CN113283511A - Multi-source information fusion method based on weight pre-distribution - Google Patents

Multi-source information fusion method based on weight pre-distribution Download PDF

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CN113283511A
CN113283511A CN202110594063.4A CN202110594063A CN113283511A CN 113283511 A CN113283511 A CN 113283511A CN 202110594063 A CN202110594063 A CN 202110594063A CN 113283511 A CN113283511 A CN 113283511A
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CN113283511B (en
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谢国
金永泽
李艳恺
穆凌霞
冯楠
梁莉莉
钱富才
辛菁
上官安琪
陈文斌
韩宁
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Guangdong Zhongkexin Micro Security Technology Co ltd
Xi'an Huaqi Zhongxin Technology Development Co ltd
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Xian University of Technology
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Abstract

The invention discloses a multisource information fusion method based on weight pre-distribution, which comprises the steps of firstly selecting a Q test method to remove abnormal monitoring data of each sensor aiming at a system containing a plurality of sensors, and pre-distributing fusion weights to the data after abnormal values are removed based on a distance criterion; then, selecting a self-attenuation unscented Kalman filter UKF based on the Mahalanobis distance as a local state estimator, evaluating the squared Mahalanobis distance of the innovation vector, and taking corresponding measures to improve the adaptability and robustness of the UKF to the modeling error of the multi-sensor nonlinear random system to obtain a local state estimation result; and finally, fusing the multi-sensor monitoring data based on a minimum variance linear weighting criterion to obtain a global state estimation result. The invention eliminates the influence of adverse factors such as sensor errors, monitoring data loss, deviation and the like on the fusion result, establishes a distributed fusion framework based on weight pre-allocation and improves the fusion accuracy of the sensor.

Description

Multi-source information fusion method based on weight pre-distribution
Technical Field
The invention belongs to the technical field of multi-source information fusion, and particularly relates to a multi-source information fusion method based on weight pre-distribution.
Background
In recent years, as sensor technology advances, monitoring data has also become diversified. Compared with a single sensor monitoring system, the multi-sensor information fusion can effectively improve the monitoring performance of the system, enhance the monitoring reliability and robustness of the system, reduce the monitoring cost of the system, improve the data monitoring precision, expand the space-time coverage capability of the system, and be widely applied to target tracking, industrial monitoring, fault diagnosis and intelligent traffic. However, in recent years, with the continuous improvement of the complexity of the system, the monitoring range of the sensor is continuously expanded, so that the actual requirements of the system are gradually difficult to meet by the existing fusion technology, and the development of more advanced fusion theory research has wide application prospects and necessity.
Disclosure of Invention
The invention aims to provide a multi-source information fusion method based on weight pre-allocation, which eliminates the influence of adverse factors such as sensor errors, monitoring data loss, deviation and the like on a fusion result, establishes a distributed fusion framework based on weight pre-allocation and improves the fusion accuracy of sensors.
The technical scheme adopted by the invention is that a multi-source information fusion method based on weight pre-distribution is implemented according to the following steps:
step 1, selecting a Q test method to remove abnormal monitoring data of each sensor aiming at a system containing a plurality of sensors, and pre-distributing fusion weight to the data after removing abnormal values based on a distance criterion;
step 2, selecting a self-attenuation unscented Kalman filter UKF based on the Mahalanobis distance as a local state estimator, evaluating the squared Mahalanobis distance of the innovation vector, and taking corresponding measures to improve the adaptability and robustness of the UKF to the modeling error of the multi-sensor nonlinear random system to obtain a local state estimation result;
and 3, fusing the multi-sensor monitoring data based on a minimum variance linear weighting criterion to obtain a global state estimation result.
The present invention is also characterized in that,
the step 1 is as follows:
step 1.1, setting the state space model of each sensor to meet the following form:
Figure BDA0003090320640000021
in the formula, xtAnd xt+1Respectively representing the state values of the tested system at the time t and the time t + 1; f (-) is the system nonlinear state function; w is atIs zero mean Gaussian white noise with variance Q more than or equal to 0; z is a radical oft+1Is the measured value at the moment of the sensor t + 1; h (-) is a sensor nonlinear measurement function; e.g. of the typet+1Zero mean Gaussian white noise with variance R not less than 0 at the moment of t + 1;
step 1.2, taking the monitoring data of each sensor at the moment t as an example, setting
Figure BDA0003090320640000026
i＝1,2,…,MsObtaining a system monitoring result Z at the t moment for a system monitoring result at the t moment of the ith sensort：
Figure BDA0003090320640000022
In the formula, MsThe number of sensors;
step 1.3, monitoring result Z of the system at the time ttArranging according to increasing order to obtain ascending sequence
Figure BDA0003090320640000023
And calculating a check value Q1：
Figure BDA0003090320640000024
Figure BDA0003090320640000025
In the formula (I), the compound is shown in the specification,
Figure BDA0003090320640000031
and
Figure BDA0003090320640000032
the maximum value and the minimum value of the monitoring data at the time t are respectively,
Figure BDA0003090320640000033
and
Figure BDA0003090320640000034
respectively measuring results of the ith sensor at the moment t and the nearest monitoring result thereof;
step 1.4, according to ascending sequence
Figure BDA0003090320640000035
Determination of the test value Q from the number of measured values and the specified confidence level2If Q is1＞Q2Then the ith sensor measurement at time t is compared
Figure BDA0003090320640000036
If the abnormal value is regarded as an abnormal value and discarded, otherwise, the abnormal value is retained, and the steps are repeated on the processed monitoring data until the moment is monitoredAll abnormal values in the data are removed to obtain an abnormal-free monitoring data sequence
Figure BDA0003090320640000037
Figure BDA0003090320640000038
In the formula (I), the compound is shown in the specification,
Figure BDA0003090320640000039
the first monitoring value at the time t for finally obtaining the abnormal data, the same principle
Figure BDA00030903206400000310
And
Figure BDA00030903206400000311
second and Nth time points respectively representing the existence of finally obtained abnormal-free datasThe monitored value.
Step 1.5, pre-distributing fusion weight to the data after the abnormal value is removed based on a distance criterion:
Figure BDA00030903206400000312
Figure BDA00030903206400000313
in the formula (I), the compound is shown in the specification,
Figure BDA00030903206400000314
pre-assigning a fusion weight to the ith sensor at time t,
Figure BDA00030903206400000315
for the ith monitoring value at the moment t with finally obtained abnormal-free data,
Figure BDA00030903206400000316
is the mean value of the finally obtained abnormal-free data, NsIn order to obtain the final abnormal-free data,
Figure BDA00030903206400000317
and the k-th monitoring value at the moment t is the finally obtained abnormal-free data.
The step 2 is as follows:
step 2.1, taking the state estimation of the jth sensor as an example, calculating the initial mean square error matrix P of the state vector0And a priori mean
Figure BDA00030903206400000318
Figure BDA00030903206400000319
Figure BDA00030903206400000320
In the formula, E [ Delta ]]Mean expectation, P, of Δ0For initial estimation of error variance, x0Is the initial value of the system state;
step 2.2, calculating an unscented transformation Sigma sampling point based on a sampling strategy:
Figure BDA0003090320640000041
in the formula (I), the compound is shown in the specification,
Figure BDA0003090320640000042
is the estimated value of the system state at the time t-1, xi0,t-1And xii,t-1Respectively the 0 th and ith system unscented transformation Sigma sampling points at the time of t-1, n is the system state vector dimension, P is used for adjusting the distance between the sampling point and the original sample point, P is the state variable covariance matrix at the time of t-1,
Figure BDA0003090320640000043
the ith main diagonal element representing the square root matrix;
step 2.3, calculating the first-order statistical characteristic weight coefficient of the sampling point
Figure BDA0003090320640000044
And weight coefficients of second order statistical characteristics
Figure BDA0003090320640000045
Figure BDA0003090320640000046
Step 2.4, calculating a one-step prediction matrix based on Sigma sampling points at the moment t
Figure BDA0003090320640000047
Sum covariance matrix Pt|t-1：
ξi,t|t-1＝f(ξi,t-1)(i＝0,1,…,2n)
Figure BDA0003090320640000048
In the formula, wtIs the state noise at time t, QtThe state noise variance at time t.
Step 2.5, for the one-step prediction matrix in step 2.4
Figure BDA0003090320640000049
The UT transform was performed again to obtain a new Sigma point set as follows:
Figure BDA0003090320640000051
in the formula, xi'0,t|t-1And ξ'i,t|t-1With respect to one-step prediction matrices for time t-1, respectively
Figure BDA0003090320640000052
And the 0 th and i th systems of (a) transform the Sigma sample points without traces.
Step 2.6, substituting the new Sigma point set obtained in the step 2.5 into the measurement equation to obtain an observation predicted value z of the ith sensor at the moment ti,t|t-1To the observed value zi,t|t-1Weighted summation is carried out to obtain an observed prediction mean value
Figure BDA0003090320640000053
zi,t|t-1＝h(ξi',t|t-1)
Figure BDA0003090320640000054
In the formula (I), the compound is shown in the specification,
Figure BDA0003090320640000055
for the observed variance at time t, etObserved noise at time t, RtIs the observed noise variance at time t.
Step 2.7, State estimation covariance matrix
Figure BDA0003090320640000056
Is updated as:
Figure BDA0003090320640000057
step 2.8, calculating Kalman gain KtUpdating the state variable estimate
Figure BDA0003090320640000058
Sum equation of state covariance Pt：
Figure BDA0003090320640000059
Figure BDA00030903206400000510
Figure BDA00030903206400000511
Step 2.9, introducing a time-varying adaptive fading factor lambdatTo prediction state covariance matrix Pt|t-1：
Figure BDA0003090320640000061
Step 2.10, with correction
Figure BDA0003090320640000062
Prediction state covariance matrix P instead of classical UKFt|t-1Completing classical UKF to update local state estimation and obtaining estimation result of jth sensor at t moment
Figure BDA0003090320640000063
Figure BDA0003090320640000064
Step 2.11, performing state parallel estimation on all sensors in the system according to the steps 2.1-2.10 to obtain a local state estimation result
Figure BDA0003090320640000065
j＝1,2,…,N。
The step 3 is as follows:
step 3.1, the global optimal state fusion value of the system at the moment t
Figure BDA0003090320640000066
Expressed as:
Figure BDA0003090320640000067
in the formula (I), the compound is shown in the specification,
Figure BDA0003090320640000068
and fusion weights representing the jth sensor estimation result at the time t.
Step 3.2, combining the fusion weight pre-distribution and linear weighting fusion criteria to obtain a global state estimation result:
Figure BDA0003090320640000069
Figure BDA00030903206400000610
Figure BDA00030903206400000611
in the formula (I), the compound is shown in the specification,
Figure BDA00030903206400000612
for the global state estimation result at the time t of the system
Figure BDA00030903206400000613
Figure BDA00030903206400000614
A weight is pre-assigned for the jth sensor estimate at time t,
Figure BDA00030903206400000615
and
Figure BDA00030903206400000616
respectively, the jth sensor local estimation result at the moment t and the fusion weight thereof.
The invention has the beneficial effects that the multisource information fusion method based on weight pre-distribution selects the Q test method to remove abnormal monitoring data of the sensor, and pre-distributes the fusion weight to the data after removing abnormal values based on the distance criterion; self-attenuation Unscented Kalman Filtering (UKF) based on the Mahalanobis distance is selected as a local state estimator, the adaptability and robustness of the UKF to modeling errors of a multi-sensor nonlinear random system are improved by evaluating the squared Mahalanobis distance of an innovation vector and taking corresponding measures to obtain a local state estimation result; and fusing the multi-sensor monitoring data based on a minimum variance linear weighting criterion to obtain a global state estimation result. The algorithm has good fusion effect and high precision, can still obtain accurate fusion results for the conditions of sensor faults, monitoring data loss and the like, and has strong referential property and practicability.
Drawings
FIG. 1 is a block diagram of a fusion filtering structure of a multi-source information fusion method based on weight pre-allocation according to the present invention;
FIG. 2 is a diagram of the system sensor monitoring results of a multi-source information fusion method based on weight pre-allocation according to the present invention;
FIG. 3 is a graph of sensor monitoring data fusion results obtained by a weight pre-distribution based multi-source information fusion method of the present invention;
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention discloses a multi-source information fusion method based on weight pre-distribution, which is implemented by combining a figure 1 according to the following steps:
step 1, selecting a Q test method to remove abnormal monitoring data of each sensor aiming at a system containing a plurality of sensors, and pre-distributing fusion weight to the data after removing abnormal values based on a distance criterion;
the step 1 is as follows:
step 1.1, setting the state space model of each sensor to meet the following form:
Figure BDA0003090320640000081
in the formula, xtAnd xt+1Respectively representing the state values of the tested system at the time t and the time t + 1; f (-) is the system nonlinear state function; w is atIs zero mean Gaussian white noise with variance Q more than or equal to 0; z is a radical oft+1Is the measured value at the moment of the sensor t + 1; h (-) is a sensor nonlinear measurement function; e.g. of the typet+1Zero mean Gaussian white noise with variance R not less than 0 at the moment of t + 1;
step 1.2, taking the monitoring data of each sensor at the moment t as an example, setting
Figure BDA0003090320640000082
i＝1,2,…,MsObtaining a system monitoring result Z at the t moment for a system monitoring result at the t moment of the ith sensort：
Figure BDA0003090320640000083
In the formula, MsThe number of sensors;
step 1.3, monitoring result Z of the system at the time ttArranging according to increasing order to obtain ascending sequence
Figure BDA0003090320640000084
And calculating a check value Q1：
Figure BDA0003090320640000085
Figure BDA0003090320640000086
In the formula (I), the compound is shown in the specification,
Figure BDA0003090320640000087
and
Figure BDA0003090320640000088
the maximum value and the minimum value of the monitoring data at the time t are respectively,
Figure BDA0003090320640000089
and
Figure BDA00030903206400000810
respectively measuring results of the ith sensor at the moment t and the nearest monitoring result thereof;
step 1.4, according to ascending sequence
Figure BDA00030903206400000811
Determination of the test value Q from the number of measured values and a specified confidence level (e.g. 90%)2If Q is1＞Q2Then the ith sensor measurement at time t is compared
Figure BDA00030903206400000812
Discarding the abnormal values, otherwise, retaining the abnormal values, repeating the steps on the processed monitoring data until all the abnormal values in the monitoring data at the moment are removed, and obtaining the abnormal-free monitoring data sequence
Figure BDA00030903206400000813
Figure BDA00030903206400000814
In the formula (I), the compound is shown in the specification,
Figure BDA00030903206400000815
the first monitoring value at the time t for finally obtaining the abnormal data, the same principle
Figure BDA00030903206400000816
And
Figure BDA00030903206400000817
second and Nth time points respectively representing the existence of finally obtained abnormal-free datasThe monitored value.
Step 1.5, pre-distributing fusion weight to the data after the abnormal value is removed based on a distance criterion:
Figure BDA0003090320640000091
Figure BDA0003090320640000092
in the formula (I), the compound is shown in the specification,
Figure BDA0003090320640000093
pre-assigning a fusion weight to the ith sensor at time t,
Figure BDA0003090320640000094
for the ith monitoring value at the moment t with finally obtained abnormal-free data,
Figure BDA0003090320640000095
is the mean value of the finally obtained abnormal-free data, NsIn order to obtain the final abnormal-free data,
Figure BDA0003090320640000096
and the k-th monitoring value at the moment t is the finally obtained abnormal-free data.
Step 2, selecting a self-attenuation unscented Kalman filter UKF based on the Mahalanobis distance as a local state estimator, evaluating the squared Mahalanobis distance of the innovation vector, and taking corresponding measures to improve the adaptability and robustness of the UKF to the modeling error of the multi-sensor nonlinear random system to obtain a local state estimation result;
the step 2 is as follows:
step 2.1, taking the state estimation of the jth sensor as an example, calculating the initial mean square error matrix P of the state vector0And a priori mean
Figure BDA0003090320640000097
Figure BDA0003090320640000098
Figure BDA0003090320640000099
In the formula, E [ Delta ]]Mean expectation, P, of Δ0For initial estimation of error variance, x0Is the initial value of the system state;
step 2.2, calculating an unscented transformation Sigma sampling point based on a sampling strategy:
Figure BDA00030903206400000910
in the formula (I), the compound is shown in the specification,
Figure BDA0003090320640000101
is the estimated value of the system state at the time t-1, xi0,t-1And xii,t-1Respectively the 0 th and ith system unscented transformation Sigma sampling points at the time of t-1, n is the system state vector dimension, P is used for adjusting the distance between the sampling point and the original sample point, P is the state variable covariance matrix at the time of t-1,
Figure BDA0003090320640000102
the ith main diagonal element representing the square root matrix;
step 2.3, calculating the first-order statistical characteristic weight coefficient of the sampling point
Figure BDA0003090320640000103
And weight coefficients of second order statistical characteristics
Figure BDA0003090320640000104
Figure BDA0003090320640000105
Step 2.4, calculating a one-step prediction matrix based on Sigma sampling points at the moment t
Figure BDA0003090320640000106
Sum covariance matrix Pt|t-1：
ξi,t|t-1＝f(ξi,t-1)(i＝0,1,…,2n)
Figure BDA0003090320640000107
In the formula, wtIs the state noise at time t, QtThe state noise variance at time t.
Step 2.5, for the one-step prediction matrix in step 2.4
Figure BDA0003090320640000108
The UT transform was performed again to obtain a new Sigma point set as follows:
Figure BDA0003090320640000109
in the formula, xi'0,t|t-1And ξ'i,t|t-1With respect to one-step prediction matrices for time t-1, respectively
Figure BDA00030903206400001010
And the 0 th and i th systems of (a) transform the Sigma sample points without traces.
Step 2.6, substituting the new Sigma point set obtained in the step 2.5 into the measurement equation to obtain an observation predicted value z of the ith sensor at the moment ti,t|t-1To the observed value zi,t|t-1Weighted summation is carried out to obtain an observed prediction mean value
Figure BDA0003090320640000111
zi,t|t-1＝h(ξi',t|t-1)
Figure BDA0003090320640000112
In the formula (I), the compound is shown in the specification,
Figure BDA0003090320640000113
for the observed variance at time t, etObserved noise at time t, RtIs the observed noise variance at time t.
Step 2.7, State estimation covariance matrix
Figure BDA0003090320640000114
Is updated as:
Figure BDA0003090320640000115
step 2.8, calculating Kalman gain KtUpdating the state variable estimate
Figure BDA0003090320640000116
Sum equation of state covariance Pt：
Figure BDA0003090320640000117
Figure BDA0003090320640000118
Figure BDA0003090320640000119
Step 2.9, introducing a time-varying adaptive fading factor lambdatTo prediction state covariance matrix Pt|t-1：
Figure BDA00030903206400001110
Step 2.10, with correction
Figure BDA00030903206400001111
Predicted state covariance matrix instead of classical UKFArray Pt|t-1Completing classical UKF to update local state estimation and obtaining estimation result of jth sensor at t moment
Figure BDA00030903206400001112
Figure BDA00030903206400001113
Step 2.11, performing state parallel estimation on all sensors in the system according to the steps 2.1-2.10 to obtain a local state estimation result
Figure BDA0003090320640000121
j＝1,2,…,N。
And 3, fusing the multi-sensor monitoring data based on a minimum variance linear weighting criterion to obtain a global state estimation result.
The step 3 is as follows:
step 3.1, under the condition of not considering the influence of the pre-distribution weight, the global optimal state fusion value of the system at the moment t
Figure BDA0003090320640000122
Expressed as:
Figure BDA0003090320640000123
in the formula (I), the compound is shown in the specification,
Figure BDA0003090320640000124
and fusion weights representing the jth sensor estimation result at the time t.
Step 3.2, combining the fusion weight pre-distribution and linear weighting fusion criteria to obtain a global state estimation result:
Figure BDA0003090320640000125
Figure BDA0003090320640000126
Figure BDA0003090320640000127
in the formula (I), the compound is shown in the specification,
Figure BDA0003090320640000128
for the global state estimation result at the time t of the system
Figure BDA0003090320640000129
Figure BDA00030903206400001210
A weight is pre-assigned for the jth sensor estimate at time t,
Figure BDA00030903206400001211
and
Figure BDA00030903206400001212
respectively, the jth sensor local estimation result at the moment t and the fusion weight thereof.
Fig. 2 is a diagram of the monitoring results of the system sensor of the invention, in which the black solid line is the real braking speed of a certain train, and the other four curves represent the four-way speed measurement results of the train. Fig. 3 shows a train speed fusion result graph obtained by the present invention, in which the black solid line is the real speed of the train, and other curves represent the monitoring data fusion results under different conditions. It can be clearly seen from the observation of fig. 3 that the method provided by the invention can effectively fuse the multi-path speed measurement results of the train, is influenced by behavior factors such as loss or abnormality of the measured data of the sensor, and has slightly higher precision than other two conditions because the measured data contains more effective information under the condition of meeting the actual precision requirement of the system.

Claims (4)

1. A multi-source information fusion method based on weight pre-distribution is characterized by being implemented according to the following steps:
step 1, selecting a Q test method to remove abnormal monitoring data of each sensor aiming at a system containing a plurality of sensors, and pre-distributing fusion weight to the data after removing abnormal values based on a distance criterion;
step 2, selecting a self-attenuation unscented Kalman filter UKF based on the Mahalanobis distance as a local state estimator, evaluating the squared Mahalanobis distance of the innovation vector, and taking corresponding measures to improve the adaptability and robustness of the UKF to the modeling error of the multi-sensor nonlinear random system to obtain a local state estimation result;
and 3, fusing the multi-sensor monitoring data based on a minimum variance linear weighting criterion to obtain a global state estimation result.
2. The multi-source information fusion method based on weight pre-allocation according to claim 1, wherein the step 1 is as follows:
step 1.1, setting the state space model of each sensor to meet the following form:
Figure FDA0003090320630000011
in the formula, xtAnd xt+1Respectively representing the state values of the tested system at the time t and the time t + 1; f (-) is the system nonlinear state function; w is atIs zero mean Gaussian white noise with variance Q more than or equal to 0; z is a radical oft+1Is the measured value at the moment of the sensor t + 1; h (-) is a sensor nonlinear measurement function; e.g. of the typet+1Zero mean Gaussian white noise with variance R not less than 0 at the moment of t + 1;
step 1.2, taking the monitoring data of each sensor at the moment t as an example, setting
Figure FDA0003090320630000013
i＝1,2,…,MsObtaining a system monitoring result Z at the t moment for a system monitoring result at the t moment of the ith sensort：
Figure FDA0003090320630000012
In the formula, MsThe number of sensors;
step 1.3, monitoring result Z of the system at the time ttArranged in ascending order to obtain ascending sequence Zts, and calculating the check value Q1：
Figure FDA0003090320630000021
Figure FDA0003090320630000022
In the formula (I), the compound is shown in the specification,
Figure FDA0003090320630000023
and
Figure FDA0003090320630000024
the maximum value and the minimum value of the monitoring data at the time t are respectively,
Figure FDA0003090320630000025
and
Figure FDA0003090320630000026
respectively measuring results of the ith sensor at the moment t and the nearest monitoring result thereof;
step 1.4, according to ascending sequence
Figure FDA0003090320630000027
Determination of the test value Q from the number of measured values and the specified confidence level2If Q is1＞Q2Then the ith sensor measurement at time t is compared
Figure FDA0003090320630000028
Discarding the abnormal values, otherwise, retaining the abnormal values, repeating the steps on the processed monitoring data until all the abnormal values in the monitoring data at the moment are removed, and obtaining the abnormal-free monitoring data sequence
Figure FDA0003090320630000029
Figure FDA00030903206300000210
In the formula (I), the compound is shown in the specification,
Figure FDA00030903206300000211
the first monitoring value at the time t for finally obtaining the abnormal data, the same principle
Figure FDA00030903206300000212
And
Figure FDA00030903206300000213
second and Nth time points respectively representing the existence of finally obtained abnormal-free datasThe monitored value.
Step 1.5, pre-distributing fusion weight to the data after the abnormal value is removed based on a distance criterion:
Figure FDA00030903206300000214
Figure FDA00030903206300000215
in the formula (I), the compound is shown in the specification,
Figure FDA00030903206300000216
pre-assigning fusion weight to ith sensor at time tThe weight of the steel is heavy,
Figure FDA00030903206300000217
for the ith monitoring value at the moment t with finally obtained abnormal-free data,
Figure FDA00030903206300000218
is the mean value of the finally obtained abnormal-free data, NsIn order to obtain the final abnormal-free data,
Figure FDA00030903206300000219
and the k-th monitoring value at the moment t is the finally obtained abnormal-free data.
3. The multi-source information fusion method based on weight pre-allocation according to claim 2, wherein the step 2 is specifically as follows:
step 2.1, taking the state estimation of the jth sensor as an example, calculating the initial mean square error matrix P of the state vector0And a priori mean
Figure FDA0003090320630000031
Figure FDA0003090320630000032
Figure FDA0003090320630000033
In the formula, E [ Delta ]]Mean expectation, P, of Δ0For initial estimation of error variance, x0Is the initial value of the system state;
step 2.2, calculating an unscented transformation Sigma sampling point based on a sampling strategy:
Figure FDA0003090320630000034
in the formula (I), the compound is shown in the specification,
Figure FDA0003090320630000035
is the estimated value of the system state at the time t-1, xi0,t-1And xii,t-1Respectively the 0 th and ith system unscented transformation Sigma sampling points at the time of t-1, n is the system state vector dimension, P is used for adjusting the distance between the sampling point and the original sample point, P is the state variable covariance matrix at the time of t-1,
Figure FDA0003090320630000036
the ith main diagonal element representing the square root matrix;
step 2.3, calculating the first-order statistical characteristic weight coefficient of the sampling point
Figure FDA0003090320630000037
And weight coefficients of second order statistical characteristics
Figure FDA0003090320630000038
Figure FDA0003090320630000039
Step 2.4, calculating a one-step prediction matrix based on Sigma sampling points at the moment t
Figure FDA00030903206300000310
Sum covariance matrix Pt|t-1：
ξi,t|t-1＝f(ξi,t-1)(i＝0,1,…,2n)
Figure FDA0003090320630000041
In the formula, wtIs the state noise at time t, QtThe state noise variance at time t.
Step 2.5, for the one-step prediction matrix in step 2.4
Figure FDA0003090320630000042
The UT transform was performed again to obtain a new Sigma point set as follows:
Figure FDA0003090320630000043
in the formula, xi'0,t|t-1And ξ'i,t|t-1With respect to one-step prediction matrices for time t-1, respectively
Figure FDA0003090320630000044
And the 0 th and i th systems of (a) transform the Sigma sample points without traces.
Step 2.6, substituting the new Sigma point set obtained in the step 2.5 into the measurement equation to obtain an observation predicted value z of the ith sensor at the moment ti,t|t-1To the observed value zi,t|t-1Weighted summation is carried out to obtain an observed prediction mean value
Figure FDA0003090320630000045
zi,t|t-1＝h(ξ′i,t|t-1)
Figure FDA0003090320630000046
In the formula (I), the compound is shown in the specification,
Figure FDA0003090320630000047
for the observed variance at time t, etObserved noise at time t, RtIs the observed noise variance at time t.
Step 2.7, State estimation covariance matrix
Figure FDA0003090320630000048
Is updated as:
Figure FDA0003090320630000049
step 2.8, calculating Kalman gain KtUpdating the state variable estimate
Figure FDA0003090320630000051
Sum equation of state covariance Pt：
Figure FDA0003090320630000052
Figure FDA0003090320630000053
Figure FDA0003090320630000054
Step 2.9, introducing a time-varying adaptive fading factor lambdatTo prediction state covariance matrix Pt|t-1：
Figure FDA0003090320630000055
Step 2.10, with correction
Figure FDA0003090320630000056
Prediction state covariance matrix P instead of classical UKFt|t-1Completing classical UKF to update local state estimation and obtaining estimation result of jth sensor at t moment
Figure FDA0003090320630000057
Figure FDA0003090320630000058
Step 2.11, performing state parallel estimation on all sensors in the system according to the steps 2.1-2.10 to obtain a local state estimation result
Figure FDA0003090320630000059
4. The multi-source information fusion method based on weight pre-allocation according to claim 3, wherein the step 3 is as follows:
step 3.1, the global optimal state fusion value of the system at the moment t
Figure FDA00030903206300000510
Expressed as:
Figure FDA00030903206300000511
in the formula (I), the compound is shown in the specification,
Figure FDA00030903206300000512
and fusion weights representing the jth sensor estimation result at the time t.
Step 3.2, combining the fusion weight pre-distribution and linear weighting fusion criteria to obtain a global state estimation result:
Figure FDA00030903206300000513
Figure FDA0003090320630000061
Figure FDA0003090320630000062
in the formula (I), the compound is shown in the specification,
Figure FDA0003090320630000063
for the global state estimation result at the time t of the system
Figure FDA0003090320630000064
Figure FDA0003090320630000065
A weight is pre-assigned for the jth sensor estimate at time t,
Figure FDA0003090320630000066
and
Figure FDA0003090320630000067
respectively, the jth sensor local estimation result at the moment t and the fusion weight thereof.
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