CN113902056B - Multidimensional heterogeneous information fusion identification method based on Copula theory - Google Patents
Multidimensional heterogeneous information fusion identification method based on Copula theory Download PDFInfo
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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
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 stepThe data space of the individual sensors being the sample spaceOn which is defined as a set of eventsAlgebraAnd measure of probabilityGenerating a space of probability measuresWherein(ii) a This is achieved byThe 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:
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;
shaft: in the vertical transverse symmetrical plane of the satellite motion direction, perpendicular toThe axis points to the outer side of the satellite orbit and is positive;
shaft: and the aboveShaft andthe 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 systemIs transformed to a coordinate system through rotationThe transformation matrix for coordinate system rotation can be obtained as follows:
secondly, translating a coordinate system;
known coordinate systemOrigin of (2)In a coordinate systemHas the coordinates ofThen coordinate systemOne point inIn a coordinate systemCoordinates of (5)Comprises the following steps:
further, in step S2, the full-dimensional signal space is constructed as follows:
in probability theory, a set of eventsAn element in (1) is called a random event, and acts asIs a specific member of (a) a group,referred to as inevitable events; definition ofOnReal measurable function, i.e. random variable(ii) a Based onThe distribution of (A) can define a measurable spaceCorresponding measure of probability;
Constructing a probabilistic measure space for single sensor dataIs to establish random variablesAnd estimatingThe key technology of this part of the content is the following two points:
WhereinThe representation of the real number field is performed,is shown inAbove Borel consisting of Borel measurable setsAlgebraic scaleIs composed ofToMeasurable mappings of (1), i.e. random variables;
is defined inThe random variables above are not unique, all that isThe mapping satisfying the above conditions isThe random variables above, so different random variables should be constructed as required;
(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 spaceInThe number of elements of (a) is,mapping it into a set of real numbers, i.e. fromThe sample observations of (a); will be estimated based on sample observations using goodness of fit testsThe 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;
If it is notIs a continuous unary distribution function ofThen, thenIs an edge distribution function ofA multivariate distribution function of (a);
order toA joint cumulative distribution function for one dimensional variable, wherein the edge cumulative distribution function for each variable is denoted asThen there is oneDimension Copula functionSo that
If the edge cumulates the distribution functionIs continuous, then the Copula functionIs unique; copula functionOnly on each sideThe function value domain of the edge cumulative distribution is uniquely determined;
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 withIs a positive definite matrix and the matrix is a negative definite matrix,,so as to makeThe multivariate normal distribution function of the covariance matrix is as follows:
(2) a multivariate Archimedean Copula function;
is provided withContinuously and strictly increasingTo do so byTo generate a primitive, a multivariate Archimedean Copula function can be constructed
kendall's as a generator for a specific Archimedean Copula functionAn expression of consistent relevance; gumbel type generatorIn the Copula function thereof
Kendall's describing variable dependenciesThe parameters are calculated as(ii) a Clayton type, generatorIn the Copula function thereof
Kendall's The parameter value is between-1 and 1; when in useTo representXVariations of (2)YThe change of the voltage is completely consistent; when in useTo representXVariations of (2)YThe reverse changes of the two are completely consistent; when in useThe correlation between the two cannot be judged; suppose thatXAndYthe Copula function ofThen Kendall' sThe relationship with the Copula function is determined by the following equation,
after introducing the integral, can be obtained
The following transformation is constructed,
jacobi matrix transformed therein
2 is re-integrated into 1, wherein the integration region is the region given by the Copula function,is an arbitrary generator of the Copula function,
i.e. for arbitrary functionsIf, ifExists in an inverse function ofCopula function as generator, its Kendall' sThe parameters must have the following form:
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;
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 signalThe 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 spaceCan be fully expressed, and thus the state spaceA 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.
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;
shaft: in the vertical transverse symmetrical plane of the satellite motion direction, perpendicular toThe axis points to the outer side of the satellite orbit and is positive;
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 systemIs transformed to a coordinate system through rotationAn 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:
secondly, translating a coordinate system;
known coordinate systemOrigin of (2)In a coordinate systemHas the coordinates ofThen coordinate systemOne point inIn a coordinate systemCoordinates of (5)Comprises the following steps:
(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 firstData space composition of individual sensorsIs a sample spaceOn which is defined as a set of eventsAlgebraAnd measure of probabilityGenerating a space of probability measuresWherein. This is achieved byThe 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 eventsAn element in (1) is called a random event, and acts asIs a specific member of (a) a group,referred to as inevitable events; definition ofOnReal measurable function, i.e. random variable. Based onThe distribution of (A) can define a measurable spaceCorresponding measure of probability。
As shown in FIG. 3, a space of probability measures is constructed for a single sensor dataIs to establish random variablesAnd estimatingThe key technology of this part of the content is the following two points:
WhereinThe representation of the real number field is performed,is shown inAbove Borel consisting of Borel measurable setsAlgebraic scaleIs composed ofToA measurable mapping of (a), i.e. a random variable.
It will be readily apparent that the definitions areThe random variables are not unique, and all the mappings satisfying the above conditions areRandom variable of (2) and is thus in practiceDifferent random variables should be constructed according to requirements in application。
(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 spaceInThe number of elements of (a) is,mapping it into a set of real numbers, i.e. fromThe sample observations of (1). Will be estimated based on sample observations using goodness of fit testsThe 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:test sumAnd (6) checking.
the inspection method is based on the totalWhen 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 ofWhen the overall distribution is tested by the test method, the original hypothesis is firstly proposed:
(ii) a WhereinAs a wholeThe distribution function of (a) is determined,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 useHypothesis testing by inspection methodWhen is inThe 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.
b) Fall intoBetween cellsThe number of sample values of (A) is recorded asCalled the measured frequency, the sum of all measured frequenciesEqual to sample capacity;
c) From the assumed theoretical distribution, a population can be calculatedFall within eachProbability of (2)Is thusIs just falling intoThe theoretical frequency of the sample values of (1);
d)the magnitude of the difference between the empirical distribution and the theoretical distribution is marked.The following statistics were introduced to represent the difference between the empirical distribution and the theoretical distribution:
e) current hypothesisTheoretical frequency at the time of establishmentAnd frequency of actual measurementShould be in close proximity, i.e.Should be small, therebyShould also be small otherwise it cannot be consideredIs established, soShould be in the range of,From the level of significanceAnd (4) determining.
if the theoretical distribution in the hypothesisHas been completely given, thenTime of day statisticsIs asymptotically distributedOf one degree of freedomDistributing; if distribution of theoryTherein is provided withThe unknown parameters are replaced by corresponding estimators, whenTime of day statisticsIs asymptotically distributedOf one degree of freedomAnd (4) distribution.
According to this theorem, for a given level of significanceAccording toDistribution table available thresholdSo that
The rejection zone is thus obtained:
If based on the given sample valueCalculate resultant statisticsIf 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.
The theorem is thatDerived when infinitely increased, and thus in use, attention is paidIs large enough andthese two conditions are not too small. Generally required in practiceAndotherwise, the intervals should be appropriately merged so thatThis requirement is met.
foregoing introducesInspection of the wholeWhether discrete or continuous, whether discrete or continuousIt 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 assumptionIf this is not true, it is still possible to:
i.e. it is possible to accept unreal original hypotheses。Inspection is overThis 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).
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 ofThe test is more effective. However, when the observed data substantially follows a normal distribution, thenK-STested not to haveThe assay is sensitive or valid.
One, single sampleK-SChecking;
the original hypothesis and the alternative hypothesis are:
whereinIs a specified one-dimensional continuous distribution function,as a wholeThe distribution function of (2).
The following limiting distribution:
When in useWhen the state is not satisfied,there is a tendency to be large. Therefore, the temperature of the molten metal is controlled,has a rejection region of,From the level of significanceIs determined for a givenFromIs defined as
Namely, it is
According toDistributed fractional digit tabulationSo thatTherefore, it is. Whereby the rejection region is
Single sampleK-SThe specific steps of the test are as follows:
c) Calculating a theoretical distribution functionAt each oneThe value of the point, and the statisticValue of (A)
d) Given level of significanceThe threshold value of the rejection region is obtainedWhen is coming into contact withWhen the temperature of the water is higher than the set temperature,this can be approximated by the following table.
e) And (3) judging: if it isIf so, the original hypothesis is rejected(ii) a If it isThe 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,Are respectively the wholeAnd the wholeThe distribution function of (a) is determined,as a wholeThe sample of (a) is selected,as a wholeAnd the two samples are independent of each other. Consider the following hypothesis testing problem:
When in use,In the case of a continuous distribution function, ifIf true, then statisticThe limit distribution is as follows:
because whenWhen the state is not satisfied,has a great tendency, thereforeThe reject domain of (a) is:
whereinDependent on the level of significanceWhen is coming into contact withAfter being given, the following formula
Determining. From the Schmilnoff test Critical value Table. When in useWhen the temperature of the water is higher than the set temperature,this can be approximated by the following table.
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.
Obviously, ifIs a continuous unary distribution function ofThen, thenIs an edge distribution function ofThe multivariate distribution function of (1).
(existence theorem) orderA joint cumulative distribution function for one dimensional variable, wherein the edge cumulative distribution function for each variable is denoted asThen there is oneDimension Copula functionSo that
If the edge cumulates the distribution functionIs continuous, then the Copula functionIs unique. Otherwise, Copula functionThe function value of the distribution is accumulated only in the region of each edgeIs uniquely determined.
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 withIs a positive definite matrix and the matrix is a negative definite matrix,,so as to makeThe multivariate normal distribution function of the covariance matrix is as follows:
(2) Multivariate Archimedean Copula function
Is provided withContinuously and strictly increasing in number, withTo generate a primitive, a multivariate Archimedean Copula function can be constructed
Kendall's are given by the existing theory aiming at the specific generating element of Archimedean Copula functionExpression of consistent correlations. Gumbel type generator as mainstreamIn the Copula function thereof
Kendall's describing variable dependenciesThe parameters are calculated as(ii) a Clayton type, generatorIn the Copula function thereof
Note Kendall' sThe parameter can measure the consistency degree of the change, and the value is between-1 and 1. When in useTo representXVariations of (2)YThe change of the voltage is completely consistent; when in useTo representXVariations of (2)YThe reverse changes of the two are completely consistent; when in useIt is impossible to determine whether there is a correlation between the two. Suppose thatXAndYthe Copula function ofThen Kendall' sThe relationship with the Copula function is determined by the following equation,
after introducing the integral, can be obtained
The following transformation is constructed,
jacobi matrix transformed therein
2 is re-integrated into 1, wherein the integration region is the region given by the Copula function,is an arbitrary generator of the Copula function,
furthermore, a conclusion can be drawn that for any functionIf, ifExists in an inverse function ofCopula function as generator, its Kendall' sThe parameters must have the following form:
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.
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
(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
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 stepThe data space of the individual sensors being the sample spaceOn which is fixedDefined as a set of eventsAlgebraAnd measure of probabilityGenerating a space of probability measuresWherein(ii) a This is achieved byThe 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:
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;
shaft: in the vertical transverse symmetrical plane of the satellite motion direction, perpendicular toThe axis points to the outer side of the satellite orbit and is positive;
shaft: and the aboveShaft andthe 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 systemIs transformed to a coordinate system through rotationThe transformation matrix for coordinate system rotation can be obtained as follows:
secondly, translating a coordinate system;
known coordinate systemOrigin of (2)In a coordinate systemHas the coordinates ofThen coordinate systemOne point inIn a coordinate systemCoordinates of (5)Comprises the following steps:
in step S2, the full-dimensional signal space is constructed as follows:
in probability theory, a set of eventsAn element in (1) is called a random event, and acts asIs a specific member of (a) a group,referred to as inevitable events; definition ofOnReal measurable function, i.e. random variable(ii) a Based onThe distribution of (A) can define a measurable spaceCorresponding measure of probability;
Constructing a probabilistic measure space for single sensor dataIs to establish random variablesAnd estimatingThe key technology of this part of the content is the following two points:
WhereinThe representation of the real number field is performed,is shown inAbove Borel consisting of Borel measurable setsAlgebraic scaleIs composed ofToMeasurable mappings of (1), i.e. random variables;
is defined inThe random variables are not unique, and all the mappings satisfying the above conditions areThe random variables above, so different random variables should be constructed as required;
(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 spaceInThe number of elements of (a) is,mapping it into a set of real numbers, i.e. fromThe sample observations of (a); will be estimated based on sample observations using goodness of fit testsA 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;
If it is notIs a continuous unary distribution function ofThen, thenIs an edge distribution function ofA multivariate distribution function of (a);
order toA joint cumulative distribution function for one dimensional variable, wherein the edge cumulative distribution function for each variable is denoted asThen there is oneDimension Copula functionSo that
If the edge cumulates the distribution functionIs continuous, then the Copula functionIs unique; copula functionThe distribution function value is only determined in the cumulative distribution function value domain of each edge;
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 withIs a positive definite matrix and the matrix is a negative definite matrix,,so as to makeThe multivariate normal distribution function of the covariance matrix is as follows:
(2) a multivariate Archimedean Copula function;
is provided withContinuously and strictly increasing in number, withTo generate a primitive, a multivariate Archimedean Copula function can be constructed
kendall's as a generator for a specific Archimedean Copula functionAn expression of consistent relevance; gumbel type generatorIn the Copula function thereof
Kendall's describing variable dependenciesThe parameters are calculated as(ii) a Clayton type, generatorIn the Copula function thereof
Kendall's The parameter value is between-1 and 1; when in useTo representXVariations of (2)YThe change of the voltage is completely consistent; when in useTo representXVariations of (2)YThe reverse changes of the two are completely consistent; when in useThe correlation between the two cannot be judged; suppose thatXAndYthe Copula function ofThen Kendall' sThe relationship with the Copula function is determined by the following equation,
after introducing the integral, can be obtained
The following transformation is constructed,
jacobi matrix transformed therein
2 is re-integrated into 1, wherein the integration region is the region given by the Copula function,is an arbitrary generator of the Copula function,
i.e. for arbitrary functionsIf, ifExists in an inverse function ofCopula function as generator, its Kendall' sThe parameters must have the following form:
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;
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