CN114491413A - Probability density hypothesis track generation method and system based on minimum cross entropy - Google Patents

Probability density hypothesis track generation method and system based on minimum cross entropy Download PDF

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CN114491413A
CN114491413A CN202210088269.4A CN202210088269A CN114491413A CN 114491413 A CN114491413 A CN 114491413A CN 202210088269 A CN202210088269 A CN 202210088269A CN 114491413 A CN114491413 A CN 114491413A
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徐从安
姚力波
王海洋
王海鹏
邓向阳
张财生
苏航
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School Of Aeronautical Combat Service Naval Aeronautical University Of Pla
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Abstract

The invention relates to a probability density hypothesis track generation method and a system based on a minimum cross entropy, comprising the following steps: obtaining a state estimation set based on an observed value observed by a sensor, and dividing the state estimation set to obtain an effective division set; determining a posterior probability density function based on the active partition set; obtaining a parameter probability density function set based on the effective partition set; based on the parameter probability density function set, adopting a minimum cross entropy optimization method to gradually optimize the posterior probability density function to obtain an optimal posterior probability density function; obtaining an optimal state partition based on the optimal posterior probability density function; and generating a track of each target based on the optimal state set. The invention can better solve the problem of track generation when the targets move adjacently or in a cross way.

Description

Probability density hypothesis track generation method and system based on minimum cross entropy
Technical Field
The invention relates to the technical field of multi-target tracking, in particular to a probability density hypothesis track generation method and system based on minimum cross entropy.
Background
The traditional multi-target tracking method based on data association converts the multi-target tracking problem into the single-target tracking problem, and a target track is naturally generated after the single-target filtering is finished. Although the Sequential Monte Carlo-Probability hypothesis density (SMC-PHD) filtering-based multi-target tracking method can complete multi-target state estimation under the conditions of real-time change of target number and uncertainty of measurement information, the method does not give attribution of each target state, and cannot form a complete target track, which brings difficulties for subsequent high-level fusion (target identification, situation evaluation, threat estimation and the like).
For the problem of flight path generation based on SMC-PHD filtering, the following two methods are mainly used:
the first approach is to combine SMC-PHD filtering with traditional data association methods (such as MHT and JPDA, etc.) to generate the target track. The method can be subdivided into two types of methods, one is that SMC-PHD filtering is used as a measurement preprocessing device, the main function of the method is to remove clutter and false alarms from the measurement set, and then the residual measurement is used as the input of the traditional data association method to complete multi-target tracking and form a target track; and the other type takes the state estimation result of the SMC-PHD as the input of the traditional data association method so as to generate the multi-target track.
The second method considers track management into the filtering process, and labels the target attribute of the state by labeling the particles while the SMC-PHD filtering is performed, so as to output a state estimation with a label, and then generates a target track.
The above two methods still have difficulty in dealing with the tracking problem when objects move adjacently or cross.
Disclosure of Invention
In view of this, the invention provides a probability density hypothesis track generation method and system based on a minimum cross entropy, which abandons the traditional data association method, resolves the track generation problem into a state estimation set division problem, and can better solve the track generation problem when targets are in adjacent or cross motion.
In order to achieve the purpose, the invention provides the following scheme:
a probability density hypothesis track generation method based on minimized cross entropy comprises the following steps:
obtaining a state estimation set based on an observed value observed by a sensor, and dividing the state estimation set to obtain an effective division set;
determining a posterior probability density function based on the active partition set; obtaining a parameter probability density function set based on the effective partition set;
based on the parameter probability density function set, adopting a minimum cross entropy optimization method to gradually optimize the posterior probability density function to obtain an optimal posterior probability density function;
obtaining an optimal state partition based on the optimal posterior probability density function; and generating the flight path of each target based on the optimal state division.
Preferably, the obtaining a state estimation set based on an observation value observed by a sensor, and dividing the state estimation set to obtain an effective division set includes:
obtaining a state estimation set based on an observed value observed by a sensor;
dividing the state estimation set to obtain an effective division set; each state vector in the active partition set
Figure BDA0003488084410000021
In the formula: cKNumber of targets, τ, appearing in the surveillance area for the first K moments0Representing all sets of spurious estimates, τiEstimating a vector for the state of the ith target;
each state vector in the effective partition set satisfies the following constraint conditions:
1) conservation of elements:the elements remain constant before and after the division,
Figure BDA0003488084410000022
in the formula:
Figure BDA0003488084410000023
Nkthe number of state estimates for time k;
2) the elements are not intersected: due to tauiEach estimate of which is either classified as a spurious estimate, or at most corresponds to a target,
Figure BDA0003488084410000024
in the formula: i represents the ith target, and j represents the jth target;
3)τiordering of the state estimates: tau isiA set of elements in ascending chronological order,
Figure BDA0003488084410000025
wherein n islFor target i at klThe number of state estimates at that moment;
4) uniqueness: since each state estimate corresponds to at most one target track,
Figure BDA0003488084410000026
5) testability: each target track corresponds to at least two target states, i.e. | τi|≥2,i＝1,2,…,CK。
Preferably, said determining a posterior probability density function based on said active partition sets; obtaining a set of parametric probability density functions based on the effective partition set, comprising:
determining the posterior probability density function based on the effective partition set;
defining a weight directed graph;
acquiring a probability weight matrix of the weight directed graph;
and constructing the parameter probability density function set based on the probability weight matrix and the effective partition set.
The invention also provides a probability density hypothesis track generation system based on the minimized cross entropy, which comprises the following steps:
the data dividing module is used for obtaining a state estimation set based on an observed value observed by the sensor and dividing the state estimation set to obtain an effective division set;
a probability density module that determines a posterior probability density function based on the active partition set; obtaining a parameter probability density function set based on the effective partition set;
the optimization module is used for gradually optimizing the posterior probability density function by adopting a minimum cross entropy optimization method based on the parameter probability density function set to obtain an optimal posterior probability density function;
the flight path generation module is used for obtaining optimal state division based on the optimal posterior probability density function; and generating the flight path of each target based on the optimal state division.
Preferably, the data dividing module includes:
the data acquisition unit is used for obtaining a state estimation set based on the observed value observed by the sensor;
the data dividing unit is used for dividing the state estimation set to obtain an effective division set; each state vector in the active partition set
Figure BDA0003488084410000031
In the formula: cKNumber of targets, τ, appearing in the surveillance area for the first K moments0Representing all sets of spurious estimates, τiEstimating a vector for the state of the ith target;
each state vector in the effective partition set satisfies the following constraint conditions:
1) conservation of elements: the elements remain constant before and after the division,
Figure BDA0003488084410000032
in the formula:
Figure BDA0003488084410000033
Nkthe number of state estimates for time k;
2) the elements are not intersected: due to tauiEach estimate of which is either classified as a spurious estimate, or at most corresponds to a target,
Figure BDA0003488084410000034
in the formula: i represents the ith target, and j represents the jth target;
3)τiordering of the state estimates: tau isiA set of elements in ascending chronological order,
Figure BDA0003488084410000041
wherein n islFor target i at klThe number of state estimates at that moment;
4) uniqueness: since each state estimate corresponds to at most one target track,
Figure BDA0003488084410000042
5) the testability: each target track corresponds to at least two target states, i.e. | τi|≥2,i＝1,2,…,CK。
Preferably, the probability density module comprises:
a posterior probability density unit that determines the posterior probability density function based on the active partition set;
the directed graph unit defines a weight directed graph;
the weight matrix unit is used for acquiring a probability weight matrix of the weight directed graph;
and the parameter probability density unit is used for constructing the parameter probability density function set based on the probability weight matrix and the effective partition set.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention relates to a probability density hypothesis track generation method and a system based on a minimum cross entropy, comprising the following steps: obtaining a state estimation set based on an observed value observed by a sensor, and dividing the state estimation set to obtain an effective division set; determining a posterior probability density function based on the active partition set; obtaining a parameter probability density function set based on the effective partition set; based on the parameter probability density function set, adopting a minimum cross entropy optimization method to gradually optimize the posterior probability density function to obtain an optimal posterior probability density function; obtaining an optimal state partition based on the optimal posterior probability density function; and generating a track of each target based on the optimal state set. The invention can better solve the problem of track generation when the targets move adjacently or in a cross way
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a probability density hypothesis track generation method based on a minimized cross entropy of the present invention;
FIG. 2 is a block diagram of a probability density hypothesis track generation system based on minimized cross entropy in accordance with the present invention.
Description of the symbols: the method comprises the following steps of 1-a data division module, 2-a probability density module, 3-an optimization module and 4-a track generation module.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a probability density hypothesis track generation method and system based on a minimum cross entropy, which abandons the traditional data association method, resolves the track generation problem into a state estimation set division problem, and can better solve the track generation problem when a target moves adjacently or in a cross mode.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
FIG. 1 is a flow chart of a probability density hypothesis track generation method based on a minimized cross entropy according to the present invention. As shown in the figure, the present invention provides a probability density hypothesis track generation method based on minimized cross entropy, which includes:
and step S1, obtaining a state estimation set based on the observed value observed by the sensor, and dividing the state estimation set to obtain an effective division set. Specifically, the method comprises the following steps:
a set of state estimates is derived based on observations observed by the sensors.
Dividing the state estimation set to obtain an effective division set; each state vector in the active partition set
Figure BDA0003488084410000051
In the formula: cKNumber of targets, τ, appearing in the surveillance area for the first K moments0Representing all sets of spurious estimates, τiA vector is estimated for the state of the ith target.
Each state vector in the effective partition set satisfies the following constraint conditions:
1) conservation of elements: the elements remain constant before and after the division,
Figure BDA0003488084410000052
in the formula:
Figure BDA0003488084410000053
Nkthe number of state estimates for time k.
2) The elements are not intersected: byAt τiEach estimate of which is either classified as a spurious estimate, or at most corresponds to a target,
Figure BDA0003488084410000054
in the formula: i represents the ith target and j represents the jth target.
3)τiOrdering of the state estimates: tau isiA set of elements in ascending chronological order,
Figure BDA0003488084410000061
wherein n islFor target i at klThe number of state estimates at the time.
4) Uniqueness: since each state estimate corresponds to at most one target track,
Figure BDA0003488084410000062
5) the testability: each target track corresponds to at least two target states, i.e. | τi|≥2,i＝1,2,…,CK。
Step S2, determining a posterior probability density function based on the effective partition set; and obtaining a parameter probability density function set based on the effective partition set.
Further, the step S2 is specifically:
divide the search for the optimal state into ω*The problem of (a) translates into an optimal estimation problem of ω in the sense of maximizing the posterior probability density function (MAP), i.e.
Figure BDA0003488084410000063
In the formula:
Figure BDA0003488084410000064
is a posterior probability density function.
For any effective division ω, assume that the number of targets at time k is nkWherein the number of new targets is bkThe number of the death target is mkAnd the number of targets detected by the sensor is dkThe number of undetected targets is ukThe number of false estimates is fkIf the state estimation number is NkThen, the above parameters have the following algebraic relationship:
Figure BDA0003488084410000065
the posterior probability density function is then expressed as follows:
Figure BDA0003488084410000066
in the formula: c0Is a constant that does not depend on the effective division ω; n (x; mu, delta) represents a Gaussian distribution with a mean value of mu and a variance of delta; tau isiEstimate the vector for the state of target i, C is the elimination of spurious estimates τ in the efficient partitioning of ω0Of the total number of estimates of (a) to (b),
Figure BDA0003488084410000067
step prediction for state;
Figure BDA0003488084410000068
is innovation covariance; p is a radical ofmA target probability of extinction; p is a radical ofdDetecting the probability for the target; p is a radical ofbIs the target probability of newborn; p is a radical offIs the target false alarm probability.
Assuming that the total estimated number is N, then
Figure BDA0003488084410000071
Defining a directed graph G with weight value as (V, E, P), wherein V is a node set of the graph, E is an edge of the graph, and P is a weight matrix. For V and E, they are represented by the formula:
Figure BDA0003488084410000072
Figure BDA0003488084410000073
in the formula, VmaxAn upper speed limit for the target; k is a radical of2-k 12 indicates that only the correlation of the estimated values for two consecutive frames is considered.
For a node without edge connection, we call an orphan, which defaults to false alarm and moves it into false track τ in actual processing0. The generation problem of the target track is to divide the nodes in the graph so as to lead the posterior probability density function
Figure BDA0003488084410000074
And max.
If using NiI-1, …, N represents the node of the graph, since the state estimation point is time-sequenced, i.e. the graph G is directed, node N is connected toiAnd NjThe connected edges are denoted (i, j). To construct a parameter vector, the following definitions are made:
1) node NiThe probability of starting a point for a certain edge in the connection graph G is pb(i)。
2) Node NiThe probability of a termination point for a certain edge in the connection graph G is pf(i)。
3) A path in the connection graph passes through node NiAnd immediately past node NjHas a probability of pij。
From the above definitions, for any NiE.g. V, then:
pf(i)+∑pij＝1；
the above formula represents the node N in the connection diagramiOccurring as termination points or intermediate nodes. So the probability weight matrix is
Figure BDA0003488084410000075
In fact, P is a parameterized vector, corresponding to v in a parameterized probability density function. In order to solve the problem of track association when the target moves in a cross mode, the state information and the course information of the target are considered to be merged into a probability weight matrix, and a node N is assumediAnd NjCorresponding time is k1And k2And k is2＞k1Probability of weight p for edges in the join graphijAs defined below:
Figure BDA0003488084410000076
in the formula, | · the luminance | |2Represents a 2 norm;
Figure BDA0003488084410000081
representing state estimation
Figure BDA0003488084410000082
K of (a)2-k1Step one, predicting; thetaijRepresenting vectors
Figure BDA0003488084410000083
And vector
Figure BDA0003488084410000084
Angle between them, thetaijThe smaller the size, the node N is indicatediAnd NjThe greater the likelihood of association; beta is a1And beta2A constant related to process noise and metrology noise; ciTo normalize the parameters, the values can be given by:
Figure BDA0003488084410000085
after the definition of the probability weight matrix P is completed, a certain path τ ═ i1,…,im) The probability of (c) is:
Figure BDA0003488084410000086
for a certain efficient partition
Figure BDA0003488084410000087
Assuming the initial node set is Θ, the parametric probability density function is:
Figure BDA0003488084410000088
and step S3, based on the parameter probability density function set, adopting a minimum cross entropy optimization method to gradually optimize the posterior probability density function to obtain an optimal posterior probability density function.
Specifically, assuming that Y is the target state space and S (-) is the performance function defined on Y, the performance function has the optimum value γ*Comprises the following steps:
Figure BDA0003488084410000089
wherein y is*Is the target state at which the performance function is optimal. For obtaining optimum value gamma of performance function*Assuming that f and h are m-dimensional parametric probability density functions associated with the performance function S (-), the cross entropy (also called Kullback-Leibler distance) of the two is defined as:
Figure BDA00034880844100000810
in the formula, EfIt is expected that D (f | h) reflects the proximity of two probability density functions, and the process of finding two closest probability density functions under certain constraint conditions is the process of minimizing cross entropy. Assuming h (-) is known, f and h are both parameterized probability density functions and can be represented by f (y, v) and h (y, u), v and u are parameter vectors, the minimum cross entropy is represented by min D (f | h), and the performance constraint conditions are as follows:
EfS(Y)＝γ；
under the above constraints, the solution of min D (f | h) is:
Figure BDA00034880844100000811
in the formula, v*The parameter vector corresponding to the solution of the minimum cross entropy, where λ is a constant, can be obtained by the following formula
Figure BDA0003488084410000091
Due to the fact that the probability distribution f (y, v) is continuous*) There is no efficient way to sample, so if we want to pass f (y, v)*) Sampling gradually approaches global optimum y*It is difficult to achieve. Suppose h (y, u) and f (y, v)*) Is a multidimensional discrete distribution, Y ═ Y1,…,Yn) Is a random vector and YiFrom the set { a1,…,anGet the value, then estimate the quantity
Figure BDA0003488084410000092
Its minimum cross entropy solution is
Figure BDA0003488084410000093
In the formula I{·}Representing an event, P representing a probability, akIs a set { a1,…,anThe elements in (c). Under the above assumptions, the following formula may be substituted:
Figure BDA0003488084410000094
constructing a sequence of parameter vectors v1,v2,…,vtSuccessive approximation to global optimum y by iterative sampling*。
In this embodiment, the optimal posterior probability density function is obtained by iteratively sampling the parameter probability density function set obtained in step S2 to gradually approach the global optimal.
Step S4, obtaining the optimal state division based on the optimal posterior probability density function; and generating a track of each target based on the optimal state set.
FIG. 2 is a block diagram of a probability density hypothesis track generation system based on minimizing cross entropy in accordance with the present invention. As shown in fig. 2, the present invention provides a probability density hypothesis track generation system based on minimized cross entropy, comprising: the system comprises a data dividing module 1, a probability density module 2, an optimizing module 3 and a track generating module 4.
The data partitioning module 1 obtains a state estimation set based on an observed value observed by a sensor, and partitions the state estimation set to obtain an effective partition set.
The probability density module 2 determines a posterior probability density function based on the active partition set; and obtaining a parameter probability density function set based on the effective partition set.
The optimization module 3 gradually optimizes the posterior probability density function based on the parameter probability density function set by adopting a minimum cross entropy optimization method to obtain an optimal posterior probability density function.
The track generation module 4 obtains the optimal state division based on the optimal posterior probability density function; and generating a track of each target based on the optimal state set.
As an optional implementation, the data partitioning module 1 of the present invention includes: a data acquisition unit and a data division unit.
The data acquisition unit obtains a state estimation set based on the observed values observed by the sensors.
The data dividing unit divides the state estimation set to obtain an effective division set; each state vector in the active partition set
Figure BDA0003488084410000101
In the formula: cKIn the monitoring area for the first K timesNumber of objects present, τ0Representing all sets of spurious estimates, τiEstimating a vector for the state of the ith target;
each state vector in the effective partition set satisfies the following constraint conditions:
1) conservation of elements: the elements remain constant before and after the division,
Figure BDA0003488084410000102
in the formula:
Figure BDA0003488084410000103
Nkthe number of state estimates for time k;
2) the elements are not intersected: due to tauiEach estimate of which is either classified as a spurious estimate, or at most corresponds to a target,
Figure BDA0003488084410000104
in the formula: i represents the ith target, and j represents the jth target;
3)τiordering of the state estimates: tau isiA set of elements in ascending chronological order,
Figure BDA0003488084410000105
wherein n islFor target i at klThe number of state estimates at that moment;
4) uniqueness: since each state estimate corresponds to at most one target track,
Figure BDA0003488084410000106
5) the testability: each target track corresponds to at least two target states, i.e. | τi|≥2,i＝1,2,…,CK。
As an alternative embodiment, the probability density module 2 of the present invention includes: the system comprises a posterior probability density unit, a directed graph unit, a weight matrix unit and a parameter probability density unit.
The posterior probability density unit determines the posterior probability density function based on the active partition set.
The directed graph unit defines a weighted directed graph.
And the weight matrix unit acquires a probability weight matrix of the weight directed graph.
And the parameter probability density unit constructs the parameter probability density function set based on the probability weight matrix and the effective partition set.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (6)

1. A probability density hypothesis track generation method based on minimum cross entropy is characterized by comprising the following steps:
obtaining a state estimation set based on an observed value observed by a sensor, and dividing the state estimation set to obtain an effective division set;
determining a posterior probability density function based on the active partition set; obtaining a parameter probability density function set based on the effective partition set;
based on the parameter probability density function set, adopting a minimum cross entropy optimization method to gradually optimize the posterior probability density function to obtain an optimal posterior probability density function;
obtaining an optimal state partition based on the optimal posterior probability density function; and generating the flight path of each target based on the optimal state division.
2. The method for generating probability density hypothesis tracks based on minimized cross entropy of claim 1, wherein the obtaining a state estimation set based on observed values observed by sensors and dividing the state estimation set to obtain an effective division set comprises:
obtaining a state estimation set based on an observed value observed by a sensor;
dividing the state estimation set to obtain an effective division set; each state vector in the active partition set
Figure FDA0003488084400000011
In the formula: cKNumber of targets, τ, appearing in the surveillance area for the first K moments0Representing all sets of spurious estimates, τiEstimating a vector for the state of the ith target;
each state vector in the effective partition set satisfies the following constraint conditions:
1) conservation of elements: the elements remain constant before and after the division,
Figure FDA0003488084400000012
in the formula:
Figure FDA0003488084400000013
Nkthe number of state estimates for time k;
2) the elements are not intersected: due to tauiEach estimate of which is either classified as a spurious estimate, or at most corresponds to a target,
Figure FDA0003488084400000014
in the formula: i represents the ith target, and j represents the jth target;
3)τiordering of state estimates in：τiA set of elements in ascending chronological order,
Figure FDA0003488084400000015
wherein n islFor target i at klThe number of state estimates at that moment;
4) uniqueness: since each state estimate corresponds to at most one target track,
Figure FDA0003488084400000021
5) the testability: each target track corresponds to at least two target states, i.e. | τi|≥2,i＝1,2,…,CK。
3. The method for probability density hypothesis path generation based on minimized cross entropy of claim 1, wherein the determining a posterior probability density function based on the active partition sets; obtaining a set of parametric probability density functions based on the effective partition set, comprising:
determining the posterior probability density function based on the active partition set;
defining a weight directed graph;
acquiring a probability weight matrix of the weight directed graph;
and constructing the parameter probability density function set based on the probability weight matrix and the effective partition set.
4. A probability density hypothesis path generation system based on minimizing cross entropy, comprising:
the data dividing module is used for obtaining a state estimation set based on an observed value observed by the sensor and dividing the state estimation set to obtain an effective division set;
a probability density module that determines a posterior probability density function based on the active partition set; obtaining a parameter probability density function set based on the effective partition set;
the optimization module is used for gradually optimizing the posterior probability density function by adopting a minimum cross entropy optimization method based on the parameter probability density function set to obtain an optimal posterior probability density function;
the flight path generation module is used for obtaining optimal state division based on the optimal posterior probability density function; and generating the flight path of each target based on the optimal state division.
5. The system of claim 1, wherein the data partitioning module comprises:
the data acquisition unit is used for obtaining a state estimation set based on the observed value observed by the sensor;
the data dividing unit is used for dividing the state estimation set to obtain an effective division set; each state vector in the active partition set
Figure FDA0003488084400000022
In the formula: cKThe number of targets, tau, appearing in the surveillance area for the first K moments0Representing all sets of spurious estimates, τiEstimating a vector for the state of the ith target;
each state vector in the effective partition set satisfies the following constraint conditions:
1) conservation of elements: the elements remain constant before and after the division,
Figure FDA0003488084400000023
in the formula:
Figure FDA0003488084400000031
Nkthe number of state estimates for time k;
2) the elements are not intersected: due to tauiEach estimate of which is either classified as a spurious estimate, or at most corresponds to a target,
Figure FDA0003488084400000032
in the formula: i represents the ith target, and j represents the jth target;
3)τiordering of the state estimates: tau isiThe element sets are arranged in ascending chronological order,
Figure FDA0003488084400000033
wherein n islFor target i at klThe number of state estimates at that moment;
4) uniqueness: since each state estimate corresponds to at most one target track,
Figure FDA0003488084400000034
5) the testability: each target track corresponds to at least two target states, i.e. | τi|≥2,i＝1,2,…,CK。
6. The system of claim 1, wherein the probability density hypothesis path generation system based on minimizing cross entropy comprises:
a posterior probability density unit that determines the posterior probability density function based on the active partition set;
the directed graph unit defines a weight directed graph;
the weight matrix unit is used for acquiring a probability weight matrix of the weight directed graph;
and the parameter probability density unit is used for constructing the parameter probability density function set based on the probability weight matrix and the effective partition set.
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