CN109670142B - Resolvable maneuver group target state estimation method based on random finite set - Google Patents

Resolvable maneuver group target state estimation method based on random finite set Download PDF

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CN109670142B
CN109670142B CN201910012689.2A CN201910012689A CN109670142B CN 109670142 B CN109670142 B CN 109670142B CN 201910012689 A CN201910012689 A CN 201910012689A CN 109670142 B CN109670142 B CN 109670142B
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刘伟峰
迟玉东
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Abstract

The invention relates to a method for estimating the state of a resolvable maneuvering group target based on a random finite set. The existing method has the defect of considering the cooperative relationship, and has insufficient estimation precision on the cooperative error, so that the tracking precision is not high. The method of the invention firstly carries out system modeling, then carries out error correction, and finally carries out state prediction and updating. The method introduces graph theory, describes the cooperative relationship among targets by utilizing the adjacency matrix of the graph theory, optimizes the position vector among the targets, corrects the cooperative error of the state estimation, effectively reduces the error of the state estimation of the group targets caused by the cooperative relationship among the targets, and solves the problem that the traditional algorithm does not consider the influence of the cooperative relationship among the targets on the state estimation effect.

Description

Resolvable maneuver group target state estimation method based on random finite set
Technical Field
The invention belongs to the technical field of computers, in particular to the technical field of multi-sensor multi-target tracking, and particularly relates to a state estimation method for a distinguishable maneuvering group target under a random finite set framework.
Background
Measuring group targets located at different resolution units of the sensor is referred to as resolvable group targets. There is a certain structural relationship and cooperation relationship between the sub-targets of the distinguishable group targets. In the case of state estimation and tracking of a resolvable group of targets that are maneuvered, a cooperative error is one of the important factors affecting the state estimation and tracking effects. The mutual relation among the group target sub-targets has errors, the prior art has the defects of considering the cooperative relation of the current research result, and has insufficient estimation precision on the cooperative errors, so that the tracking precision is not high.
Disclosure of Invention
The invention aims to provide a distinguishable maneuvering group target state estimation method based on a random finite set. The invention provides a new error by utilizing the interrelation between the group target sub-targets, corrects the cooperative error and improves the estimation precision and the tracking precision.
The method comprises the following specific steps:
step (1), system modeling:
suppose that the resolvable group object moves at a cloud rotational speed, wherein the dynamic equation of the object x at the time k+1 is as follows:
x k+1 ＝F k x k +Γω k ；
wherein ,Fk Is a state transition matrix, Γ is a state noise matrix, ω k Is system noise; when each target node has a single parent node, the resolved group target dynamic model is as follows:
x k+1,i ＝F k,l X k,l +b k (l,i)+Γ k,i ω k,i ；
z k+1,i ＝H k+1 x k+1,i +v k+1,i ；
wherein ,xk+1,i Indicating the state of the object i at time k+1, z k+1,i The measurement state of the target i at the time k+1 is represented; f (F) k,l For the state transition matrix of the object l at the moment k, Γ k,i For the state noise matrix of the target i at the k moment omega k,i Representing the system noise of target i at time k, b k (l, i) is the positional relationship between the object i and the object i at the time k, i.e. the displacement vector; h k+1 An observation matrix at time k+1, v k+1,i Indicating that the target i observes noise at the k moment; omega k,i and vk+1,i All obey normal distribution;
Figure GDA0004137168940000021
Figure GDA0004137168940000022
and />
Figure GDA0004137168940000023
Representing the position and velocity of object i on the x-axis,/->
Figure GDA0004137168940000024
and />
Figure GDA0004137168940000025
Representing the position and velocity of the object i on the y-axis, x k,i ∈X k ，X k T represents transposition for a set of states of all targets at time k; in the maneuvering process of the target, the included angle beta between the movement direction of the father node and the direction of the father node is assumed to be in a stable state, and the angle theta of the movement direction of the father node at the moment k v The acquisition mode is as follows:
Figure GDA0004137168940000026
in the maneuvering group target, the displacement vector b k (l, i) satisfy:
Figure GDA0004137168940000027
Figure GDA0004137168940000028
is the distance between the parent node and the child node;
when the target does not have a parent node, the movement of the head node is not influenced by other targets, and the compensation vector in the movement model when the target does not have the parent node, b k (l, i) =0, and at this time x k,l The state of the target itself at time k is shown;
when a target has multiple parents and is in linear condition:
Figure GDA0004137168940000029
z k+1,i ＝H k+1 x k+1,i +v k+1,i ；
Figure GDA00041371689400000210
wherein ,
Figure GDA00041371689400000211
set of all parent nodes for target i, w k (l, i) represents kThe target l is carved as the weight of the father node of the target i;
step (2) error correction:
step (2.1) it is assumed that all targets have the same matrix, i.e. F k,l ＝F k Then:
x k+1,i ＝F k x k,l +Δb k (l,i)+Γ k,i ω k,i ；
Figure GDA00041371689400000212
wherein ,
Figure GDA00041371689400000213
for the moment k, the true position vector of the father target l and the son target i is direct; Δb k (l, i) is a collaborative displacement, which depends on the collaborative relationship between group targets;
thus, a new collaboration error is proposed:
Figure GDA0004137168940000031
step (2.2) for each object i, the object state x is passed through it k,i Adjacency matrix A d Cooperative error
Figure GDA0004137168940000032
To build a new model and to derive the following propositions:
proposition 1: it is assumed that the dynamic model of the group target satisfies the following two conditions: the movement of the group is simple movement; displacement vector { b } k (l, i) } is a random quantity and is gaussian distributed, then the cooperative error
Figure GDA0004137168940000033
Also gaussian:
Figure GDA0004137168940000034
then the collaboration error
Figure GDA0004137168940000035
Also gaussian, and is obtained by the following formula:
Figure GDA0004137168940000036
Figure GDA0004137168940000037
wherein ,Qk,i As covariance matrix of process noise, P k For the state covariance of the target, S k Covariance of displacement distribution;
step (3), predicting and updating the state:
the state transition probabilities are written as:
Figure GDA0004137168940000038
1) And (3) predicting: the initial state of the distinguishable group target is x k The predicted density function in this state can be given by the Champan-Kolmogorov equation:
Figure GDA0004137168940000039
/>
and (3) making:
Figure GDA00041371689400000310
the predicted density is:
Figure GDA00041371689400000311
μ k+1|k,i ＝F k,i x k,i ；
Figure GDA00041371689400000312
μ k+1|k,i predicting a distribution for the target;
2) And a state updating step: predicted density p k+1,i For gaussian distribution, the corresponding posterior function is:
Figure GDA0004137168940000041
wherein g (z|x) is a multi-objective likelihood function; the molecular part derivation method of the posterior function is as follows:
Figure GDA0004137168940000042
in the formula ：
Figure GDA0004137168940000043
μ k+1,i ＝μ k+1|k,i +K k+1,i (z k+1 -H k+1 μ k+1|k,i )；
P k+1,i ＝(I-K k+1,i H k+1 )P k+1|k,i ；
Figure GDA0004137168940000044
where R is the covariance of the process noise.
The method introduces graph theory, describes the cooperative relationship among targets by utilizing the adjacency matrix of the graph theory, optimizes the position vector among the targets on the basis, corrects the cooperative error of the state estimation, effectively reduces the error of the state estimation of the group targets caused by the cooperative relationship among the targets, and solves the problem that the traditional algorithm does not consider the influence of the cooperative relationship among the targets on the state estimation effect.
Drawings
FIG. 1.8 is a schematic diagram of the true trajectory of a sub-target;
FIG. 2 is a schematic diagram of state estimation obtained by a UKF filtering algorithm;
FIG. 3 is an OSPA distance comparison pictorial illustration;
FIG. 4 is a schematic diagram of target number estimation;
Detailed Description
The invention is further described below with reference to the accompanying drawings.
A resolvable maneuvering group target state estimation method based on a random finite set comprises the following specific steps:
step (1), system modeling:
suppose that the resolvable group object moves at a cloud rotational speed, wherein the dynamic equation of the object x at the time k+1 is as follows:
x k+1 ＝F k x k +Γω k (1)；
wherein ,Fk Is a state transition matrix, Γ is a state noise matrix, ω k Is system noise; when each target node has a single parent node, the resolved group target dynamic model is as follows:
x k+1,i ＝F k,l X k,l +b k (l,i)+Γ k,i ω k,i (2)；
z k+1,i ＝H k+1 x k+1,i +v k+1,i (3)；
wherein ,xk+1,i Indicating the state of the object i at time k+1, z k+1,i The measurement state of the target i at the time k+1 is represented; f (F) k,l For the state transition matrix of the object l at the moment k, Γ k,i For the state noise matrix of the target i at the k moment omega k,i Representing the system noise of target i at time k, b k (l, i) is the positional relationship between the object i and the object i at the time k, i.e. the displacement vector; h k+1 An observation matrix at time k+1, v k+1,i Indicating that the target i observes noise at the k moment; omega k,i and vk+1,i All obey normal distribution;
Figure GDA0004137168940000051
Figure GDA0004137168940000052
and />
Figure GDA0004137168940000053
Representing the position and velocity of object i on the x-axis,/->
Figure GDA0004137168940000054
and />
Figure GDA0004137168940000055
Representing the position and velocity of the object i on the y-axis, x k,i ∈X k ，X k A set of states at time k for all targets; in the maneuvering process of the target, the included angle beta between the movement direction of the father node and the direction of the father node is assumed to be in a stable state, and the angle theta of the movement direction of the father node at the moment k v The acquisition mode is as follows:
Figure GDA0004137168940000056
in the maneuvering group target, the displacement vector b k (l, i) satisfy:
Figure GDA0004137168940000057
Figure GDA0004137168940000058
is the distance between the parent node and the child node;
when the target does not have a parent node, the movement of the head node is not influenced by other targets, and the compensation vector in the movement model when the target does not have the parent node, b k (l, i) =0, and at this time x k,l The state of the target itself at time k is shown;
when a target has multiple parents and is in linear condition:
Figure GDA0004137168940000059
z k+1,i ＝H k+1 x k+1,i +v k+1,i (8)；
Figure GDA00041371689400000510
wherein ,
Figure GDA0004137168940000061
set of all parent nodes for target i, w k (l, i) represents the weight of the parent node whose target l is target i at time k.
Step (2) error correction:
step (2.1) it is assumed that all targets have the same matrix, i.e. F k,l ＝F k Then equation (9) translates into:
x k+1,i ＝F k x k,l +Δb k (l,i)+Γ k,i ω k,i (10)；
Figure GDA0004137168940000062
wherein ,
Figure GDA0004137168940000063
for the moment k, the true position vector of the father target l and the son target i is direct; Δb k (l, i) is a collaborative displacement, which depends on the collaborative relationship between group targets;
thus, a new collaboration error is proposed:
Figure GDA0004137168940000064
/>
step (2.2) according to formulas (11), (12), it can be seen that the new noiseThe influence of sound depends only on the cooperative relationship between the objects, so for each object i, the object state x through it k,i Adjacency matrix A d Cooperative error
Figure GDA0004137168940000065
To build a new model and to derive the following propositions:
proposition 1: assuming that the dynamic model of the group target is as shown in formulas (7) (8) (9), if the following two conditions are satisfied: the movement of the group is simple movement; displacement vector { b } k (l, i) } is a random quantity and is gaussian distributed, then the cooperative error
Figure GDA0004137168940000066
Also Gaussian distribution->
Figure GDA0004137168940000067
Then the collaboration error
Figure GDA0004137168940000068
Is also gaussian and can be obtained by the following formula:
Figure GDA0004137168940000069
Figure GDA00041371689400000610
wherein ,Qk,i As covariance matrix of process noise, P k For the state covariance of the target, S k Is the displacement distribution covariance.
Step (3), predicting and updating the state:
from equation (12), the cooperative error conforms to a mean of 0 and a variance of
Figure GDA00041371689400000611
Is defined by formula (13), +.>
Figure GDA00041371689400000612
Acquisition of the adjacency matrix A depends on k The state transition probabilities are written as follows:
Figure GDA0004137168940000071
1) And (3) predicting: the initial state of the distinguishable group target is x k The predicted density function in this state can be given by the Champan-Kolmogorov equation:
Figure GDA0004137168940000072
and (3) making:
Figure GDA0004137168940000073
the predicted density is:
Figure GDA0004137168940000074
μ k+1|k,i ＝F k,i x k,i (19)；
Figure GDA0004137168940000075
μ k+1|k,i a distribution is predicted for the target.
2) And a state updating step: predicted density p k+1,i For gaussian distribution, the corresponding posterior function is:
Figure GDA0004137168940000076
wherein g (z|x) is a multi-objective likelihood function; the molecular part derivation method of the posterior function is as follows:
Figure GDA0004137168940000077
in the formula ：
Figure GDA0004137168940000078
μ k+1,i ＝μ k+1|k,i +K k+1,i (z k+1 -H k+1 μ k+1|k,i ) (24)；
P k+1,i ＝(I-K k+1,i H k+1 )P k+1|k,i (25)；
Figure GDA0004137168940000079
where R is the covariance of the process noise.
Fig. 1 shows the true motion trajectories of 8 objects contained in two sub-group objects. The two sub-group targets respectively comprise 4 targets, and the array types and the motion tracks of the two sub-group targets are different.
Fig. 2 shows a state estimation effect diagram obtained by the UKF filtering algorithm.
To better illustrate the invention, in our experiments we selected an unscented kalman filter to verify the tracking process. Probability of detection of target P D (x k ) =0.98. Monitoring area s= [ -pi/2, pi/2]×[0,3000]m 2 Clutter density ranges from 1.592 ×10 -3 m -2 。
Fig. 3 shows an optimal sub-mode allocation (OSPA) distance map under a kf filter.
Fig. 4 shows a graph of the number estimation of the target number by the present algorithm under the UKF filter.
From the comparative analysis of fig. 2-4, we can conclude that: the algorithm effectively reduces the state estimation error of the maneuvering distinguishable group target by correcting the cooperative error, and improves the state estimation precision.
Finally, the above description is only intended to illustrate the technical solution of the present invention and not to limit the scope thereof, i.e. the technical solution of the present invention is modified or equivalent, without departing from the purpose and scope thereof, and is intended to be covered by the scope of the claims of the present invention.

Claims (1)

1. A method for estimating the state of a resolvable maneuvering group target based on a random finite set is characterized by comprising the following specific steps:
step (1), system modeling:
suppose that the resolvable group object moves at a cloud rotational speed, wherein the dynamic equation of the object x at the time k+1 is as follows:
x k+1 ＝F k x k +Γω k ；
wherein ,Fk Is a state transition matrix, Γ is a state noise matrix, ω k Is system noise; when each target node has a single parent node, the resolved group target dynamic model is as follows:
x k+1,i ＝F k,l X k,l +b k (l,i)+Γ k,i ω k,i ；
z k+1,i ＝H k+1 x k+1,i +v k+1,i ；
wherein ,xk+1,i Indicating the state of the object i at time k+1, z k+1,i The measurement state of the target i at the time k+1 is represented; f (F) k,l For the state transition matrix of the object l at the moment k, Γ k,i For the state noise matrix of the target i at the k moment omega k,i Representing the system noise of target i at time k, b k (l, i) is the positional relationship between the object i and the object i at the time k, i.e. the displacement vector; h k+1 An observation matrix at time k+1, v k+1,i Indicating that the target i observes noise at the k moment; omega k,i and vk+1,i All obey normal distribution;
Figure FDA0004137168930000011
Figure FDA0004137168930000012
and />
Figure FDA0004137168930000013
Representing the position and velocity of object i on the x-axis,/->
Figure FDA0004137168930000014
and />
Figure FDA0004137168930000015
Representing the position and velocity of the object i on the y-axis, x k,i ∈X k ，X k T represents transposition for a set of states of all targets at time k; in the maneuvering process of the target, the included angle beta between the movement direction of the father node and the direction of the father node is assumed to be in a stable state, and the angle theta of the movement direction of the father node at the moment k v The acquisition mode is as follows:
Figure FDA0004137168930000016
in the maneuvering group target, the displacement vector b k (l, i) satisfy:
Figure FDA0004137168930000017
Figure FDA0004137168930000018
is the distance between the parent node and the child node;
when the target does not have a parent node, the movement of the head node is not influenced by other targets, and the compensation vector in the movement model when the target does not have the parent node, b k (l, i) =0, and at this time x k,l The state of the target itself at time k is shown;
when a target has multiple parents and is in linear condition:
Figure FDA0004137168930000021
z k+1,i ＝H k+1 x k+1,i +v k+1,i ；
Figure FDA0004137168930000022
wherein ,
Figure FDA0004137168930000023
set of all parent nodes for target i, w k (l, i) represents the weight of the parent node of which the target l is the target i at the moment k;
step (2) error correction:
step (2.1) it is assumed that all targets have the same matrix, i.e. F k,l ＝F k Then:
x k+1,i ＝F k x k,l +Δb k (l,i)+Γ k,i ω k,i ；
Figure FDA0004137168930000024
wherein ,
Figure FDA0004137168930000025
for the moment k, the true position vector of the father target l and the son target i is direct; Δb k (l, i) is a collaborative displacement, which depends on the collaborative relationship between group targets;
thus, a new collaboration error is proposed:
Figure FDA0004137168930000026
step (2.2) for each object i, the object state x is passed through it k,i Adjacency matrix A d Cooperative error
Figure FDA0004137168930000027
To build a new model and to derive the following propositions:
proposition 1: it is assumed that the dynamic model of the group target satisfies the following two conditions: the movement of the group is simple movement; displacement vector { b } k (l, i) } is a random quantity and is gaussian distributed, then the cooperative error
Figure FDA0004137168930000028
Also gaussian:
Figure FDA0004137168930000029
then the collaboration error
Figure FDA00041371689300000210
Also gaussian, and is obtained by the following formula:
Figure FDA00041371689300000211
Figure FDA00041371689300000212
wherein ,Qk,i As covariance matrix of process noise, P k For the state covariance of the target, S k Covariance of displacement distribution;
step (3), predicting and updating the state:
the state transition probabilities are written as:
Figure FDA0004137168930000031
1) And (3) predicting: the initial state of the distinguishable group target is x k The predicted density function in this state can be given by the Champan-Kolmogorov equation:
Figure FDA0004137168930000032
and (3) making:
Figure FDA0004137168930000033
the predicted density is:
Figure FDA0004137168930000034
μ k+1|k,i ＝F k,i x k,i ；
Figure FDA0004137168930000035
μ k+1|k,i predicting a distribution for the target;
2) And a state updating step: predicted density p k+1,i For gaussian distribution, the corresponding posterior function is:
Figure FDA0004137168930000036
wherein g (z|x) is a multi-objective likelihood function; the molecular part derivation method of the posterior function is as follows:
Figure FDA0004137168930000037
/>
in the formula ：
Figure FDA0004137168930000038
μ k+1,i ＝μ k+1|k,i +K k+1,i (z k+1 -H k+1 μ k+1|k,i )；
P k+1,i ＝(I-K k+1,i H k+1 )P k+1|k,i ；
Figure FDA0004137168930000039
where R is the covariance of the process noise.
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