CN113902056B - Multidimensional heterogeneous information fusion identification method based on Copula theory - Google Patents

Multidimensional heterogeneous information fusion identification method based on Copula theory Download PDF

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CN113902056B
CN113902056B CN202111223384.XA CN202111223384A CN113902056B CN 113902056 B CN113902056 B CN 113902056B CN 202111223384 A CN202111223384 A CN 202111223384A CN 113902056 B CN113902056 B CN 113902056B
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data
coordinate system
copula
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CN113902056A (en
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邓科
罗懋康
张霄
周薛雪
梁倩云
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Sichuan University
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Abstract

The invention relates to a multidimensional heterogeneous information fusion identification method based on a Copula theory, belonging to the technical field of information fusion; the method comprises the following steps: performing space registration based on a geodetic coordinate system and a sensor coordinate system transformation equation; after the spatial registration is finished, finishing the time registration of interpolation extrapolation, curve fitting and data interpolation; constructing a full-dimensional signal space; and establishing the connection of edge distribution of each single-dimensional data by using a Copula function in the constructed full-dimensional signal space capable of containing different heterogeneous information, recovering the correlation among all-dimensional characteristic data, inverting the high-dimensional combination characteristics of the target and the like. The combined feature detection method based on Copula combined distribution has higher combined identification accuracy on the target than a single feature detection method based on each edge distribution, and embodies the advantages of combined detection.

Description

Multidimensional heterogeneous information fusion identification method based on Copula theory
Technical Field
The invention belongs to the technical field of information fusion, and particularly relates to a multidimensional heterogeneous information fusion identification method based on a Copula theory.
Background
With the increasing complexity of the environment, the reconnaissance platform formed by only a single sensor cannot well meet the requirement of good performance under different environments, and is not enough to cope with the multi-target severe complex environment.
At present, a plurality of sensors have certain problems in the wide application of environmental reconnaissance. The method mainly comprises the following steps:
1. failure to achieve multi-sensor multi-dimensional cooperative detection
The multi-sensor resource is not fully utilized, complementary auxiliary or redundant information of each sensor in time and space is not considered to be integrated according to a certain algorithm, so that consistency description of the target is obtained, and multi-dimensional cooperative detection is realized.
2. Failure to study the objective multidimensional combinatorial Properties
In the current research in the field of multi-sensor information fusion, the fusion processing mainly aims at the similar sensors and has the same data type; heterogeneous data can only be subjected to fusion processing at a decision level, and each sensor completes recognition or judgment respectively and cannot acquire the combined characteristics of the target.
Foreign countries have some countries aimed at the corresponding information aggregation problem and have made some progress. For example, in 2002, a unified convergence rule framework is designed in the wireless sensor network convergence by the Lefevre team, so that the problem of decision conflict in the distribution process can be solved. 2007, Altincay improves the classical EkNN algorithm, using a fusion of multiple EkNN classifiers to achieve higher classification accuracy. In 2016, Zhang Z provides a set of heterogeneous data fusion algorithm based on Dempster rule by researching evidence theory and uncertainty theory, and the method can convert observed data into credibility, thereby carrying out comprehensive consideration at decision level. However, the aggregation of the multi-source or all-source information is performed on a decision level, and has few feature layers, which are not processed from a data layer.
Therefore, at the present stage, a multidimensional heterogeneous information fusion identification method based on Copula theory needs to be designed to solve the above problems.
Disclosure of Invention
The invention aims to provide a multidimensional heterogeneous information fusion identification method based on a Copula theory, which is used for solving the technical problems in the prior art and aiming at the key problem of how to carry out multidimensional comprehensive detection by heterogeneous data of different types of sensors in reconnaissance, and an abstract mathematical space capable of containing heterogeneous information of different types is constructed on the basis of the time-space registration of the multisource heterogeneous observation data of each sensor so as to realize the unified organization and the structuralization processing of the heterogeneous information and lay a foundation for the inversion of target combination characteristics and the establishment of a high-dimensional full-spectrum characteristic library.
In order to achieve the purpose, the technical scheme of the invention is as follows:
the multidimensional heterogeneous information fusion identification method based on the Copula theory comprises the following steps:
s1: heterogeneous information registration; performing space-time registration on the observation data of the air sensors at different times; the method specifically comprises the following steps: performing space registration based on a geodetic coordinate system and a sensor coordinate system transformation equation; after the spatial registration is finished, finishing the time registration of interpolation extrapolation, curve fitting and data interpolation;
s2: on the basis of step S1, the second step
Figure DEST_PATH_IMAGE002
The data space of the individual sensors being the sample space
Figure DEST_PATH_IMAGE004
On which is defined as a set of events
Figure DEST_PATH_IMAGE006
Algebra
Figure DEST_PATH_IMAGE008
And measure of probability
Figure DEST_PATH_IMAGE010
Generating a space of probability measures
Figure DEST_PATH_IMAGE012
Wherein
Figure DEST_PATH_IMAGE014
(ii) a This is achieved by
Figure DEST_PATH_IMAGE016
The product measurement space of each space forms an abstract mathematical space which can contain different types of heterogeneous information, namely a full-dimensional signal space;
s3: on the basis of the step S2, in the constructed full-dimensional signal space capable of including different heterogeneous information, the Copula function is used to establish the connection of the edge distribution of each single-dimensional data, recover the correlation between each dimension of feature data, and invert the high-dimensional combined feature of the target.
Further, in step S1, the spatial registration based on the transformation equation of the geodetic coordinate system and the sensor coordinate system is as follows:
1) establishing a geodetic coordinate system
Figure DEST_PATH_IMAGE018
；
Origin: presetting a point on the ground as the origin of coordinates
Figure DEST_PATH_IMAGE020
；
Figure DEST_PATH_IMAGE022
Shaft: presetting any direction;
Figure DEST_PATH_IMAGE024
shaft: vertically upwards;
Figure DEST_PATH_IMAGE026
shaft: and
Figure 27737DEST_PATH_IMAGE022
a shaft,
Figure 882560DEST_PATH_IMAGE024
The axes form a right-hand coordinate system;
2) sensor coordinate system
Figure DEST_PATH_IMAGE028
；
Origin: geometric center of the sensor
Figure DEST_PATH_IMAGE030
；
Figure DEST_PATH_IMAGE032
Shaft: the direction of the head pointing to the direction of the satellite is positive and is consistent with the axis of the satellite motion direction;
Figure DEST_PATH_IMAGE034
shaft: in the vertical transverse symmetrical plane of the satellite motion direction, perpendicular to
Figure DEST_PATH_IMAGE036
The axis points to the outer side of the satellite orbit and is positive;
Figure DEST_PATH_IMAGE038
shaft: and the above
Figure 973882DEST_PATH_IMAGE032
Shaft and
Figure 696987DEST_PATH_IMAGE034
the axes constitute the pointing direction of a right-hand coordinate system;
3) a coordinate system transformation equation;
the coordinate system transformation can be divided into two steps, the first step is to rotate the coordinate system, and the second step is to translate the coordinate system:
firstly, a transformation matrix of coordinate system rotation;
from the coordinate system
Figure DEST_PATH_IMAGE040
Is transformed to a coordinate system through rotation
Figure DEST_PATH_IMAGE042
The transformation matrix for coordinate system rotation can be obtained as follows:
Figure DEST_PATH_IMAGE044
，
Figure DEST_PATH_IMAGE046
。
secondly, translating a coordinate system;
known coordinate system
Figure DEST_PATH_IMAGE048
Origin of (2)
Figure DEST_PATH_IMAGE050
In a coordinate system
Figure DEST_PATH_IMAGE051
Has the coordinates of
Figure DEST_PATH_IMAGE053
Then coordinate system
Figure 896980DEST_PATH_IMAGE048
One point in
Figure DEST_PATH_IMAGE055
In a coordinate system
Figure 100002_DEST_PATH_IMAGE056
Coordinates of (5)
Figure 100002_DEST_PATH_IMAGE058
Comprises the following steps:
Figure 100002_DEST_PATH_IMAGE060
。
further, in step S2, the full-dimensional signal space is constructed as follows:
in probability theory, a set of events
Figure 100002_DEST_PATH_IMAGE062
An element in (1) is called a random event, and acts as
Figure 47338DEST_PATH_IMAGE062
Is a specific member of (a) a group,
Figure 100002_DEST_PATH_IMAGE064
referred to as inevitable events; definition of
Figure 32481DEST_PATH_IMAGE064
On
Figure 637906DEST_PATH_IMAGE062
Real measurable function, i.e. random variable
Figure 100002_DEST_PATH_IMAGE066
(ii) a Based on
Figure 493735DEST_PATH_IMAGE066
The distribution of (A) can define a measurable space
Figure 100002_DEST_PATH_IMAGE068
Corresponding measure of probability
Figure 100002_DEST_PATH_IMAGE070
；
Constructing a probabilistic measure space for single sensor data
Figure 100002_DEST_PATH_IMAGE072
Is to establish random variables
Figure 142891DEST_PATH_IMAGE066
And estimating
Figure 631641DEST_PATH_IMAGE066
The key technology of this part of the content is the following two points:
(1) establishing
Figure 775178DEST_PATH_IMAGE064
On
Figure 95301DEST_PATH_IMAGE062
Measurable function of real value
Figure 446516DEST_PATH_IMAGE066
；
First, establish
Figure 94667DEST_PATH_IMAGE068
To
Figure 100002_DEST_PATH_IMAGE074
Is mapped to
Figure 822320DEST_PATH_IMAGE066
：
Figure 100002_DEST_PATH_IMAGE076
，
And for arbitrary
Figure 100002_DEST_PATH_IMAGE078
Is provided with
Figure 100002_DEST_PATH_IMAGE080
，
Wherein
Figure 100002_DEST_PATH_IMAGE082
The representation of the real number field is performed,
Figure 100002_DEST_PATH_IMAGE084
is shown in
Figure 590425DEST_PATH_IMAGE082
Above Borel consisting of Borel measurable sets
Figure 100002_DEST_PATH_IMAGE086
Algebraic scale
Figure 456750DEST_PATH_IMAGE066
Is composed of
Figure 592196DEST_PATH_IMAGE068
To
Figure 100002_DEST_PATH_IMAGE088
Measurable mappings of (1), i.e. random variables;
is defined in
Figure 202169DEST_PATH_IMAGE068
The random variables above are not unique, all that isThe mapping satisfying the above conditions is
Figure 355938DEST_PATH_IMAGE068
The random variables above, so different random variables should be constructed as required
Figure 862006DEST_PATH_IMAGE066
；
(2) Distribution estimation based on a goodness-of-fit method;
observing the target by using a sensor, wherein the obtained observation data is a measurable space
Figure 609382DEST_PATH_IMAGE068
In
Figure 898412DEST_PATH_IMAGE062
The number of elements of (a) is,
Figure 985317DEST_PATH_IMAGE066
mapping it into a set of real numbers, i.e. from
Figure 459024DEST_PATH_IMAGE066
The sample observations of (a); will be estimated based on sample observations using goodness of fit tests
Figure 818330DEST_PATH_IMAGE066
The distribution function of (2).
Further, step S3 is specifically as follows:
establishing connection of edge distribution of each single-dimensional data by using a Copula function in a constructed full-dimensional signal space capable of containing different heterogeneous information, recovering a correlation relation between each pair of dimensional characteristic data, and inverting a high-dimensional combination characteristic of a target;
on the first hand, a Copula function construction scheme is completed, a data consistency representation method of applicability is established, and a Copula function family construction method based on edge distribution of each single feature data and different correlations among the feature data is initially established;
is provided with
Figure 100002_DEST_PATH_IMAGE090
A meta Copula function refers to a function having the following properties
Figure 100002_DEST_PATH_IMAGE092
：
a）
Figure 100002_DEST_PATH_IMAGE094
,
Figure 100002_DEST_PATH_IMAGE096
And is
Figure 100002_DEST_PATH_IMAGE098
,
Figure DEST_PATH_IMAGE100
；
b）
Figure 894739DEST_PATH_IMAGE092
Is of zero basal plane and is
Figure 773833DEST_PATH_IMAGE090
Dimension increment is carried out;
c）
Figure 621704DEST_PATH_IMAGE092
edge distribution function of
Figure DEST_PATH_IMAGE102
Satisfies the following conditions:
Figure DEST_PATH_IMAGE104
wherein
Figure DEST_PATH_IMAGE106
,
Figure DEST_PATH_IMAGE108
；
If it is not
Figure DEST_PATH_IMAGE110
Is a continuous unary distribution function of
Figure DEST_PATH_IMAGE112
Then, then
Figure DEST_PATH_IMAGE114
Is an edge distribution function of
Figure DEST_PATH_IMAGE116
A multivariate distribution function of (a);
order to
Figure DEST_PATH_IMAGE118
A joint cumulative distribution function for one dimensional variable, wherein the edge cumulative distribution function for each variable is denoted as
Figure 796202DEST_PATH_IMAGE116
Then there is one
Figure 817247DEST_PATH_IMAGE090
Dimension Copula function
Figure 534537DEST_PATH_IMAGE092
So that
Figure DEST_PATH_IMAGE120
If the edge cumulates the distribution function
Figure 350046DEST_PATH_IMAGE116
Is continuous, then the Copula function
Figure 169097DEST_PATH_IMAGE092
Is unique; copula function
Figure 931517DEST_PATH_IMAGE092
Only on each sideThe function value domain of the edge cumulative distribution is uniquely determined;
for the case of continuous edge distribution, for all
Figure DEST_PATH_IMAGE122
All are provided with
Figure DEST_PATH_IMAGE124
Therefore, based on the edge distribution, a plurality of Copula functions satisfying the definition conditions, that is, a multivariate normal Copula function and an Archimedean Copula function, are constructed by adopting different generation modes:
(1) a multivariate normal Copula function;
is provided with
Figure DEST_PATH_IMAGE126
Is a positive definite matrix and the matrix is a negative definite matrix,
Figure DEST_PATH_IMAGE128
，
Figure DEST_PATH_IMAGE130
so as to make
Figure 34471DEST_PATH_IMAGE126
The multivariate normal distribution function of the covariance matrix is as follows:
Figure DEST_PATH_IMAGE132
，
wherein
Figure DEST_PATH_IMAGE134
Is a one-dimensional standard normal distribution function;
(2) a multivariate Archimedean Copula function;
is provided with
Figure DEST_PATH_IMAGE136
Continuously and strictly increasingTo do so by
Figure DEST_PATH_IMAGE138
To generate a primitive, a multivariate Archimedean Copula function can be constructed
Figure DEST_PATH_IMAGE140
Figure DEST_PATH_IMAGE142
，
Wherein
Figure DEST_PATH_IMAGE144
In that
Figure DEST_PATH_IMAGE146
Up monotonous;
kendall's as a generator for a specific Archimedean Copula function
Figure DEST_PATH_IMAGE148
An expression of consistent relevance; gumbel type generator
Figure DEST_PATH_IMAGE150
In the Copula function thereof
Figure DEST_PATH_IMAGE152
Kendall's describing variable dependencies
Figure 219551DEST_PATH_IMAGE148
The parameters are calculated as
Figure DEST_PATH_IMAGE154
(ii) a Clayton type, generator
Figure DEST_PATH_IMAGE156
In the Copula function thereof
Figure DEST_PATH_IMAGE158
Kendall's describing variable dependencies
Figure 712849DEST_PATH_IMAGE148
The parameters are calculated as
Figure DEST_PATH_IMAGE160
；
Kendall's
Figure 731490DEST_PATH_IMAGE148
The parameter value is between-1 and 1; when in use
Figure DEST_PATH_IMAGE162
To representXVariations of (2)YThe change of the voltage is completely consistent; when in use
Figure DEST_PATH_IMAGE164
To representXVariations of (2)YThe reverse changes of the two are completely consistent; when in use
Figure DEST_PATH_IMAGE166
The correlation between the two cannot be judged; suppose thatXAndYthe Copula function of
Figure DEST_PATH_IMAGE168
Then Kendall' s
Figure 236420DEST_PATH_IMAGE148
The relationship with the Copula function is determined by the following equation,
Figure DEST_PATH_IMAGE170
，
after introducing the integral, can be obtained
Figure DEST_PATH_IMAGE172
，
The following transformation is constructed,
Figure DEST_PATH_IMAGE174
；
jacobi matrix transformed therein
Figure DEST_PATH_IMAGE176
Wherein
Figure DEST_PATH_IMAGE178
；
2 is re-integrated into 1, wherein the integration region is the region given by the Copula function,
Figure DEST_PATH_IMAGE180
is an arbitrary generator of the Copula function,
Figure DEST_PATH_IMAGE182
i.e. for arbitrary functions
Figure DEST_PATH_IMAGE184
If, if
Figure DEST_PATH_IMAGE186
Exists in an inverse function of
Figure 767634DEST_PATH_IMAGE186
Copula function as generator, its Kendall' s
Figure DEST_PATH_IMAGE188
The parameters must have the following form:
Figure DEST_PATH_IMAGE190
，
whereinAAndBis a determined constant;
in the second aspect, an optimal Copula function selection method based on a maximum likelihood criterion is completed, basic connection between different dimensions of multi-source heterogeneous data is established, and further basic mapping from multi-source heterogeneous data vectors to a high-dimensional probability space is given;
based on the edge distribution of single sensor data and the related information of the data, a family of Copula functions can be generated by using a Copula function structure, and the optimal Copula function for better describing the related relation of multi-dimensional data is selected from the Copula functions based on the maximum likelihood criterion;
is provided with
Figure DEST_PATH_IMAGE192
Is the generated Copula function family,
Figure DEST_PATH_IMAGE194
is a training data set, then
Figure DEST_PATH_IMAGE196
，
Figure DEST_PATH_IMAGE198
Basic connection among different dimensions of the multivariate heterogeneous data is established, and the multivariate heterogeneous data is naturally mapped to a high-dimensional probability space to serve as a basis for establishing a full-dimensional signal space.
Compared with the prior art, the invention has the beneficial effects that:
the innovation point of the invention is that, as shown in fig. 9, each of the SAR radar, infrared, optical, etc. signal spaces is regarded as a measurement space and then as a composite dimension as a whole according to its own existing measurement relationship. And for each target, a group of multi-source heterogeneous data signals obtained by once detection of each sensor form a high-dimensional point. The high-dimensional points obtained by a plurality of times of detection form a high-dimensional joint distribution generated by the joint of all composite dimensions, and the high-dimensional joint distribution already contains the whole information of the target, so that the heterogeneous signal data structurally form a whole in a uniform manner. The Copula theory and the method in the random process theory ensure that the association between the combined distribution formed by the high-dimensional points and each composite dimension, namely the marginal distribution in each sensor signal space, can be established by a Copula connection function, so that a feature level fusion result can be obtained through the marginal distribution in each sensor signal space.
The multi-source heterogeneous sensor information has strong correlation, diversity and complementarity, and in order to better improve the perception capability of the target state, a common representation form and measurement mode are required to be given to the multi-source heterogeneous sensor information, namely a unified identification of a multi-source heterogeneous data composite dimension is constructed. As shown in fig. 10, a structured metric space, referred to as a "full-dimensional signal space", is then formed from one or more composite dimensions. A unified mathematical model and a mathematical space containing signal types of each sensor are established in the full-dimensional signal space, and a brand-new framework is established for target identification, so that support on a mathematical theory is provided for single feature identification and full-spectrum feature identification. The composite measurement signal of any target in the full-dimensional space is a multi-dimensional signal
Figure DEST_PATH_IMAGE200
The multi-dimensional signal has information of multiple dimensions such as SAR radar, infrared and optics, and measurement signals of all dimensions are independent from each other, and can carry information based on time dimensions respectively without influencing state information of other dimensions. The composite measurement signal of any target uses a full-dimensional space
Figure DEST_PATH_IMAGE202
Can be fully expressed, and thus the state space
Figure DEST_PATH_IMAGE202A
A plurality of mutually independent ways of re-fully expressing the target state are provided. According to different characteristics of heterogeneous data, data rules are mined, and Copula functions suitable for marginal distribution and internal relation of target heterogeneous characteristic data are constructed in a targeted mode to obtain combined distribution. Thereby establishing a full-dimensional feature data space.
The combined feature detection method based on Copula combined distribution has higher combined identification accuracy on the target than a single feature detection method based on each edge distribution, and embodies the advantages of combined detection.
Drawings
FIG. 1 is a schematic geodetic coordinate system of an embodiment of the present application.
Fig. 2 is a schematic diagram of coordinate system rotation according to an embodiment of the present application.
Fig. 3 is a schematic time registration diagram according to an embodiment of the present application.
Fig. 4 is a schematic diagram of a probability density function of the sample data generation model according to the embodiment of the present application.
Fig. 5 is a schematic diagram of a reconstruction density function based on a normal Copula function according to an embodiment of the present application.
Fig. 6 is a schematic diagram of a reconstruction error based on a normal Copula function according to an embodiment of the present application.
Fig. 7 is a schematic diagram of a reconstruction density function based on an Archimedean Copula function according to an embodiment of the present application.
Fig. 8 is a schematic diagram of a reconstruction error based on an Archimedean Copula function according to an embodiment of the present application.
Fig. 9 is a schematic diagram of heterogeneous data connection according to an embodiment of the present application.
Fig. 10 is a schematic diagram of establishing a full-dimensional signal space according to an embodiment of the present application.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to fig. 1 to 10 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.
Example (b):
as shown in fig. 1, a multidimensional heterogeneous information fusion identification method based on Copula theory is proposed, which constructs an innovative abstract mathematical space, namely a full-dimensional signal space, capable of incorporating different types of heterogeneous information based on the time-space registration of sensor observation data, and realizes the unified representation of the heterogeneous data of three sensors (radar, infrared and visible light).
First, heterogeneous information registration section.
The space-time registration of sensor observation data in different space-time mainly comprises two aspects:
(1) spatial registration based on a geodetic coordinate system and a sensor coordinate system transformation equation;
when spatial registration is performed, the geodetic coordinate system and the sensor coordinate system are mainly considered.
1) Geodetic coordinate system
Figure DEST_PATH_IMAGE203
(ii) a As shown in fig. 1;
origin: presetting a point on the ground as the origin of coordinates
Figure DEST_PATH_IMAGE204
；
Figure DEST_PATH_IMAGE205
Shaft: presetting any direction;
Figure DEST_PATH_IMAGE206
shaft: vertically upwards;
Figure DEST_PATH_IMAGE207
shaft: and
Figure 59812DEST_PATH_IMAGE205
a shaft,
Figure 164035DEST_PATH_IMAGE206
The axes constitute a right-hand coordinate system.
2) Sensor coordinate system
Figure DEST_PATH_IMAGE208
；
Origin: geometric center of the sensor
Figure DEST_PATH_IMAGE209
；
Figure DEST_PATH_IMAGE210
Shaft: the direction of the head pointing to the direction of the satellite is positive and is consistent with the axis of the satellite motion direction;
Figure DEST_PATH_IMAGE211
shaft: in the vertical transverse symmetrical plane of the satellite motion direction, perpendicular to
Figure DEST_PATH_IMAGE212
The axis points to the outer side of the satellite orbit and is positive;
Figure DEST_PATH_IMAGE213
shaft: and the above
Figure 116947DEST_PATH_IMAGE210
Shaft and
Figure 835373DEST_PATH_IMAGE211
the axes constitute the sense of the right-hand coordinate system.
3) A coordinate system transformation equation;
the coordinate system transformation can be divided into two steps, the first step is to rotate the coordinate system, and the second step is to translate the coordinate system:
firstly, a transformation matrix of coordinate system rotation;
from the coordinate system
Figure DEST_PATH_IMAGE214
Is transformed to a coordinate system through rotation
Figure DEST_PATH_IMAGE215
An angle as shown in fig. 2 is required.
From the geometrical relationships in fig. 2, the transformation matrix for coordinate system rotation can be derived as follows:
Figure DEST_PATH_IMAGE216
，
Figure DEST_PATH_IMAGE217
。
secondly, translating a coordinate system;
known coordinate system
Figure DEST_PATH_IMAGE218
Origin of (2)
Figure DEST_PATH_IMAGE219
In a coordinate system
Figure DEST_PATH_IMAGE220
Has the coordinates of
Figure DEST_PATH_IMAGE221
Then coordinate system
Figure 427898DEST_PATH_IMAGE218
One point in
Figure DEST_PATH_IMAGE222
In a coordinate system
Figure DEST_PATH_IMAGE223
Coordinates of (5)
Figure DEST_PATH_IMAGE224
Comprises the following steps:
Figure DEST_PATH_IMAGE225
。
(2) completing the time registration of interpolation extrapolation, curve fitting and data interpolation;
due to the fact that sampling periods and starting-up time of the sensors are not consistent, time references are not consistent, instability of data link transmission, system control errors and the like, measurement data of different sensors are asynchronous. As shown in fig. 3, the time registration is to unify the time-asynchronous measurement data of each sensor with respect to the same target to a synchronous fusion processing time after being processed by a suitable algorithm.
Three algorithms are mainly used for time registration: interpolation extrapolation, curve fitting and data interpolation.
1) Interpolation and extrapolation;
the interpolation extrapolation method is to interpolate and extrapolate target observation data collected by each sensor in the same time interval, and extrapolate the data on high-precision observation time to low-precision observation time points so as to achieve the time synchronization of different sensors. The algorithm is divided into three steps:
the first step is as follows: time division
The time slice division is different with specific moving targets, the states of the targets can be divided into static, low-speed movement, high-speed movement and the like, and the corresponding fusion time slice can be selected to be in the order of hours, minutes or seconds.
The second step is that: incremental sorting
And (4) performing incremental sequencing on the observation data of various sensors in each time interval according to the measurement precision.
The third step: interpolation extrapolation
And interpolating and extrapolating the data on the high-precision observation time to the low-precision time points in each time interval to form a series of target observation data at equal intervals, wherein the observation data in the same time slice are generally multiple.
2) Fitting a curve;
the curve fitting method is to perform curve fitting on the data of each sensor to obtain a fitting curve under the principle of keeping the fitting error to be minimum (such as the least square criterion) and then to perform sampling according to a selected sampling interval, so as to obtain the data at the registration moment and realize the time registration of the target. The algorithm is divided into three steps:
the first step is as follows: time division
The time slice division is different with specific moving targets, the states of the targets can be divided into static, low-speed movement, high-speed movement and the like, and the corresponding fusion time slice can be selected to be in the order of hours, minutes or seconds.
The second step is that: fitting of curves
And in each time interval, fitting the observed data of each sensor according to a principle (such as a least square criterion) with the minimum fitting error to obtain respective data curves.
The third step: data sampling
And sampling in the same sampling period to obtain sampling data at the same fusion moment.
3) Data interpolation;
the data interpolation method is to obtain an equation (or a curve) from known sampling point data of each sensor by an interpolation method, and then obtain data at the registration time by the equation (or an analytic expression of the curve), wherein an interpolation algorithm comprises Lagrange polynomial interpolation, spline interpolation and the like. The algorithm is divided into three steps:
the first step is as follows: time division
The time slice division is different with specific moving targets, the states of the targets can be divided into static, low-speed movement, high-speed movement and the like, and the corresponding fusion time slice can be selected to be in the order of hours, minutes or seconds.
The second step is that: data interpolation
And in each time interval, carrying out Lagrange polynomial interpolation or spline interpolation on the observation data of each sensor to obtain a data equation (curve).
The third step: data sampling
And calculating to obtain the sampling data at the same fusion moment according to a data equation (curve) obtained by interpolation.
And constructing a second full-dimensional signal space.
On the basis of spatio-temporal registration, the premise that heterogeneous data can be aggregated is that they can be transformed in some way to a common representation and consistent metric. Will be first
Figure DEST_PATH_IMAGE226
Data space composition of individual sensorsIs a sample space
Figure DEST_PATH_IMAGE227
On which is defined as a set of events
Figure DEST_PATH_IMAGE228
Algebra
Figure DEST_PATH_IMAGE229
And measure of probability
Figure DEST_PATH_IMAGE230
Generating a space of probability measures
Figure DEST_PATH_IMAGE231
Wherein
Figure DEST_PATH_IMAGE232
. This is achieved by
Figure DEST_PATH_IMAGE233
The product measure space of the spaces constitutes the abstract mathematical space we wish to be able to incorporate different types of heterogeneous information, i.e. the full-dimensional signal space.
In probability theory, a set of events
Figure DEST_PATH_IMAGE234
An element in (1) is called a random event, and acts as
Figure 626491DEST_PATH_IMAGE234
Is a specific member of (a) a group,
Figure DEST_PATH_IMAGE235
referred to as inevitable events; definition of
Figure 902751DEST_PATH_IMAGE235
On
Figure 729762DEST_PATH_IMAGE234
Real measurable function, i.e. random variable
Figure DEST_PATH_IMAGE236
. Based on
Figure 91473DEST_PATH_IMAGE236
The distribution of (A) can define a measurable space
Figure DEST_PATH_IMAGE237
Corresponding measure of probability
Figure DEST_PATH_IMAGE238
。
As shown in FIG. 3, a space of probability measures is constructed for a single sensor data
Figure DEST_PATH_IMAGE239
Is to establish random variables
Figure 130973DEST_PATH_IMAGE236
And estimating
Figure 730582DEST_PATH_IMAGE236
The key technology of this part of the content is the following two points:
(1) establishing
Figure 790810DEST_PATH_IMAGE235
On
Figure 46342DEST_PATH_IMAGE234
Measurable function of real value
Figure 92796DEST_PATH_IMAGE236
；
First, establish
Figure 733862DEST_PATH_IMAGE237
To
Figure DEST_PATH_IMAGE240
Is mapped to
Figure 981303DEST_PATH_IMAGE236
：
Figure DEST_PATH_IMAGE241
，
And for arbitrary
Figure DEST_PATH_IMAGE242
Is provided with
Figure DEST_PATH_IMAGE243
，
Wherein
Figure DEST_PATH_IMAGE244
The representation of the real number field is performed,
Figure DEST_PATH_IMAGE245
is shown in
Figure 160350DEST_PATH_IMAGE244
Above Borel consisting of Borel measurable sets
Figure DEST_PATH_IMAGE246
Algebraic scale
Figure 400707DEST_PATH_IMAGE236
Is composed of
Figure 771645DEST_PATH_IMAGE237
To
Figure DEST_PATH_IMAGE247
A measurable mapping of (a), i.e. a random variable.
It will be readily apparent that the definitions are
Figure 658830DEST_PATH_IMAGE237
The random variables are not unique, and all the mappings satisfying the above conditions are
Figure 607063DEST_PATH_IMAGE237
Random variable of (2) and is thus in practiceDifferent random variables should be constructed according to requirements in application
Figure 119953DEST_PATH_IMAGE236
。
(2) Distribution estimation based on a goodness-of-fit method;
observing the target by using a sensor, wherein the obtained observation data is a measurable space
Figure 610977DEST_PATH_IMAGE237
In
Figure 669063DEST_PATH_IMAGE234
The number of elements of (a) is,
Figure 979959DEST_PATH_IMAGE236
mapping it into a set of real numbers, i.e. from
Figure 30960DEST_PATH_IMAGE236
The sample observations of (1). Will be estimated based on sample observations using goodness of fit tests
Figure 376491DEST_PATH_IMAGE236
The distribution function of (2). Under the condition that the sample observed value obeys certain determined distribution, the distribution parameters are estimated according to a moment estimation method or a maximum likelihood estimation method, then proper statistics are constructed according to a statistical principle, the statistics are calculated by utilizing the observed data and are compared with a threshold value, if the statistics fall into a rejection region, a small probability event is shown to occur, and therefore the observed data do not obey the theoretical distribution. The goodness of fit test method is as follows:
Figure DEST_PATH_IMAGE249
test sum
Figure DEST_PATH_IMAGE251
And (6) checking.
1）
Figure 261270DEST_PATH_IMAGE249
Checking;
Figure DEST_PATH_IMAGE253
the inspection method is based on the total
Figure DEST_PATH_IMAGE255
When the distribution of (a) is unknown, a test method of testing hypotheses about the distribution of the population from a sample from the population.
Use of
Figure 117186DEST_PATH_IMAGE253
When the overall distribution is tested by the test method, the original hypothesis is firstly proposed:
Figure DEST_PATH_IMAGE257
(ii) a Wherein
Figure DEST_PATH_IMAGE259
As a whole
Figure DEST_PATH_IMAGE261
The distribution function of (a) is determined,
Figure DEST_PATH_IMAGE263
is the theoretical distribution function to be examined. Whether to accept the original hypothesis is then determined based on how well the empirical distribution of the samples matches the hypothesized theoretical distribution. This test is commonly referred to as a goodness-of-fit test, which is a non-parametric test.
In use
Figure DEST_PATH_IMAGE265
Hypothesis testing by inspection method
Figure DEST_PATH_IMAGE267
When is in
Figure 706299DEST_PATH_IMAGE267
The type of the lower distribution is known, but the parameters are unknown, and the parameters need to be estimated by a maximum likelihood estimation method and then checked.
Fitting of the distribution
Figure 499812DEST_PATH_IMAGE265
The basic principle and steps of the assay are as follows:
a) will be overall
Figure 289913DEST_PATH_IMAGE261
Is divided into
Figure DEST_PATH_IMAGE269
The cells not overlapping each other are denoted as
Figure DEST_PATH_IMAGE271
；
b) Fall into
Figure DEST_PATH_IMAGE273
Between cells
Figure DEST_PATH_IMAGE275
The number of sample values of (A) is recorded as
Figure DEST_PATH_IMAGE277
Called the measured frequency, the sum of all measured frequencies
Figure DEST_PATH_IMAGE279
Equal to sample capacity
Figure DEST_PATH_IMAGE281
；
c) From the assumed theoretical distribution, a population can be calculated
Figure 886986DEST_PATH_IMAGE261
Fall within each
Figure 358418DEST_PATH_IMAGE275
Probability of (2)
Figure DEST_PATH_IMAGE283
Is thus
Figure DEST_PATH_IMAGE285
Is just falling into
Figure 68754DEST_PATH_IMAGE275
The theoretical frequency of the sample values of (1);
d）
Figure DEST_PATH_IMAGE287
the magnitude of the difference between the empirical distribution and the theoretical distribution is marked.
Figure DEST_PATH_IMAGE289
The following statistics were introduced to represent the difference between the empirical distribution and the theoretical distribution:
Figure DEST_PATH_IMAGE291
；
e) current hypothesis
Figure 967440DEST_PATH_IMAGE267
Theoretical frequency at the time of establishment
Figure 864858DEST_PATH_IMAGE285
And frequency of actual measurement
Figure DEST_PATH_IMAGE293
Should be in close proximity, i.e.
Figure DEST_PATH_IMAGE295
Should be small, thereby
Figure DEST_PATH_IMAGE297
Should also be small otherwise it cannot be considered
Figure 874402DEST_PATH_IMAGE267
Is established, so
Figure 252294DEST_PATH_IMAGE267
Should be in the range of
Figure DEST_PATH_IMAGE299
，
Figure DEST_PATH_IMAGE301
From the level of significance
Figure DEST_PATH_IMAGE303
And (4) determining.
Figure 446515DEST_PATH_IMAGE289
The following are demonstrated:
if the theoretical distribution in the hypothesis
Figure DEST_PATH_IMAGE305
Has been completely given, then
Figure DEST_PATH_IMAGE307
Time of day statistics
Figure DEST_PATH_IMAGE309
Is asymptotically distributed
Figure DEST_PATH_IMAGE311
Of one degree of freedom
Figure DEST_PATH_IMAGE313
Distributing; if distribution of theory
Figure DEST_PATH_IMAGE315
Therein is provided with
Figure DEST_PATH_IMAGE317
The unknown parameters are replaced by corresponding estimators, when
Figure 565649DEST_PATH_IMAGE307
Time of day statistics
Figure 300256DEST_PATH_IMAGE309
Is asymptotically distributed
Figure DEST_PATH_IMAGE319
Of one degree of freedom
Figure 329392DEST_PATH_IMAGE313
And (4) distribution.
According to this theorem, for a given level of significance
Figure DEST_PATH_IMAGE321
According to
Figure 38722DEST_PATH_IMAGE313
Distribution table available threshold
Figure DEST_PATH_IMAGE323
So that
Figure DEST_PATH_IMAGE325
The rejection zone is thus obtained:
Figure DEST_PATH_IMAGE327
(without estimating parameters)
Figure DEST_PATH_IMAGE329
(estimation of
Figure 582836DEST_PATH_IMAGE317
Parameters)
If based on the given sample value
Figure DEST_PATH_IMAGE331
Calculate resultant statistics
Figure 996500DEST_PATH_IMAGE309
If the observed value falls into the rejection region, the original hypothesis is rejected, otherwise, the difference is considered to be not significant and the original hypothesis is accepted.
Figure 4776DEST_PATH_IMAGE289
The theorem is that
Figure DEST_PATH_IMAGE333
Derived when infinitely increased, and thus in use, attention is paid
Figure 150586DEST_PATH_IMAGE333
Is large enough and
Figure DEST_PATH_IMAGE335
these two conditions are not too small. Generally required in practice
Figure DEST_PATH_IMAGE337
And
Figure DEST_PATH_IMAGE339
otherwise, the intervals should be appropriately merged so that
Figure 509892DEST_PATH_IMAGE335
This requirement is met.
2）
Figure DEST_PATH_IMAGE341
Checking;
foregoing introduces
Figure DEST_PATH_IMAGE343
Inspection of the whole
Figure DEST_PATH_IMAGE345
Whether discrete or continuous, whether discrete or continuous
Figure 664930DEST_PATH_IMAGE345
It applies whether the distribution of the original hypothesis contains unknown parameters, one-dimensional or multi-dimensional. It relies on the partitioning of intervals, even if the original assumption
Figure DEST_PATH_IMAGE347
If this is not true, it is still possible to:
Figure DEST_PATH_IMAGE349
i.e. it is possible to accept unreal original hypotheses
Figure DEST_PATH_IMAGE351
。
Figure 730975DEST_PATH_IMAGE341
Inspection is over
Figure 313266DEST_PATH_IMAGE343
This disadvantage was examined, but it required that the overall distribution had to be continuous and that the original hypothetical distribution generally did not contain unknown parameters (exceptions may be made to large samples, normal distributions, and exponential distributions).
Figure 35235DEST_PATH_IMAGE341
Examination (K-STest) is based on a cumulative distribution function to check whether one empirical distribution fits a theoretical distribution or to compare whether two empirical distributions differ significantly. Two samplesK-SThe test is one of the most useful and conventional nonparametric methods of comparing two samples because it is sensitive to differences in both the location and shape parameters of the empirical distribution functions of the two samples.
K-SThe test has many advantages, such as: (a) as a nonparametric method, the method has robustness; (b) mean-independent position; (c) is insensitive to scaling; (d) ratio of
Figure 993963DEST_PATH_IMAGE343
The test is more effective. However, when the observed data substantially follows a normal distribution, thenK-STested not to have
Figure DEST_PATH_IMAGE353
The assay is sensitive or valid.
One, single sampleK-SChecking;
the original hypothesis and the alternative hypothesis are:
Figure DEST_PATH_IMAGE355
；
wherein
Figure DEST_PATH_IMAGE357
Is a specified one-dimensional continuous distribution function,
Figure DEST_PATH_IMAGE359
as a whole
Figure DEST_PATH_IMAGE361
The distribution function of (2).
If it is not
Figure DEST_PATH_IMAGE363
If true, then statistic
Figure DEST_PATH_IMAGE365
The following limiting distribution:
Figure DEST_PATH_IMAGE367
wherein
Figure DEST_PATH_IMAGE369
As a whole
Figure DEST_PATH_IMAGE371
The sample empirical distribution function of (1).
When in use
Figure DEST_PATH_IMAGE373
When the state is not satisfied,
Figure DEST_PATH_IMAGE375
there is a tendency to be large. Therefore, the temperature of the molten metal is controlled,
Figure 237818DEST_PATH_IMAGE373
has a rejection region of
Figure DEST_PATH_IMAGE377
，
Figure DEST_PATH_IMAGE379
From the level of significance
Figure DEST_PATH_IMAGE381
Is determined for a given
Figure 256590DEST_PATH_IMAGE381
From
Figure 403537DEST_PATH_IMAGE381
Is defined as
Figure DEST_PATH_IMAGE383
Namely, it is
Figure DEST_PATH_IMAGE385
According to
Figure DEST_PATH_IMAGE387
Distributed fractional digit tabulation
Figure DEST_PATH_IMAGE389
So that
Figure DEST_PATH_IMAGE391
Therefore, it is
Figure DEST_PATH_IMAGE393
. Whereby the rejection region is
Figure DEST_PATH_IMAGE395
Single sampleK-SThe specific steps of the test are as follows:
a) extract the volume of the total
Figure DEST_PATH_IMAGE397
And observing the sample
Figure DEST_PATH_IMAGE399
Arranged in order from small to large
Figure DEST_PATH_IMAGE401
；
b) Calculating an empirical distribution function
Figure DEST_PATH_IMAGE403
Figure DEST_PATH_IMAGE405
c) Calculating a theoretical distribution function
Figure DEST_PATH_IMAGE407
At each one
Figure DEST_PATH_IMAGE409
The value of the point, and the statistic
Figure DEST_PATH_IMAGE411
Value of (A)
Figure DEST_PATH_IMAGE413
d) Given level of significance
Figure DEST_PATH_IMAGE415
The threshold value of the rejection region is obtained
Figure DEST_PATH_IMAGE417
When is coming into contact with
Figure DEST_PATH_IMAGE419
When the temperature of the water is higher than the set temperature,
Figure DEST_PATH_IMAGE421
this can be approximated by the following table.
TABLE 1
Figure DEST_PATH_IMAGE423
Figure DEST_PATH_IMAGE425
e) And (3) judging: if it is
Figure DEST_PATH_IMAGE427
If so, the original hypothesis is rejected
Figure DEST_PATH_IMAGE429
(ii) a If it is
Figure DEST_PATH_IMAGE431
The original hypothesis is accepted and the theoretical distribution function of the original hypothesis is considered to fit well to the subsample data.
Two and two samples thereofK-SChecking;
assuming there are two samples from two independent populations respectively, to examine the null hypothesis that the population distributions behind them are the same, one can proceed with two independent samplesK-SAnd (6) checking. The principle is completely the same as the single sample case, and only the distribution of the zero hypothesis in the test statistic needs to be changed into the empirical distribution of another sample.
Is provided with
Figure DEST_PATH_IMAGE433
，
Figure DEST_PATH_IMAGE435
Are respectively the whole
Figure DEST_PATH_IMAGE437
And the whole
Figure DEST_PATH_IMAGE439
The distribution function of (a) is determined,
Figure DEST_PATH_IMAGE441
as a whole
Figure 241656DEST_PATH_IMAGE437
The sample of (a) is selected,
Figure DEST_PATH_IMAGE443
as a whole
Figure 564184DEST_PATH_IMAGE439
And the two samples are independent of each other. Consider the following hypothesis testing problem:
Figure DEST_PATH_IMAGE445
；
is provided with
Figure DEST_PATH_IMAGE447
，
Figure DEST_PATH_IMAGE449
Are respectively a sample
Figure DEST_PATH_IMAGE451
And a sample
Figure DEST_PATH_IMAGE453
Empirical distribution function of
Figure DEST_PATH_IMAGE455
Figure DEST_PATH_IMAGE457
When in use
Figure DEST_PATH_IMAGE459
，
Figure DEST_PATH_IMAGE461
In the case of a continuous distribution function, if
Figure DEST_PATH_IMAGE463
If true, then statistic
Figure DEST_PATH_IMAGE465
The limit distribution is as follows:
Figure DEST_PATH_IMAGE467
because when
Figure 799862DEST_PATH_IMAGE463
When the state is not satisfied,
Figure 621056DEST_PATH_IMAGE465
has a great tendency, therefore
Figure 718325DEST_PATH_IMAGE463
The reject domain of (a) is:
Figure DEST_PATH_IMAGE469
wherein
Figure DEST_PATH_IMAGE471
Dependent on the level of significance
Figure DEST_PATH_IMAGE473
When is coming into contact with
Figure 426518DEST_PATH_IMAGE473
After being given, the following formula
Figure DEST_PATH_IMAGE475
Determining
Figure 505201DEST_PATH_IMAGE471
. From the Schmilnoff test Critical value Table
Figure 626741DEST_PATH_IMAGE471
. When in use
Figure DEST_PATH_IMAGE477
When the temperature of the water is higher than the set temperature,
Figure 934226DEST_PATH_IMAGE471
this can be approximated by the following table.
TABLE 2
Figure DEST_PATH_IMAGE479
Figure DEST_PATH_IMAGE481
And thirdly, connecting heterogeneous data.
In order to check and embody the connection effectiveness of the full-dimensional signal space and the target combination characteristic inversion method in one stage, a Copula function-based different-dimension connection method part in the next stage is adopted.
Because each sensor observes the same target, the acquired data may have a certain incidence relation, and therefore, in the constructed mathematical space capable of containing different heterogeneous information, the Copula function is used for establishing connection of edge distribution of each single-dimensional data, the correlation relation between each two-dimensional characteristic data is recovered, and the high-dimensional combination characteristic of the target is inverted. The main contents include the following two aspects:
on the first hand, a Copula function construction scheme is completed, a data consistency representation method with wider applicability than the existing research result is established, and a Copula function family construction method based on edge distribution of each single feature data and different relativity among each feature data is initially established.
Is provided with
Figure DEST_PATH_IMAGE483
A meta Copula function refers to a function having the following properties
Figure DEST_PATH_IMAGE485
：
a）
Figure DEST_PATH_IMAGE487
,
Figure DEST_PATH_IMAGE489
And is
Figure DEST_PATH_IMAGE491
,
Figure DEST_PATH_IMAGE493
；
b）
Figure DEST_PATH_IMAGE495
Is zero basal (grouped) and is
Figure DEST_PATH_IMAGE497
Dimensional increment (n-increment);
c）
Figure 542931DEST_PATH_IMAGE495
edge distribution function of
Figure DEST_PATH_IMAGE499
Satisfies the following conditions:
Figure DEST_PATH_IMAGE501
wherein
Figure DEST_PATH_IMAGE502
,
Figure DEST_PATH_IMAGE503
。
Obviously, if
Figure DEST_PATH_IMAGE504
Is a continuous unary distribution function of
Figure DEST_PATH_IMAGE505
Then, then
Figure DEST_PATH_IMAGE506
Is an edge distribution function of
Figure DEST_PATH_IMAGE507
The multivariate distribution function of (1).
(existence theorem) order
Figure DEST_PATH_IMAGE508
A joint cumulative distribution function for one dimensional variable, wherein the edge cumulative distribution function for each variable is denoted as
Figure 413472DEST_PATH_IMAGE507
Then there is one
Figure DEST_PATH_IMAGE509
Dimension Copula function
Figure DEST_PATH_IMAGE510
So that
Figure DEST_PATH_IMAGE511
If the edge cumulates the distribution function
Figure 5996DEST_PATH_IMAGE507
Is continuous, then the Copula function
Figure 586013DEST_PATH_IMAGE510
Is unique. Otherwise, Copula function
Figure 331115DEST_PATH_IMAGE510
The function value of the distribution is accumulated only in the region of each edgeIs uniquely determined.
For the case of continuous edge distribution, for all
Figure DEST_PATH_IMAGE512
All are provided with
Figure DEST_PATH_IMAGE513
Therefore, based on the edge distribution, a plurality of Copula functions satisfying the definition conditions are constructed by adopting different generation modes, such as a multivariate normal Copula function and an Archimedean Copula function:
(1) multivariate normal Copula function
Is provided with
Figure DEST_PATH_IMAGE514
Is a positive definite matrix and the matrix is a negative definite matrix,
Figure DEST_PATH_IMAGE515
，
Figure DEST_PATH_IMAGE516
so as to make
Figure 220442DEST_PATH_IMAGE514
The multivariate normal distribution function of the covariance matrix is as follows:
Figure DEST_PATH_IMAGE517
，
wherein
Figure DEST_PATH_IMAGE518
Is a one-dimensional standard normal distribution function.
(2) Multivariate Archimedean Copula function
Is provided with
Figure DEST_PATH_IMAGE519
Continuously and strictly increasing in number, with
Figure DEST_PATH_IMAGE520
To generate a primitive, a multivariate Archimedean Copula function can be constructed
Figure DEST_PATH_IMAGE521
Figure DEST_PATH_IMAGE522
，
Wherein
Figure DEST_PATH_IMAGE523
In that
Figure DEST_PATH_IMAGE524
The upper is monotonous.
Kendall's are given by the existing theory aiming at the specific generating element of Archimedean Copula function
Figure DEST_PATH_IMAGE525
Expression of consistent correlations. Gumbel type generator as mainstream
Figure DEST_PATH_IMAGE526
In the Copula function thereof
Figure DEST_PATH_IMAGE527
Kendall's describing variable dependencies
Figure 565842DEST_PATH_IMAGE525
The parameters are calculated as
Figure DEST_PATH_IMAGE528
(ii) a Clayton type, generator
Figure DEST_PATH_IMAGE529
In the Copula function thereof
Figure DEST_PATH_IMAGE530
Kendall's describing variable dependencies
Figure 933238DEST_PATH_IMAGE525
The parameters are calculated as
Figure DEST_PATH_IMAGE531
。
Note Kendall' s
Figure 267268DEST_PATH_IMAGE525
The parameter can measure the consistency degree of the change, and the value is between-1 and 1. When in use
Figure DEST_PATH_IMAGE532
To representXVariations of (2)YThe change of the voltage is completely consistent; when in use
Figure DEST_PATH_IMAGE533
To representXVariations of (2)YThe reverse changes of the two are completely consistent; when in use
Figure DEST_PATH_IMAGE534
It is impossible to determine whether there is a correlation between the two. Suppose thatXAndYthe Copula function of
Figure DEST_PATH_IMAGE535
Then Kendall' s
Figure 999600DEST_PATH_IMAGE525
The relationship with the Copula function is determined by the following equation,
Figure DEST_PATH_IMAGE536
，
after introducing the integral, can be obtained
Figure DEST_PATH_IMAGE537
，
The following transformation is constructed,
Figure DEST_PATH_IMAGE538
.
jacobi matrix transformed therein
Figure DEST_PATH_IMAGE539
Wherein
Figure DEST_PATH_IMAGE540
。
2 is re-integrated into 1, wherein the integration region is the region given by the Copula function,
Figure DEST_PATH_IMAGE541
is an arbitrary generator of the Copula function,
Figure DEST_PATH_IMAGE542
furthermore, a conclusion can be drawn that for any function
Figure DEST_PATH_IMAGE543
If, if
Figure DEST_PATH_IMAGE544
Exists in an inverse function of
Figure 425771DEST_PATH_IMAGE544
Copula function as generator, its Kendall' s
Figure DEST_PATH_IMAGE545
The parameters must have the following form:
Figure DEST_PATH_IMAGE546
，
whereinAAndBis a certain constant.
And secondly, completing preliminary research of an optimal Copula function selection method based on a maximum likelihood criterion, establishing basic connection between different dimensions of multi-source heterogeneous data, and further providing basic mapping from multi-source heterogeneous data vectors to a high-dimensional probability space.
Based on the edge distribution of single sensor data and the related information of the data, a family of Copula functions can be generated by using a Copula function construction technology, and an optimal Copula function capable of better describing the related relation of multi-dimensional data is hopefully selected based on a maximum likelihood criterion.
Is provided with
Figure DEST_PATH_IMAGE547
Is the generated Copula function family,
Figure DEST_PATH_IMAGE548
is a training data set, then
Figure DEST_PATH_IMAGE549
，
Figure DEST_PATH_IMAGE550
The basic connection between different dimensions of the multivariate heterogeneous data is established, and the multivariate heterogeneous data is naturally mapped to a high-dimensional probability space, thereby laying the most important foundation for establishing a full-dimensional signal space.
Next, a preliminary simulation verification is performed on the feasibility of the Copula function construction technology, and the results are shown in fig. 4, 5, 6, 7 and 8.
Example (c): the test target is a 1:40 all-metal scaling model (the coxswain is 4 meters and 3 meters respectively) of a ship A and a ship B, three sensors of infrared, visible light and millimeter wave radars are adopted to test and acquire actual target data, and an abstract mathematical space construction technology capable of containing different types of heterogeneous information is verified according to the actual target data;
(1) taking all real experimental data of the two ships as sample data to perform identification calculation, wherein the identification result is as follows:
TABLE 3 identification results of real experimental data
Figure DEST_PATH_IMAGE552
(2) We perform recognition calculation by using 10000 sets of data randomly generated from Copula joint distributions F1 and F2 as sample data, and the recognition results are as follows:
TABLE 4 Generation of sample data identification results
Figure DEST_PATH_IMAGE554
The results show that the combined feature detection method based on Copula combined distribution has higher combined identification accuracy on the target than a single feature detection method based on each edge distribution, and embodies the advantages of combined detection.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.

Claims (1)

1. The multidimensional heterogeneous information fusion identification method based on the Copula theory is characterized by comprising the following steps of:
s1: heterogeneous information registration; performing space-time registration on the observation data of the air sensors at different times; the method specifically comprises the following steps: performing space registration based on a geodetic coordinate system and a sensor coordinate system transformation equation; after the spatial registration is finished, finishing the time registration of interpolation extrapolation, curve fitting and data interpolation;
s2: on the basis of step S1, the second step
Figure DEST_PATH_IMAGE001
The data space of the individual sensors being the sample space
Figure 919406DEST_PATH_IMAGE002
On which is fixedDefined as a set of events
Figure DEST_PATH_IMAGE003
Algebra
Figure 544422DEST_PATH_IMAGE004
And measure of probability
Figure DEST_PATH_IMAGE005
Generating a space of probability measures
Figure 682755DEST_PATH_IMAGE006
Wherein
Figure DEST_PATH_IMAGE007
(ii) a This is achieved by
Figure 88328DEST_PATH_IMAGE008
The product measurement space of each space forms an abstract mathematical space which can contain different types of heterogeneous information, namely a full-dimensional signal space;
s3: on the basis of the step S2, in the constructed full-dimensional signal space that can be included in different heterogeneous information, establishing connection of edge distribution of each single-dimensional data by using Copula function, recovering correlation between each dimensional feature data, and inverting the high-dimensional combination feature of the target;
in step S1, the spatial registration based on the geodetic coordinate system and the sensor coordinate system transformation equation is specifically as follows:
1) establishing a geodetic coordinate system
Figure DEST_PATH_IMAGE009
；
Origin: presetting a point on the ground as the origin of coordinates
Figure 730662DEST_PATH_IMAGE010
；
Figure DEST_PATH_IMAGE011
Shaft: presetting any direction;
Figure 351131DEST_PATH_IMAGE012
shaft: vertically upwards;
Figure DEST_PATH_IMAGE013
shaft: and
Figure 115824DEST_PATH_IMAGE011
a shaft,
Figure 477536DEST_PATH_IMAGE012
The axes form a right-hand coordinate system;
2) sensor coordinate system
Figure 392402DEST_PATH_IMAGE014
；
Origin: geometric center of the sensor
Figure DEST_PATH_IMAGE015
；
Figure 867377DEST_PATH_IMAGE016
Shaft: the direction of the head pointing to the direction of the satellite is positive and is consistent with the axis of the satellite motion direction;
Figure DEST_PATH_IMAGE017
shaft: in the vertical transverse symmetrical plane of the satellite motion direction, perpendicular to
Figure 802972DEST_PATH_IMAGE018
The axis points to the outer side of the satellite orbit and is positive;
Figure DEST_PATH_IMAGE019
shaft: and the above
Figure 855241DEST_PATH_IMAGE016
Shaft and
Figure 449165DEST_PATH_IMAGE017
the axes constitute the pointing direction of a right-hand coordinate system;
3) a coordinate system transformation equation;
the coordinate system transformation can be divided into two steps, the first step is to rotate the coordinate system, and the second step is to translate the coordinate system:
firstly, a transformation matrix of coordinate system rotation;
from the coordinate system
Figure 700018DEST_PATH_IMAGE020
Is transformed to a coordinate system through rotation
Figure DEST_PATH_IMAGE021
The transformation matrix for coordinate system rotation can be obtained as follows:
Figure 806514DEST_PATH_IMAGE022
，
Figure DEST_PATH_IMAGE023
；
secondly, translating a coordinate system;
known coordinate system
Figure 346080DEST_PATH_IMAGE024
Origin of (2)
Figure DEST_PATH_IMAGE025
In a coordinate system
Figure 6344DEST_PATH_IMAGE026
Has the coordinates of
Figure DEST_PATH_IMAGE027
Then coordinate system
Figure 314965DEST_PATH_IMAGE024
One point in
Figure 389100DEST_PATH_IMAGE028
In a coordinate system
Figure 884804DEST_PATH_IMAGE026
Coordinates of (5)
Figure DEST_PATH_IMAGE029
Comprises the following steps:
Figure 351688DEST_PATH_IMAGE030
；
in step S2, the full-dimensional signal space is constructed as follows:
in probability theory, a set of events
Figure DEST_PATH_IMAGE031
An element in (1) is called a random event, and acts as
Figure 842713DEST_PATH_IMAGE031
Is a specific member of (a) a group,
Figure 759853DEST_PATH_IMAGE032
referred to as inevitable events; definition of
Figure 8432DEST_PATH_IMAGE032
On
Figure 747849DEST_PATH_IMAGE031
Real measurable function, i.e. random variable
Figure DEST_PATH_IMAGE033
(ii) a Based on
Figure 765483DEST_PATH_IMAGE033
The distribution of (A) can define a measurable space
Figure 119104DEST_PATH_IMAGE034
Corresponding measure of probability
Figure DEST_PATH_IMAGE035
；
Constructing a probabilistic measure space for single sensor data
Figure 182875DEST_PATH_IMAGE036
Is to establish random variables
Figure 725983DEST_PATH_IMAGE033
And estimating
Figure 394862DEST_PATH_IMAGE033
The key technology of this part of the content is the following two points:
(1) establishing
Figure 857067DEST_PATH_IMAGE032
On
Figure 204872DEST_PATH_IMAGE031
Measurable function of real value
Figure 207463DEST_PATH_IMAGE033
；
First, establish
Figure 934111DEST_PATH_IMAGE034
To
Figure DEST_PATH_IMAGE037
Is mapped to
Figure 185793DEST_PATH_IMAGE033
：
Figure 755315DEST_PATH_IMAGE038
，
And for arbitrary
Figure DEST_PATH_IMAGE039
Is provided with
Figure 577909DEST_PATH_IMAGE040
，
Wherein
Figure DEST_PATH_IMAGE041
The representation of the real number field is performed,
Figure 80434DEST_PATH_IMAGE042
is shown in
Figure 618863DEST_PATH_IMAGE041
Above Borel consisting of Borel measurable sets
Figure DEST_PATH_IMAGE043
Algebraic scale
Figure 957571DEST_PATH_IMAGE033
Is composed of
Figure 239648DEST_PATH_IMAGE034
To
Figure 3205DEST_PATH_IMAGE044
Measurable mappings of (1), i.e. random variables;
is defined in
Figure 102748DEST_PATH_IMAGE034
The random variables are not unique, and all the mappings satisfying the above conditions are
Figure 522228DEST_PATH_IMAGE034
The random variables above, so different random variables should be constructed as required
Figure 748941DEST_PATH_IMAGE033
；
(2) Distribution estimation based on a goodness-of-fit method;
observing the target by using a sensor, wherein the obtained observation data is a measurable space
Figure 367004DEST_PATH_IMAGE034
In
Figure 512815DEST_PATH_IMAGE031
The number of elements of (a) is,
Figure 544225DEST_PATH_IMAGE033
mapping it into a set of real numbers, i.e. from
Figure 230421DEST_PATH_IMAGE033
The sample observations of (a); will be estimated based on sample observations using goodness of fit tests
Figure 171832DEST_PATH_IMAGE033
A distribution function of (a);
step S3 is specifically as follows:
establishing connection of edge distribution of each single-dimensional data by using a Copula function in a constructed full-dimensional signal space capable of containing different heterogeneous information, recovering a correlation relation between each pair of dimensional characteristic data, and inverting a high-dimensional combination characteristic of a target;
on the first hand, a Copula function construction scheme is completed, a data consistency representation method of applicability is established, and a Copula function family construction method based on edge distribution of each single feature data and different correlations among the feature data is initially established;
is provided with
Figure DEST_PATH_IMAGE045
A meta Copula function refers to a function having the following properties
Figure 360980DEST_PATH_IMAGE046
：
a）
Figure DEST_PATH_IMAGE047
,
Figure 82949DEST_PATH_IMAGE048
And is
Figure DEST_PATH_IMAGE049
,
Figure 41677DEST_PATH_IMAGE050
；
b）
Figure 447382DEST_PATH_IMAGE046
Is of zero basal plane and is
Figure 997312DEST_PATH_IMAGE045
Dimension increment is carried out;
c）
Figure 878681DEST_PATH_IMAGE046
edge distribution function of
Figure 968996DEST_PATH_IMAGE051
Satisfies the following conditions:
Figure DEST_PATH_IMAGE052
wherein
Figure 885000DEST_PATH_IMAGE053
,
Figure DEST_PATH_IMAGE054
；
If it is not
Figure 684460DEST_PATH_IMAGE055
Is a continuous unary distribution function of
Figure DEST_PATH_IMAGE056
Then, then
Figure 381020DEST_PATH_IMAGE057
Is an edge distribution function of
Figure DEST_PATH_IMAGE058
A multivariate distribution function of (a);
order to
Figure 415972DEST_PATH_IMAGE059
A joint cumulative distribution function for one dimensional variable, wherein the edge cumulative distribution function for each variable is denoted as
Figure 796269DEST_PATH_IMAGE058
Then there is one
Figure 688002DEST_PATH_IMAGE045
Dimension Copula function
Figure 278383DEST_PATH_IMAGE046
So that
Figure DEST_PATH_IMAGE060
If the edge cumulates the distribution function
Figure 241660DEST_PATH_IMAGE058
Is continuous, then the Copula function
Figure 601097DEST_PATH_IMAGE046
Is unique; copula function
Figure 663731DEST_PATH_IMAGE046
The distribution function value is only determined in the cumulative distribution function value domain of each edge;
for the case of continuous edge distribution, for all
Figure 613845DEST_PATH_IMAGE061
All are provided with
Figure DEST_PATH_IMAGE062
Therefore, based on the edge distribution, a plurality of Copula functions satisfying the definition conditions, that is, a multivariate normal Copula function and an Archimedean Copula function, are constructed by adopting different generation modes:
(1) a multivariate normal Copula function;
is provided with
Figure 256179DEST_PATH_IMAGE063
Is a positive definite matrix and the matrix is a negative definite matrix,
Figure DEST_PATH_IMAGE064
，
Figure 63598DEST_PATH_IMAGE065
so as to make
Figure 375762DEST_PATH_IMAGE063
The multivariate normal distribution function of the covariance matrix is as follows:
Figure DEST_PATH_IMAGE066
，
wherein
Figure 940735DEST_PATH_IMAGE067
Is a one-dimensional standard normal distribution function;
(2) a multivariate Archimedean Copula function;
is provided with
Figure DEST_PATH_IMAGE068
Continuously and strictly increasing in number, with
Figure 245815DEST_PATH_IMAGE069
To generate a primitive, a multivariate Archimedean Copula function can be constructed
Figure DEST_PATH_IMAGE070
Figure 924052DEST_PATH_IMAGE071
，
Wherein
Figure DEST_PATH_IMAGE072
In that
Figure 797330DEST_PATH_IMAGE073
Up monotonous;
kendall's as a generator for a specific Archimedean Copula function
Figure DEST_PATH_IMAGE074
An expression of consistent relevance; gumbel type generator
Figure 443075DEST_PATH_IMAGE075
In the Copula function thereof
Figure DEST_PATH_IMAGE076
Kendall's describing variable dependencies
Figure 36998DEST_PATH_IMAGE074
The parameters are calculated as
Figure 225534DEST_PATH_IMAGE077
(ii) a Clayton type, generator
Figure DEST_PATH_IMAGE078
In the Copula function thereof
Figure 394347DEST_PATH_IMAGE079
Kendall's describing variable dependencies
Figure 668334DEST_PATH_IMAGE074
The parameters are calculated as
Figure DEST_PATH_IMAGE080
；
Kendall's
Figure 328598DEST_PATH_IMAGE074
The parameter value is between-1 and 1; when in use
Figure 637219DEST_PATH_IMAGE081
To representXVariations of (2)YThe change of the voltage is completely consistent; when in use
Figure DEST_PATH_IMAGE082
To representXVariations of (2)YThe reverse changes of the two are completely consistent; when in use
Figure 914617DEST_PATH_IMAGE083
The correlation between the two cannot be judged; suppose thatXAndYthe Copula function of
Figure DEST_PATH_IMAGE084
Then Kendall' s
Figure 816845DEST_PATH_IMAGE074
The relationship with the Copula function is determined by the following equation,
Figure 877205DEST_PATH_IMAGE085
，
after introducing the integral, can be obtained
Figure DEST_PATH_IMAGE086
，
The following transformation is constructed,
Figure 430546DEST_PATH_IMAGE087
；
jacobi matrix transformed therein
Figure DEST_PATH_IMAGE088
Wherein
Figure 629577DEST_PATH_IMAGE089
；
2 is re-integrated into 1, wherein the integration region is the region given by the Copula function,
Figure DEST_PATH_IMAGE090
is an arbitrary generator of the Copula function,
Figure 737211DEST_PATH_IMAGE091
i.e. for arbitrary functions
Figure DEST_PATH_IMAGE092
If, if
Figure 601261DEST_PATH_IMAGE093
Exists in an inverse function of
Figure 494262DEST_PATH_IMAGE093
Copula function as generator, its Kendall' s
Figure DEST_PATH_IMAGE094
The parameters must have the following form:
Figure 316725DEST_PATH_IMAGE095
，
whereinAAndBis a determined constant;
in the second aspect, an optimal Copula function selection method based on a maximum likelihood criterion is completed, basic connection between different dimensions of multi-source heterogeneous data is established, and further basic mapping from multi-source heterogeneous data vectors to a high-dimensional probability space is given;
based on the edge distribution of single sensor data and the related information of the data, a family of Copula functions can be generated by using a Copula function structure, and the optimal Copula function for better describing the related relation of multi-dimensional data is selected from the Copula functions based on the maximum likelihood criterion;
is provided with
Figure DEST_PATH_IMAGE096
Is the generated Copula function family,
Figure 380496DEST_PATH_IMAGE097
is a training data set, then
Figure DEST_PATH_IMAGE098
，
Figure 932393DEST_PATH_IMAGE099
Basic connection among different dimensions of the multivariate heterogeneous data is established, and the multivariate heterogeneous data is naturally mapped to a high-dimensional probability space to serve as a basis for establishing a full-dimensional signal space.
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