阅读说明：本技术 具有类型概率的l-rfs混合目标结构建模与估计方法 (L-RFS mixed target structure modeling and estimation method with type probability ) 是由 刘伟峰 黄梓龙 王志 于 2020-06-02 设计创作，主要内容包括：本发明提出了一种具有类型概率的L-RFS混合目标结构建模与估计方法,该方法包括三个方面：混合目标动态建模,混合目标的形状类型分析和混合目标的跟踪估计。首先,结合广义标签多伯努利滤波器建立了混合目标的量测混合模型,并对目标类型进行分析,利用Gibbs采样和BIC准则推导出有限混合模型的参数来对混合目标进行学习跟踪,然后采用等效量测方法来替代扩展目标和群目标所构成的多量测目标产生的量测,对多量测目标形状采用椭圆逼近建模,实现多量测目标形状的估计。该方法可以有效的判断目标类型,并跟踪混合目标。(The invention provides a modeling and estimation method of an L-RFS mixed target structure with type probability, which comprises the following three aspects: dynamic modeling of the mixed target, shape type analysis of the mixed target and tracking estimation of the mixed target. Firstly, a measuring mixed model of a mixed target is established by combining a generalized label multi-Bernoulli filter, the type of the target is analyzed, parameters of the limited mixed model are deduced by utilizing Gibbs sampling and BIC criteria to learn and track the mixed target, then an equivalent measuring method is adopted to replace measurement generated by a plurality of measuring targets formed by an extended target and a swarm target, and ellipse approximation modeling is adopted for the shape of the plurality of measuring targets to realize the estimation of the shape of the plurality of measuring targets. The method can effectively judge the type of the target and track the mixed target.)

1. The L-RFS mixed target structure modeling and estimation method with the type probability is characterized by comprising the following steps:

step (1) setting a multi-target mixed state set X at the moment k_k：

Multi-target hybrid state X at time k_kRepresented by a random finite set:

X_k＝{(x_k,1),(x_k,2),…,(x_k,N(k)) } ∈ F (χ); f (χ) represents a set of a finite set of state spaces χ; n (k) is the number of targets at time k, x_k,iRepresenting the ith multi-target state, each value being in state space χ, i ═ 1,2, …, n (k);

the hybrid target state of the tape-flag type is represented as:

X_k＝{(x_k,1,l₁,t₁),(x_k,2,l₂,t₂),…,(x_k,n(k),l_n(k),t_N(k)) }; label (R)

since the GLMB filtering algorithm requires different and unique labels for different targets, the label constraint Δ (X) is:

M (k) represents the number of measurements at time k, Z_k,jRepresents the j-th observed state, j ═ 1,2, …, m (k);

extended target metrology set at time kWhereinRepresenting the metrology set generated by the M' (k) th extended target at time k;

measurement set of distinguishable group targets at time kWhereinRepresenting the metrology set generated at time k for the M "(k) th resolvable cluster target;

Z_kclutter, target measurement and missing detection information are included; the target measurement comprises observed values of a point target, an extended target and a distinguishable group target; step (3), establishing a target finite mixture model:

the multi-metric observation data set is described by the following mixture distribution function:

wherein the measurement setWhile

the constraint conditions of the mixing proportion weight are as follows:

the bayesian estimate is described as: is posterior distribution;

step (4) establishing likelihood function

The measured likelihood function is calculated by the following equation:

wherein

Rewritten as the following equation:

wherein the missing variable

missing variables

wherein the content of the first and second substances,

in the mixed target tracking engineering, three types of targets are mixed together, and classification tracking is needed, so type judgment is needed;

(5-1) for the point target, the measurement corresponds to the state point one by one, namely, only one measurement can be carried out on one target state point;

point targets obey a single Bernoulli distribution

Wherein P is_D(x) For survival probability, α ∈ (0,1), the closer the measurement value is to the target value, the larger the α value, and (| Z | -P)_D) N (0, 0.1); the probability that the ith target is considered as the point target is:

(5-2) multiple measurement targets: the target capable of generating a plurality of measurements is a plurality of measurement targets, namely a group target or an extended target; the parameters of different multiple measuring targets have different dimensions, so that the following type jump matrix can be established;

in the above formula, the element P_r(j₁,j₂) Is denoted as the j-th₂Type target jump to jth₁The hopping probability of the type target; it is not required, however, that the matrix must be a symmetric matrix, i.e., P_r(j₁,j₂) May not be equal to P_r(j₂,j₁)；

The sum of the probabilities of the type targets jumping to each target is 1, namely the sum of each row vector is 1; with the following constraints

Since the object type is known, the structure type of each object is described by the following type probability vector

Wherein, the superscript i represents the ith target, the subscript k represents the kth step, and the subscript t_jDenotes the t-th_jThe number of the types of the objects,

(5-3) multiple measurement target observation space passing

namely:

wherein r is the radius of the circle after target fitting;

the measurement values in the extended target follow a poisson distribution, then:

for Δ n distributed in the X axis_z,1+Δn_z,2+…+Δn_z,nChecking;

that is to say that the first and second electrodes,

then at 3 sigma standard deviation, the type probability density satisfying the extended target distribution is foundWherein Δ n_zIs a middleA variable;

(5-4) obtaining the measurement value and the number of indistinguishable objects in the indistinguishable objects

And carrying out normalization processing on various target probabilities under multiple measurements, wherein the processing is as follows:

the type probability density of the hybrid target is therefore expressed as follows:

wherein the content of the first and second substances,

(5-5) updating of the type probabilities of the extended targets and the group targets as follows:

wherein the intensity function

each time the update probability is calculatedThen, normalization processing is carried out on various target probabilities, and then the prediction updating process is carried out in a circulating mode;

step (6) tracking the mixed target by using a GLMB filtering algorithm, wherein the tracking is divided into a prediction step and an updating step;

the formula of GLMB is:

(6-1) the formula of the prediction step is as follows:

in the following formula, P (T) is type probability, adoptingIndicating a new labelThe weight of (a) is determined,

(6-2) an updating step, which can be realized by a Gibbs sampling iterative learning algorithm;

wherein, θ:

further learning the shapes of a plurality of measured targets in the mixed target on the basis of obtaining the target state estimation;

step (7), estimating the mean covariance of Gaussian distribution and the weight of each Gaussian distribution by using a Gibbs sampling algorithm, and evaluating the fitting truth of the Gaussian distributions by using a BIC (binary arithmetic coding) criterion; outputting to obtain weight, mean, covariance and BIC value, and adopting nth_kEquivalent measurement of a mixed target

Technical Field

The invention belongs to the technical field of sensors, particularly relates to the field of mixed target tracking, and relates to an L-RFS (Label-Random finish Set) mixed target structure modeling and estimation problem algorithm with type probability.

Background

In many fields such as civil and military, target tracking has an indispensable application meaning all the time. Due to the limitation of the previous sensing technology, the conventional target tracking algorithm assumes that the detected target is a point, i.e. one target can only produce one measurement at most. With the continuous development of modern sensor technology, the radar equipment can receive test data from different scattering points on an extended target, namely, one target can generate a plurality of measurements at different moments, and the target is called an extended target. In another case, a plurality of targets may exhibit a certain formation flight or similar motion pattern, and exhibit certain motion characteristics of a group of targets, which are collectively referred to as group targets. The tracking of extended targets and group targets can provide us with an accurate number and motion state of the tracked targets. In the target tracking process, multiple types of targets are often mixed together, and certain interference is generated on the tracking of the targets, so that the tracking effect is poor.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a modeling and estimation method of an L-RFS mixed target structure with type probability.

In order to obtain the overall optimal tracking performance in the tracking of mixed targets (including point targets, extended targets and distinguishable group targets), the method establishes a measurement mixed model of the mixed targets by combining a generalized label multi-Bernoulli filter, analyzes the types of the targets, deduces parameters of a finite mixed model by utilizing Gibbs sampling and BIC criteria to learn and track the mixed targets, then replaces the measurement generated by a plurality of measurement targets formed by the extended targets and the group targets by adopting an equivalent measurement method, and adopts ellipse approximation modeling for the shapes of the plurality of measurement targets to realize the tracking of the mixed targets.

The invention discloses a modeling and estimation method of an L-RFS mixed target structure with type probability, which specifically comprises the following steps:

step (1) setting a multi-target mixed state set X at the moment k_k：

Multi-target hybrid state X at time k_kBy random finiteSet representation:

X_k＝{(x_k,1),(x_k,2),…,(x_k,N(k)) } ∈ F (χ); f (χ) represents a set of a finite set of state spaces χ; n (k) is the number of targets at time k, x_k,iRepresents the ith multi-target state, each value being in the state space χ, i ═ 1,2, …, n (k).

The hybrid target state of the tape-flag type is represented as:

X_k＝{(x_k,1,l₁,t₁),(x_k,2,l₂,t₂),…,(x_k,n(k),l_n(k),t_N(k)) }; label (R)In order to have a label space that is distributed discretely,representing a set of positive integers, α_iIndicates a difference; the type component T e (T) of the hybrid target₀,T₁,T₂)，T₀Indicating a point target, T₁Denotes the extended target, T₂Indicating a resolvable group target.

Since the GLMB filtering algorithm requires different and unique labels for different targets, the label constraint Δ (X) is:

wherein, X's label set

A set of labels representing x, x representing (x, l, t); step (2) setting an observation state set Z in the k-time system model_k：

M (k) represents the number of measurements at time k, Z_k,jRepresents the j-th observed state, j ═ 1,2, …, m (k);

representing a state space

All of the limited subsets of (a).

Extended target metrology set at time k

Wherein

Representing the metrology set generated by the M' (k) th extended target at time k;

measurement set of distinguishable group targets at time k

Wherein

Represents the metrology set generated by the M' (k) th resolvable cluster target at time k.

Z_kClutter, target measurement and missing detection information are included; the target measurement comprises observed values of a point target, an extended target and a distinguishable group target; step (3), establishing a target finite mixture model:

the multi-metric observation data set is described by the following mixture distribution function:

wherein the measurement setWhileRepresents the position and speed of the centroid point at the j-th target k on the xy axis, r_k+1Parameters representing the position, velocity and type of the centroid point at time k +1 on the xy axis

Is the mixing ratio weight, ω, at the jth target time k_k+1Represents the weight of the mixing ratio at the time of k +1, j is an indicator variable of the target, and the number of variables is m_kJ-0 represents a clutter measurement,is a measure of the centroid point at the jth target time k +1, y_k+1Represents the measurement of the target centroid point at time k +1,represents the observation set at time k +1 under label l, y_k+1Representing a measured set of target centroid points;

the constraint conditions of the mixing proportion weight are as follows:

the bayesian estimate is described as:

is posterior distribution;in order to be a function of the likelihood,to a prior distribution, C^-1Is a constant for the normalization of the signals,

step (4) establishing likelihood function

The measured likelihood function is calculated by the following equation:

wherein

Rewritten as the following equation:

wherein the missing variable

And satisfies the following constraints:

missing variablesFrom conditional meanThe estimation gives:

wherein the content of the first and second substances,

and (5) in the mixed target tracking engineering, the three types of targets are mixed together, and classification tracking is required, so that type judgment is required.

(5-1) for point targets, the measurements correspond to state points one-to-one, i.e., there is only one measurement for a target state point.

Point targets obey a single Bernoulli distribution

Wherein P is_D(x) For survival probability, α ∈ (0,1), the closer the measurement value is to the target value, the larger the α value, and (| Z | -P)_D) N (0, 0.1). The probability that the ith target is considered as the point target is:

(5-2) multiple measurement targets: the target capable of generating a plurality of measurements is a plurality of measurement targets, namely a group target or an extended target. And the parameters of different multiple measuring targets have different dimensions, so that the following type jump matrix can be established.

In the above formula, the element P_r(j₁,j₂) Is denoted as the j-th₂Type target jump to jth₁Hop probability of type object. It is not required, however, that the matrix must be a symmetric matrix, i.e., P_r(j₁,j₂) May not be equal to P_r(j₂,j₁)。

And the sum of the probability of the type target jumping to each target is 1, i.e. the sum of each row vector is 1. With the following constraints

Since the object type is known, the structure type of each object is described by the following type probability vector

Wherein the superscript i denotesI th target, subscript k denotes the k th step, subscript t_jDenotes the t-th_jThe number of the types of the objects,indicates belonging to the t-th_jProbability of individual structure types. The component corresponding to the maximum probability value in the type probability vector of each target is the type to which the multiple targets belong.

(5-3) multiple measurement target observation space passing

Obtaining a covariance matrix through covariance, solving an eigenvalue and an eigenvector of the matrix through an eig function, calculating a long axis a and a short axis b of the shape of the target, and taking a 3 sigma standard deviation as a standard for measuring an extended target;

namely:

wherein r is the radius of the circle after target fitting;

the measurement values in the extended target follow a poisson distribution, then:

for Δ n distributed in the X axis_z,1+Δn_z,2+…+Δn_z,nChecking;

that is to say that the first and second electrodes,

then at 3 sigma standard deviation, the type probability density satisfying the extended target distribution is foundWherein Δ n_zIs an intermediate variable.

(5-4) the biggest difference between the group target and the extended target is that in the target tracking, one target generates a plurality of measurements, and the measurement values surroundWith the same extended target, most of the measurements are in an indistinguishable volume. The distinguishable group target is composed of a plurality of point targets, the structure is fixed, a plurality of sub targets generate a plurality of measurements, and the sub target values correspond to the measurement values one by one. Point targets within a cluster are distinguishable, and an indistinguishable object cannot encompass the entire cluster of targets. Generally, the number of point targets in a cluster is equal to the number of indistinguishable objects. Can be obtained by measuring the amount of the indistinguishable substance and the number of the indistinguishable substances

And carrying out normalization processing on various target probabilities under multiple measurements, wherein the processing is as follows:

the type probability density of the hybrid target is therefore expressed as follows:

wherein the content of the first and second substances,and detecting the target type through a max criterion.

(5-5) updating of the type probabilities of the extended targets and the group targets as follows:

wherein the intensity functionThe formula is as follows:

each time the update probability is calculated

Then, normalization processing needs to be carried out on various target probabilities, and then the prediction updating process is carried out in a circulating mode.

And (6) tracking the mixed target by using a GLMB filtering algorithm, wherein the tracking is divided into a prediction step and an updating step.

The formula of GLMB is:

(6-1) the formula of the prediction step is as follows:

in the following formula, P (T) is type probability, adoptingIndicating a new label

The weight of (a) is determined,

indicating a survival tag

The weight of (c). Probability density of newborn target is represented by p_B(. l) represents the survival target density

From a prior density p_S(. l) yields the probability density of surviving targets represented by f (. l).

And (6-2) an updating step, which can be realized by a Gibbs sampling iterative learning algorithm.

Wherein the content of the first and second substances,θ (i) ═ θ (i ') > 0 means i ═ i'. In a fixed (I, xi), at maximum weight

Next, the M elements of theta are represented by theta^(M)＝{ξ⁽¹⁾,…,ξ^(M)And (c) represents.

Expressed as the truncated normalized weight, p (t) represents the probability under each type. It is related toThe parameters are defined as follows.

And further learning the shapes of a plurality of measurement targets in the mixed target on the basis of obtaining the target state estimation.

And (7) estimating the mean covariance of the Gaussian distributions and the weight of each Gaussian distribution by using a Gibbs sampling algorithm, and evaluating the fitting truth of the Gaussian distributions by using a BIC (binary arithmetic coding) criterion.

Through the algorithm, the weight, the mean value, the covariance and the BIC value are obtained through output, and the nth value is adopted_kEquivalent measurement of a mixed target

And replacing the mixed target measurement, modeling the shapes of the multiple measurement targets by adopting ellipse approximation, and continuously learning the shapes of the multiple measurement targets by a Gibbs parameter learning algorithm.

The invention has the beneficial effects that: aiming at the problems of state estimation, target number estimation and target shape estimation of a mixed target consisting of a point target, an extended target and a group target (indistinguishable) under a filtering condition, an L-RFS mixed target structure modeling and estimation problem algorithm with type probability is provided. Firstly, a measuring mixed model of a mixed target is established by combining a generalized label multi-Bernoulli filter, the type of the target is analyzed, parameters of the limited mixed model are deduced by utilizing Gibbs sampling and BIC criteria to learn and track the mixed target, then an equivalent measuring method is adopted to replace measurement generated by a plurality of measuring targets formed by an extended target and a swarm target, and ellipse approximation modeling is adopted for the shape of the plurality of measuring targets to realize the estimation of the shape of the plurality of measuring targets. The method can effectively track the mixed target.

Drawings

FIG. 1: mixing target motion tracks;

FIG. 2: mixing the real tracks of the targets;

FIG. 3: state estimation obtained by a GLMB filtering algorithm;

FIG. 4: OSPA distance (10 times);

FIG. 5: the number of mixed targets was estimated (10 times).

The specific implementation mode is as follows:

the invention provides an L-RFS mixed target structure modeling and estimation problem algorithm with type probability, which comprises the following steps:

step (1) the state of multiple targets at the time k is represented by the following RFS set

X_k＝{(x_k,1),(x_k,2),…,(x_k,N(k))}∈F(χ) (1)

Where N (k) is the number of targets at time k, there are N (k) multi-target states x_k,1,x_k,2,…x_k,N(k)Each value is on the state space χ, while F (χ) represents the set of the finite set of χ.

The mixed target state of the tape-flag type is expressed as follows:

X_k＝{(x_k,1,l₁,t₁),(x_k,2,l₂,t₂),…,(x_k,n(k),l_n(k),t_N(k))} (2)

label space in which the labels are discretely distributedWhereinRepresenting a set of positive integers, α_iRepresenting a difference, a label

T represents the type component of the mixing target, T ∈ (T)₀,T₁,T₂),T₀Indicating a point target, T₁Denotes the extended target, T₂Representing a resolvable group target;

since the GLMB filtering algorithm requires different and unique labels for different targets, the following are used as label constraints:

wherein, X's label setStep (2) setting an observation state in the system modelM (k) represents the number of measurements at time k,

representsAll of the limited subsets of (a).Representing the metrology set of the extended target at time k,

wherein

Represents the measurement set generated by the M (k) th extended target at the k time.Representing the measurement set of resolvable cluster targets at time k,

whereinRepresents the measurement set generated by the M (k) th resolvable group target at time k.

Z_kThe clutter, target measurement and missing detection information are included, target measurement comprises observed values of point targets, extended targets and distinguishable group targets, and a total measurement set comprises target measurement, measurement generated by unknown clutter and false alarm measurement.

Step (3) target finite mixed model

The multi-metric observed data set may be described by the following mixed distribution function:

wherein the measurement set

n_kIs the total number of measurements at time k,

while

Representing the position and velocity of the centroid point of the target on the xy-axis,

is a type parameter.Is the weight of the mixture ratio, j is the indicator variable of the target, the number of variables is m_kJ-0 represents a clutter measurement,is a measure of the target centroid point.

The mixing ratio weight constraint is as follows:

bayesian estimation can be described as:

wherein the content of the first and second substances,z_1:k:＝{z₁,…z_k}，

is a posterior distribution, C^-1Is a normalization constant.In order to be a function of the likelihood,

is a prior distribution.

And (4) likelihood function. The measured likelihood function can be calculated by the following equation:

wherein

Rewritten as the following equation:

wherein the missing variable

And satisfies the following constraints:

missing variables

Can be derived from conditional mean

The estimation gives:

wherein the content of the first and second substances,

and (5) in the mixed target tracking engineering, the three types of targets are mixed together, and classification tracking is required, so that type judgment is required.

(5-1) for point targets, the measurements correspond to state points one-to-one, i.e., there is only one measurement for a target state point.

Point targets obey a single Bernoulli distribution

Wherein P is_D(x) For survival probability, α ∈ (0,1), the closer the measurement value is to the target value, the larger the α value, and (| Z | -P)_D) N (0, 0.1). The probability that the ith target is a point target can be considered as:

(5-2) multiple measurement targets: the target capable of generating a plurality of measurements is a plurality of measurement targets, namely a group target or an extended target. And the parameters of different multiple measuring targets have different dimensions, so that the following type jump matrix can be established.

In the above formula, the element P_r(j₁,j₂) Is denoted as the j-th₂Type target jump to jth₁Hop probability of type object. It is not required, however, that the matrix must be a symmetric matrix, i.e., P_r(j₁,j₂) May not be equal to P_r(j₂,j₁)。

And the sum of the probability of the type target jumping to each target is 1, i.e. the sum of each row vector is 1. The following constraints can be used

Since the object type is known, the structure type of each object can be described by the following type probability vector

Wherein, the superscript i represents the ith target, the subscript k represents the kth step, and the subscript t_jDenotes the t-th_jThe number of the types of the objects,indicates belonging to the t-th_jProbability of individual structure types. The component corresponding to the maximum probability value in the type probability vector of each target is the type to which the multiple targets belong.

(5-3) the observation space of the multiple measurement targets is

z_k＝Hx_k+v_k(17)

Then can pass through

And obtaining a covariance matrix through covariance, solving an eigenvalue and an eigenvector of the matrix through an eig function, calculating a long axis a and a short axis b of the shape of the target, and taking a 3 sigma standard deviation as a standard for measuring the extended target.

Namely:

the measurement values in the extended target follow a poisson distribution, then:

for Δ n distributed in the X axis_z,1+Δn_z,2+…+Δn_z,nFor inspection

That is to say that the first and second electrodes,

then at 3 sigma standard deviation, the type probability density satisfying the extended target distribution is found

(5-4) the biggest difference between the group target and the extended target is that in target tracking, one target generates multiple measurements, and the measurement values all surround the same extended target, and most of the measurements are in an indistinguishable body (constant). The distinguishable group target is composed of a plurality of point targets, the structure is fixed, a plurality of sub targets generate a plurality of measurements, and the sub target values correspond to the measurement values one by one. Point targets within a cluster are distinguishable, and an indistinguishable object cannot encompass the entire cluster of targets. Generally, the number of point targets in a cluster is equal to the number of indistinguishable objects. Can be obtained by measuring the amount of the indistinguishable substance and the number of the indistinguishable substances

And carrying out normalization processing on various target probabilities under multiple measurements, wherein the processing is as follows:

the type probability density of the hybrid target is therefore expressed as follows:

wherein the content of the first and second substances,

and detecting the target type through a max criterion.

(5-5) updating of the type probabilities of the extended targets and the group targets as follows:

wherein the intensity functionThe formula is as follows:

each time the update probability is calculated

Then, normalization processing needs to be carried out on the probabilities of various targets (matrix row vectors), and then the prediction updating process is carried out in a circulating mode.

And (6) tracking the mixed target by using a GLMB filtering algorithm, wherein the tracking can be divided into a prediction step and an updating step.

The formula of GLMB is:

(6-1) the formula of the prediction step is as follows:

in the following formula, P (T) is type probability, adoptingIndicating a new labelThe weight of (a) is determined,indicating a survival tag

The weight of (c). Probability density of newborn target is represented by p_B(. l) represents the survival target densityFrom a prior density p_S(. l) yields the probability density of surviving targets represented by f (. l).

And (6-2) an updating step, which can be realized by a Gibbs sampling iterative learning algorithm.

Wherein the content of the first and second substances,

θ (i) ═ θ (i ') > 0 means i ═ i'. In a fixed (I, xi), at maximum weight

Next, the M elements of theta are represented by theta^(M)＝{ξ⁽¹⁾,…,ξ^(M)And (c) represents.

Expressed as the truncated normalized weight, p (t) represents the probability under each type. The relevant parameters are defined as follows.

And further learning the shapes of a plurality of measurement targets in the mixed target on the basis of obtaining the target state estimation.

And (7) estimating the mean covariance of the Gaussian distributions and the weight of each Gaussian distribution by using a Gibbs sampling algorithm, and evaluating the fitting truth of the Gaussian distributions by using a BIC (binary arithmetic coding) criterion.

Through the algorithm, the weight, the mean value, the covariance and the BIC value are obtained through output, and the nth value is adopted_kEquivalent measurement of a mixed target

And replacing the mixed target measurement, modeling the shapes of the multiple measurement targets by adopting ellipse approximation, and continuously learning the shapes of the multiple measurement targets by a Gibbs parameter learning algorithm.

For better explanation of the present invention, assume that there are 4 extended targets in the observation area containing clutter, 3 single targets, 3 group targets (indistinguishable) moving, the number of targets changing every moment, and the probability of a target being detected is P_D0.8, clutter is uniformly distributed, 20 clutter intensity lambada c, 1000 clutter area S [ -1000,1000]×[-1000,1000]m²。

The four extended target intensities are respectively lambda_e1＝16,λ_e2＝18，λ_e3＝20，λ_e418. The extended targets do uniform linear (CV) motion on a 2-dimensional plane, the detection time is 100s, and the four extended targets are respectively born and consumed at different times and different placesAnd (7) death.

The state equation for the target is:

x_k+1,i＝Gx_k,i+v_k,i

wherein the state transition matrix is:

where T-1 s denotes the sampling time,indicating position and velocity in the x and y directions, respectively.

The observation equation for the target is:

z_k+1,i＝Hx_k,i+w_k,i

wherein the observation matrix H ═ 1000; 0010] observing a noise covariance of diag ([ 10; 10]) × diag ([ 10; 10]), i representing the ith target. The initial states of the four extended targets are respectively:

TABLE 1 extended target motion initial state and Presence time

TABLE 2 initial state and Presence time of movement of object

Assuming that the number of the group targets (indistinguishable) is 3, three targets do uniform linear (CV) motion on a 2-dimensional plane, the detection time is 100s, and the four group targets are born and die at different times and different places respectively.

When a certain scattering point in the extended target does not have a parent node, the scattering point is called a head node, the motion of the head node is not influenced by any node, and the state equation of the head node is as follows:

x_k+1＝G_kx_k+β_kw_k

when a parent node exists, the scattered node is called a child node, the motion of the scattered node is influenced by the parent node, and the state equation of the scattered node is defined as follows:

as shown above, assuming that the number of scattering points of the group target is M, the scattering point M ∈ [1, …, M ∈]，b_k(i, m) represents the compensation vector between the scattering point m and its parent node, b_kAnd (i, m) represents the direction and distance information between nodes, a state transition matrix G and a state noise matrix beta.

Assume weight w_k(i, m) are equal weights, and the main steps for establishing the group target motion model are as follows:

traversing n nodes in the group, then finding out a father node of the node through a given adjacency matrix, judging whether the father node exists, if so, then:

wherein, in the above formula

Represents the jth parent node of the scattering point m.

If not, then:

x_k+1,m＝G_k,ix_k.i+β_k,mw_k,m

TABLE 3 group target motion initialization and Presence time

Fig. 1 is a model of scattering points of the three types of objects at 20, 60, 80, and 99 in the presence of noise.

In the whole tracking process, if 10 targets are mutually independent, the real track of the target motion is represented in the lower graph, different curves in the graph respectively represent the respective motion tracks of the targets, the starting point of the target motion is marked by a small circle, and the motion end point is represented by a small triangle.

Fig. 2 is a real trajectory of a hybrid target.

Fig. 3 is a state estimation of an object, tracks of different colors represent track estimations of different object motions, and a first graph and a second graph respectively represent tracking tracks in x-axis and y-axis directions. The first and second extended targets, the first point target, and the first group target appear at 1 second; a third extended target, a second point target, and a second cluster target appear at 20 seconds; a third cluster target occurs at 30 seconds; a third point target occurs at 40 seconds; the fourth expansion target occurs at 50 seconds; at the 100 th second, only the third, fourth, extended object, the second, third point object, and the third group object are stored. It can be seen in fig. 2 that the algorithm performs relatively good tracking on multiple types of targets.

The performance of the algorithm presented herein was evaluated by using the OSPA distance:

wherein X andthe number of the real state set and the estimated state set is m and n respectively. N shape_nExpressed as a factorial from 1 to n, with a precondition of 1. ltoreq. p.ltoreq. ∞ andc is greater than 0. FIG. 4 shows OSPA results from ten Monte Carlo simulations of the GLMB algorithm.

As can be seen from fig. 4, the OSPA distance is large in the first few scans, mainly due to the radix error, since both filters need to perform multiple scans to build the trace.

Fig. 5 shows the number estimation of targets, which is basically consistent with the actual target value under GLMB, and the number of targets is 4 from 0s to 20 s: at the 20 th s, the extension target 3, the point target 2, the group target 2 are born, and the number of targets becomes 7: at 30s, a group target 3 was born, and the number of targets became 8: at 40s, a point target 3 is born, and the number of targets becomes 9: at 50s, the extension target 3, the point target 2, the group target 2 are born, and the number of targets becomes 10: at the time of 60s, the number of targets 1 died, the number of extended targets 1 died at the 70s, the number of group targets 1 died at the 80s, and the number of group targets 2 died at the 80 s.