CN113537302B - Multi-sensor randomized data association fusion method - Google Patents

Multi-sensor randomized data association fusion method Download PDF

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CN113537302B
CN113537302B CN202110703559.0A CN202110703559A CN113537302B CN 113537302 B CN113537302 B CN 113537302B CN 202110703559 A CN202110703559 A CN 202110703559A CN 113537302 B CN113537302 B CN 113537302B
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沈晓静
王艺
孙佳婕
刘海琪
刘冰
张栩琪
孟凡钦
袁学东
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93209 Troops Of Chinese Pla
Sichuan University
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Abstract

The invention discloses a multi-sensor randomized data association fusion method, and belongs to the field of information fusion. The method comprises the steps of providing a multi-sensor randomized data association fusion algorithm, relaxing a traditional multi-sensor multi-hypothesis data association linear programming problem into a 0-1 integer programming problem through a convex relaxation technology, and solving to obtain a local hypothesis probability value; and further estimating the target state by a random coefficient matrix Kalman filtering fusion method. The method can reduce the computational complexity of the traditional NP-difficult association problem, fully utilizes the information of multiple sensors in consideration of the association uncertainty in a complex scene, and improves the estimation accuracy of a fusion center on the target; numerical analysis shows that the estimation effect of the new method on the target state can be more scientifically and reasonably related to and fused with the multi-sensor information.

Description

Multi-sensor randomized data association fusion method
Technical Field
The invention relates to the field of information processing and fusion, in particular to a multi-sensor randomized data association fusion method.
Background
The multi-sensor system has the advantages of higher estimation precision, wider coverage range, stronger survivability and the like, and is widely applied to the fields of target tracking and the like. The multi-sensor data association is one of the basic problems of multi-sensor information fusion. In complex scenes such as near target distance and target interaction, the matching relation between the multi-sensor observations is difficult to determine, so that the accuracy of the association algorithm is reduced, and the fusion effect is affected. Therefore, establishing a reliable multi-sensor data association fusion method is still a problem to be solved.
One of the key points of the multi-sensor data fusion problem is to determine the association matching relationship among the multiple sensors, but due to the fact that the number of the sensors is large, the observation distance of the local sensors is short, clutter exists in the observation, and the like, the accurate multi-sensor data association relationship is difficult to obtain, and the fusion effect is difficult to guarantee. A multi-sensor multi-hypothesis data association method proposed by poura B, which has been widely used so far [ document 1: multidimensinal assignment foumulation of data association problems arising from multitarget and multisensor tracking, computational Optimization & Applications,1994,3 (1): 27-57]. The determined matching relationship is obtained by modeling the multi-sensor association problem as a 0-1 integer programming problem. However, when the targets are dense and interaction exists between the targets, the association accuracy of the method is reduced, and the tracking effect is reduced.
The main idea of the method is that: for each local hypothesis (i c ，i 1 ，…，i L ) Defining binary associationsVariables, namely:
Figure BDA0003131201500000011
the multi-sensor association problem is modeled as the following multi-dimensional allocation problem:
Figure BDA0003131201500000012
s.t.：
Figure BDA0003131201500000013
Figure BDA0003131201500000014
for i l ＝0，...，N l and l＝2，...，L-1，
Figure BDA0003131201500000015
Figure BDA0003131201500000016
wherein
Figure BDA0003131201500000017
To select the local hypothesis (i c ，i 1 ，…，i L ) Can be calculated by taking the negative logarithm of the likelihood of the local hypothesis. The multidimensional allocation problem is a problem that NP-hard and the computational complexity thereof will take on an exponentially growing form depending on the size of the problem. After the local hypothesis to be selected is obtained, a central or distributed Kalman fusion filtering method is adopted to perform state estimation on the target.
Term interpretation:
multi-sensor data fusion: and a plurality of groups of data generated by a plurality of sensors are adopted, and useful information contained in the plurality of groups of data is fully utilized to estimate quantity-parameters and the like. The information of the plurality of sensors can be mutually complemented, so that the state estimation precision of the target can be improved, and the system has wider coverage range, observability and the like. The central fusion directly transmits the most original data to the fusion center, so that the fusion center can obtain all potential information, and an optimal estimation result is obtained. However, due to the inclusion of a large amount of clutter observation, certain pressure is caused to traffic, storage of fusion centers, calculation capacity of the centers and the like. The distributed method adopts a method of processing and transmitting the data first by the center, namely each sensor processes the original observed data first and then only transmits the processed data to the center processor. Compared with the central type, the distributed type has smaller traffic, and can reduce the calculation power and storage requirements of the central processor. But this causes a certain loss in performance, since the center can only receive the processed data.
Kalman filtering: a discrete time dynamic system of local sensors/is:
x k+1，l ＝F k，l x k，l +v k，l
y k+1，l ＝H k+1，l x k+1，l +w k+1，l
where k is the time index, x is the system state, and y is the observation. F and H are the state transition matrix and the observation matrix, respectively. v and w are process noise and observation noise, respectively. And the system satisfies the following conditions:
(1){F k，l ，H k+1，l ，v k，l ，w k+1，l k=0, 1,2, … } is a sample sequence of independent random variables, initial state x 0 Independent of them.
(2)x k，1 and {Fk，l ，H k+1，l K=0, 1,2, … } are independent.
(3) Initial state x 0 And noise v k，l ，w k+1，l Are all of (1)The values and covariance satisfy the following properties:
E(x 0，l )＝μ 0，l ，E(x 0，l -μ 0，l )(x 0，l -μ 0，l )′＝P 0|0，l
E(v k，l )＝0，E(v k，l (v k，l )′)＝Q k，l
E(w k+1，l )＝0，E(w k+1，l (w k+1，l )′)＝R k+1，l·
the linear least squares recursive state estimation of the above system is as follows:
Figure BDA0003131201500000031
x k+1|k，l ＝H l x k|k，l
P k+1|k，l ＝F l P k|k，l F′ l +Q k，l
Figure BDA00031312015000000314
P k+1|k+1，l ＝(I-K k+1，l H l )P k+1|k，l
R k+1，l ＝E(w k+1，l (w k+1，l )′)
Q k，l ＝E(v k，l (v k，l )′)
E(x k+1，l x′ k+1，l )＝F l E(x k，l x′ k，l )F′ l +Q k，l
x 0|0，l ＝Ex 0，l ，P 0|0，l ＝Cov(x 0，l )
E(x 0，l x′ 0，l )＝Ex 0，l Ex′ 0，l +P 0|0，l·
disclosure of Invention
In view of the above problems, the present invention aims to provide a multi-sensor randomized data association fusion method. The problem of multi-sensor data association can be better solved, so that the randomized association still has good association effect under complex scenes such as near target distance or target interaction. The technical proposal is as follows:
a multi-sensor randomized data association fusion method comprises the following steps:
step 1: inputting state estimation set of all targets of the k-th moment fusion center to the fusion center
Figure BDA0003131201500000032
And the corresponding covariance matrix set of all target state estimates +.>
Figure BDA0003131201500000033
Step 2: collecting all observation data generated by L sensors at time k+1 to obtain an observation set Y k+1 ；
Step 3: pair estimation set by state equation of discrete dynamic system
Figure BDA0003131201500000034
Each target state estimate in (a)
Figure BDA0003131201500000035
Covariance matrix set +.>
Figure BDA0003131201500000036
Is +.>
Figure BDA0003131201500000037
Forecasting to obtain a forecasting state estimation set of the target +.>
Figure BDA0003131201500000038
Forecast covariance matrix set +.>
Figure BDA0003131201500000039
Each target x k|k The calculation method of the prediction state estimation and prediction covariance matrix comprises the following steps:
Figure BDA00031312015000000310
Figure BDA00031312015000000311
wherein ,Qk Is state noise, F is a state transition matrix; f' is the transpose of F;
step 4: estimating a set by the forecasted state
Figure BDA00031312015000000312
Observation set Y k+1 Establishing a linear programming problem associated with the multisensor randomized data and solving to obtain the probability of local hypothesis +.>
Figure BDA00031312015000000313
The linear programming problem of the multi-sensor randomized data association is as follows:
Figure BDA0003131201500000041
s.t.：
Figure BDA0003131201500000042
Figure BDA0003131201500000043
for i l ＝0，...，N l and l＝2，...，L-1，
Figure BDA0003131201500000044
Figure BDA0003131201500000045
wherein ,
Figure BDA0003131201500000046
and />
Figure BDA0003131201500000047
Respectively, selecting local hypothesis (i c ，i 1 ，…，i L ) Corresponding losses and probabilities; n (N) c N is the target number of the fusion center l Generating an observed number for the first local sensor;
step 5: kalman filtering using a matrix of random coefficients and probability of the local hypothesis
Figure BDA0003131201500000048
Updating the set of predictor state estimates +.>
Figure BDA0003131201500000049
Is estimated +.>
Figure BDA00031312015000000410
To->
Figure BDA00031312015000000411
Updating the set of prediction covariance matrices>
Figure BDA00031312015000000412
Forecast covariance matrix of each target state +.>
Figure BDA00031312015000000413
To->
Figure BDA00031312015000000414
Get state estimation set of object update +.>
Figure BDA00031312015000000415
Updated state covariance matrix +.>
Figure BDA00031312015000000416
The association problem adopts a randomization decision, and the following observation matrix is considered to be in the form of a random parameter matrix; the observation equation of the center is
y k+1 ＝H k+1 x k+1 +w k+1
wherein ,Hk+1 and wk+1 Is a random matrix with a discrete distribution of M c The specific expression forms are as follows:
Figure BDA00031312015000000417
probability of->
Figure BDA00031312015000000427
…
Figure BDA00031312015000000418
Probability of->
Figure BDA00031312015000000419
wherein ,
Figure BDA00031312015000000420
is the mth c Probability of implementation; />
Figure BDA00031312015000000421
and />
Figure BDA00031312015000000422
Is the mth c Realizing corresponding observation matrix and observation noise, m c ＝1，…，M c ；
Observation y k+1 Viewing and lookingMeasuring matrix
Figure BDA00031312015000000423
And observation noise->
Figure BDA00031312015000000424
Are all stacked matrices, and are specifically expressed as follows:
y k+1 ＝(y′ k+1，1 ，…，y′ k+1，L )′
Figure BDA00031312015000000425
Figure BDA00031312015000000426
wherein ,mc Represents the mth of the observation equation c Implementation is performed; the updated state estimate and covariance calculation method for each target taking the randomized decisions is then:
Figure BDA0003131201500000051
x k+1|k ＝Fx k|k
Figure BDA0003131201500000052
Figure BDA0003131201500000053
Figure BDA0003131201500000054
wherein ,Kk+1 Is a gain matrix;
Figure BDA0003131201500000055
for observing matrix H k+1 Is not limited to the desired one; />
Figure BDA0003131201500000056
Represents the mth c Covariance matrix of observed noise in several implementations, < >>
Figure BDA0003131201500000057
As a random vector w k+1 Is a covariance matrix of (a);
step 6: output of a set of target state estimates at time k+1
Figure BDA00031312015000000517
Sum covariance matrix set +.>
Figure BDA0003131201500000058
Furthermore, in the step 2, the method of fusion of the center, which is the observation processed by the transmission local sensor, is adopted to change the calculation modes of the data collection in the step 2, the linear programming problem in the step 4 and the filtering update in the step 5 in the multi-sensor randomized data association fusion method; the method comprises the following steps:
collecting L local sensors to obtain state estimation set
Figure BDA0003131201500000059
Status forecast set->
Figure BDA00031312015000000510
Covariance matrix set +.>
Figure BDA00031312015000000511
Covariance matrix forecast set +.>
Figure BDA00031312015000000512
Observations used to update states
Figure BDA00031312015000000513
wherein />
Figure BDA00031312015000000514
and />
Figure BDA00031312015000000515
Data transmitted to the fusion center for the first partial sensor and the data quantity is +.>
Figure BDA00031312015000000516
The linear programming problem of the data correlation in step 4 is:
Figure BDA0003131201500000061
s.t.：
Figure BDA0003131201500000062
Figure BDA0003131201500000063
Figure BDA0003131201500000064
Figure BDA0003131201500000065
Figure BDA0003131201500000066
from the above-defined linear programming problem, probability of local hypothesis is obtained
Figure BDA0003131201500000067
And the filtering update in step 5 is obtained using the estimation result of the local sensor:
Figure BDA0003131201500000068
Figure BDA0003131201500000069
wherein
Figure BDA00031312015000000610
Represents Moore-Penrose generalized inverse, < ->
Figure BDA00031312015000000611
Representation matrix->
Figure BDA00031312015000000612
Is the first column block of (c).
The beneficial effects of the invention are as follows:
1) The invention provides a multi-sensor randomized data association fusion method, which aims to solve the problem that in complex scenes such as dense targets, the conventional multi-sensor multi-hypothesis association method adopts a deterministic decision, and association errors are easy to cause so as to influence fusion effect.
2) The invention innovatively relaxes the original multi-dimensional distribution problem of NP-difficult multi-sensor multi-hypothesis data association into a linear programming problem by adopting a linear relaxation mode, reduces the complexity of calculating the multi-sensor association matching problem, considers the uncertainty of observation, fully utilizes the multi-sensor information by adopting a central and distributed random coefficient matrix Kalman filtering fusion method, and improves the estimation precision of the target state.
3) The invention provides a multi-sensor randomization association fusion method, which supports scientific and reasonable algorithm equivalent test design; the multi-sensor association fusion problem can be applied, and belongs to one of basic problems in algorithm test evaluation in the multi-sensor association fusion algorithm test experiment design process.
Drawings
FIG. 1 is a flow chart of the multi-sensor randomized data correlation fusion algorithm of the present invention.
Fig. 2 is a data real track in an embodiment of the present invention.
FIG. 3 is an observation diagram generated by a sensor in an embodiment of the invention.
FIG. 4 is a graph of error curves for a multi-sensor distributed randomized data correlation fusion algorithm for center fusion and local sensors in an example embodiment of the invention.
FIG. 5 is a graph of error for a distributed fusion of multiple sensor distributed randomized data correlation fusion algorithm and a local sensor in an example embodiment of the invention.
Detailed Description
The invention will now be described in further detail with reference to the drawings and to specific examples. As shown in fig. 1, the method of the multi-sensor randomized data association fusion algorithm of the present invention comprises the following steps:
step 1: inputting state estimation set of all targets of the k-th moment fusion center to the fusion center
Figure BDA0003131201500000071
And the corresponding covariance matrix set of all target state estimates +.>
Figure BDA0003131201500000072
Step 2: collecting all observation data generated by L sensors at time k+1 to obtain an observation set Y k+1 ；
Step 3: pair estimation set by state equation of discrete dynamic system
Figure BDA0003131201500000073
Each target state estimate in (a)
Figure BDA0003131201500000074
Covariance matrix set +.>
Figure BDA0003131201500000075
Is +.>
Figure BDA0003131201500000076
Forecasting to obtain a forecasting state estimation set of the target +.>
Figure BDA0003131201500000077
Forecast covariance matrix set +.>
Figure BDA0003131201500000078
Each target x k|k The calculation method of the prediction state estimation and prediction covariance matrix comprises the following steps:
Figure BDA0003131201500000079
Figure BDA00031312015000000710
wherein ,Qk Is state noise, F is a state transition matrix; f' is the transpose of F;
step 4: estimating a set by the forecasted state
Figure BDA00031312015000000711
Observation set Y k+1 Establishing a linear programming problem associated with the multisensor randomized data and solving to obtain the probability of local hypothesis +.>
Figure BDA00031312015000000712
The linear programming problem of the multi-sensor randomized data association is as follows:
Figure BDA0003131201500000081
s.t.：
Figure BDA0003131201500000082
Figure BDA0003131201500000083
for i l ＝0，...，N l and l＝2，...，L-1，
Figure BDA0003131201500000084
/>
Figure BDA0003131201500000085
wherein ,
Figure BDA0003131201500000086
and />
Figure BDA0003131201500000087
Respectively, selecting local hypothesis (i c ，i 1 ，…，i L ) Corresponding losses and probabilities; n (N) c N is the target number of the fusion center l Generating an observed number for the first local sensor;
step 5: kalman filtering using a matrix of random coefficients and probability of the local hypothesis
Figure BDA0003131201500000088
Updating the set of predictor state estimates +.>
Figure BDA0003131201500000089
Is estimated +.>
Figure BDA00031312015000000810
To->
Figure BDA00031312015000000811
Updating the set of prediction covariance matrices>
Figure BDA00031312015000000812
Forecast covariance matrix of each target state +.>
Figure BDA00031312015000000813
To->
Figure BDA00031312015000000814
Get state estimation set of object update +.>
Figure BDA00031312015000000815
Updated state covariance matrix +.>
Figure BDA00031312015000000816
The association problem adopts a randomization decision, and the following observation matrix is considered to be in the form of a random parameter matrix; the observation equation of the center is
y k+1 ＝H k+1 x k+1 +w k+1
wherein ,Hk+1 and wk+1 Is a random matrix with a discrete distribution of M c The specific expression forms are as follows:
Figure BDA00031312015000000817
probability of->
Figure BDA00031312015000000818
…
Figure BDA00031312015000000819
Probability of->
Figure BDA00031312015000000820
wherein ,
Figure BDA00031312015000000821
is the mth c Probability of implementation; />
Figure BDA00031312015000000822
and />
Figure BDA00031312015000000823
Is the mth c Realizing corresponding observation matrix and observation noise, m c ＝1，…，M c ；
Observation y k+1 Observation matrix
Figure BDA00031312015000000824
And observation noise->
Figure BDA00031312015000000825
Are all stacked matrices, and are specifically expressed as follows:
y k+1 ＝(y′ k+1，1 ，…，y′ k+1，L )′
Figure BDA00031312015000000826
Figure BDA00031312015000000827
wherein ,mc Represents the mth of the observation equation c Implementation is performed; the updated state estimate and covariance calculation method for each target taking the randomized decisions is then:
Figure BDA0003131201500000091
x k+1|k ＝Fx k|k
Figure BDA0003131201500000092
Figure BDA0003131201500000093
Figure BDA0003131201500000094
wherein ,Kk+1 Is a gain matrix;
Figure BDA0003131201500000095
for observing matrix H k+1 Is not limited to the desired one; />
Figure BDA0003131201500000096
Represents the mth c Covariance matrix of observed noise in several implementations, < >>
Figure BDA0003131201500000097
As a random vector w k+1 Is a covariance matrix of (a);
step 6: output of a set of target state estimates at time k+1
Figure BDA0003131201500000098
Sum covariance matrix set +.>
Figure BDA0003131201500000099
Furthermore, in the step 2, the method of fusion of the center, which is the observation processed by the transmission local sensor, is adopted to change the calculation modes of the data collection in the step 2, the linear programming problem in the step 4 and the filtering update in the step 5 in the multi-sensor randomized data association fusion method; the method comprises the following steps:
collecting L local sensors to obtain state estimation set
Figure BDA00031312015000000910
Status forecast set->
Figure BDA00031312015000000911
Covariance matrix set +.>
Figure BDA00031312015000000912
Covariance matrix forecast set +.>
Figure BDA00031312015000000913
Observations used to update states
Figure BDA00031312015000000914
wherein />
Figure BDA00031312015000000915
and />
Figure BDA00031312015000000916
Data transmitted to the fusion center for the first partial sensor and the data quantity is +.>
Figure BDA00031312015000000917
The linear programming problem of the data correlation in step 4 is:
Figure BDA0003131201500000101
s.t.：
Figure BDA0003131201500000102
Figure BDA0003131201500000103
Figure BDA0003131201500000104
Figure BDA0003131201500000105
Figure BDA0003131201500000106
from the above-defined linear programming problem, probability of local hypothesis is obtained
Figure BDA0003131201500000107
And the filtering update in step 5 is obtained using the estimation result of the local sensor:
Figure BDA0003131201500000108
Figure BDA0003131201500000109
wherein
Figure BDA00031312015000001012
Represents Moore-Penrose generalized inverse, < ->
Figure BDA00031312015000001010
Representation matrix->
Figure BDA00031312015000001011
Is the first column block of (c).
The embodiment specifically describes that the multi-sensor randomized data association fusion algorithm provided by the invention is used for target association tracking under a multi-sensor multi-target scene and is used for performing a simulation test.
Description of the problem: and simulating the observation of a plurality of radar sensors on a plurality of targets by adopting simulation, and tracking the plurality of targets through a multi-sensor association fusion algorithm.
Data sources: the present embodiment simulates observation of a plurality of targets by a plurality of radar sensors by simulation, giving a simulated scene as in fig. 2. There are 7 targets in the two-dimensional monitoring area, and the movement duration of the targets is 100 seconds. We employ 4 sensors to monitor together 7 targets in the scene. The movement of the 7 objects in particular is shown in fig. 2 by circles representing the starting position of each object; the boxes represent the location of each target endpoint; the four triangles represent the positions of the four sensors, respectively. The state of the object at time k is represented as a vector of two-dimensional position and velocity:
Figure BDA0003131201500000111
the state transition density for each target is:
Figure BDA0003131201500000112
wherein ：
Figure BDA0003131201500000113
and I 2 Is a 2 x 2 unit array, delta=1 is the sampling period,
Figure BDA0003131201500000114
is the standard deviation of the process noise +.>
Figure BDA0003131201500000115
Representing the kronecker product. Fig. 3 is an observation diagram generated by 4 sensors, and in particular, the detail of observation is shown by the arrow in fig. 3.
The algorithm is implemented: according to the multisensor randomized data associative fusion algorithm, we first collected the observations of 4 sensors. Calculating a forecast state estimation and a forecast covariance matrix of each target through a state equation; establishing a linear programming problem of multi-sensor randomization association matching through the predicted target state and the observation information of 4 local sensors, and solving to obtain the probability of local hypothesis; and updating the state forecast and covariance forecast of the fusion center to the current moment by using the observation equation and the obtained local hypothesis probability, and finally outputting the updated target state and covariance.
And (3) effect analysis: the square errors of the 4 partial sensors and the center were calculated, respectively, and fig. 4 and 5 were obtained. The error of the center and local sensors at each instant is the sum of the state estimates of 7 targets and the square difference of the true state. Each point on the graph is the sum of the errors of 50 monte carlo experiments. In the error curve obtained by 50 Monte Carlo, no matter the central data association fusion or the distributed data association fusion method, the center can well execute data association, and the estimated error is obviously lower than the error of all local sensors.
Standard: the present embodiment uses an average squared error (Mean Square Error), which is used for the target-associative fusion problem.

Claims (2)

1. The multi-sensor randomized data association fusion method is characterized by comprising the following steps of:
step 1: inputting state estimation set of all targets of the k-th moment fusion center to the fusion center
Figure FDA0003131201490000011
And the corresponding covariance matrix set of all target state estimates +.>
Figure FDA0003131201490000012
Step 2: collecting all observation data generated by L sensors at time k+1 to obtain an observation set Y k+1 ；
Step 3: pair estimation set by state equation of discrete dynamic system
Figure FDA0003131201490000013
Is estimated by the state of each object in (1)>
Figure FDA0003131201490000014
Covariance matrix set +.>
Figure FDA0003131201490000015
Is +.>
Figure FDA0003131201490000016
Forecasting to obtain a forecasting state estimation set of the target +.>
Figure FDA0003131201490000017
Forecast covariance matrix set +.>
Figure FDA0003131201490000018
Each target x k|k The calculation method of the prediction state estimation and prediction covariance matrix comprises the following steps:
Figure FDA0003131201490000019
Figure FDA00031312014900000110
wherein ,Qk Is state noise, F is a state transition matrix; f' is the transpose of F;
step 4: estimating a set by the forecasted state
Figure FDA00031312014900000111
Observation set Y k+1 Establishing a linear programming problem associated with the multisensor randomized data and solving to obtain the probability of local hypothesis +.>
Figure FDA00031312014900000118
The linear programming problem of the multi-sensor randomized data association is as follows:
Figure FDA00031312014900000112
s.t.：
Figure FDA00031312014900000119
Figure FDA00031312014900000113
for i l ＝0，...，N l and l＝2，...，L-1，
Figure FDA00031312014900000114
Figure FDA00031312014900000120
wherein ,
Figure FDA00031312014900000121
and />
Figure FDA00031312014900000122
Respectively, selecting local hypothesis (i c ，i 1 ，…，i L ) Corresponding losses and probabilities; n (N) c N is the target number of the fusion center l Generating an observed number for the first local sensor;
step 5: kalman filtering using a matrix of random coefficients and probability of the local hypothesis
Figure FDA00031312014900000123
Updating the set of predictor state estimates +.>
Figure FDA00031312014900000115
Is estimated +.>
Figure FDA00031312014900000116
To->
Figure FDA00031312014900000117
Updating the set of prediction covariance matrices>
Figure FDA0003131201490000021
Forecast covariance matrix of each target state +.>
Figure FDA0003131201490000022
To->
Figure FDA0003131201490000023
Get state estimation set of object update +.>
Figure FDA0003131201490000024
Updated state covariance matrix +.>
Figure FDA0003131201490000025
The association problem adopts a randomization decision, and the following observation matrix is considered to be in the form of a random parameter matrix; the observation equation of the center is
y k+1 ＝H t+1 x k+1 +w k+1
wherein ,Hk+1 and wk+1 Is a random matrix with a discrete distribution of M c The specific expression forms are as follows:
Figure FDA0003131201490000026
probability of->
Figure FDA0003131201490000027
…
Figure FDA0003131201490000028
Probability of->
Figure FDA0003131201490000029
wherein ,
Figure FDA00031312014900000210
is the mth c Probability of implementation; />
Figure FDA00031312014900000211
and />
Figure FDA00031312014900000212
Is the mth c Realizing corresponding observation matrix and observation noise, m c ＝1，…，M c ；
Observation y k+1 Observation matrix
Figure FDA00031312014900000213
And observation noise->
Figure FDA00031312014900000214
Are all stacked matrices, and are specifically expressed as follows:
y k+1 ＝(y′ k+1，1 ，…，y′ k+1，L )′
Figure FDA00031312014900000215
Figure FDA00031312014900000216
wherein ,mc Represents the mth of the observation equation c Implementation is performed; the updated state estimate and covariance calculation method for each target taking the randomized decisions is then:
Figure FDA00031312014900000217
Figure FDA00031312014900000226
Figure FDA00031312014900000218
Figure FDA00031312014900000219
Figure FDA00031312014900000220
wherein ,Kk+1 Is a gain matrix;
Figure FDA00031312014900000221
for observing matrix H k+1 Is not limited to the desired one; />
Figure FDA00031312014900000222
Represents the mth c Covariance matrix of observed noise in several implementations, < >>
Figure FDA00031312014900000223
As a random vector w k+1 Is a covariance matrix of (a);
step 6: target state estimation at output k+1 timeAggregation
Figure FDA00031312014900000224
Sum covariance matrix set +.>
Figure FDA00031312014900000225
2. The multi-sensor randomized data association fusion method according to claim 1, wherein in the step 2, a fusion method of transmitting observations processed by local sensors, i.e., a center, is adopted to change the calculation modes of the step 2 data collection, the linear programming problem of the step 4, and the filtering update of the step 5 in the multi-sensor randomized data association fusion method; the method comprises the following steps:
collecting L local sensors to obtain state estimation set
Figure FDA0003131201490000031
Status forecast set->
Figure FDA0003131201490000032
Covariance matrix set +.>
Figure FDA0003131201490000033
Covariance matrix forecast set +.>
Figure FDA0003131201490000034
Observations used to update states
Figure FDA0003131201490000035
wherein />
Figure FDA0003131201490000036
and />
Figure FDA0003131201490000037
For transmission of the first partial sensor to the fusion centerData and data volume is +.>
Figure FDA0003131201490000038
The linear programming problem of the data correlation in step 4 is:
Figure FDA0003131201490000039
s.t.：
Figure FDA00031312014900000310
Figure FDA00031312014900000311
Figure FDA00031312014900000312
Figure FDA00031312014900000313
Figure FDA00031312014900000316
from the above-defined linear programming problem, probability of local hypothesis is obtained
Figure FDA00031312014900000317
And the filtering update in step 5 is obtained using the estimation result of the local sensor:
Figure FDA00031312014900000314
Figure FDA00031312014900000315
wherein
Figure FDA0003131201490000043
Represents Moore-Penrose generalized inverse, < ->
Figure FDA0003131201490000041
Representation matrix->
Figure FDA0003131201490000042
Is the first column block of (c). />
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