CN115390560A - Ground target track tracking method based on mixed grid multi-model - Google Patents

Ground target track tracking method based on mixed grid multi-model Download PDF

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CN115390560A
CN115390560A CN202210992794.9A CN202210992794A CN115390560A CN 115390560 A CN115390560 A CN 115390560A CN 202210992794 A CN202210992794 A CN 202210992794A CN 115390560 A CN115390560 A CN 115390560A
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coarse
probability
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CN115390560B (en
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王小刚
白瑜亮
荣思远
王瑞鹏
单永志
周宏宇
张龙
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Harbin Institute of Technology
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Abstract

The invention relates to the field of target tracks, in particular to a ground target track tracking method based on a mixed grid multi-model. Step 1: dividing a model set M of the ground target into a coarse model subset and a fine model subset; and 2, step: processing the coarse model subset according to the classification in the step 1 to obtain a coarse model subset with updated probability and carrying out estimation fusion on the coarse model subset; and step 3: step 1, the classified fine model subset is adaptively adjusted according to online data and priori knowledge; and 4, step 4: respectively carrying out probability updating on the rough model subset in the step 2 and the fine model subset in the step 3; and 5: and (4) performing global estimation fusion again on the coarse model subset and the fine model subset which are updated in the step (4). The method is used for solving the problem that the prior technical scheme can not carry out accurate state estimation on the ground target track.

Description

Ground target track tracking method based on mixed grid multi-model
Technical Field
The invention relates to the field of target tracks, in particular to a ground target track tracking method based on a mixed grid multi-model and a readable storage medium.
Background
Since the last 70 s, a variety of fixed structure multi-model algorithms have been applied to state estimation of ground target trajectories. It features that the model set used in the whole state estimation process
Figure BDA0003804566510000014
Fixed and time invariant, and assuming a set of models
Figure BDA0003804566510000015
And the real mode space
Figure BDA0003804566510000016
The same is true. However, when a multi-model algorithm is used to estimate the state of an object with multiple motion patterns, all possible motion patterns cannot be listed, and the model set is
Figure BDA0003804566510000013
And the real mode space
Figure BDA0003804566510000012
The same assumption is no longer true.
Disclosure of Invention
The invention provides a ground target track tracking method based on a mixed grid multi-model, which can not accurately estimate the state of a ground target track by utilizing the existing fixed structure multi-model algorithm when the ground target moves in various forms.
The invention is realized by the following technical scheme:
a ground target track tracking method based on a mixed grid multi-model comprises the following steps:
step 1: model set of ground target
Figure BDA0003804566510000011
Into coarse model subsets M (i =1, \8230;, n) M ) And a fine model subset A (r =1, \8230;, n) A );
Step 2: sorting according to step 1 on the coarse model subset M (i =1, \ 8230;, n) M ) The processing results in a coarse model subset M (i =1, \ 8230;, n) with probability update M ) And carrying out estimation fusion on the two;
and step 3: step 1 classified fine model subset a (r =1, \8230;, n) A ) Self-adaptive adjustment is carried out according to online data and priori knowledge;
and 4, step 4: for the coarse model subset M of step 2 (i =1, \ 8230;, n) M ) And the fine model subset a of step 3 (r =1, \8230;, n) A ) Respectively updating the probability;
and 5: coarse model subset M (i =1, \ 8230;, n) for step 4 probabilistic update M ) And a fine model subset A (r =1, \8230;, n) A ) And carrying out global state estimation fusion again to realize ground target track tracking.
A ground target track tracking method based on a mixed grid multi-model is disclosed, wherein in the step 2, a coarse model subset M (i =1, \ 8230;, n) is subjected to M ) The treatment specifically comprises the following steps:
step 2.1: sorting according to step 1 on the coarse model subset M (i =1, \ 8230;, n) M ) Performing input interaction;
step 2.2: coarse model subset M (i =1, \ 8230;, n) after input interaction for step 2 M ) And carrying out parallel filtering.
A ground target track tracking method based on a mixed grid multi-model is disclosed, wherein in the step 3, a fine model subset A (r =1, \8230; n) A ) The self-adaptive adjustment according to the online data and the prior knowledge specifically comprises the following steps:
step 3.1: classifying according to step 1 on a fine model subset A (r =1, \8230;, n) A ) Designing;
step 3.2: for the fine model subset A (r =1, \8230;, n) designed in step 3.1 A ) And carrying out parallel filtering.
A ground target track tracking method based on a mixed grid multi-model includes the following steps:
Figure BDA0003804566510000021
Figure BDA0003804566510000022
where k denotes the time, x denotes the state quantity, f (-) denotes the state equation, h (-) denotes the measurement equation, w denotes process noise, v denotes measurement noise,
Figure BDA0003804566510000023
represents an event m k =m (j) I.e. model m (j) Acting at time k;
in a hybrid mesh multi-model algorithm, a set of models
Figure BDA0003804566510000024
The method comprises two parts, namely a coarse model subset M represented by a coarse grid and a fine model subset A represented by a fine grid; model set for time k
Figure BDA0003804566510000025
Is provided with
Figure BDA0003804566510000026
Wherein, the coarse model set M is kept unchanged in the whole state estimation process, and the fine model set A is adaptively adjusted according to online data and priori knowledge;
the optimal state estimate based on the minimum mean square error criterion is expressed as
Figure BDA0003804566510000027
In the formula (I), the compound is shown in the specification,
Figure BDA0003804566510000028
in order to be a global state estimate,
Figure BDA0003804566510000029
representing the sequence of measurements from the initial time to time k,
Figure BDA00038045665100000210
and
Figure BDA00038045665100000211
respectively a coarse model subset M and a fine model subset A k The posterior probability at time k,
Figure BDA00038045665100000212
and
Figure BDA00038045665100000213
based on a coarse model subset M and a fine model subset A, respectively k The state estimate obtained at time k.
3.2, designing a detailed model subset comprises calculating mode moments;
definition of
Figure BDA00038045665100000214
i =1,2, \ 8230, n is the ith model m (i) First two orders of moment, mu i Is a model m (i) When designing the fine model subset, the desired pattern of the fine model subset at time k
Figure BDA00038045665100000215
And probability
Figure BDA00038045665100000216
Not yet acquired, and therefore often utilize the expected pattern at time k-1
Figure BDA00038045665100000217
And probability
Figure BDA00038045665100000218
Carrying out replacement; thus, the desired mode
Figure BDA00038045665100000219
Can be obtained by the following calculation
Figure BDA0003804566510000031
In the formula (I), the compound is shown in the specification,
Figure BDA0003804566510000032
a desired pattern that is a subset of the coarse patterns;
from the equation, the desired mode covariance can be obtained as ∑ k Comprises the following steps:
Figure BDA0003804566510000033
the expected pattern at time k is given by equations (5) and (6)
Figure BDA0003804566510000034
And covariance ∑ k Next, a set of detailed model subsets is designed by using the method of moment matching
Figure BDA0003804566510000035
Respectively matching the first two moments of the model subset with the expected patterns
Figure BDA0003804566510000036
Sum covariance Σ k Equal;
for a ground moving target, designing a model set by considering a constant-speed model and cooperative turning models with different parameters, and adaptively refining the model set
Figure BDA0003804566510000037
Is designed as follows
Figure BDA0003804566510000038
In the formula, p is more than or equal to 0 0 < 1 is a predetermined parameter, and subscript n is a vector
Figure BDA0003804566510000039
Dimension of (2), number of models n A = n +2, number of models n for cooperative turning model A =3;
In-process model set
Figure BDA00038045665100000310
After the design of (2), further utilize
Figure BDA00038045665100000311
Computing a subset of the fine models
Figure BDA00038045665100000312
Where B may be represented by ρ Σ k Obtained by Cholseky decomposition and meets rho sigma k =BB T (ii) a Thereby completing the design of the fine model set.
A ground target track tracking method based on mixed grid multi-model is used for tracking coarse model subset M (i =1, \8230;, n) M ) Performing input interactions includes model probability prediction
Figure BDA00038045665100000313
Hybrid weights
Figure BDA00038045665100000314
Hybrid state estimation and covariance
Figure BDA00038045665100000315
Figure BDA0003804566510000041
The coarse model subset M is filtered in parallel into
Figure BDA0003804566510000042
Wherein KF (·) denotes Kalman filtering;
the probability update of the subset M of the coarse model comprises a likelihood function
Figure BDA0003804566510000043
Normalized constant
Figure BDA0003804566510000044
Figure BDA0003804566510000045
Model probability update
Figure BDA0003804566510000046
Estimating and fusing the rough model subset M;
Figure BDA0003804566510000047
where EF (-) denotes the estimated fusion.
A ground target track tracking method based on mixed grid multi-model is obtained by designing a fine model subset A
Figure BDA0003804566510000048
Wherein FMD (-) represents a fine model subset design;
carrying out parallel filtering on the fine model subset A;
Figure BDA0003804566510000049
wherein KF (·) represents Kalman filtering;
the probability update of the fine model subset A comprises a likelihood function
Figure BDA00038045665100000410
Probability of model
Figure BDA00038045665100000411
Figure BDA0003804566510000051
Normalized constant
Figure BDA0003804566510000052
Model probability update
Figure BDA0003804566510000053
The state estimation fusion of the fine model subset A is specifically
Figure BDA0003804566510000054
Where EF (-) denotes the estimated fusion.
A ground target track tracking method based on mixed grid multi-model for estimation fusionThe combined coarse model subset M (i =1, \8230;, n) M ) The probability updating is carried out specifically as
Figure BDA0003804566510000055
Figure BDA0003804566510000056
For the estimated fused fine model subset A (r =1, \8230;, n) A ) The probability updating is carried out specifically as
Figure BDA0003804566510000057
Figure BDA0003804566510000058
A ground target track tracking method based on mixed grid multi-model is used for updating the probability of a coarse model subset M (i =1, \ 8230;, n) M ) And a probability updated fine model subset a (r =1, \8230;, n) A ) The global estimation fusion is performed again specifically in that,
Figure BDA0003804566510000059
a computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the above-mentioned method steps.
The invention has the beneficial effects that:
the method adaptively designs the fine model set by using a moment matching method based on the estimation result, and completes the state estimation of the ground target by performing weighted fusion on the estimation result of the fine model set, so that the method has higher estimation precision than a single model algorithm and an interactive multi-model algorithm.
Drawings
Fig. 1 is a schematic diagram of the principle of the present invention.
Fig. 2 is a schematic diagram of the filter structure of the present invention.
FIG. 3 is a graph of the initial moment model distribution and corresponding probability of the present invention.
FIG. 4 is a diagram of the first two moments of the initial time model of the present invention.
Fig. 5 is a diagram of the target motion trajectory of the present invention.
Fig. 6 is a schematic diagram of the target speed profile of the present invention.
FIG. 7 is a schematic diagram of a position estimation error curve of the present invention.
FIG. 8 is a schematic diagram of the velocity estimation error curve of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying 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.
A hybrid mesh multi-model algorithm is applied to track tracking of ground maneuvering targets. The hybrid grid is formed by mixing a coarse grid representing a coarse model and a fine grid representing a fine model (as shown in fig. 1), each grid point corresponds to one target motion model, coordinates of the grid points are relevant parameters in the target motion model, and different grid points represent different models.
A ground target track tracking method based on a mixed grid multi-model comprises the following steps:
step 1: model set of ground target
Figure BDA0003804566510000061
Into coarse model subsets M (i =1, \8230;, n) M ) And a fine model subset A (r =1, \8230;, n) A );
The coarse model set M is kept unchanged in the whole state estimation process, and the fine model set A is adaptively adjusted according to online data and priori knowledge;
step 2: classifying the coarse model subset M (i =1, \ 8230;, n) according to step 1 M ) The processing results in a coarse model subset M (i =1, \ 8230;, n) with probability update M ) And carrying out estimation fusion on the two;
and step 3: step 1 classified fine model subset a (r =1, \8230;, n) A ) Self-adaptive adjustment is carried out according to online data and priori knowledge;
and 4, step 4: for the coarse model subset M of step 2 (i =1, \ 8230;, n) M ) And the fine model subset a of step 3 (r =1, \8230;, n) A ) Respectively updating the probability;
and 5: coarse model subset M (i =1, \ 8230;, n) for step 4 probabilistic update M ) And a fine model subset A (r =1, \8230;, n) A ) And carrying out global state estimation fusion again to realize ground target track tracking.
A ground target track tracking method based on mixed grid multi-model is disclosed, in the step 2, a coarse model subset M (i =1, \8230; n) M ) The treatment specifically comprises the following steps:
step 2.1: sorting according to step 1 on the coarse model subset M (i =1, \ 8230;, n) M ) Performing input interaction;
step 2.2: coarse model subset M (i =1, \ 8230;, n) after input interaction for step 2 M ) And carrying out parallel filtering.
A ground target track tracking method based on a mixed grid multi-model is disclosed, wherein in the step 3, a fine model subset A (r =1, \8230; n) A ) The self-adaptive adjustment according to the online data and the prior knowledge specifically comprises the following steps:
step 3.1: classifying according to step 1 on a fine model subset A (r =1, \8230;, n) A ) Designing;
step 3.2: for the fine model subset A (r =1, \8230;, n) designed in step 3.2 A ) And carrying out parallel filtering.
A ground target track tracking method based on a mixed grid multi-model includes the following steps:
Figure BDA0003804566510000071
Figure BDA0003804566510000072
where k denotes the time, x denotes the state quantity, f (-) denotes the state equation, h (-) denotes the measurement equation, w denotes process noise, v denotes measurement noise,
Figure BDA0003804566510000073
represents an event m k =m (j) I.e. model m (j) Acting at time k;
in a hybrid mesh multi-model algorithm, a set of models
Figure BDA0003804566510000074
The method comprises two parts, namely a coarse model subset M represented by a coarse grid and a fine model subset A represented by a fine grid; model set for time k
Figure BDA0003804566510000075
Is provided with
Figure BDA0003804566510000076
Wherein, the coarse model set M is kept unchanged in the whole state estimation process, and the fine model set A is adaptively adjusted according to online data and priori knowledge;
the optimal state estimate based on the minimum mean square error criterion is expressed as
Figure BDA0003804566510000077
In the formula (I), the compound is shown in the specification,
Figure BDA0003804566510000078
in order to be a global state estimate,
Figure BDA0003804566510000079
representing the sequence of measurements from the initial time to time k,
Figure BDA00038045665100000710
and
Figure BDA00038045665100000711
respectively a coarse model subset M and a fine model subset A k The posterior probability at time k,
Figure BDA00038045665100000712
and
Figure BDA00038045665100000713
based on a coarse model subset M and a fine model subset A, respectively k The state estimate obtained at time k.
3.2, designing a detailed model subset comprises calculating mode moments;
in the mixed grid multi-model method, the models in the adaptive fine model subset are not fixed, and are correspondingly adjusted according to the output results of the filters corresponding to other models, so that the accuracy of describing the target motion mode can be improved in the limited number of models. The design of the detailed model subset mainly comprises two parts, namely the calculation of mode moments, namely the calculation of first moment and second moment of grid point coordinates, and the generation of the detailed model subset. Definition of
Figure BDA0003804566510000081
i =1,2, \ 8230, n is the ith model m (i) First two orders of moment, mu i Is a model m (i) When designing the fine model subset, the desired pattern of the fine model subset at time k
Figure BDA0003804566510000082
And probability
Figure BDA0003804566510000083
Not yet acquired, and therefore often utilize the expected pattern at time k-1
Figure BDA0003804566510000084
And probability
Figure BDA0003804566510000085
Carrying out replacement; thus, the desired mode
Figure BDA0003804566510000086
Can be obtained by the following calculation
Figure BDA0003804566510000087
In the formula (I), the compound is shown in the specification,
Figure BDA0003804566510000088
a desired pattern that is a subset of the coarse patterns;
from the equation, the covariance of the desired pattern is ∑ k Comprises the following steps:
Figure BDA0003804566510000089
the expected pattern at time k is given by equations (5) and (6)
Figure BDA00038045665100000810
And covariance ∑ k Next, a set of detailed model subsets is designed by using the method of moment matching
Figure BDA00038045665100000811
Respectively connecting the first two moments of the model subset with the expected mode
Figure BDA00038045665100000812
Sum covariance Σ k Equal;
for a ground moving target, designing a model set by considering a constant-speed model and cooperative turning models with different parameters, and adaptively refining the model set
Figure BDA00038045665100000813
Is designed as follows
Figure BDA00038045665100000814
In the formula, p is more than or equal to 0 0 < 1 is a predetermined parameter, and subscript n is a vector
Figure BDA00038045665100000820
Dimension of (2), number of models n A = n +2, number of models n for cooperative turning model A =3;
In-process model set
Figure BDA00038045665100000815
After the design of (2), further utilize
Figure BDA00038045665100000816
Computing a subset of the fine models
Figure BDA00038045665100000817
Where B may be represented by ρ Σ k Obtained by Cholseky decomposition and meets rho sigma k =BB T (ii) a Thereby completing the design of the fine model set.
A ground target track tracking method based on mixed grid multi-model is used for tracking coarse model subset M (i =1, \8230;, n) M ) Performing input interactions includes model probability prediction
Figure BDA00038045665100000818
Mixing weights
Figure BDA00038045665100000819
Hybrid state estimation and covariance
Figure BDA0003804566510000091
Figure BDA0003804566510000092
Parallel filtering the coarse model subset M into
Figure BDA0003804566510000093
Wherein KF (·) denotes Kalman filtering;
the probability update of the subset M of the coarse model comprises a likelihood function
Figure BDA0003804566510000094
Normalized constant
Figure BDA0003804566510000095
Figure BDA0003804566510000096
Model probability update
Figure BDA0003804566510000097
Estimating and fusing the rough model subset M;
Figure BDA0003804566510000098
where EF (-) denotes the estimated fusion.
A ground target track tracking method based on mixed grid multi-model is obtained by designing a fine model subset A
Figure BDA0003804566510000099
Wherein FMD (-) represents a fine model subset design;
performing parallel filtering on the fine model subset A;
Figure BDA00038045665100000910
wherein KF (·) represents Kalman filtering;
the probability update of the fine model subset A comprises a likelihood function
Figure BDA00038045665100000911
Probability of model
Figure BDA0003804566510000101
Figure BDA0003804566510000102
Normalized constant
Figure BDA0003804566510000103
Model probability update
Figure BDA0003804566510000104
The estimation fusion of the fine model subset A is specifically
Figure BDA0003804566510000105
Where EF (-) represents the estimated fusion.
A ground target track tracking method based on mixed grid multi-model is used for estimating a fused coarse model subset M (i =1, \8230; n) M ) The probability updating is carried out specifically as
Figure BDA0003804566510000106
Figure BDA0003804566510000107
For the estimated fused fine model subset A (r =1, \8230;, n) A ) The probability updating is carried out specifically as
Figure BDA0003804566510000108
Figure BDA0003804566510000109
A ground target track tracking method based on mixed grid multi-model is used for updating the probability of a coarse model subset M (i =1, \ 8230;, n) M ) And a probability updated fine model subset a (r =1, \8230;, n) A ) The global estimation fusion is performed again specifically in that,
Figure BDA00038045665100001010
a computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the above-mentioned method steps.
To obtain global state estimates
Figure BDA00038045665100001011
Need to calculate
Figure BDA00038045665100001012
And
Figure BDA00038045665100001013
four variables. Since the coarse model subset M remains unchanged throughout the state estimation process, the state estimation can be performed using an interactive multi-model algorithm
Figure BDA00038045665100001014
And its covariance
Figure BDA00038045665100001015
Calculating and outputting a coarse model
Figure BDA00038045665100001016
Probabilities in the coarse model subset M
Figure BDA00038045665100001017
And the like.
After the state estimation based on the coarse model subset is completed, the state estimation result based on the fine model subset is calculated. First, a fine model subset A at time k is defined k Is composed of
Figure BDA0003804566510000111
In the formula, m (r) Representing models in a subset of fine models, n A The number of models in the subset of fine models.
State estimation based on a subset of the fine models
Figure BDA0003804566510000112
And state error covariance
Figure BDA0003804566510000113
Can be expressed as
Figure BDA0003804566510000114
Figure BDA0003804566510000115
In the formula (I), the compound is shown in the specification,
Figure BDA0003804566510000116
for a fine model m at time k (r) The probability in the fine-model subset a,
Figure BDA0003804566510000117
and
Figure BDA0003804566510000118
based on a thin model
Figure BDA0003804566510000119
State estimation and covariance of
According to the Bayes' theorem,
Figure BDA00038045665100001110
can be calculated by
Figure BDA00038045665100001111
In the formula (I), the compound is shown in the specification,
Figure BDA00038045665100001112
is a thin model
Figure BDA00038045665100001113
A priori probabilities in the fine model subset A, the probabilities being associated with the fine model
Figure BDA00038045665100001114
A likelihood function generated according to a certain criterion in the design of the self-adaptive fine model set
Figure BDA00038045665100001115
And a normalization constant c 2 Are respectively as
Figure BDA00038045665100001116
Figure BDA00038045665100001117
In the formula (I), the compound is shown in the specification,
Figure BDA00038045665100001118
and
Figure BDA00038045665100001119
which are the measured residual and residual covariance at time k output by the sub-filter r.
Fine model subset A k The posterior probability at time k can be expanded to
Figure BDA0003804566510000121
In the traditional multi-model algorithm, jump between models is usually represented by a first-order Markov chain, and then the models are refined in the formula
Figure BDA0003804566510000122
Is predicted with probability of
Figure BDA0003804566510000123
Can be rewritten as
Figure BDA0003804566510000124
In the formula (I), the compound is shown in the specification,
Figure BDA0003804566510000125
π jr representation model
Figure BDA0003804566510000126
To model
Figure BDA0003804566510000127
The transition probability of (2).
However, in the mixed grid multi-model algorithm, the model in the fine model set changes in real time according to the output result of each sub-filter, and it is difficult to give a suitable transition probability matrix [ pi ] jr ]。
Therefore, the invention utilizes another way to calculate the model prediction probability
Figure BDA0003804566510000128
Namely, it is
Figure BDA0003804566510000129
In the formula (I), the compound is shown in the specification,
Figure BDA00038045665100001210
is a thin model
Figure BDA00038045665100001211
In the fine model subset A k A prior probability of (2).
Neglecting the jumps between the subset of fine models and the set of coarse models, have
Figure BDA00038045665100001212
Substitution of formula (17) into formula (16) gives
Figure BDA00038045665100001213
In combination of formulae (12), (13) and (18), formula (14) can be further derived as
Figure BDA00038045665100001214
In the formula (I), the compound is shown in the specification,
Figure BDA0003804566510000131
is the probability of the coarse model subset M at time k-1.
According to the relation between the probability of the coarse model subset and the probability of the fine model subset, the probability of the coarse model subset M at the time k can be obtained
Figure BDA0003804566510000132
Is composed of
Figure BDA0003804566510000133
Therefore, global state estimation of ground target track tracking can be carried out according to the formula.
TABLE 1 hybrid grid Multi-model Algorithm flow
Figure BDA0003804566510000134
Figure BDA0003804566510000141
In the above table, KF (·) represents kalman filtering, EF (·) represents estimated fusion, and FMD (·) represents fine model subset design.
And (3) performing track tracking mathematical simulation by respectively using an IMM (inertial measurement model) algorithm and a mixed grid multi-model algorithm by using the ground moving target model as a model set template and angular velocity in the cooperative turning model as a grid point coordinate parameter.
(1) Model set parameters
In addition to the constant velocity model, the coarse model set is defined to include two cooperative turning model components, the turning rate of which is [ 2 ]-15°15°]. Transition probability matrix pi between coarse models HG Is composed of
Figure BDA0003804566510000142
Initial coarse model probability of
Figure BDA0003804566510000143
In the fine model design, n A =3 is the number of models in the subset of fine models, and the other preset parameters ρ =0.2 0 =0.4。
For the interactive multi-model, a constant-speed model and two cooperative turning models are selected from the model set, and the turning speed of the model is [ -15 degrees and 15 degrees ].
(2) Parameters of object motion
The motion trail of the ground target is shown in fig. 5, and a speed change curve of the target is shown in fig. 6;
the interactive multi-model tracking filter and the hybrid grid multi-model tracking filter are respectively utilized to perform 100 Monte Carlo mathematical simulations, and the obtained simulation results are summarized as shown in FIGS. 7-8:
TABLE 2 root mean square error
Figure BDA0003804566510000144
The method establishes a coarse model set based on prior information, adaptively designs a fine model set based on an estimation result by using a moment matching method, and completes state estimation of a target by performing weighted fusion on the estimation result of the coarse model set, so that the method has higher estimation precision than an interactive multi-model algorithm.

Claims (10)

1. A ground target track tracking method based on a mixed grid multi-model is characterized by comprising the following steps:
step 1: model set of ground target
Figure FDA0003804566500000014
Into coarse model subsets M (i =1, \8230;, n) M ) And a fine model subset A (r =1, \8230;, n) A );
And 2, step: sorting according to step 1 on the coarse model subset M (i =1, \ 8230;, n) M ) The processing results in a coarse model subset M (i =1, \ 8230;, n) with probability update M ) And carrying out estimation fusion on the two;
and step 3: step 1 classified fine model subset a (r =1, \8230;, n) A ) Self-adaptive adjustment is carried out according to online data and priori knowledge;
and 4, step 4: for the coarse model subset M of step 2 (i =1, \ 8230;, n) M ) And the fine model subset a of step 3 (r =1, \8230;, n) A ) Respectively updating the probability;
and 5: coarse model subset M (i =1, \ 8230;, n) for step 4 probabilistic update M ) And a fine model subset A (r =1, \8230;, n) A ) And carrying out global state estimation fusion again to realize ground target track tracking.
2. The method for tracking the ground target trajectory based on the mixed grid multi-model as claimed in claim 1, wherein in the step 2, the coarse model subset M (i =1, \8230;, n) is selected M ) The treatment specifically comprises the following steps:
step 2.1: sorting according to step 1 on the coarse model subset M (i =1, \ 8230;, n) M ) Performing input interaction;
step 2.2: coarse model subset M (i =1, \ 8230;, n) after input interaction for step 2 M ) And performing parallel filtering.
3. The method for tracking the ground target trajectory based on the mixed grid multi-model as claimed in claim 1, wherein the step 3 is performed on a subset A of fine models (r =1, \8230;, n) A ) The self-adaptive adjustment according to the online data and the prior knowledge specifically comprises the following steps:
step 3.1: classifying according to step 1 on a fine model subset A (r =1, \8230;, n) A ) Designing;
step 3.2: for the fine model subset A (r =1, \8230;, n) designed in step 3.1 A ) And carrying out parallel filtering.
4. The method for tracking the ground target trajectory based on the hybrid grid multi-model as claimed in claim 1, wherein the step 1 is specifically a discrete hybrid system as follows:
Figure FDA0003804566500000011
Figure FDA0003804566500000012
where k denotes the time, x denotes the state quantity, f (-) denotes the state equation, h (-) denotes the measurement equation, w denotes process noise, v denotes measurement noise,
Figure FDA0003804566500000013
represents an event m k =m (j) I.e. model m (j) Acting at time k;
in the mixed grid multi-model algorithm, a model set
Figure FDA0003804566500000021
The method comprises two parts, namely a coarse model subset M represented by a coarse grid and a fine model subset A represented by a fine grid; model set for time k
Figure FDA0003804566500000022
Is provided with
Figure FDA0003804566500000023
Wherein, the coarse model set M is kept unchanged in the whole state estimation process, and the fine model set A is adaptively adjusted according to online data and priori knowledge;
the optimal state estimate based on the minimum mean square error criterion is expressed as
Figure FDA0003804566500000024
In the formula (I), the compound is shown in the specification,
Figure FDA00038045665000000212
in order to be a global state estimate,
Figure FDA0003804566500000025
representing the sequence of measurements from the initial time to time k,
Figure FDA0003804566500000026
and
Figure FDA0003804566500000027
respectively a coarse model subset M and a fine model subset A k The posterior probability at time k is,
Figure FDA00038045665000000213
and
Figure FDA00038045665000000214
based on a coarse model subset M and a fine model subset A, respectively k The state estimate obtained at time k.
5. The method for tracking the ground target track based on the hybrid grid multi-model as claimed in claim 3, wherein the step 3.2 of designing the subset of the detailed models comprises calculating mode moments;
definition of
Figure FDA00038045665000000220
n is the ith model m (i) First two orders of moment, mu i Is a model m (i) When designing the fine model subset, the desired pattern of the fine model subset at time k
Figure FDA00038045665000000216
And probability
Figure FDA00038045665000000215
Not yet acquired, and therefore often utilize the expected pattern at time k-1
Figure FDA00038045665000000217
And probability
Figure FDA00038045665000000218
Carrying out replacement; thus, the desired mode
Figure FDA00038045665000000219
Can be obtained by the following calculation
Figure FDA0003804566500000028
In the formula (I), the compound is shown in the specification,
Figure FDA0003804566500000029
a desired pattern that is a subset of the coarse patterns;
from the equation, the covariance of the desired pattern is ∑ k Comprises the following steps:
Figure FDA00038045665000000210
the expected pattern at time k is given by equations (5) and (6)
Figure FDA00038045665000000221
And covariance ∑ k Below, ofDesigning a group of fine model subsets by using a method of moment matching
Figure FDA00038045665000000222
Respectively matching the first two moments of the model subset with the expected patterns
Figure FDA00038045665000000223
Sum covariance Σ k Equal;
for a ground moving target, the design of a model set is carried out by considering a constant-speed model and cooperative turning models with different parameters, and the model set is adaptive to a fine model set
Figure FDA00038045665000000224
Is designed as follows
Figure FDA00038045665000000211
In the formula, p is not less than 0 0 < 1 is a predetermined parameter, and subscript n is a vector
Figure FDA00038045665000000314
Dimension of (2), number of models n A = n +2, number of models n for cooperative turning model A =3;
In-process model set
Figure FDA00038045665000000312
After the design of (2), further utilize
Figure FDA00038045665000000311
Computing a subset of the fine models
Figure FDA00038045665000000313
Where B may be represented by ρ Σ k Obtained by Cholseky decomposition and meets rho sigma k =BB T (ii) a Thereby completing the design of the fine model set.
6. The method for tracking the ground target trajectory based on the hybrid grid multi-model as claimed in claim 2, wherein the coarse model subset M (i =1, \8230;, n) is selected M ) Performing input interactions includes model probability prediction
Figure FDA0003804566500000031
Hybrid weights
Figure FDA0003804566500000032
Hybrid state estimation and covariance
Figure FDA0003804566500000033
Figure FDA0003804566500000034
The coarse model subset M is filtered in parallel into
Figure FDA0003804566500000035
Wherein KF (·) denotes Kalman filtering;
the probability update of the subset M of the coarse model comprises a likelihood function
Figure FDA0003804566500000036
Normalized constant
Figure FDA0003804566500000037
Figure FDA0003804566500000038
Model probability update
Figure FDA0003804566500000039
Estimating and fusing the rough model subset M;
Figure FDA00038045665000000310
where EF (-) denotes the estimated fusion.
7. The ground target track tracking method based on the hybrid grid multi-model as claimed in claim 3, characterized in that the fine model subset A is designed to obtain
Figure FDA0003804566500000041
Wherein FMD (-) represents a fine model subset design;
performing parallel filtering on the fine model subset A;
Figure FDA0003804566500000042
wherein KF (·) represents kalman filtering;
the probability update of the fine model subset A comprises a likelihood function
Figure FDA0003804566500000043
Probability of model
Figure FDA0003804566500000044
Figure FDA0003804566500000045
Normalized constant
Figure FDA0003804566500000046
Model probability update
Figure FDA0003804566500000047
The estimation fusion of the fine model subset A is specifically
Figure FDA0003804566500000048
Where EF (-) represents the estimated fusion.
8. The method for tracking the ground target trajectory based on the hybrid grid multi-model as claimed in claim 1, wherein the subset M (i =1, \8230;, n) of the coarse models after the estimation fusion is performed M ) The probability updating is carried out specifically as
Figure FDA0003804566500000049
Figure FDA00038045665000000410
For the estimation of the fused fine model subset A (r =1, \8230;, n) A ) The probability updating is carried out specifically as
Figure FDA0003804566500000051
Figure FDA0003804566500000052
9. The method for tracking the ground target trajectory based on the hybrid grid multi-model as claimed in claim 1, wherein the probability-updated coarse model subset M (i =1, \8230;, n) is selected from M ) And a probability updated fine model subset a (r =1, \8230;, n) A ) The global estimation fusion is performed again specifically in that,
Figure FDA0003804566500000053
10. a computer-readable storage medium, characterized in that a computer program is stored in the computer-readable storage medium, which computer program, when being executed by a processor, carries out the method steps of any one of the claims 1-9.
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