CN112688667A - Design method of GM-PHD filter - Google Patents

Design method of GM-PHD filter Download PDF

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CN112688667A
CN112688667A CN202011529403.7A CN202011529403A CN112688667A CN 112688667 A CN112688667 A CN 112688667A CN 202011529403 A CN202011529403 A CN 202011529403A CN 112688667 A CN112688667 A CN 112688667A
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薛永宏
韩晓亚
乔凯
樊士伟
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63921 Troops of PLA
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Abstract

The invention relates to a design method of a GM-PHD filter, which comprises the following steps: s1, determining whether prior distribution is in a mixed Gaussian form under a linear Gaussian distribution condition based on an assumed condition of a GM-PHD filter, and if so, assuming that the posterior probability at the k-1 moment assumes a density Dk‑1|k‑1(x) S2. at time k, using the prediction equation and the state transition matrix F to obtain the predicted Dk|k‑1(x) S3. Using predicted Dk|k‑1(x) Performing state update to obtain updated Dk|k(x) (ii) a S4, acquiring Gaussian component weight of the PHD based on the updated PHD
Figure DDA0002851773970000011
And a measure of the current time zkThe correlation between them; s5, measuring z by using the previous momentk‑1Replacing a prediction function of a new object
Figure DDA0002851773970000012
Obtaining new target Gaussian components of new filterThe formula is updated with the quantity weights and their states. The improved GM-PHD filter can realize new target detection more quickly, and has better performance by converging the target number.

Description

Design method of GM-PHD filter
Technical Field
The invention relates to a design method of a GM-PHD filter.
Background
The Random Finish Sets (RFS) theory is a new approach to solving the multi-objective tracking problem. The target state set model and the measurement set model are established, the posterior probability density of the target is recurred in real time under a Bayes framework, and the problem of 'combined explosion' in the association of measurement and the target can be effectively avoided, so that the target track association is well carried out. The GM-PHD filter is a typical implementation method of a random finite set theory, and the computation efficiency is improved through Gaussian term management, clipping and the like, but the method usually assumes that the generation position of a target is known (such as an aircraft carrier, an airport and the like), and for an unknown state target with strong burstiness and unpredictable emission time and spatial position, the clipping method is easy to clip a new target, so that the target is lost or a long time is needed for completing the tracking of the target.
Disclosure of Invention
The invention aims to provide a design method of a GM-PHD filter, which solves the problem that a new target of a traditional GM-PHD filter is lost.
In order to achieve the above object, the present invention provides a method for designing a GM-PHD filter, comprising:
s1, determining whether the distribution is in a Gaussian mixture form under the condition of linear Gaussian distribution based on the assumed condition of a GM-PHD filter, and if so, assuming the posterior probability at the moment of k-1 to assume a density Dk-1|k-1(x) The gaussian mixture of (a) is:
Figure BDA0002851773950000011
wherein ω represents the weight of the gaussian components, N () represents the gaussian distribution function of x, x is a state parameter, m represents the mean of the state parameter, P represents the covariance matrix of the state parameter, and J represents the number of the gaussian components;
s2, at the moment k, the state transition matrix F is utilized to obtain the predictionDk|k-1(x) Comprises the following steps: dk|k-1(x)＝γk(x)+Dβ,k|k-1(x)+DS,k|k-1(x) Wherein D isβ,k|k-1(x) And DS,k|k-1(x) Probability hypothesis densities representing the split target and the surviving target, respectively;
s3. Using predicted Dk|k-1(x) Performing state update to obtain updated Dk|k(x) Comprises the following steps:
Figure BDA0002851773950000021
wherein (1-p)D)Dk|k-1(x) A PHD representing a missed inspection target;
Figure BDA0002851773950000022
indicating the PHD updated with the detected object,
in the updated PHD, DD,k(x; z) is represented by:
Figure BDA0002851773950000023
Figure BDA0002851773950000024
wherein, κk(z) represents clutter density, z represents an observation state parameter, H represents an observation matrix, and U represents a covariance matrix of observation noise;
s4, acquiring Gaussian component weight of the PHD based on the updated PHD
Figure BDA0002851773950000025
And a measure of the current time zkThe correlation between them;
s5, measuring z by using the previous momentk-1Replacing a prediction function of a new object
Figure BDA0002851773950000026
Obtaining new target Gaussian component weight of a new filter and a state updating formula thereof:
Figure BDA0002851773950000027
according to one aspect of the invention, in step S2, the probability hypothesis density D of the split targetβ,k|k-1(x) Expressed as:
Figure BDA0002851773950000031
where F denotes a state transition matrix, Q denotes a covariance matrix of state transition noise, and P denotes a covariance matrix of state parameters.
According to one aspect of the invention, in step S2, the probability of surviving objects is assumed to be density DS,k|k-1(x) Expressed as:
Figure BDA0002851773950000032
according to one aspect of the invention, the density D is assumed based on the probability of splitting the targetβ,k|k-1(x) And probability hypothesis density of surviving objects DS,k|k-1(x) D with predictionk|k-1(x) To obtain:
Figure BDA0002851773950000033
wherein the number of predicted targets is:
Figure BDA0002851773950000034
which represents the sum of the number of surviving targets, split targets, and newly generated targets.
According to an aspect of the present invention, in step S3, the updated target numbers are:
Figure BDA0002851773950000035
including the number of missed targets and the number of targets updated with measurements.
According to an aspect of the present invention, in step S1, the feedback GM-PHD filter is assumed to have the following conditions:
the state transition density function and the observation likelihood function of the target are subjected to linear Gaussian distribution, wherein the state transition model and the observation model of the target visual axis pointing vector both meet the linear Gaussian condition, and the state transition density function and the observation likelihood function can be expressed as follows by adopting a Gaussian distribution form:
Figure BDA0002851773950000041
in the formula, N () represents a gaussian distribution function; q is a covariance matrix of state transition noise; u is a covariance matrix of observation noise;
the survival probability and the detection probability of the target are independent of the target state and are constant, and are expressed as:
pS,k(x)＝pS,pD,k(x)＝pD
wherein p iss,k(x) Indicates the probability of survival, pD,k(x) Representing a detection probability;
the PHD of both the split target and the newly generated target have a gaussian mixture form, expressed as:
Figure BDA0002851773950000042
according to one scheme of the invention, the improved GM-PHD Filter (IGM-PHD Filter) can realize new target detection more quickly, converge the target number and have better performance.
According to the scheme of the invention, the measurement at the previous moment is used as the new target state estimator, and a feedback filtering mode is used, so that the problem that the new target of the unknown state is lost in the GM-PHD filter is solved, and the convergence speed of the estimation of the new target state of the unknown state is improved.
Drawings
FIG. 1 is a flow chart schematically representing a GM-PHD filter according to the present invention;
FIG. 2 is a graph schematically illustrating the distance relationship between measurements and likelihood values for a GM-PHD filter according to one embodiment of the present invention;
FIG. 3 is a graph schematically illustrating a comparison of performance of a GM-PHD filter according to the present invention with a conventional GM-PHD filter at a target number estimation;
fig. 4 is a graph schematically showing the comparison of performance of the GM-PHD filter according to the present invention with the conventional GM-PHD filter at OSPA distances.
Detailed Description
In order to more clearly illustrate the embodiments of the present invention, the following detailed description of the present invention is provided with reference to the drawings and the specific embodiments, which are not repeated herein, but the embodiments of the present invention are not limited to the following embodiments.
According to one embodiment of the present invention, the GM-PHD filter uses gaussian components as basic units, and usually has the following three assumptions:
first, the state transition density function and the observation likelihood function of the target both obey a linear gaussian distribution. Wherein, the state transition model and the observation model of the target visual axis pointing vector both satisfy the linear Gaussian condition, and the Gaussian distribution form can be expressed as:
Figure BDA0002851773950000051
wherein N (-) represents a Gaussian distribution function; x is a state parameter, F is a state transition matrix, and Q is a covariance matrix of state transition noise; z is an observation parameter, H is an observation matrix, and U is a covariance matrix of observation noise. (ii) a
Second, the survival probability and the detection probability of the target are independent of the target state and are constant, and are expressed as:
pS,k(x)＝pS,pD,k(x)＝pD
wherein p iss,k(x) Indicates the probability of survival, pD,k(x) Representing a detection probability;
third, the PHD of the split target and the newly generated target both have a gaussian mixture form, expressed as:
Figure BDA0002851773950000061
where J denotes the number of gaussian components, ω denotes the weight of the gaussian components, m denotes the mean of the state parameters, and P denotes the covariance matrix of the state parameters.
Beta represents a split target, and when the target is at a subscript or superscript position, the parameter represents that the parameter is a parameter of the split target; gamma represents a newly generated target, and when the target is located at the subscript or superscript position, the parameter represents the parameter of the newly generated target; s represents a living target, and when the living target is positioned at a subscript or superscript position, the parameter is a parameter of the living target; k. k-1 each represents a time instant.
As shown in fig. 1, according to an embodiment of the present invention, a method for designing a GM-PHD filter includes:
s1, determining whether prior distribution is in a mixed Gaussian form or not under a linear Gaussian distribution condition based on an assumed condition of a feedback GM-PHD filter, and if so, expressing updated posterior distribution in a mixed Gaussian sum form; i.e. the estimation of the posterior probability density function can be obtained by recursion of the weight, mean and covariance of the gaussian mixture components. Further, assume a posterior probability hypothesis density D at time k-1k-1|k-1(x) The gaussian mixture of (a) is:
Figure BDA0002851773950000062
wherein, ω is(i) k-1Representing the weight of the ith Gaussian component, N () representing the Gaussian distribution function of x, x being a state parameter, m representing the mean of the state parameter, P representing the covariance matrix of the state parameter, and J representing the number of Gaussian components;
s2, at the moment k, obtaining predicted D by using a prediction equation and a state transition matrix Fk|k-1(x) Comprises the following steps: dk|k-1(x)＝γk(x)+Dβ,k|k-1(x)+DS,k|k-1(x) Wherein D isβ,k|k-1(x) And DS,k|k-1(x) Probability hypothesis densities representing the split target and the surviving target, respectively;
s3. Using predicted Dk|k-1(x) Performing state update to obtain updated Dk|k(x) Comprises the following steps:
Figure BDA0002851773950000063
wherein (1-p)D)Dk|k-1(x) A PHD representing a missed inspection target;
Figure BDA0002851773950000064
representing the PHD updated with a detected target, the detected target representing the detected target;
in the updated PHD, DD,k(x; z) is represented by:
Figure BDA0002851773950000071
Figure BDA0002851773950000072
wherein, κk(z) represents clutter density, z represents an observation state parameter, H represents an observation matrix, and U represents a covariance matrix of observation noise;
s4, acquiring Gaussian component weight of the PHD based on the updated PHD
Figure BDA0002851773950000073
And a measure of the current time zkThe correlation therebetween; as shown in fig. 2, in this step, since the gaussian component clipping is performed according to the weight thereof, the gaussian component weight is weighted in step S3
Figure BDA0002851773950000074
The updated formula shows that the weight and the current measurement zkAnd likelihood value Hx of current time prediction statek|k-1Are closely related. The absence of a priori information results from the assumption of a new target state xγ,k|k-1Predicted likelihood value Hxγ,k|k-1With new target measurement zkThere is a long distance therebetweenTherefore, the weight of the Gaussian component of the new target is too small to be cut off, and the new target is difficult to find in time. In practice, the measurement of a new target always appears in the measurement space (p)D> 0) and measurements (z) made by new targets in the measurement space at adjacent timeskAnd zk-1) Always between the predicted likelihood of ratio (z)kAnd Hxγ,k|k-1) With a smaller distance (see fig. 2).
S5, measuring z by using the previous momentk-1Replacing a prediction function of a new object
Figure BDA0002851773950000075
Obtaining new target Gaussian component weight of a new filter and a state updating formula thereof:
Figure BDA0002851773950000081
according to one embodiment of the invention, in step S2, the probability hypothesis density D of the split targetβ,k|k-1(x) Expressed as:
Figure BDA0002851773950000082
where F denotes a state transition matrix, Q denotes a covariance matrix of state transition noise, and P denotes a covariance matrix of state parameters.
According to one embodiment of the invention, in step S2, the probability of surviving objects is assumed to have a density DS,k|k-1(x) Expressed as:
Figure BDA0002851773950000083
according to one embodiment of the invention, the density D is assumed based on the probability of splitting the targetβ,k|k-1(x) And probability hypothesis density of surviving objects DS,k|k-1(x) D with predictionk|k-1(x) To obtain:
Figure BDA0002851773950000084
wherein the predicted number of targets is:
Figure BDA0002851773950000085
which represents the sum of the number of surviving targets, split targets, and newly generated targets.
According to an embodiment of the present invention, in step S3, the updated target numbers are:
Figure BDA0002851773950000091
including the number of missed targets and the number of targets updated with measurements.
As shown in fig. 3 and 4, the performance of the GM-PHD Filter (GM-PHD Filter) and the performance of the improved GM-PHD Filter (IGM-PHD Filter) are compared using the target number estimation performance and the OSPA distance, respectively. The scene comprises 3 targets which appear at different time and different positions, wherein the target 1 appears immediately from the beginning of the simulation, the target 2 appears 40s from the beginning of the simulation, the target 3 appears 80s from the beginning of the simulation, and the simulation duration is 140 s. It can be seen that the improved GM-PHD Filter (IGM-PHD Filter) can achieve new target detection faster, converge the number of targets, and have better performance.
The foregoing is merely exemplary of particular aspects of the present invention and reference should be made to apparatus and structures not specifically described herein which are illustrated as such, but are instead understood to be implemented in the general manner of apparatus and methods known in the art.
The above description is only one embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made without departing from the spirit and principle of the present invention shall fall within the protection scope of the present invention.

Claims (6)

1. A design method of a GM-PHD filter comprises the following steps:
s1, determining prior under the condition of linear Gaussian distribution based on the assumed condition of a GM-PHD filterIf the distribution is in a Gaussian mixture form, if so, the posterior probability at the k-1 moment is assumed to assume a density Dk-1|k-1(x) The gaussian mixture of (a) is:
Figure FDA0002851773940000011
wherein ω represents the weight of the gaussian components, N () represents the gaussian distribution function of x, x is a state parameter, m represents the mean of the state parameter, P represents the covariance matrix of the state parameter, and J represents the number of the gaussian components;
s2, at the moment k, obtaining predicted D by using the state transition matrix Fk|k-1(x) Comprises the following steps: dk|k-1(x)＝γk(x)+Dβ,k|k-1(x)+DS,k|k-1(x) Wherein D isβ,k|k-1(x) And DS,k|k-1(x) Respectively representing probability hypothesis densities of the split target and the survival target;
s3. Using predicted Dk|k-1(x) Performing state update to obtain updated Dk|k(x) Comprises the following steps:
Figure FDA0002851773940000012
wherein (1-p)D)Dk|k-1(x) A PHD representing a missed inspection target;
Figure FDA0002851773940000013
indicating the PHD updated with the detected object,
in the updated PHD, DD,k(x; z) is represented by:
Figure FDA0002851773940000014
Figure FDA0002851773940000015
wherein, κk(z) represents clutter density, z represents an observation state parameter, H represents an observation matrix, and U represents a covariance matrix of observation noise;
s4, acquiring Gaussian component weight of the PHD based on the updated PHD
Figure FDA0002851773940000021
And a measure of the current time zkThe correlation between them;
s5, measuring z by using the previous momentk-1Replacing a prediction function of a new object
Figure FDA0002851773940000022
Obtaining new target Gaussian component weight of a new filter and a state updating formula thereof:
Figure FDA0002851773940000023
2. the design method according to claim 1, wherein in step S2, the probability hypothesis density D of the split targetβ,k|k-1(x) Expressed as:
Figure FDA0002851773940000024
where F denotes a state transition matrix, Q denotes a covariance matrix of state transition noise, and P denotes a covariance matrix of state parameters.
3. The design method according to claim 2, wherein in step S2, the probability of surviving objects is assumed to have a density DS,k|k-1(x) Expressed as:
Figure FDA0002851773940000025
4. the design method of claim 3, wherein the density D is assumed based on the probability of splitting the targetβ,k|k-1(x) And probability hypothesis density of surviving objects DS,k|k-1(x) D with predictionk|k-1(x) To obtain:
Figure FDA0002851773940000026
wherein the number of predicted targets is:
Figure FDA0002851773940000031
which represents the sum of the number of surviving targets, dividing targets and newly generated targets.
5. The designing method according to claim 4, wherein in step S3, the updated target numbers are:
Figure FDA0002851773940000032
including the number of missed targets and the number of targets updated with measurements.
6. The design method according to claim 5, wherein in step S1, the feedback GM-PHD filter is assumed to be:
the state transition density function and the observation likelihood function of the target are subjected to linear Gaussian distribution, wherein the state transition model and the observation model of the target visual axis pointing vector both meet the linear Gaussian condition, and the state transition density function and the observation likelihood function can be expressed as follows by adopting a Gaussian distribution form:
Figure FDA0002851773940000033
in the formula, N () represents a gaussian distribution function; q is a covariance matrix of state transition noise; u is a covariance matrix of observation noise;
the survival probability and the detection probability of the target are independent of the target state and are constant, and are expressed as:
pS,k(x)＝pS,pD,k(x)＝pD
wherein p iss,k(x) The probability of survival is indicated and is,pD,k(x) Representing a detection probability;
the PHD of both the split target and the newly generated target have a gaussian mixture form, expressed as:
Figure FDA0002851773940000034
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113959428A (en) * 2021-09-27 2022-01-21 桂林电子科技大学 PHD filtering method for tracking non-rigid multi-extension target

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107423539A (en) * 2017-03-29 2017-12-01 中国电子科技集团公司第三十八研究所 A kind of label distribution method of GM PHD wave filters
CN109525220A (en) * 2018-12-10 2019-03-26 中国人民解放军国防科技大学 Gaussian mixture CPHD filtering method with track association and extraction capability
CN110780269A (en) * 2019-10-08 2020-02-11 河海大学 Explicit multi-target tracking method based on GM-PHD filter under self-adaptive new growth intensity
CN111488552A (en) * 2020-04-24 2020-08-04 商丘师范学院 Close-proximity multi-target tracking method based on Gaussian mixture probability hypothesis density

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107423539A (en) * 2017-03-29 2017-12-01 中国电子科技集团公司第三十八研究所 A kind of label distribution method of GM PHD wave filters
CN109525220A (en) * 2018-12-10 2019-03-26 中国人民解放军国防科技大学 Gaussian mixture CPHD filtering method with track association and extraction capability
CN110780269A (en) * 2019-10-08 2020-02-11 河海大学 Explicit multi-target tracking method based on GM-PHD filter under self-adaptive new growth intensity
CN111488552A (en) * 2020-04-24 2020-08-04 商丘师范学院 Close-proximity multi-target tracking method based on Gaussian mixture probability hypothesis density

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
赵斌等: "多机动目标跟踪的BFG-GMPHD算法", 《火力与指挥控制》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113959428A (en) * 2021-09-27 2022-01-21 桂林电子科技大学 PHD filtering method for tracking non-rigid multi-extension target
CN113959428B (en) * 2021-09-27 2024-05-28 桂林电子科技大学 PHD filtering method for tracking non-rigid multi-expansion target

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