In this paper,the concept of a random rough set which includes the mechanisms of numeric and non-numeric aspects of uncertain knowledge is introduced.It is proved that for any belief structure and its inducing belief ...In this paper,the concept of a random rough set which includes the mechanisms of numeric and non-numeric aspects of uncertain knowledge is introduced.It is proved that for any belief structure and its inducing belief and plausibility measures there exists a random approximation space such that the associated lower and upper probabilities are respectively the given belief and plausibility measures,and vice versa.And for a random approximation space generated from a totally random set,its inducing lower and upper probabilities are respectively a pair of necessity and possibility measures.展开更多
We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson construct...We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson constructed a class of strictly self\|similar sets and got many important results on fractal properties.Graf investigated the fractal properties of a special statistically self\|similar set. We have investigated various self\|similar sets and their probability properties and fractal properties.\;展开更多
A set is called regular if its Hausdorff dimension and upper box-counting dimension coincide. In this paper,we prove that the random self-conformal set is regular almost surely. Also we determine the dimensions for a ...A set is called regular if its Hausdorff dimension and upper box-counting dimension coincide. In this paper,we prove that the random self-conformal set is regular almost surely. Also we determine the dimensions for a class of random self-conformal sets.展开更多
First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction ...First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.展开更多
In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.
The finite set statistics provides a mathematically rig- orous single target Bayesian filter (STBF) for tracking a target that generates multiple measurements in a cluttered environment. However, the target maneuver...The finite set statistics provides a mathematically rig- orous single target Bayesian filter (STBF) for tracking a target that generates multiple measurements in a cluttered environment. However, the target maneuvers may lead to the degraded track- ing performance and even track loss when using the STBF. The multiple-model technique has been generally considered as the mainstream approach to maneuvering the target tracking. Moti- vated by the above observations, we propose the multiple-model extension of the original STBF, called MM-STBF, to accommodate the possible target maneuvering behavior. Since the derived MM- STBF involve multiple integrals with no closed form in general, a sequential Monte Carlo implementation (for generic models) and a Gaussian mixture implementation (for linear Gaussian models) are presented. Simulation results show that the proposed MM-STBF outperforms the STBF in terms of root mean squared errors of dynamic state estimates.展开更多
In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure...In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure function and the integal test of packing measure.展开更多
A novel slow-down set waveform is proposed to improve the set performance and a 1 kb phase change random access memory chip fabricated with a 13nm CMOS technology is implemented to investigate the set performance by d...A novel slow-down set waveform is proposed to improve the set performance and a 1 kb phase change random access memory chip fabricated with a 13nm CMOS technology is implemented to investigate the set performance by different set programming strategies based on this new set pulse. The amplitude difference (I1 - I2) of the set pulse is proved to be a crucial parameter for set programming. We observe and analyze the cell characteristics with different I1 - I2 by means of thermal simulations and high-resolution transmission electron microscopy, which reveal that an incomplete set programming will occur when the proposed slow-down pulse is set with an improperly high I1 - I2. This will lead to an amorphous residue in the active region. We also discuss the programming method to avoid the set performance degradations.展开更多
A systematic approach is proposed to the theme of safety,reliability and global quality of complex networks(material and immaterial)by means of special mathematical tools that allow an adequate geometric characterizat...A systematic approach is proposed to the theme of safety,reliability and global quality of complex networks(material and immaterial)by means of special mathematical tools that allow an adequate geometric characterization and study of the operation,even in the presence of multiple obstacles along the path.To that end,applying the theory of graphs to the problem under study and using a special mathematical model based on stochastic geometry,in this article we consider some regular lattices in which it is possible to schematize the elements of the network,with the fundamental cell with six,eight or 2(n+2)obstacles,calculating the probability of Laplace.In this way it is possible to measure the“degree of impedance”exerted by the anomalies along the network by the obstacles examined.The method can be extended to other regular and/or irregular geometric figures,whose union together constitutes the examined network,allowing to optimize the functioning of the complex system considered.展开更多
Abstract In this paper we investigate the quasi-shadowing property for C1 random dynamical sys-terns on their random partially hyperbolic sets. It is shown that for any pseudo orbit {xk}+∞ -∞ on a random partially ...Abstract In this paper we investigate the quasi-shadowing property for C1 random dynamical sys-terns on their random partially hyperbolic sets. It is shown that for any pseudo orbit {xk}+∞ -∞ on a random partially hyperbolic set there exists a "center" pseudo orbit {Yk}+∞ -∞ shadowing it in the sense that yk+l is obtained from the image of yk by a motion along the center direction. Moreover, when the random partially hyperbolic set has a local product structure, the above "center" pseudo orbit{yk}+∞ -∞ can be chosen such that yk+1 and the image of yk lie in their common center leaf.展开更多
<div style="text-align:justify;"> In recent years, multi-target tracking technology based on Gaussian Mixture- Probability Hypothesis Density (GM-PHD) filtering has become a hot field of information fu...<div style="text-align:justify;"> In recent years, multi-target tracking technology based on Gaussian Mixture- Probability Hypothesis Density (GM-PHD) filtering has become a hot field of information fusion research. This article outlines the generation and development of multi-target tracking methods based on GM-PHD filtering, and the principle and implementation method of GM-PHD filtering are explained, and the application status based on GM-PHD filtering is summarized, and the key issues of the development of GM-PHD filtering technology are analyzed. </div>展开更多
Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pytha...Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton’s kinetic energy E = 1/2mv<sup>2</sup> leads to Einstein’s celebrated maximal energy equation E = mc<sup>2</sup> and how in turn this can be dissected into the ordinary energy density E(O) = mc<sup>2</sup>/22 and the dark energy density E(D) = mc<sup>2</sup>(21/22) of the cosmos where m is the mass;v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and ‘tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.展开更多
This paper presents a multi-Bernoulli filter for tracking the direction of arrival(DOAs)of time-varying number of targets using sensor array.Our method operates directly on the measurements of sensor array and does no...This paper presents a multi-Bernoulli filter for tracking the direction of arrival(DOAs)of time-varying number of targets using sensor array.Our method operates directly on the measurements of sensor array and does not require any detection.Firstly,more information is reserved and compared with the after-detection measurements using a finite set of detected points.It can significantly improve the tracking performance,especially in low signal-to-noise ratio.Secondly,it inherits the advantages of the multi-Bernoulli approximation which models each of the targets individually.This allows more accurate multi-target state estimation,especially when targets cross.The proposed filter does not need clustering step and simulation results showcase the improved performance of the proposed filter.展开更多
We have studied statistically self similar measures together with statistically self similar sets in this paper.A special kind of statistically self similar measures has been constructed and a class of statisticall...We have studied statistically self similar measures together with statistically self similar sets in this paper.A special kind of statistically self similar measures has been constructed and a class of statistically self similar sets as well.展开更多
With the great development of Multi-Target Tracking(MTT)technologies,many MTT algorithms have been proposed with their own advantages and disadvantages.Due to the fact that requirements to MTT algorithms vary from the...With the great development of Multi-Target Tracking(MTT)technologies,many MTT algorithms have been proposed with their own advantages and disadvantages.Due to the fact that requirements to MTT algorithms vary from the application scenarios,performance evaluation is significant to select an appropriate MTT algorithm for the specific application scenario.In this paper,we propose a performance evaluation method on the sets of trajectories with temporal dimension specifics to compare the estimated trajectories with the true trajectories.The proposed method evaluates the estimate results of an MTT algorithm in terms of tracking accuracy,continuity and clarity.Furthermore,its computation is based on a multi-dimensional assignment problem,which is formulated as a computable form using linear programming.To enhance the influence of recent estimated states of the trajectories in the evaluation,an attention function is used to reweight the trajectory errors at different time steps.Finally,simulation results show that the proposed performance evaluation method is able to evaluate many aspects of the MTT algorithms.These evaluations are worthy for selecting suitable MTT algorithms in different application scenarios.展开更多
In this study,we provide an overview of recent advances in multisensor multitarget tracking based on the random finite set(RFS)approach.The fusion that plays a fundamental role in multisensor filtering is classified i...In this study,we provide an overview of recent advances in multisensor multitarget tracking based on the random finite set(RFS)approach.The fusion that plays a fundamental role in multisensor filtering is classified into data-level multitarget measurement fusion and estimate-level multitarget density fusion,which share and fuse local measurements and posterior densities between sensors,respectively.Important properties of each fusion rule including the optimality and sub-optimality are presented.In particulax,two robust multitarget density-averaging approaches,arithmetic-and geometric-average fusion,are addressed in detail for various RFSs.Relevant research topics and remaining challenges are highlighted.展开更多
We demonstrate a heuristic approach for optimizing the posterior density of the data association tracking algorithm via the random finite set(RFS)theory.Specifically,we propose an adjusted version of the joint probabi...We demonstrate a heuristic approach for optimizing the posterior density of the data association tracking algorithm via the random finite set(RFS)theory.Specifically,we propose an adjusted version of the joint probabilistic data association(JPDA)filter,known as the nearest-neighbor set JPDA(NNSJPDA).The target labels in all possible data association events are switched using a novel nearest-neighbor method based on the Kullback-Leibler divergence,with the goal of improving the accuracy of the marginalization.Next,the distribution of the target-label vector is considered.The transition matrix of the target-label vector can be obtained after the switching of the posterior density.This transition matrix varies with time,causing the propagation of the distribution of the target-label vector to follow a non-homogeneous Markov chain.We show that the chain is inherently doubly stochastic and deduce corresponding theorems.Through examples and simulations,the effectiveness of NNSJPDA is verified.The results can be easily generalized to other data association approaches under the same RFS framework.展开更多
The coalescence and missed detection are two key challenges in Multi-Target Tracking(MTT).To balance the tracking accuracy and real-time performance,the existing Random Finite Set(RFS)based filters are generally diffi...The coalescence and missed detection are two key challenges in Multi-Target Tracking(MTT).To balance the tracking accuracy and real-time performance,the existing Random Finite Set(RFS)based filters are generally difficult to handle the above problems simultaneously,such as the Track-Oriented marginal Multi-Bernoulli/Poisson(TOMB/P)and Measurement-Oriented marginal Multi-Bernoulli/Poisson(MOMB/P)filters.Based on the Arithmetic Average(AA)fusion rule,this paper proposes a novel fusion framework for the Poisson Multi-Bernoulli(PMB)filter,which integrates both the advantages of the TOMB/P filter in dealing with missed detection and the advantages of the MOMB/P filter in dealing with coalescence.In order to fuse the different PMB distributions,the Bernoulli components in different Multi-Bernoulli(MB)distributions are associated with each other by Kullback-Leibler Divergence(KLD)minimization.Moreover,an adaptive AA fusion rule is designed on the basis of the exponential fusion weights,which utilizes the TOMB/P and MOMB/P updates to solve these difficulties in MTT.Finally,by comparing with the TOMB/P and MOMB/P filters,the performance of the proposed filter in terms of accuracy and efficiency is demonstrated in three challenging scenarios.展开更多
It is difficult to build accurate model for measurement noise covariance in complex backgrounds. For the scenarios of unknown sensor noise variances, an adaptive multi-target tracking algorithm based on labeled random...It is difficult to build accurate model for measurement noise covariance in complex backgrounds. For the scenarios of unknown sensor noise variances, an adaptive multi-target tracking algorithm based on labeled random finite set and variational Bayesian (VB) approximation is proposed. The variational approximation technique is introduced to the labeled multi-Bernoulli (LMB) filter to jointly estimate the states of targets and sensor noise variances. Simulation results show that the proposed method can give unbiased estimation of cardinality and has better performance than the VB probability hypothesis density (VB-PHD) filter and the VB cardinality balanced multi-target multi-Bernoulli (VB-CBMeMBer) filter in harsh situations. The simulations also confirm the robustness of the proposed method against the time-varying noise variances. The computational complexity of proposed method is higher than the VB-PHD and VB-CBMeMBer in extreme cases, while the mean execution times of the three methods are close when targets are well separated.展开更多
Classical decision tree model is one of the classical machine learning models for its simplicity and effectiveness in applications. However, compared to the DT model, probability estimation trees (PETs) give a bette...Classical decision tree model is one of the classical machine learning models for its simplicity and effectiveness in applications. However, compared to the DT model, probability estimation trees (PETs) give a better estimation on class probability. In order to get a good probability estimation, we usually need large trees which are not desirable with respect to model transparency. Linguistic decision tree (LDT) is a PET model based on label semantics. Fuzzy labels are used for building the tree and each branch is associated with a probability distribution over classes. If there is no overlap between neighboring fuzzy labels, these fuzzy labels then become discrete labels and a LDT with discrete labels becomes a special case of the PET model. In this paper, two hybrid models by combining the naive Bayes classifier and PETs are proposed in order to build a model with good performance without losing too much transparency. The first model uses naive Bayes estimation given a PET, and the second model uses a set of small-sized PETs as estimators by assuming the independence between these trees. Empirical studies on discrete and fuzzy labels show that the first model outperforms the PET model at shallow depth, and the second model is equivalent to the naive Bayes and PET.展开更多
基金NationalNaturalScienceFoundationofChina (No .60373078)
文摘In this paper,the concept of a random rough set which includes the mechanisms of numeric and non-numeric aspects of uncertain knowledge is introduced.It is proved that for any belief structure and its inducing belief and plausibility measures there exists a random approximation space such that the associated lower and upper probabilities are respectively the given belief and plausibility measures,and vice versa.And for a random approximation space generated from a totally random set,its inducing lower and upper probabilities are respectively a pair of necessity and possibility measures.
文摘We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson constructed a class of strictly self\|similar sets and got many important results on fractal properties.Graf investigated the fractal properties of a special statistically self\|similar set. We have investigated various self\|similar sets and their probability properties and fractal properties.\;
文摘A set is called regular if its Hausdorff dimension and upper box-counting dimension coincide. In this paper,we prove that the random self-conformal set is regular almost surely. Also we determine the dimensions for a class of random self-conformal sets.
基金Supported by the National Natural Science Foundation of China (10371092)the Foundation of Wuhan University
文摘First of all the authors introduce the concepts of random sub-self-similar set and random shift set and then construct the random sub-self-similar set by a random shift set and a collection of statistical contraction operators.
基金supported by the National Natural Science Foundation of China(10371092)Foundation of Ningbo University(8Y0600036).
文摘In this article, the Hausdorff dimension and exact Hausdorff measure function of any random sub-self-similar set are obtained under some reasonable conditions. Several examples are given at the end.
基金supported by the National Natural Science Foundation of China (61101181)
文摘The finite set statistics provides a mathematically rig- orous single target Bayesian filter (STBF) for tracking a target that generates multiple measurements in a cluttered environment. However, the target maneuvers may lead to the degraded track- ing performance and even track loss when using the STBF. The multiple-model technique has been generally considered as the mainstream approach to maneuvering the target tracking. Moti- vated by the above observations, we propose the multiple-model extension of the original STBF, called MM-STBF, to accommodate the possible target maneuvering behavior. Since the derived MM- STBF involve multiple integrals with no closed form in general, a sequential Monte Carlo implementation (for generic models) and a Gaussian mixture implementation (for linear Gaussian models) are presented. Simulation results show that the proposed MM-STBF outperforms the STBF in terms of root mean squared errors of dynamic state estimates.
文摘In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure function and the integal test of packing measure.
基金Supported by the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No XDA09020402the National Key Basic Research Program of China under Grant Nos 2013CBA01900,2010CB934300,2011CBA00607,and 2011CB932804+2 种基金the National Integrate Circuit Research Program of China under Grant No 2009ZX02023-003the National Natural Science Foundation of China under Grant Nos 61176122,61106001,61261160500,and 61376006the Science and Technology Council of Shanghai under Grant Nos 12nm0503701,13DZ2295700,12QA1403900,and 13ZR1447200
文摘A novel slow-down set waveform is proposed to improve the set performance and a 1 kb phase change random access memory chip fabricated with a 13nm CMOS technology is implemented to investigate the set performance by different set programming strategies based on this new set pulse. The amplitude difference (I1 - I2) of the set pulse is proved to be a crucial parameter for set programming. We observe and analyze the cell characteristics with different I1 - I2 by means of thermal simulations and high-resolution transmission electron microscopy, which reveal that an incomplete set programming will occur when the proposed slow-down pulse is set with an improperly high I1 - I2. This will lead to an amorphous residue in the active region. We also discuss the programming method to avoid the set performance degradations.
文摘A systematic approach is proposed to the theme of safety,reliability and global quality of complex networks(material and immaterial)by means of special mathematical tools that allow an adequate geometric characterization and study of the operation,even in the presence of multiple obstacles along the path.To that end,applying the theory of graphs to the problem under study and using a special mathematical model based on stochastic geometry,in this article we consider some regular lattices in which it is possible to schematize the elements of the network,with the fundamental cell with six,eight or 2(n+2)obstacles,calculating the probability of Laplace.In this way it is possible to measure the“degree of impedance”exerted by the anomalies along the network by the obstacles examined.The method can be extended to other regular and/or irregular geometric figures,whose union together constitutes the examined network,allowing to optimize the functioning of the complex system considered.
基金supported by NSFC(Grant Nos.11371120 and 11771118)supported by Fundamental Research Funds for the Central University,China(Grant No.20720170004)
文摘Abstract In this paper we investigate the quasi-shadowing property for C1 random dynamical sys-terns on their random partially hyperbolic sets. It is shown that for any pseudo orbit {xk}+∞ -∞ on a random partially hyperbolic set there exists a "center" pseudo orbit {Yk}+∞ -∞ shadowing it in the sense that yk+l is obtained from the image of yk by a motion along the center direction. Moreover, when the random partially hyperbolic set has a local product structure, the above "center" pseudo orbit{yk}+∞ -∞ can be chosen such that yk+1 and the image of yk lie in their common center leaf.
文摘<div style="text-align:justify;"> In recent years, multi-target tracking technology based on Gaussian Mixture- Probability Hypothesis Density (GM-PHD) filtering has become a hot field of information fusion research. This article outlines the generation and development of multi-target tracking methods based on GM-PHD filtering, and the principle and implementation method of GM-PHD filtering are explained, and the application status based on GM-PHD filtering is summarized, and the key issues of the development of GM-PHD filtering technology are analyzed. </div>
文摘Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton’s kinetic energy E = 1/2mv<sup>2</sup> leads to Einstein’s celebrated maximal energy equation E = mc<sup>2</sup> and how in turn this can be dissected into the ordinary energy density E(O) = mc<sup>2</sup>/22 and the dark energy density E(D) = mc<sup>2</sup>(21/22) of the cosmos where m is the mass;v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and ‘tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.
文摘This paper presents a multi-Bernoulli filter for tracking the direction of arrival(DOAs)of time-varying number of targets using sensor array.Our method operates directly on the measurements of sensor array and does not require any detection.Firstly,more information is reserved and compared with the after-detection measurements using a finite set of detected points.It can significantly improve the tracking performance,especially in low signal-to-noise ratio.Secondly,it inherits the advantages of the multi-Bernoulli approximation which models each of the targets individually.This allows more accurate multi-target state estimation,especially when targets cross.The proposed filter does not need clustering step and simulation results showcase the improved performance of the proposed filter.
文摘We have studied statistically self similar measures together with statistically self similar sets in this paper.A special kind of statistically self similar measures has been constructed and a class of statistically self similar sets as well.
基金supported by the National Natural Science Foundation of China(No.62276204,No.62306222)the Natural Science Basic Research Program of Shaanxi,China(No.2023-JC-QN-0710)。
文摘With the great development of Multi-Target Tracking(MTT)technologies,many MTT algorithms have been proposed with their own advantages and disadvantages.Due to the fact that requirements to MTT algorithms vary from the application scenarios,performance evaluation is significant to select an appropriate MTT algorithm for the specific application scenario.In this paper,we propose a performance evaluation method on the sets of trajectories with temporal dimension specifics to compare the estimated trajectories with the true trajectories.The proposed method evaluates the estimate results of an MTT algorithm in terms of tracking accuracy,continuity and clarity.Furthermore,its computation is based on a multi-dimensional assignment problem,which is formulated as a computable form using linear programming.To enhance the influence of recent estimated states of the trajectories in the evaluation,an attention function is used to reweight the trajectory errors at different time steps.Finally,simulation results show that the proposed performance evaluation method is able to evaluate many aspects of the MTT algorithms.These evaluations are worthy for selecting suitable MTT algorithms in different application scenarios.
基金Project supported by the Key Laboratory Foundation of National Defence Technology,China(No.61424010306)the Joint Fund of Equipment Development and Aerospace Science and Technology,China(No.6141B0624050101)the National Natural Science Foundation of China(Nos.61901489 and 62071389)。
文摘In this study,we provide an overview of recent advances in multisensor multitarget tracking based on the random finite set(RFS)approach.The fusion that plays a fundamental role in multisensor filtering is classified into data-level multitarget measurement fusion and estimate-level multitarget density fusion,which share and fuse local measurements and posterior densities between sensors,respectively.Important properties of each fusion rule including the optimality and sub-optimality are presented.In particulax,two robust multitarget density-averaging approaches,arithmetic-and geometric-average fusion,are addressed in detail for various RFSs.Relevant research topics and remaining challenges are highlighted.
基金Project supported by the National Key Research and Development Program of China(No.2017YFB1402102)the National Natural Science Foundation of China(Nos.61907028 and 11872036)+2 种基金the Natural Science Foundation of Shaanxi Province,China(Nos.2020JQ-423,2019JQ-574,and 2019ZDLSF07-01)the Fundamental Research Funds for the Central Universities,China(No.GK201903103)the China Postdoctoral Science Foundation(No.2018M640950)。
文摘We demonstrate a heuristic approach for optimizing the posterior density of the data association tracking algorithm via the random finite set(RFS)theory.Specifically,we propose an adjusted version of the joint probabilistic data association(JPDA)filter,known as the nearest-neighbor set JPDA(NNSJPDA).The target labels in all possible data association events are switched using a novel nearest-neighbor method based on the Kullback-Leibler divergence,with the goal of improving the accuracy of the marginalization.Next,the distribution of the target-label vector is considered.The transition matrix of the target-label vector can be obtained after the switching of the posterior density.This transition matrix varies with time,causing the propagation of the distribution of the target-label vector to follow a non-homogeneous Markov chain.We show that the chain is inherently doubly stochastic and deduce corresponding theorems.Through examples and simulations,the effectiveness of NNSJPDA is verified.The results can be easily generalized to other data association approaches under the same RFS framework.
基金supported by the National Natural Science Foundation of China(No.61871301)。
文摘The coalescence and missed detection are two key challenges in Multi-Target Tracking(MTT).To balance the tracking accuracy and real-time performance,the existing Random Finite Set(RFS)based filters are generally difficult to handle the above problems simultaneously,such as the Track-Oriented marginal Multi-Bernoulli/Poisson(TOMB/P)and Measurement-Oriented marginal Multi-Bernoulli/Poisson(MOMB/P)filters.Based on the Arithmetic Average(AA)fusion rule,this paper proposes a novel fusion framework for the Poisson Multi-Bernoulli(PMB)filter,which integrates both the advantages of the TOMB/P filter in dealing with missed detection and the advantages of the MOMB/P filter in dealing with coalescence.In order to fuse the different PMB distributions,the Bernoulli components in different Multi-Bernoulli(MB)distributions are associated with each other by Kullback-Leibler Divergence(KLD)minimization.Moreover,an adaptive AA fusion rule is designed on the basis of the exponential fusion weights,which utilizes the TOMB/P and MOMB/P updates to solve these difficulties in MTT.Finally,by comparing with the TOMB/P and MOMB/P filters,the performance of the proposed filter in terms of accuracy and efficiency is demonstrated in three challenging scenarios.
基金supported by the National High Technology Research and Development Program of China (No.2014AA7014061)the National Natural Science Foundation of China (No.61501484)
文摘It is difficult to build accurate model for measurement noise covariance in complex backgrounds. For the scenarios of unknown sensor noise variances, an adaptive multi-target tracking algorithm based on labeled random finite set and variational Bayesian (VB) approximation is proposed. The variational approximation technique is introduced to the labeled multi-Bernoulli (LMB) filter to jointly estimate the states of targets and sensor noise variances. Simulation results show that the proposed method can give unbiased estimation of cardinality and has better performance than the VB probability hypothesis density (VB-PHD) filter and the VB cardinality balanced multi-target multi-Bernoulli (VB-CBMeMBer) filter in harsh situations. The simulations also confirm the robustness of the proposed method against the time-varying noise variances. The computational complexity of proposed method is higher than the VB-PHD and VB-CBMeMBer in extreme cases, while the mean execution times of the three methods are close when targets are well separated.
文摘Classical decision tree model is one of the classical machine learning models for its simplicity and effectiveness in applications. However, compared to the DT model, probability estimation trees (PETs) give a better estimation on class probability. In order to get a good probability estimation, we usually need large trees which are not desirable with respect to model transparency. Linguistic decision tree (LDT) is a PET model based on label semantics. Fuzzy labels are used for building the tree and each branch is associated with a probability distribution over classes. If there is no overlap between neighboring fuzzy labels, these fuzzy labels then become discrete labels and a LDT with discrete labels becomes a special case of the PET model. In this paper, two hybrid models by combining the naive Bayes classifier and PETs are proposed in order to build a model with good performance without losing too much transparency. The first model uses naive Bayes estimation given a PET, and the second model uses a set of small-sized PETs as estimators by assuming the independence between these trees. Empirical studies on discrete and fuzzy labels show that the first model outperforms the PET model at shallow depth, and the second model is equivalent to the naive Bayes and PET.