) and q (ct)；
The calculating of clutter density parameter in S4, measurement: keep the approximate posterior probability density of each state variable constant, most
The likelihood function lower bound that bigization monitoring system measures calculates the clutter density parameter θ in measuring,
The estimated value calculating of S5, each state variable: according to the approximate posterior probability density q (x of each state variablet), q (Xt),
q(wt) and q (ct) and clutter density parameter θ in measuring, the mathematic expectaion of each state variable is calculated to obtain each state variable
Estimated value, repeat step S2-S4 predetermined number of times, it is believed that tracking terminate；
The tracking estimation of S6, multiple targets: real according to the estimated value and clutter density parameter of finally obtained each state variable
The estimation of existing multiple targets motion state, shape and environment clutter density.
Next the present invention is described in detail.
Robust multiple targets Union Movement state and shape tracking provided in this embodiment based on stochastic matrix models,
It is tested by the test data that the sensor and background environment using simulation true environment generate, implementation steps are as follows:
Step 1, in the ideal case, observation noise may be assumed that Gaussian distributed.In practical applications, since environment is disliked
It is bad, interfere the factors such as more, accuracy of instrument, observation noise often and disobeys ideal Gaussian Profile and obeys some heavy-tailed points
Cloth causes sensor often to return to some outlier, and state estimation variance is caused to become larger, and in turn results in multiple targets state estimation performance
Decline.Secondly, in view of, there are clutter, needing to consider clutter to the shadow of multiple targets state estimation during tracking in environment
It rings.Therefore be distributed using student t come the heavytailed distribution to observation noise and measure outlier and model, using being uniformly distributed or limited
Mixed model models environment clutter.Introduce one group of weight variable wtTo characterize contribution of each observation to state estimation.
Similarly, one group of binary variable c is introducedtBelong to target or clutter to characterize the measurement.
Step 2, the complete data joint probability density p (x of each state variable of computing system and measurementt,Xt,wt,ct,Zt|
Zt-1).According to Bayes' theorem, according to variable wtAnd ctIndependently of system mode xtAnd Xt, each state variable and measurement it is complete
Data aggregate probability density p (xt,Xt,wt,ct,Zt|Zt-1) can be analyzed to
N(xt；xt|t-1,Pt|t-1)IW(Xt；vt|t-1,Vt|t-1)
Step 3, according to variational Bayesian method, the approximate posterior probability density of each state variable can be close by minimizing
Like probability density q (xt), q (Xt), q (wt) and q (ct) with each state variable of system join probability density p (xt,Xt,wt,ct|Zt)
Between Kullback-Leibler divergence acquire following analytic formula:
Wherein E [] represents the expectation of stochastic variable.Const is relative to state variable xt, Xt, wtAnd ctConstant.On
State the complete data joint probability density logarithm logp (x of each state variable of system and measurement in formulat,Xt,wt,ct,Zt|Zt -1) expressed intact it is as follows:
Q after (i+1) secondary iterationx(·)、qX(·)、qw() and qc() expression formula is respectivelyWithHereinafter, subscript (i) and (i+1) indicate i-th and i+1 time
Expression formula.Wherein WithRespectively represent variable wtj、xt、And ctjExpectation, i.e., With
Weight variable wtjIt obeysDistribution, wherein γtjFor temporary variable, expressed to simplify
Formula,
Motion state xtIt obeysDistribution, wherein
Configuration variable XtIt obeysDistribution, wherein
Measure class variable ctjBernoulli Jacob's distribution is obeyed, i.e.,Wherein
Based on the above-mentioned probability density being derived byIterative solution
Process.
Step 4, in the case where keeping each state variable posterior probability density constant, by maximizing log-likelihood function
Lower bound pair unknown parameter θ is estimated.By seeking likelihood function lower bound the derivative of parameter θ and it being enabled to be equal to 0, solution can must be joined
The value of number θ.
In calculating process, work as ctjOccur will affect the stability of program when minimum and algorithm being caused to dissipate.Therefore, exist
C is defined in programtjThreshold value, when be more than predetermined threshold value then measurement source in target.In the iterative process of each round, greatly
In the c of threshold valuetjIt is placed in 1；And it is less than the c of threshold valuetjThen it is placed in 0.The calculation formula of unknown parameter θ are as follows:
Step 5, step 2- step 4 predetermined number of times is repeated, it is believed that algorithm has been restrained, and is calculated mathematic expectaion and is obtained
Each variable estimated value, i.e.,
Robust multiple targets track algorithm provided by the invention based on stochastic matrix models, can have in sensor observation noise
There is heavytailed distribution characteristic and generate abnormal measurement, monitors that there are realize to move shape to multiple targets in the case of noise jamming in environment
The Combined estimator of state, shape and environment clutter density.The test that sensor and background environment for simulation true environment generate
Data obtain the meter of multiple targets tracking system complete data log-likelihood function based on student t distribution and variational Bayesian method
Calculation method.Using the mathematical method of expectation maximization, is calculated by way of estimating and maximizing the continuous iteration of two steps and be
The probability density and estimated value of each variable of system state.The algorithm proposed is very flexible, can be using to measurement iterative processing
Implementation, so that computation complexity meets Practical Project demand.In addition to this, that clutter can be obtained by Maximum-likelihood estimation is close
Spend parameter.This algorithm frame is clearly conducive to realize, can achieve the performance requirement calculated in real time.So as in real scene group's mesh
Mark, which is traced and monitored in system, is used widely, and provides important technical support for the fusion of good information.
One skilled in the art will appreciate that in addition to realizing system provided by the invention in a manner of pure computer readable program code
It, completely can be by the way that method and step be carried out programming in logic come so that the present invention provides and its other than each device, module, unit
System and its each device, module, unit with logic gate, switch, specific integrated circuit, programmable logic controller (PLC) and embedding
Enter the form of the controller that declines etc. to realize identical function.So system provided by the invention and its every device, module, list
Member is considered a kind of hardware component, and to include in it can also for realizing the device of various functions, module, unit
To be considered as the structure in hardware component；It can also will be considered as realizing the device of various functions, module, unit either real
The software module of existing method can be the structure in hardware component again.
Specific embodiments of the present invention are described above.It is to be appreciated that the invention is not limited to above-mentioned
Particular implementation, those skilled in the art can make a variety of changes or modify within the scope of the claims, this not shadow
Ring substantive content of the invention.In the absence of conflict, the feature in embodiments herein and embodiment can any phase
Mutually combination.
Claims (10)
1. a kind of robust multiple targets tracking towards monitoring system, which comprises the following steps:
S1, the foundation for mixing observation model: the mixing observation model of monitoring system measurement is established, the mixing observation model is by source
Observation model from multiple targets and the observation model composition from environment clutter, construct monitoring system amount according to mixing observation model
The likelihood function of survey；
The calculating of S2, joint probability density: the likelihood function measured according to monitoring system calculates each state variable of monitoring system
With the complete data joint probability density of measurement；
The calculating of S3, approximate posterior probability density: the Kullback- of the approximate posterior probability density of each state variable is minimized
Leibler divergence, the complete data joint probability density for being then based on each state variable and measurement that step S2 is obtained calculate respectively
The approximate posterior probability density of state variable；
The calculating of clutter density parameter in S4, measurement: keeping the approximate posterior probability density of each state variable constant, maximizes
The likelihood function lower bound that monitoring system measures calculates the clutter density parameter in measuring；
The estimated value calculating of S5, each state variable: according to the clutter in the approximate posterior probability density of each state variable and measurement
Density parameter calculates the mathematic expectaion of each state variable to obtain the estimated value of each state variable, repeats step S2-
S4 predetermined number of times, it is believed that tracking terminates；
The tracking estimation of S6, multiple targets: according to the estimated value and clutter density parameter of finally obtained each state variable, group is realized
The estimation of target state, shape and environment clutter density.
2. the robust multiple targets tracking according to claim 1 towards monitoring system, which is characterized in that the step
In S1, the measurement of the observation model from multiple targets obeys heavy-tailed student t and is distributed St (Cxt,Xt, v), the sight from environment clutter
The measurement obedience for surveying model is uniformly distributedTherefore the mixing observation model that monitoring system measures obedience is as follows:
Wherein, ztjFor j-th of measurement of moment t, xtFor t moment multiple targets motion state, ctjFor the class variable of measurement, value
It represents to measure for 1 and is generated by multiple targets and obeyed heavy-tailed student t distribution, value is 0 to represent to measure and generate and take as environment clutter
From being uniformly distributed, C is the observing matrix of monitoring system, XtFor the shape state of t moment multiple targets, parameter v >=1 controls student
T is distributed heavy-tailed degree, and Θ represents monitor area.
3. the robust multiple targets tracking according to claim 1 towards monitoring system, which is characterized in that the step
In S1, multiple targets are originated from by one group and obeys the measurement of heavy-tailed student t distribution and is originated from environment clutter and obedience is uniformly distributedMeasurement ask product obtain monitoring system measurement likelihood function p (Zt|xt,Xt,wt,ct), wherein ZtIt is moment t source
From the measurement of multiple targets and environment clutter, xtFor t moment multiple targets motion state, XtFor the shape state of t moment multiple targets, wt
For the weight variable of one group of measurement, ctFor the two-valued variable of one group of measurement.
4. the robust multiple targets tracking according to claim 1 towards monitoring system, which is characterized in that the step
In S2, each state variable of monitoring system and the complete data joint probability density p (x of measurementt,Xt,wt,ct,Zt|Zt-1) by supervising
Likelihood function p (the Z that viewing system measurest|xt,Xt,wt,ct)、xtAnd XtJoint probability density p (xt,Xt|Zt-1), weight variable
wtProbability density p (wt), the two-valued variable c of one group of measurementtProbability density p (ct), multiplication obtains, wherein xtFor t moment group
Target state, XtFor the shape state of t moment multiple targets, wtFor the weight variable of one group of measurement, ctIt is the two of one group of measurement
It is worth variable, ZtIt is the measurement that moment t is originated from multiple targets and environment clutter, Zt-1For from the beginning of time to the cumulant of moment t-1
It surveys.
5. the robust multiple targets tracking according to claim 1 towards monitoring system, which is characterized in that the step
In S3, the Kullback-Leibler divergence of the approximate posterior probability density of each state variable is minimized, step S2 is then based on
The complete data joint probability density p (x of obtained each state variable and measurementt,Xt,wt,ct,Zt|Zt-1), pass through iterative solution method
Calculate the approximate posterior probability density q (x of each state variablet), q (Xt), q (wt) and q (ct), wherein xtFor t moment multiple targets fortune
Dynamic state, XtFor the shape state of t moment multiple targets, wtFor the weight variable of one group of measurement, ctBecome for the two-value of one group of measurement
Amount, ZtIt is the measurement that moment t is originated from multiple targets and environment clutter, Zt-1To be measured from the beginning of time to the accumulation of moment t-1.
6. the robust multiple targets tracking according to claim 1 towards monitoring system, which is characterized in that the step
In S4, keeps the approximate posterior probability density of each state variable constant, asked by the likelihood function lower bound measured to monitoring system
The derivative of clutter density parameter θ simultaneously enables it be equal to 0, and solution obtains the value of clutter density parameter θ.
7. the robust multiple targets tracking according to claim 1 towards monitoring system, which is characterized in that the step
In S5, multiple targets motion state x is calculated separatelyt, multiple targets shape state Xt, one group of measurement weight variable wt, one group of measurement
Two-valued variable ctMathematic expectaionTo obtain the estimated value of each state variable, wherein wtObey gamma
Distribution, xtGaussian distributed, XtObey inverse Wishart distribution, ctObey bi-distribution.
8. a kind of robust multiple targets tracking system towards monitoring system, which is characterized in that including,
Mix the building module of observation model: for constructing the mixing observation model of monitoring system measurement, mould is observed in the mixing
Observation model of the type by being originated from the observation model of multiple targets and from environment clutter forms, according to mixing observation model building monitoring
The likelihood function of system measurements；
The computing module of joint probability density: the likelihood function measured according to monitoring system, each state for calculating monitoring system become
Amount and the complete data joint probability density measured；
The computing module of approximate posterior probability density: the Kullback- of the approximate posterior probability density of each state variable is minimized
Leibler divergence is then based on the complete data joint of each state variable and measurement that joint probability density computing module obtains
Probability density calculates the approximate posterior probability density of each state variable；
The computing module of clutter density parameter: keeping the approximate posterior probability density of each state variable constant, maximizes monitoring system
The likelihood function lower bound that system measures calculates the clutter density parameter in measuring；
The computing module of each state variable estimate: according to the clutter in the approximate posterior probability density of each state variable and measurement
Density parameter calculates the mathematic expectaion of each state variable to obtain the estimated value of each state variable, it is specified to repeat calculating
Number, it is believed that tracking terminates；
The tracking estimation module of multiple targets: it according to the estimated value and clutter density parameter of finally obtained each state variable, realizes
The estimation of multiple targets motion state, shape and environment clutter density.
9. a kind of robust multiple targets tracking system towards monitoring system according to claim 8, which is characterized in that described
It mixes in observation model, the measurement of the observation model from multiple targets obeys heavy-tailed student t and is distributed St (Cxt,Xt, v), it is originated from ring
The measurement obedience of the observation model of border clutter is uniformly distributedTherefore it is as follows to measure the mixing observation model obeyed:
Wherein, ztjFor j-th of measurement of moment t, xtFor t moment multiple targets motion state, ctjFor the class variable of measurement, value
It represents to measure for 1 and is generated by multiple targets and obeyed heavy-tailed student t distribution, value is 0 to represent to measure and generate and take as environment clutter
From being uniformly distributed, C is the observing matrix of monitoring system, XtFor the shape state of t moment multiple targets, parameter v >=1 controls student
T is distributed heavy-tailed degree, and Θ represents monitor area.
10. a kind of robust multiple targets tracking system towards monitoring system according to claim 8, which is characterized in that institute
In the computing module for stating clutter density parameter, the method for solving of clutter density parameter is the approximate posteriority for keeping each state variable
Probability density is constant, seeks the derivative of clutter density parameter θ by the likelihood function lower bound measured to monitoring system and it is enabled to be equal to
0, solution obtains the value of clutter density parameter θ.
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