CN111709438A - Heterogeneous sensor information fusion method - Google Patents

Heterogeneous sensor information fusion method Download PDF

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CN111709438A
CN111709438A CN202010356456.7A CN202010356456A CN111709438A CN 111709438 A CN111709438 A CN 111709438A CN 202010356456 A CN202010356456 A CN 202010356456A CN 111709438 A CN111709438 A CN 111709438A
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陆科林
符启恩
薛磊
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Nanjing Yunzhikong Industrial Technology Research Institute Co ltd
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Abstract

The invention discloses a heterogeneous sensor information fusion method which comprises a local estimation part and a fusion estimation part. Each local sensor calculates pseudo-measures, constitutes a local measure lineage, and obtains a generalized covariance intersection of local estimates. In the fusion estimation part, based on Sklar's theorem, a Copula function representing the dependency relationship between the modes is used for estimating the correlation relationship between the random variables of different sensors; optimizing a correlation coefficient of a Copula function according to a minimum resolution information criterion by comparing Kullback-Leibler divergence between fusion estimation and local estimation; carrying out importance sampling by utilizing a generalized covariance intersection so as to improve the calculation efficiency, and constructing a Gaussian approximation of fusion density by utilizing kernel density estimation; and recursively updating the fusion estimation in a layered mode to realize fusion of any number of heterogeneous sensors. The invention reduces the requirements on the communication rate of the local sensor and the correlation calculation.

Description

Heterogeneous sensor information fusion method
Technical Field
The invention relates to the technical field of data fusion, in particular to a heterogeneous sensor information fusion method.
Background
Distributed state estimation of a dynamic system is an important technology in the field of digital signal processing, and is widely applied to aspects of cooperative target tracking, distributed formation of space telescopes, remote environment monitoring and the like. At present, the development of a data fusion technology of a distributed estimation system is greatly promoted by the rapid development of wireless sensor hardware with advanced sensing, computing and communication capabilities. The sensor fusion method provides a larger sensing range than a single sensor by expanding the geographical range and improving the filtering accuracy.
A distributed tracking method is provided in the Comparison of dual-sensor tracking methods Based on State Vector Fusion And Measurement Fusion, which is described in the IEEE Aerospace And Electronic Systems Collection (J Roecker, C McGillem.' Comparison of Two-sensor tracking methods Based on State Vector Fusion, IEEEtransactions on Aerospace And Electronic Systems,1988,24:447-449.), And is characterized in that: the observed quantities from different sensors are directly combined in an augmentation mode, and then a standard Kalman filtering method based on a centralized measurement model can be used for estimating the system state at a fusion node. The centralized measurement fusion method realizes the optimal estimation performance based on the minimum mean square error. However, the method of transmitting measurement data from the sensors to the fusion node is not energy efficient due to some practical constraints, such as power constraints of the sensors and bandwidth constraints of the wireless communication.
Compared with the measurement fusion structure, the track-to-track fusion structure has the advantages of reducing the bandwidth requirement and improving the reliability. For example, in "a Solution to the problem of Track-to-Track fusion at An Arbitrary Communication rate", IEEE Aerospace and electronics Systems Collection (F Govars, W Koch.' An Exact Solution to Track-to-Track-fusion at architecture Communication Rates, IEEE Transactions on An aeronautical and electronic Systems,2012,48: 2718. 2729.): in a typical track-to-track approach, each sensor corresponds to a local filter, and the local measurement data is preprocessed and then the preprocessed estimation result is transmitted to the fusion node. The fusion node re-fuses the received local estimation data to obtain a global estimation value which is more accurate than an estimation value calculated by a single sensor. Therefore, fusion algorithms that fuse local estimates in a multi-sensor system are attracting attention of many scholars due to their flexibility and power savings. However, conventional methods lack extensive consideration and study of the inherent correlation between individual local estimates.
One of the key points of the track fusion problem is to construct the internal relationships between the local estimates to be fused. Although the sensor measurements are generally assumed to be independent of each other, the local estimates are correlated due to the common process measurement noise model. Ignoring this correlation term may result in inconsistent fusion results and even filter divergence.
For The inconsistency, The influence of general process Noise on The Covariance of The dual-sensor fusion track is reported in The IEEE aviation and Electronic Systems, namely, IEEE Transactions on Aero-and Electronic Systems, and a single-scan track fusion algorithm is provided by using a cross Covariance matrix to reconstruct an accurate correlation term between local tracks and using a static linear estimation model on The basis of an experimental filtering system model. Although the fusion algorithm is optimal in the maximum likelihood sense, it is not practical in practice due to the complexity and computational difficulty of the cross covariance matrix required in the fusion process. Second, this method of cross covariance complete reconstruction is inefficient in transmission because it requires full rate transmission of the local kalman gain for each sensor. Moreover, the early communication between the fusion node and the local sensor further increases the complexity of the internal relationship between the local estimation values, so that the precise relationship of the related items becomes difficult to construct. Therefore, regardless of the intrinsic relationship model to be constructed, there are a number of suboptimal robust trajectory fusion algorithms. Typically, as a Non-divergent estimation algorithm with Unknown Correlations, The covariance intersection algorithm is given In The American Conference Of controls theory set (S J Julier, J K Uhlmann. 'A Non-divergent estimation algorithm In The Presence Of The Presence Of Unknown Correlations' In Proceedings Of The American Control Conference, 1997), which yields convex combinations Of locally estimated means and covariances with Unknown Correlations.
In recent studies, In order to reduce the conservatism of the covariance intersection algorithm, the "fused ellipsoid method Comparative Analysis of Distributed data problem" In the twelfth set of International Conference papers for Distributed data Management and dissemination (M a Bakr, slide. 'comprehensive Analysis of interactive Methods for Distributed data fusion'. In Proceedings of the 12th International Conference on unavailability information Management and Communication, Langkawi, Malaysia, 2018) proposes a method for obtaining public information In the maximized local estimation by using the ellipsoid intersection method and the inverse covariance intersection method by introducing additional parameters. The performance of these intersection-based fusion algorithms is still limited due to the omission of the internal relationships between the local tracks.
New sensor fusion systems require different sensors to increase the diversity of information, where the observation model used by the local sensors may be different. For the problem of trajectory fusion of homogeneous sensors, cross covariance terms due to common process noise have been theoretically established. However, existing sensor fusion methods rely on known correlations, so correlation data from different sources cannot be combined in an optimal manner, and the results of these suboptimal fusion algorithms are conservative and less accurate to estimate. There is currently no general modeling method to construct the joint probability density between the inter-modal dependency structure and the observed values of statistically relevant sensors.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a heterogeneous sensor information fusion method with high fusion degree and estimation accuracy.
The technical scheme is as follows: the invention discloses a heterogeneous sensor information fusion method, which comprises the following steps:
(1) calculating local estimation of a local track according to local measurement historical data of each local sensor;
(2) estimating the correlation between any two sensors based on a Copula theory and Bayesian probabilistic inference, and obtaining an original fusion estimation of a local flight path by using a Copula function;
(3) obtaining an optimal original fusion estimation result between the two sensors by comparing Kullback-Leibler divergence between original fusion estimation and local estimation and selecting an optimal Copula function correlation coefficient according to a minimum resolution information criterion;
(4) obtaining generalized covariance intersection GCI of local estimation and using the GCI as importance density, performing related importance sampling on the optimal original fusion estimation to obtain a uniform weighted sample, and constructing Gaussian approximation of the uniform weighted sample by using kernel density estimation to obtain a local fusion estimation result between two sensors;
(5) and the fusion nodes sequentially fuse the local fusion estimation results and send the obtained fusion flight path back to each local sensor.
Further, the step (1) includes:
obtaining historical data of each sensor, and calculating false measurement of the ith sensor
Figure BDA0002473625570000031
Forming a local measurement pedigree to obtain local estimation of a local flight path; wherein i is the sensor number, k is the time series number,
Figure BDA0002473625570000032
representing the measurement taken by the ith sensor at step k.
Further, the step (2) includes:
(21) based on Copula theory and Bayesian probabilistic reasoning, the conditional independence of local observation data between any two sensors is constructed:
Figure BDA0002473625570000033
wherein X is the system state;
(22) based on Sklar's theorem, a Copula function representing the dependency relationship between the modes is used to estimate the correlation relationship between random variables of different sensors, and the original fusion estimation of the local flight path is obtained:
Figure BDA0002473625570000041
Figure BDA0002473625570000042
wherein c (·,. cndot.) represents a Copula function,
Figure BDA0002473625570000043
f (X) represents a multidimensional distribution function of the variable X.
Further, the step (3) includes:
(31) selecting a Copula function:
Figure BDA0002473625570000044
wherein,
Figure BDA0002473625570000045
ρ ∈ (-1, 1) represents the Copula function correlation coefficient, Φ (·) is the cumulative distribution function of the standard gaussian distribution;
(32) define Kullback-Leibler divergence:
Figure BDA0002473625570000046
wherein p is1、p2Two probability density functions are respectively provided;
(33) defining the Copula function correlation coefficient optimization index as:
Figure BDA0002473625570000047
(34) selecting an optimal Copula function correlation coefficient rho according to the following minimum resolution information criterion*：
Figure BDA0002473625570000048
(35) According to rho*And calculating an optimal Copula function to obtain a local track fusion estimation result between the two sensors.
Further, the step (4) includes:
(41) generalized covariance intersection with local estimation using Monte Carlo significance sampling
Figure BDA0002473625570000049
As the importance density, and the correlation importance sampling is performed. Extracting a small number of original weighted sample sets from the local estimate of the desired fusion
Figure BDA00024736255700000410
Representing N sampled from the importance densities g (X)sA sample, wherein
Figure BDA00024736255700000411
Denotes the importance density, w ∈ (0, 1) denotes the fusion coefficient;
(42) and obtaining a Gaussian approximation of the fusion density by using kernel density estimation to obtain a local fusion estimation result:
Figure BDA0002473625570000051
wherein d is the dimension of the vector X, K (·, h) is the kernel function, h is the kernel function bandwidth,
Figure BDA0002473625570000052
are uniformly weighted samples obtained from systematic resampling of the original weighted samples. In the present method, a normal density is used as a kernel function.
Further, the step (5) further comprises: and (4) sequentially fusing local fusion estimation results of the sensors in a sequential mode according to the steps (1) to (4), synthesizing a fusion track, and sending back each local sensor.
Has the advantages that: the heterogeneous sensor information fusion method provided by the invention has good heterogeneous sensor fusion estimation performance and stronger robustness; moreover, the difficulty of fusion density calculation is reduced, and the calculation speed is accelerated. By introducing a hierarchical structure, the local estimates are fused in a sequential manner by the above-mentioned fusion steps, so that it can contain more sensors. Therefore, the method has expandability and can process any number of heterogeneous sensors.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a process diagram for parallel implementation of Copula function correlation coefficient optimization algorithm;
FIG. 3 is a process diagram of a kernel density estimation algorithm;
FIG. 4 is a flow chart of layered expansion of a sensor fusion system;
FIG. 5 is a graph comparing the mean square error of the position of the CI at full rate in accordance with the method of the present invention;
FIG. 6 is a plot of the mean square error of the position of the CI at rate 1/2 in accordance with the method of the present invention;
FIG. 7 is a plot comparing the mean square error of the location of the CI at rate 1/4 in accordance with the method of the present invention;
FIG. 8 is a graph comparing the mean square error of the position of the CI and the method of the present invention at different sensor counts.
Detailed Description
The technical scheme of the invention is further described in the following by combining the attached drawings and the detailed description.
For a distributed estimation system with a plurality of nodes, the sensor fusion system is composed of a plurality of local sensors and a plurality of fusion nodes. The information fusion method of the heterogeneous sensor comprises two parts of local estimation and fusion estimation, as shown in figure 1, wherein each local sensor estimates the state of a local system according to the observed value of the local sensor, then, the local estimation is fused into a global estimation result at a fusion node in a hierarchical recursive mode, and a fusion track is sent back to each local sensor to improve the performance.
In the local estimation section, pseudo-measures are calculated from each local sensor, constituting a local measurement lineage. Further, since the fusion density cannot be calculated in the parameterized form, the fusion result of the locally estimated generalized covariance intersection is obtained as the importance density, and the correlation importance sampling is performed to improve the calculation efficiency. Finally, the result constructs an original sample set.
In the fusion estimation part, firstly, a mathematical basis based on Copula theory and Bayesian probabilistic reasoning is deduced, a mathematical formula about local observation independence is constructed, and a Copula function representing the dependence relationship among the modes is used for estimating the correlation relationship among random variables of different sensors based on Sklar's theorem. In addition, the correlation coefficient of the Copula function is optimized according to the minimum resolution information criterion by comparing the Kullback-Leibler divergence between the fusion estimation and the local estimation. And finally, performing system resampling on the original weighted sample to obtain a uniform weighted sample, and constructing Gaussian approximation of fusion density by using kernel density estimation.
The method specifically comprises the following steps:
(1) local estimation
Obtaining historical data of each sensor to obtain a pseudo measurement of the ith sensor
Figure BDA0002473625570000061
(ii) make up a local measurement lineage; wherein i is the sensor number, k is the time series number,
Figure BDA0002473625570000062
representing the measurement taken by the ith sensor at step k.
(2) Raw fusion estimation
(21) Based on a Copula function representing the dependency relationship between the modalities and Bayesian probabilistic reasoning, the conditional independence of local observation data between any two sensors is constructed to estimate the correlation relationship between random variables of different sensors:
Figure BDA0002473625570000063
wherein X is the system state;
(22) based on Sklar's theorem, a Copula function representing the dependency relationship between the modes is used to estimate the correlation relationship between random variables of different sensors, and the original fusion estimation of the local flight path is obtained:
Figure BDA0002473625570000064
Figure BDA0002473625570000065
wherein X is the system state, c (-) represents the Copula density function,
Figure BDA0002473625570000066
Figure BDA0002473625570000067
f (X) represents a multidimensional distribution function of the variable X.
(3) Optimizing fusion estimation
(31) The Copula function of the following form is used in the method:
Figure BDA0002473625570000071
wherein,
Figure BDA0002473625570000072
ρ ∈ (-1, 1) represents the correlation coefficient to be optimized, and Φ (-) is the cumulative distribution function of the standard gaussian distribution.
(32) Defining the Kullback-Leibler divergence of the information gain obtained after updating the probability density function:
Figure BDA0002473625570000073
wherein p is1、p2Two probability density functions, respectively.
(33) Defining the Copula function correlation coefficient optimization index as:
Figure BDA0002473625570000074
rho is a parameter to be optimized in the Copula function, and optimization is carried out by taking values of M possible coefficients
Figure BDA0002473625570000075
Using a grid search.
When the correlation coefficient satisfies the cost function J (p) minimum for Kullback-Leibler divergence, i.e. the
Figure BDA0002473625570000076
The Copula function can get a consistent result, which is consistent with the minimum resolution information criterion. Therefore, by comparing the Kullback-Leibler divergence between the fusion estimate and the local estimate, the correlation coefficient of the Copula function is optimized according to the minimum resolution information criterion and the computation time is reduced, as shown in fig. 2. And obtaining an optimal track original fusion estimation result between the two sensors based on the optimal Copula function.
(4) Nuclear density estimation
(41) Generalized covariance intersection with local estimation using Monte Carlo significance sampling
Figure BDA0002473625570000077
As the importance density, and the correlation importance sampling is performed, as in fig. 3. Extracting a small number of original weighted sample sets from the local estimate of the desired fusion
Figure BDA0002473625570000078
Representing N sampled from the importance densities g (X)sSamples, where the importance density is expressed as:
Figure BDA0002473625570000079
w ∈ (0, 1) represents a fusion coefficient;
(42) and obtaining a Gaussian approximation of the fusion density by using kernel density estimation to obtain a local fusion estimation result:
Figure BDA00024736255700000710
wherein d is the dimension of the vector X, K (·, h) is the kernel function, h is the kernel function bandwidth,
Figure BDA0002473625570000081
are uniformly weighted samples obtained from systematic resampling of the original weighted samples. In the present method, a normal density is used as a kernel function.
(5) Structure layered structure
When the number of local sensors is greater than two, a hierarchical structure is introduced, as in fig. 4, to fuse the method proposed by the invention (CF below) with a plurality of local estimates in a sequential manner, so that it can contain more sensors. Assume that there are three sensors whose local tracks are SiI is numbered 1,2,3, the estimates of the first two sensors are first fused, i.e., S1And S2To obtain an initial fusion track F12. Thereafter, the local track S of the third sensor is used3Fusion is performed.
First, an information fusion system used in the scenario is configured with one fusion node and two heterogeneous sensors. When the fusion process is completed, each sensor gets a feedback of the fusion estimate from the fusion node, and then replaces its local track with the fusion estimate. Under this fusion setting, when the sensor communicates with the fusion node at a non-full rate, the measurement is correlated to the previous observation state due to the presence of process noise. Comparing the method of the present invention with the cross Covariance (CI) method, fig. 5-7 compare the position mean square errors of CF and CI at full rate, 1/2 rate, 1/4 rate, respectively. As seen in fig. 5, the estimation accuracy between CF and CI is very close in the full rate case. However, if the communication frequency is lowered to reduce the communication load, the CI method may degrade in performance as shown in fig. 6 and 7 because it explains the unknown correlation between the local tracks in a conservative manner. Meanwhile, with the proposed CF method, the result shows that it can guarantee consistent estimation accuracy regardless of the communication frequency. The reason for this is that Copula's equation provides a reliable mechanism for estimating unknown correlations between local sensor data. The extended fusion system was simulated and the performance of sequential fusion systems with different numbers of sensors was analyzed.
As shown in fig. 8, as the number of sensors increases, the RMSE offset remains above 0, so the proposed CF consistently performs better than the CI. In addition, as can be seen from fig. 8, as the number of local tracks to be fused increases, the difference of the fusion accuracy between CF and CI becomes larger. The reason is that as more and more tracks are fused in the fusion process, the complexity of the correlation between the estimates to be fused is increasing. While CI does not require precise correlation between sensor data, it preserves the robustness of the estimation at the expense of a more conservative fusion approach. Meanwhile, for the proposed CF, it employs a Copula function to represent the inter-modal correlation of local sensor data, which helps to optimize the combination of local estimates by considering the correlation between them.

Claims (6)

1. A heterogeneous sensor information fusion method; the method is characterized by comprising the following steps:
(1) calculating local estimation of a local track according to local measurement historical data of each local sensor;
(2) estimating the correlation between any two sensors based on a Copula theory and Bayesian probabilistic inference, and obtaining an original fusion estimation of a local flight path by using a Copula function;
(3) the Kullback-Leibler divergence between the original fusion estimation and the local estimation is compared, and the optimal Copula function correlation coefficient is selected according to the minimum resolution information criterion to obtain the local track fusion estimation result between the two sensors;
(4) obtaining a fusion result of locally estimated generalized covariance intersection GCI as an importance density, executing related importance sampling, constructing an original sampling set, performing system resampling on the original sampling set to obtain a uniform weighted sample, and constructing Gaussian approximation of a local track fusion estimation result by using kernel density estimation to obtain a local fusion estimation result;
(5) and the fusion nodes sequentially fuse the local fusion estimation results and send the obtained fusion flight path back to each local sensor.
2. The heterogeneous sensor information fusion method according to claim 1, wherein the step (1) comprises:
obtaining historical data of each sensor, and calculating false measurement of the ith sensor
Figure FDA0002473625560000011
Forming a local measurement pedigree to obtain local estimation of a local flight path; wherein i is the sensor number, k is the time series number,
Figure FDA0002473625560000012
representing the measurement taken by the ith sensor at step k.
3. The heterogeneous sensor information fusion method according to claim 1, wherein the step (2) comprises:
(21) based on Copula theory and Bayesian probabilistic reasoning, the conditional independence of local observation data between any two sensors is constructed:
Figure FDA0002473625560000013
wherein X is the system state;
(22) based on Sklar's theorem, a Copula function representing the dependency relationship between the modes is used to estimate the correlation relationship between random variables of different sensors, and the original fusion estimation of the local flight path is obtained:
Figure FDA0002473625560000014
wherein c (·,. cndot.) represents a Copula function,
Figure FDA0002473625560000015
f (X) represents a multidimensional distribution function of the variable X.
4. The heterogeneous sensor information fusion method according to claim 1, wherein the step (3) comprises:
(31) selecting a Copula function:
Figure FDA0002473625560000021
wherein,
Figure FDA0002473625560000022
ρ ∈ (-1, 1) represents the Copula function correlation coefficient, Φ (·) is the cumulative distribution function of the standard gaussian distribution;
(32) define Kullback-Leibler divergence:
Figure FDA0002473625560000023
wherein p is1、p2Two probability density functions are respectively provided;
(33) defining the Copula function correlation coefficient optimization index as:
Figure FDA0002473625560000024
(34) selecting an optimal Copula function correlation coefficient rho according to the following minimum resolution information criterion*：
Figure FDA0002473625560000025
(35) According to rho*And calculating an optimal Copula function to obtain a local track fusion estimation result between the two sensors.
5. The heterogeneous sensor information fusion method according to claim 1, wherein the step (4) comprises:
(41) generalized covariance intersection with local estimation using Monte Carlo significance sampling
Figure FDA0002473625560000026
As the importance density, and the correlation importance sampling is performed. Extracting a small number of original weighted sample sets from the local estimate of the desired fusion
Figure FDA0002473625560000027
Representing N sampled from the importance densities g (X)sA sample, wherein
Figure FDA0002473625560000028
Denotes the importance density, w ∈ (0, 1) denotes the fusion coefficient;
(42) and obtaining a Gaussian approximation of the fusion density by using kernel density estimation to obtain a local fusion estimation result:
Figure FDA0002473625560000029
wherein d is the dimension of the vector X, K (·, h) is the kernel function, h is the kernel function bandwidth,
Figure FDA00024736255600000210
are uniformly weighted samples obtained from systematic resampling of the original weighted samples. In the present method, a normal density is used as a kernel function.
6. The heterogeneous sensor information fusion method according to claim 1, wherein the step (5) further comprises: and (4) sequentially fusing local fusion estimation results of the sensors in a sequential mode according to the steps (1) to (4), synthesizing a fusion track, and sending back each local sensor.
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CN113902056A (en) * 2021-10-20 2022-01-07 四川大学 Multidimensional heterogeneous information fusion identification method based on Copula theory

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CN106291533A (en) * 2016-07-27 2017-01-04 电子科技大学 A kind of distributed multi-sensor blending algorithm based on AMD
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CN113902056B (en) * 2021-10-20 2022-04-19 四川大学 Multidimensional heterogeneous information fusion identification method based on Copula theory

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