CN106707272B - A kind of multi-object tracking method based on random set theory - Google Patents

A kind of multi-object tracking method based on random set theory Download PDF

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CN106707272B
CN106707272B CN201610522044.XA CN201610522044A CN106707272B CN 106707272 B CN106707272 B CN 106707272B CN 201610522044 A CN201610522044 A CN 201610522044A CN 106707272 B CN106707272 B CN 106707272B
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probability density
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CN106707272A (en
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易伟
王佰录
李帅
李溯琪
孔令讲
杨晓波
崔国龙
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/66—Radar-tracking systems; Analogous systems
    • G01S13/72—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar
    • G01S13/723—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar by using numerical data
    • G01S13/726—Multiple target tracking

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
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  • Radar Systems Or Details Thereof (AREA)

Abstract

In order to realize effective tracking of multiple target state under complex scene, the present invention provides a kind of multi-object tracking methods based on random set theory under limited resources restrictive condition.This method is first depending on bayesian criterion in the Trajectory Prediction stage and carries out one-step prediction to each track that continues to survive, and is then adaptively born targetpath according to target prior information；In track with the new stage, is calculated first under each hypothesis accordingly there are weight probability and joint multiple target probability density function, then calculate the posterior probability parameter of each target label, including existing probability and corresponding probability density function.This method tool approximated cost is small, has excellent performance under limited resources, is applicable in the advantages that robustness of any measurement model.In addition, the system resources in computation as occupied by algorithm of the invention is few, has good future in engineering applications.

Description

Multi-target tracking method based on random set theory
Technical Field
The invention belongs to the field of multi-target tracking, and particularly relates to the technical field of multi-target tracking under a random set theory.
Background
In recent years, a multi-target detection tracking technology based on a random set statistical theory is widely concerned, and the method avoids data association of traditional multi-target tracking and can process the condition that the number of targets is unknown and time-varying. Currently, most random set tracking algorithms, such as probability hypothesis density filters, primatized probability hypothesis density filters, labeled multi-target bernoulli filters, etc., are designed for standard metrology models (see documents r. mahler, statistical multiple source-multiple Information Fusion, Norwood, MA: Artech House, 2007.). However, in an actual multi-target tracking scenario, a standard measurement model has many limitations, and many sensor models cannot be described by the standard measurement model, such as a tracking model before radar detection, multi-user positioning in a wireless sensor network, multi-target positioning in a multi-input multi-output radar, a sonar amplitude sensor, a radio frequency tomography tracking system, a video tracking system, and the like.
Aiming at the problem of multi-target tracking under a Generalized measurement model (especially a highly nonlinear non-standard measurement model), a Generalized label multi-target Bernoulli filter is proposed in documents (F.Papi, B.N.Vo, B.T.Vo, C.Fantaci and M.Beard, and ' Generalized label separation-Bernoulli amplification of multi-target properties ', and ' IEEE trans.on Signal Process.Vol.63, No.20, pp.5487-5497,2015.), wherein the filter realizes effective tracking of multiple targets under the non-standard measurement model, can effectively identify target identities and form target tracks. However, the number of the multi-target posterior components of the filter is increased in a super-exponential manner along with the increase of the number of the targets, so that the required computing resources are extremely large, the real-time performance is poor, and the practical application is greatly limited.
Disclosure of Invention
The invention aims to solve the technical problem that the system computing resources occupied by the conventional random set multi-target tracking method aiming at the non-standard measurement model are exponentially increased along with the number of targets, so that the actual engineering application is not facilitated.
The technical scheme adopted by the invention for solving the technical problems is that the multi-target tracking method based on the random set theory comprises the following steps:
step 1, initializing system parameters
Initializing system parameters includes: radar monitoring range: namely a data plane, radar range resolution delta r, a radar scanning period T and an observation total frame number K; probability of target survivalSingle target transition probability density function fk|k-1(xk|xk-1) (ii) a The birth target model is a multi-target Bernoulli distributionWhereinIs shown asThe probability of the existence of an individual birth target track,is shown asA distribution probability density function corresponding to each birth target track,representing a birth target label set space; a multi-target likelihood function g (Z | X), wherein Z represents a measurement set and X represents a multi-target state set;
step 2: initializing label multi-target-bernoulli parametersAnd orderWhereinA target label set space representing a current frame; the initialization iteration time k is 1,is shown asThe probability of existence of a continued-to-live target track,is shown asA probability density function of the surviving objects;
step 3, calculating the predicted track of the kth frame:
3.1, based on prior information of the target birth positionThe target birth model is a multi-target Bernoulli distribution
3.2 prediction of surviving tracks according to Bayesian prediction equationProbability of existence of a bar surviving track predictionAnd corresponding probability density functionThe following are respectively given,
wherein, the mathematical symbols<f1(x),f2(x)>Representing function f1(x) And function f2(x) The inner product between;representing a continued survival target track label set space;
step 3, constructing a limited subset space of the predicted target label set;
3.1 determining a target set of labelsThe target label set is a union of the target birth label set and the target survival label set;
3.2 building target set of labelsOf all finite subsets of (a) whose mathematical symbols are expressed asThe limited number of subsets ofHerein is defined as+For a limited subset spaceAnd its mathematical symbol is expressed as
Step 4, calculating each limited subset of the kth frame according to the Bayesian criterionThe posterior weight probability and the corresponding multi-target probability density function thereof;
4.1. computing each subsetIs given by the prior weight probability w+(I+)：
Wherein the mathematical symbol pi represents a successive multiplication symbol,is shown asThe probability of existence of the predicted target track,a representation indicating function, which is defined as follows: indicating function
4.2. Computing each subsetMultiple target posterior probability density function normalization factor etaZ(I+)：
WhereinIs shown asA probability density function of each predicted target track;
4.3. computing each subsetA posteriori weight probability w (I)+)：
w(I+)＝w+(I+)ηZ(I+)
4.4. Computing each subsetThe multi-objective posterior probability density function of (1):
step 5, for each subsetA posteriori weight probability w (I)+) And (3) carrying out normalization treatment:
step 6, calculating each target labelProbability of existence ofAnd its corresponding probability density function
6.1 calculating the target labelsProbability of existence ofThe subsets of step 5Target mark of middle ladleA posteriori weight probability w (I)+) Summing to obtain the target labelProbability of existence of
6.2 calculating the target labelsA posterior probability density function ofThe subsets of step 5Target mark of middle ladleEdge probability density function ofPerforming weighted summation with the weighted weight of the posterior weight probability w (I) of the corresponding subset+) And the existence probability obtained in step 6.1A posteriori probability density function obtained by weighting and summingAnd (3) carrying out normalization:
whereinWhereinRepresenting a subset of reference numerals I+Comprises thatThe multi-objective posterior probability density function P (X | Z); step 7, extracting a target state; the cardinal number corresponding to the maximum distribution value of the set cardinal numbers is the estimation N of the target number at the moment kkAnd estimating the N separatelykThe status of the individual target;
and 8, if K is less than K, enabling K to be equal to K +1, and returning to the step 3, wherein K is the frame number.
The innovation point of the method is that 1) in the prediction stage, independent prediction is carried out among multiple Bernoulli components, so that the calculation resources required by multi-target tracking are greatly saved; 2) in the updating stage, a multi-target probability density function under various assumptions is considered in a combined manner by constructing a limited subset space of the target labels, so that the tracking method can be suitable for a more generalized multi-target measurement model.
The invention has the advantages that the multi-target tracking method which occupies less computing resources and has excellent tracking performance is provided, and the target tracking algorithm provided by the invention can be suitable for any measurement model and has stronger algorithm robustness.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of an algorithm of the present invention;
FIG. 3 is a simulation scene diagram in a typical scene of the algorithm of the present invention;
fig. 4 is a tracking effect diagram of the algorithm of the present invention.
Detailed Description
For the convenience of describing the present invention, the following terms are first defined:
and (3) random aggregation: refers to a given state spaceByAll the finite subsets of (A) constitute a hyperspaceIs defined inThe random variables above are referred to as random sets.
Set cardinality: refers to the number of elements in the set.
The invention mainly adopts a computer simulation method to verify, and all steps and conclusions are verified to be correct on MATLAB-R2014 b. The specific implementation steps are as follows:
step 1, initializing system parameters.
Initializing system parameters includes: radar monitoring range [0,60m]×[0,60m]The radar range resolution Δ r is 1m, the radar scanning period T is 1s, and the total observation frame number K is 28; probability of target survivalThe birth target model is a multi-target Bernoulli distributionWherein Vector for measurement value of current frameRepresentation of mathematical symbols thereinRepresenting the real number field, zj(j equals 1, …, M) represents the measurement value of the jth radar resolution cell, the number of resolution cells M equals 3600, and the mathematical expression of the multi-target likelihood function g (Z | X) is:
wherein the mathematical symbolsA probability density function representing a measured value of the jth resolution cell under the condition of the multiple target state X, wherein a Gaussian distribution is adopted, and a mathematical expression is as follows:
whereinRepresenting a gaussian distribution with mean μ, covariance matrix Γ,representing the power contribution, σ, of the target state x to the j-th resolution cellN(x) Representing the noise power.
Step 2: initializing label multi-target-bernoulli parametersAnd orderWhereinA target label set space representing a current frame; the initialization iteration time k is 1.
Step 3, calculating the predicted track of the kth frame:
3.1, generating a new target track according to the prior information of the target birth position and based on a target birth model, wherein the birth target model is multi-target Bernoulli distribution
3.2 continue prediction of survival track. According to Bayesian prediction equations, noProbability of existence of a bar surviving track predictionAnd corresponding probability density functionThe following are respectively given,
wherein, the mathematical symbols<f1(x),f2(x)>Representing function f1(x) And function f2(x) Inner product of which is mathematically defined asRepresenting a surviving target track label set space.
And 3, constructing a limited subset space of the predicted target label set.
3.1 determining a target set of labelsThe target label set is the union of the target birth label set and the target survival label set, i.e. the target birth label set and the target survival label setWherein. The number of elements in the target label set isWhere the symbol | f | represents the length of f.
3.2 building target set of labelsOf all finite subsets of (a) whose mathematical symbols are expressed asThe limited number of subsets ofHerein is defined as+For a limited subset spaceAnd its mathematical symbol is expressed as
Step 4, calculating each limited subset of the kth frame according to the Bayesian criterionAnd the corresponding multi-target probability density function.
4.1. Computing each subsetIs given by the prior weight probability w+(I+) The mathematical calculation expression is
Where the mathematical symbol pi represents a continuous multiplication symbol.
4.2. Computing each subsetMultiple target posterior probability density function normalization factor etaZ(I+) The mathematical calculation expression is
4.3. Computing each subsetA posteriori weight probability w (I)+) The mathematical calculation expression is
w(I+)＝w+(I+)ηZ(I+)
4.4. Computing each subsetThe mathematical calculation expression of the multi-target posterior probability density function of
Step 5, for each subsetA posteriori weight probability w (I)+) Performing a normalization process, i.e.
Step 6, calculating each target labelProbability of existence ofAnd its corresponding probability density function
6.1 calculating the target labelsProbability of existence ofThe subsets of step 5Target mark of middle ladleA posteriori weight probability w (I)+) Summing to obtain the target labelProbability of existence ofNamely, it is
6.2 calculating the target labelsA posterior probability density function ofThe subsets of step 5Target mark of middle ladleEdge probability density function ofPerforming weighted summation with the weighted weight of the posterior weight probability w (I) of the corresponding subset+) And the existence probability obtained in step 6.1A posteriori probability density function obtained by weighting and summingAnd (3) carrying out normalization:
whereinWhereinIndicating signThe number set comprisesThe multi-objective posterior probability density function P (X | Z); and 7, extracting a target state. The cardinal number corresponding to the maximum distribution value of the set cardinal numbers is the estimation N of the target number at the moment kkAnd estimating the N separatelykThe status of the individual targets.
And 8, if K is less than K, enabling K to be equal to K +1, and returning to the step 3, wherein K is the frame number.
Through the steps, the multi-target tracking under the complex scene can be effectively realized under the limited resources of the system.

Claims (1)

1. A multi-target tracking method based on a random set theory comprises the following steps:
step 1, initializing system parameters
Initializing system parameters includes: radar monitoring range: namely a data plane, radar range resolution delta r, a radar scanning period T and an observation total frame number K; probability of target survival pS(l) Probability density function f of single target transitionk|k-1(xk|xk-1) (ii) a The birth target model is a multi-target Bernoulli distributionWhereinIndicating the probability of the presence of the ith birth target track,representing the distribution probability density function corresponding to the ith birth target track,representing a birth target label set space; a multi-target likelihood function g (Z | X), wherein Z represents a measurement set and X represents a multi-target state set;
step 2: initializing label multi-target-bernoulli parametersAnd orderWhereinA target label set space representing a current frame; initialization iteration frame number k is 1, r(l)Indicating the probability of existence of the ith surviving target track, p(l)A probability density function representing the ith survival target;
step 3, calculating the predicted track of the kth frame:
3.1, generating a new target track according to the prior information of the target birth position and based on a target birth model, wherein the birth target model is multi-target Bernoulli distribution
3.2 prediction of surviving track, according to Bayes prediction equation, the existence probability of the prediction of the l-th surviving trackAnd corresponding probability density functionThe following are respectively given,
wherein,mathematical symbol < f1(x),f2(x) Represents the function f1(x) And function f2(x) The inner product between;representing a continued survival target track label set space;
step 4, constructing a limited subset space of the predicted target label set;
4.1 determining a target set of labelsThe target label set is a union of the target birth label set and the target survival label set;
4.2 building target set of labelsOf all finite subsets of (a) whose mathematical symbols are expressed as The limited number of subsets ofHerein is defined as+For a limited subset spaceAnd its mathematical symbol is expressed as
Step 5, calculating each limited subset of the kth frame according to the Bayesian criterionThe posterior weight probability and the corresponding multi-target probability density function thereof;
5.1 computing each subsetIs given by the prior weight probability w+(I+)：
Wherein the mathematical symbol Π represents a continuous multiplication symbol,indicating the probability of existence of the ith predicted target track,a representation indicating function, which is defined as follows: indicating function
5.2 calculate each subsetMultiple target posterior probability density function normalization factor etaZ(I+)：
Wherein p is+(xi,li) A probability density function representing the ith predicted target track;
5.3 computing each subsetA posteriori weight probability of
5.4 calculate each subsetThe multi-objective posterior probability density function of (1):
step 6, for each subsetA posteriori weight probability w (I)+) And (3) carrying out normalization treatment:
step 7, calculating the existence probability r of each target label l(l)And its corresponding probability density function p(l)(x)；
7.1 calculating the probability of existence r of each target label l(l)(ii) a The step 6 subsetsThe posterior weighted probability w (I) of the target label l+) Summing to obtain the existence probability r of the target label l(l)：
7.2 calculating the posterior probability density function p of each target label l(l)(x) (ii) a The edge of the parameter P (X | Z) in step 5 is calculated by the following formulaFunction of probability density
Wherein P ({ (x, l) } { (x)1,l1),…,(xn,ln) Z) denotes index subset I+A multi-objective posterior probability density function P (X | Z) comprising l; each subset is divided intoEdge probability density function containing target label lWeighted summation is carried out, the weighted weights of the weighted summation are normalized to the posterior weight probability w (I) of the corresponding subset+) And with the existence probability r obtained in step 7.1(l)Normalizing the posterior probability density function obtained by weighting and summing:
step 8, extracting a target state; the cardinal number corresponding to the maximum distribution value of the set cardinal numbers is the estimation N of the target number at the moment kkAnd estimating the N separatelykThe status of the individual target;
and 9, if K is less than K, enabling K to be equal to K +1, and returning to the step 3, wherein K is the frame number.
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