In this paper,a Millimeter wave(mmWave)beam tracking problem is studied in orthogonal time frequency space(OTFS)systems.Considering the nonlinearity of beamforming and the constraints of existing Kalman-filtering base...In this paper,a Millimeter wave(mmWave)beam tracking problem is studied in orthogonal time frequency space(OTFS)systems.Considering the nonlinearity of beamforming and the constraints of existing Kalman-filtering based beam tracking schemes,we propose a novel Cubature Kalman Filter(CKF)framework tracking the channel state information(CSI)to manage the challenge of highspeed channel variation in single-user moving scene for OTFS systems.Aiming for low complexity for mobile settings,this paper trains only one beam pair to track a path to maintain the reliable communication link in the analog beamforming architecture.Simulation results show that our proposed method has better tracking performance to improve the accuracy of the estimated beam angle compared with prior work.展开更多
Aiming at improving the estimation accuracy and real-time of nonlinear system with linear Gaussian sub-structure,a novel marginalized cubature Kalman filter is proposed in Bayesian estimation framework. Firstly,the ma...Aiming at improving the estimation accuracy and real-time of nonlinear system with linear Gaussian sub-structure,a novel marginalized cubature Kalman filter is proposed in Bayesian estimation framework. Firstly,the marginalized technique is adopted to model the target system dynamics with nonlinear state and linear state separately,and the two parts are estimated by cubature Kalman filter and standard Kalman filter respectively. Therefore,the linear part avoids the generation and propagation process of cubature points. Accordingly,the computational complexity is reduced.Meanwhile,the accuracy of state estimation is improved by taking the difference of nonlinear state estimation as the measurement of linear state. Furthermore,the computational complexity of marginalized cubature Kalman filter is discussed by calculating the number of floating-point operation. Finally,simulation experiments and analysis show that the proposed algorithm can improve the performance of filtering precision and real-time effectively in target tracking system.展开更多
In this paper, adaptive sensor fusion INS/GNSS is proposed to solve specific problem of non linear time variant state space estimation with measurement outliers, different algorithms are used to solve this specific pr...In this paper, adaptive sensor fusion INS/GNSS is proposed to solve specific problem of non linear time variant state space estimation with measurement outliers, different algorithms are used to solve this specific problem generally occurs in intentional and non-intentional interferences caused by other radio navigation sources, or by the GNSS receiver’s deterioration. Non linear approximation techniques such as Extended Kalman filter EKF, Sigma Point Kalman Filters such as UKF and CDKF are computed to estimate the navigation states for UAV flight control. Several comparisons are conduced and analyzed in order to compare the accuracy and the convergence of different approaches usually applied in navigation data fusion purposes. The last non linear filter algorithm developed is the Cubature Kalman Filter CKF which provides more accurate estimation with more stability in Tracking data fusion application. In this work, CKF is compared with SPKF and EKF in ideal conditions and during GNSS outliers supposed to occur during specific interval of time, innovation based adaptive approach is selected and used to modify the covariance calculation of the non linear filters performed in this paper. Interesting results are observed, discussed with real perspectives in navigation data fusion for real time applications. Three parallel modified algorithms are simulated and compared to non-adaptive forms according to Root Mean Square Error (RMSE) criteria.展开更多
A novel low-cost adaptive square-root cubature Kalmanfilter (LCASCKF) is proposed to enhance the robustness of processmodels while only increasing the computational load slightly.It is well-known that the Kalman fil...A novel low-cost adaptive square-root cubature Kalmanfilter (LCASCKF) is proposed to enhance the robustness of processmodels while only increasing the computational load slightly.It is well-known that the Kalman filter cannot handle uncertainties ina process model, such as initial state estimation errors, parametermismatch and abrupt state changes. These uncertainties severelyaffect filter performance and may even provoke divergence. Astrong tracking filter (STF), which utilizes a suboptimal fading factor,is an adaptive approach that is commonly adopted to solvethis problem. However, if the strong tracking SCKF (STSCKF)uses the same method as the extended Kalman filter (EKF) tointroduce the suboptimal fading factor, it greatly increases thecomputational load. To avoid this problem, a low-cost introductorymethod is proposed and a hypothesis testing theory is applied todetect uncertainties. The computational load analysis is performedby counting the total number of floating-point operations and it isfound that the computational load of LCASCKF is close to that ofSCKF. Experimental results prove that the LCASCKF performs aswell as STSCKF, while the increase in computational load is muchlower than STSCKF.展开更多
The stochastic convergence of the cubature Kalmanfilter with intermittent observations (CKFI) for general nonlinearstochastic systems is investigated. The Bernoulli distributed ran-dom variable is employed to descri...The stochastic convergence of the cubature Kalmanfilter with intermittent observations (CKFI) for general nonlinearstochastic systems is investigated. The Bernoulli distributed ran-dom variable is employed to describe the phenomenon of intermit-tent observations. According to the cubature sample principle, theestimation error and the error covariance matrix (ECM) of CKFIare derived by Taylor series expansion, respectively. Afterwards, itis theoretically proved that the ECM will be bounded if the obser-vation arrival probability exceeds a critical minimum observationarrival probability. Meanwhile, under proper assumption corre-sponding with real engineering situations, the stochastic stabilityof the estimation error can be guaranteed when the initial estima-tion error and the stochastic noise terms are sufficiently small. Thetheoretical conclusions are verified by numerical simulations fortwo illustrative examples; also by evaluating the tracking perfor-mance of the optical-electric target tracking system implementedby CKFI and unscented Kalman filter with intermittent observa-tions (UKFI) separately, it is demonstrated that the proposed CKFIslightly outperforms the UKFI with respect to tracking accuracy aswell as real time performance.展开更多
Nonlinear initial alignment is a significant research topic for strapdown inertial navigation system(SINS).Cubature Kalman filter(CKF)is a popular tool for nonlinear initial alignment.Standard CKF assumes that the sta...Nonlinear initial alignment is a significant research topic for strapdown inertial navigation system(SINS).Cubature Kalman filter(CKF)is a popular tool for nonlinear initial alignment.Standard CKF assumes that the statics of the observation noise are pre-given before the filtering process.Therefore,any unpredicted outliers in observation noise will decrease the stability of the filter.In view of this problem,improved CKF method with robustness is proposed.Multiple fading factors are introduced to rescale the observation noise covariance.Then the update stage of the filter can be autonomously tuned,and if there are outliers exist in the observations,the update should be less weighted.Under the Gaussian assumption of KF,the Mahalanobis distance of the innovation vector is supposed to be Chi-square distributed.Therefore a judging index based on Chi-square test is designed to detect the noise outliers,determining whether the fading tune are required.The proposed method is applied in the nonlinear alignment of SINS,and vehicle experiment proves the effective of the proposed method.展开更多
A new Gaussian approximation nonlinear filter called generalized cubature quadrature Kalman filter (GCQKF) is introduced for nonlinear dynamic systems. Based on standard GCQKF, two extensions are developed, namely squ...A new Gaussian approximation nonlinear filter called generalized cubature quadrature Kalman filter (GCQKF) is introduced for nonlinear dynamic systems. Based on standard GCQKF, two extensions are developed, namely square root generalized cubature quadrature Kalman filter (SR-GCQKF) and iterated generalized cubature quadrature Kalman filter (I-GCQKF). In SR-GCQKF, the QR decomposition is exploited to alter the Cholesky decomposition and both predicted and filtered error covariances have been propagated in square root format to make sure the numerical stability. In I-GCQKF, the measurement update step is executed iteratively to make full use of the latest measurement and a new terminal criterion is adopted to guarantee the increase of likelihood. Detailed numerical experiments demonstrate the superior performance on both tracking stability and estimation accuracy of I-GCQKF and SR-GCQKF compared with GCQKF.展开更多
In order to improve tracking accuracy when initial estimate is inaccurate or outliers exist,a bearings-only tracking approach called the robust range-parameterized cubature Kalman filter(RRPCKF)was proposed.Firstly,th...In order to improve tracking accuracy when initial estimate is inaccurate or outliers exist,a bearings-only tracking approach called the robust range-parameterized cubature Kalman filter(RRPCKF)was proposed.Firstly,the robust extremal rule based on the pollution distribution was introduced to the cubature Kalman filter(CKF)framework.The improved Turkey weight function was subsequently constructed to identify the outliers whose weights were reduced by establishing equivalent innovation covariance matrix in the CKF.Furthermore,the improved range-parameterize(RP)strategy which divides the filter into some weighted robust CKFs each with a different initial estimate was utilized to solve the fuzzy initial estimation problem efficiently.Simulations show that the result of the RRPCKF is more accurate and more robust whether outliers exist or not,whereas that of the conventional algorithms becomes distorted seriously when outliers appear.展开更多
This paper focuses on the cubature Kalman filters (CKFs) for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical–radial cu...This paper focuses on the cubature Kalman filters (CKFs) for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical–radial cubature rule which makes it possible to compute the integrals encountered in nonlinear filtering problems. However, the rule not only requires computing the integration over an n-dimensional spherical region, but also combines the spherical cubature rule with the radial rule, thereby making it difficult to construct higher-degree CKFs. Moreover, the cubature formula used to construct the CKF has some drawbacks in computation. To address these issues, we present a more general class of the CKFs, which completely abandons the spherical–radial cubature rule. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes a fifth-degree extension of the CKF. Two target tracking problems are used to verify the proposed algorithm. The results of both experiments demonstrate that the higher-degree CKF outperforms the conventional nonlinear filters in terms of accuracy.展开更多
Reasonable selection and optimization of a filter used in model estimation for a multiple model structure is the key to improve tracking accuracy of maneuvering target.Combining with the cubature Kalman filter with it...Reasonable selection and optimization of a filter used in model estimation for a multiple model structure is the key to improve tracking accuracy of maneuvering target.Combining with the cubature Kalman filter with iterated observation update and the interacting multiple model method,a novel interacting multiple model algorithm based on the cubature Kalman filter with observation iterated update is proposed.Firstly,aiming to the structural features of cubature Kalman filter,the cubature Kalman filter with observation iterated update is constructed by the mechanism of iterated observation update.Secondly,the improved cubature Kalman filter is used as the model filter of interacting multiple model,and the stability and reliability of model identification and state estimation are effectively promoted by the optimization of model filtering step.In the simulations,compared with classic improved interacting multiple model algorithms,the theoretical analysis and experimental results show the feasibility and validity of the proposed algorithm.展开更多
To solve the problem that the choice of softening factor in conventional adaptive strong tracking filter( STF) greatly relies on the experience and computer simulation,a new concept of softening factor matrix is intro...To solve the problem that the choice of softening factor in conventional adaptive strong tracking filter( STF) greatly relies on the experience and computer simulation,a new concept of softening factor matrix is introduced and a fuzzy adaptive strong tracking cubature Kalman filter( FASTCKF) based on fuzzy logic controller is proposed. This method monitors residual absolute mean and standard deviation of each measurement component with fuzzy logic adaptive controller( FLAC),and adjusts the softening factor matrix dynamically by fuzzy rules,which is capable to modify suboptimal fading factor of STF adaptively and improve the filter's robust adaptive capacity. The simulation results show that the improved filtering performance is superior to the conventional square root cubature Kalman filter( SCKF) and the strong tracking square root cubature Kalman filter( STSCKF).展开更多
The GM-PHD framework as recursion realization of PHD filter is extensively applied to multitarget tracking system. A new idea of improving the estimation precision of time-varying multi-target in non-linear system is ...The GM-PHD framework as recursion realization of PHD filter is extensively applied to multitarget tracking system. A new idea of improving the estimation precision of time-varying multi-target in non-linear system is proposed due to the advantage of computation efficiency in this paper. First,a novel cubature Kalman probability hypothesis density filter is designed for single sensor measurement system under the Gaussian mixture framework. Second,the consistency fusion strategy for multi-sensor measurement is proposed through constructing consistency matrix. Furthermore,to take the advantage of consistency fusion strategy,fused measurement is introduced in the update step of cubature Kalman probability hypothesis density filter to replace the single-sensor measurement. Then a cubature Kalman probability hypothesis density filter based on multi-sensor consistency fusion is proposed. Capabilily of the proposed algorithm is illustrated through simulation scenario of multi-sensor multi-target tracking.展开更多
A novel variational Bayesian inference based on adaptive cubature Kalman filter(VBACKF)algorithm is proposed for the problem of state estimation in a target tracking system with time-varying measurement noise and rand...A novel variational Bayesian inference based on adaptive cubature Kalman filter(VBACKF)algorithm is proposed for the problem of state estimation in a target tracking system with time-varying measurement noise and random measurement losses.Firstly,the Inverse-Wishart(IW)distribution is chosen to model the covariance matrix of time-varying measurement noise in the cubature Kalman filter framework.Secondly,the Bernoulli random variable is introduced as the judgement factor of the measurement losses,and the Beta distribution is selected as the conjugate prior distribution of measurement loss probability to ensure that the posterior distribution and prior distribution have the same function form.Finally,the joint posterior probability density function of the estimated variables is approximately decoupled by the variational Bayesian inference,and the fixed-point iteration approach is used to update the estimated variables.The simulation results show that the proposed VBACKF algorithm considers the comprehensive effects of system nonlinearity,time-varying measurement noise and unknown measurement loss probability,moreover,effectively improves the accuracy of target state estimation in complex scene.展开更多
Traditional cubature Kalman filter(CKF)is a preferable tool for the inertial navigation system(INS)/global positioning system(GPS)integration under Gaussian noises.The CKF,however,may provide a significantly biased es...Traditional cubature Kalman filter(CKF)is a preferable tool for the inertial navigation system(INS)/global positioning system(GPS)integration under Gaussian noises.The CKF,however,may provide a significantly biased estimate when the INS/GPS system suffers from complex non-Gaussian disturbances.To address this issue,a robust nonlinear Kalman filter referred to as cubature Kalman filter under minimum error entropy with fiducial points(MEEF-CKF)is proposed.The MEEF-CKF behaves a strong robustness against complex nonGaussian noises by operating several major steps,i.e.,regression model construction,robust state estimation and free parameters optimization.More concretely,a regression model is constructed with the consideration of residual error caused by linearizing a nonlinear function at the first step.The MEEF-CKF is then developed by solving an optimization problem based on minimum error entropy with fiducial points(MEEF)under the framework of the regression model.In the MEEF-CKF,a novel optimization approach is provided for the purpose of determining free parameters adaptively.In addition,the computational complexity and convergence analyses of the MEEF-CKF are conducted for demonstrating the calculational burden and convergence characteristic.The enhanced robustness of the MEEF-CKF is demonstrated by Monte Carlo simulations on the application of a target tracking with INS/GPS integration under complex nonGaussian noises.展开更多
Aiming at the adverse effect caused by observation noise on system state estimation precision,a novel distributed cubature Kalman filter(CKF) based on observation bootstrap sampling is proposed.Firstly,combining with ...Aiming at the adverse effect caused by observation noise on system state estimation precision,a novel distributed cubature Kalman filter(CKF) based on observation bootstrap sampling is proposed.Firstly,combining with the extraction and utilization of the latest observation information and the prior statistical information from observation noise modeling,an observation bootstrap sampling strategy is designed.The objective is to deal with the adverse influence of observation uncertainty by increasing observations information.Secondly,the strategy is dynamically introduced into the cubature Kalman filter,and the distributed fusion framework of filtering realization is constructed.Better filtering precision is obtained by promoting observation reliability without increasing the hardware cost of observation system.Theory analysis and simulation results show the proposed algorithm feasibility and effectiveness.展开更多
Mobile robot systems performing simultaneous localization and mapping(SLAM) are generally plagued by non-Gaussian noise.To improve both accuracy and robustness under non-Gaussian measurement noise,a robust SLAM algori...Mobile robot systems performing simultaneous localization and mapping(SLAM) are generally plagued by non-Gaussian noise.To improve both accuracy and robustness under non-Gaussian measurement noise,a robust SLAM algorithm is proposed.It is based on the square-root cubature Kalman filter equipped with a Huber' s generalized maximum likelihood estimator(GM-estimator).In particular,the square-root cubature rule is applied to propagate the robot state vector and covariance matrix in the time update,the measurement update and the new landmark initialization stages of the SLAM.Moreover,gain weight matrices with respect to the measurement residuals are calculated by utilizing Huber' s technique in the measurement update step.The measurement outliers are suppressed by lower Kalman gains as merging into the system.The proposed algorithm can achieve better performance under the condition of non-Gaussian measurement noise in comparison with benchmark algorithms.The simulation results demonstrate the advantages of the proposed SLAM algorithm.展开更多
This paper evaluates the state estimation performance for processing nonlinear/non-Gaussian systems using the cubature particle lter(CPF),which is an estimation algorithm that combines the cubature Kalman lter(CKF)and...This paper evaluates the state estimation performance for processing nonlinear/non-Gaussian systems using the cubature particle lter(CPF),which is an estimation algorithm that combines the cubature Kalman lter(CKF)and the particle lter(PF).The CPF is essentially a realization of PF where the third-degree cubature rule based on numerical integration method is adopted to approximate the proposal distribution.It is benecial where the CKF is used to generate the importance density function in the PF framework for effectively resolving the nonlinear/non-Gaussian problems.Based on the spherical-radial transformation to generate an even number of equally weighted cubature points,the CKF uses cubature points with the same weights through the spherical-radial integration rule and employs an analytical probability density function(pdf)to capture the mean and covariance of the posterior distribution using the total probability theorem and subsequently uses the measurement to update with Bayes’rule.It is capable of acquiring a maximum a posteriori probability estimate of the nonlinear system,and thus the importance density function can be used to approximate the true posterior density distribution.In Bayesian ltering,the nonlinear lter performs well when all conditional densities are assumed Gaussian.When applied to the nonlinear/non-Gaussian distribution systems,the CPF algorithm can remarkably improve the estimation accuracy as compared to the other particle lterbased approaches,such as the extended particle lter(EPF),and unscented particle lter(UPF),and also the Kalman lter(KF)-type approaches,such as the extended Kalman lter(EKF),unscented Kalman lter(UKF)and CKF.Two illustrative examples are presented showing that the CPF achieves better performance as compared to the other approaches.展开更多
文摘In this paper,a Millimeter wave(mmWave)beam tracking problem is studied in orthogonal time frequency space(OTFS)systems.Considering the nonlinearity of beamforming and the constraints of existing Kalman-filtering based beam tracking schemes,we propose a novel Cubature Kalman Filter(CKF)framework tracking the channel state information(CSI)to manage the challenge of highspeed channel variation in single-user moving scene for OTFS systems.Aiming for low complexity for mobile settings,this paper trains only one beam pair to track a path to maintain the reliable communication link in the analog beamforming architecture.Simulation results show that our proposed method has better tracking performance to improve the accuracy of the estimated beam angle compared with prior work.
基金Supported by the National Natural Science Foundation of China(No.61771006)the Open Foundation of Key Laboratory of Spectral Imaging Technology of the Chinese Academy of Sciences(No.LSIT201711D)+1 种基金the Outstanding Young Cultivation Foundation of Henan University(No.0000A40366)the Excellent Chinese and Foreign Youth Exchange Programme of China Science and Technology Association(2017CASTQNJL046)
文摘Aiming at improving the estimation accuracy and real-time of nonlinear system with linear Gaussian sub-structure,a novel marginalized cubature Kalman filter is proposed in Bayesian estimation framework. Firstly,the marginalized technique is adopted to model the target system dynamics with nonlinear state and linear state separately,and the two parts are estimated by cubature Kalman filter and standard Kalman filter respectively. Therefore,the linear part avoids the generation and propagation process of cubature points. Accordingly,the computational complexity is reduced.Meanwhile,the accuracy of state estimation is improved by taking the difference of nonlinear state estimation as the measurement of linear state. Furthermore,the computational complexity of marginalized cubature Kalman filter is discussed by calculating the number of floating-point operation. Finally,simulation experiments and analysis show that the proposed algorithm can improve the performance of filtering precision and real-time effectively in target tracking system.
文摘In this paper, adaptive sensor fusion INS/GNSS is proposed to solve specific problem of non linear time variant state space estimation with measurement outliers, different algorithms are used to solve this specific problem generally occurs in intentional and non-intentional interferences caused by other radio navigation sources, or by the GNSS receiver’s deterioration. Non linear approximation techniques such as Extended Kalman filter EKF, Sigma Point Kalman Filters such as UKF and CDKF are computed to estimate the navigation states for UAV flight control. Several comparisons are conduced and analyzed in order to compare the accuracy and the convergence of different approaches usually applied in navigation data fusion purposes. The last non linear filter algorithm developed is the Cubature Kalman Filter CKF which provides more accurate estimation with more stability in Tracking data fusion application. In this work, CKF is compared with SPKF and EKF in ideal conditions and during GNSS outliers supposed to occur during specific interval of time, innovation based adaptive approach is selected and used to modify the covariance calculation of the non linear filters performed in this paper. Interesting results are observed, discussed with real perspectives in navigation data fusion for real time applications. Three parallel modified algorithms are simulated and compared to non-adaptive forms according to Root Mean Square Error (RMSE) criteria.
基金supported by the National Natural Science Foundation of China(61573283)
文摘A novel low-cost adaptive square-root cubature Kalmanfilter (LCASCKF) is proposed to enhance the robustness of processmodels while only increasing the computational load slightly.It is well-known that the Kalman filter cannot handle uncertainties ina process model, such as initial state estimation errors, parametermismatch and abrupt state changes. These uncertainties severelyaffect filter performance and may even provoke divergence. Astrong tracking filter (STF), which utilizes a suboptimal fading factor,is an adaptive approach that is commonly adopted to solvethis problem. However, if the strong tracking SCKF (STSCKF)uses the same method as the extended Kalman filter (EKF) tointroduce the suboptimal fading factor, it greatly increases thecomputational load. To avoid this problem, a low-cost introductorymethod is proposed and a hypothesis testing theory is applied todetect uncertainties. The computational load analysis is performedby counting the total number of floating-point operations and it isfound that the computational load of LCASCKF is close to that ofSCKF. Experimental results prove that the LCASCKF performs aswell as STSCKF, while the increase in computational load is muchlower than STSCKF.
基金supported by the National Natural Science Foundation of China(6110418661273076)
文摘The stochastic convergence of the cubature Kalmanfilter with intermittent observations (CKFI) for general nonlinearstochastic systems is investigated. The Bernoulli distributed ran-dom variable is employed to describe the phenomenon of intermit-tent observations. According to the cubature sample principle, theestimation error and the error covariance matrix (ECM) of CKFIare derived by Taylor series expansion, respectively. Afterwards, itis theoretically proved that the ECM will be bounded if the obser-vation arrival probability exceeds a critical minimum observationarrival probability. Meanwhile, under proper assumption corre-sponding with real engineering situations, the stochastic stabilityof the estimation error can be guaranteed when the initial estima-tion error and the stochastic noise terms are sufficiently small. Thetheoretical conclusions are verified by numerical simulations fortwo illustrative examples; also by evaluating the tracking perfor-mance of the optical-electric target tracking system implementedby CKFI and unscented Kalman filter with intermittent observa-tions (UKFI) separately, it is demonstrated that the proposed CKFIslightly outperforms the UKFI with respect to tracking accuracy aswell as real time performance.
基金This work is supported by National Natural Science Foundation of China under Grant No.41574069The Major National Projects of China under Grant No.GFZX0301040303.
文摘Nonlinear initial alignment is a significant research topic for strapdown inertial navigation system(SINS).Cubature Kalman filter(CKF)is a popular tool for nonlinear initial alignment.Standard CKF assumes that the statics of the observation noise are pre-given before the filtering process.Therefore,any unpredicted outliers in observation noise will decrease the stability of the filter.In view of this problem,improved CKF method with robustness is proposed.Multiple fading factors are introduced to rescale the observation noise covariance.Then the update stage of the filter can be autonomously tuned,and if there are outliers exist in the observations,the update should be less weighted.Under the Gaussian assumption of KF,the Mahalanobis distance of the innovation vector is supposed to be Chi-square distributed.Therefore a judging index based on Chi-square test is designed to detect the noise outliers,determining whether the fading tune are required.The proposed method is applied in the nonlinear alignment of SINS,and vehicle experiment proves the effective of the proposed method.
基金supported by the National Natural Science Foundation of China(6147322711472222)+2 种基金the Aerospace Technology Support Fund of China(2014-HT-XGD)the Natural Science Foundation of Shaanxi Province(2015JM6304)the Aeronautical Science Foundation of China(20151353018)
文摘A new Gaussian approximation nonlinear filter called generalized cubature quadrature Kalman filter (GCQKF) is introduced for nonlinear dynamic systems. Based on standard GCQKF, two extensions are developed, namely square root generalized cubature quadrature Kalman filter (SR-GCQKF) and iterated generalized cubature quadrature Kalman filter (I-GCQKF). In SR-GCQKF, the QR decomposition is exploited to alter the Cholesky decomposition and both predicted and filtered error covariances have been propagated in square root format to make sure the numerical stability. In I-GCQKF, the measurement update step is executed iteratively to make full use of the latest measurement and a new terminal criterion is adopted to guarantee the increase of likelihood. Detailed numerical experiments demonstrate the superior performance on both tracking stability and estimation accuracy of I-GCQKF and SR-GCQKF compared with GCQKF.
基金Projects(51377172,51577191) supported by the National Natural Science Foundation of China
文摘In order to improve tracking accuracy when initial estimate is inaccurate or outliers exist,a bearings-only tracking approach called the robust range-parameterized cubature Kalman filter(RRPCKF)was proposed.Firstly,the robust extremal rule based on the pollution distribution was introduced to the cubature Kalman filter(CKF)framework.The improved Turkey weight function was subsequently constructed to identify the outliers whose weights were reduced by establishing equivalent innovation covariance matrix in the CKF.Furthermore,the improved range-parameterize(RP)strategy which divides the filter into some weighted robust CKFs each with a different initial estimate was utilized to solve the fuzzy initial estimation problem efficiently.Simulations show that the result of the RRPCKF is more accurate and more robust whether outliers exist or not,whereas that of the conventional algorithms becomes distorted seriously when outliers appear.
基金Supported by the National Natural Science Foundation of China (50979017, NSFC60775060) the National High Technology Ship Research Project of China (GJCB09001)
文摘This paper focuses on the cubature Kalman filters (CKFs) for the nonlinear dynamic systems with additive process and measurement noise. As is well known, the heart of the CKF is the third-degree spherical–radial cubature rule which makes it possible to compute the integrals encountered in nonlinear filtering problems. However, the rule not only requires computing the integration over an n-dimensional spherical region, but also combines the spherical cubature rule with the radial rule, thereby making it difficult to construct higher-degree CKFs. Moreover, the cubature formula used to construct the CKF has some drawbacks in computation. To address these issues, we present a more general class of the CKFs, which completely abandons the spherical–radial cubature rule. It can be shown that the conventional CKF is a special case of the proposed algorithm. The paper also includes a fifth-degree extension of the CKF. Two target tracking problems are used to verify the proposed algorithm. The results of both experiments demonstrate that the higher-degree CKF outperforms the conventional nonlinear filters in terms of accuracy.
基金Supported by the National Nature Science Foundations of China(No.61300214,U1204611,61170243)the Science and Technology Innovation Team Support Plan of Education Department of Henan Province(No.13IRTSTHN021)+3 种基金the Science and Technology Research Key Project of Education Department of Henan Province(No.13A413066)the Basic and Frontier Technology Research Plan of Henan Province(No.132300410148)the Funding Scheme of Young Key Teacher of Henan Province Universitiesthe Key Project of Teaching Reform Research of Henan University(No.HDXJJG2013-07)
文摘Reasonable selection and optimization of a filter used in model estimation for a multiple model structure is the key to improve tracking accuracy of maneuvering target.Combining with the cubature Kalman filter with iterated observation update and the interacting multiple model method,a novel interacting multiple model algorithm based on the cubature Kalman filter with observation iterated update is proposed.Firstly,aiming to the structural features of cubature Kalman filter,the cubature Kalman filter with observation iterated update is constructed by the mechanism of iterated observation update.Secondly,the improved cubature Kalman filter is used as the model filter of interacting multiple model,and the stability and reliability of model identification and state estimation are effectively promoted by the optimization of model filtering step.In the simulations,compared with classic improved interacting multiple model algorithms,the theoretical analysis and experimental results show the feasibility and validity of the proposed algorithm.
基金National Natural Science Foundations of China(Nos.51175082,60874092,51375088)
文摘To solve the problem that the choice of softening factor in conventional adaptive strong tracking filter( STF) greatly relies on the experience and computer simulation,a new concept of softening factor matrix is introduced and a fuzzy adaptive strong tracking cubature Kalman filter( FASTCKF) based on fuzzy logic controller is proposed. This method monitors residual absolute mean and standard deviation of each measurement component with fuzzy logic adaptive controller( FLAC),and adjusts the softening factor matrix dynamically by fuzzy rules,which is capable to modify suboptimal fading factor of STF adaptively and improve the filter's robust adaptive capacity. The simulation results show that the improved filtering performance is superior to the conventional square root cubature Kalman filter( SCKF) and the strong tracking square root cubature Kalman filter( STSCKF).
基金Supported by the National Natural Science Foundation of China(No.61300214)the Science and Technology Innovation Team Support Plan of Education Department of Henan Province(No.13IRTSTHN021)+1 种基金the Post-doctoral Science Foundation of China(No.2014M551999) the Outstanding Young Cultivation Foundation of Henan University(No.0000A40366)
文摘The GM-PHD framework as recursion realization of PHD filter is extensively applied to multitarget tracking system. A new idea of improving the estimation precision of time-varying multi-target in non-linear system is proposed due to the advantage of computation efficiency in this paper. First,a novel cubature Kalman probability hypothesis density filter is designed for single sensor measurement system under the Gaussian mixture framework. Second,the consistency fusion strategy for multi-sensor measurement is proposed through constructing consistency matrix. Furthermore,to take the advantage of consistency fusion strategy,fused measurement is introduced in the update step of cubature Kalman probability hypothesis density filter to replace the single-sensor measurement. Then a cubature Kalman probability hypothesis density filter based on multi-sensor consistency fusion is proposed. Capabilily of the proposed algorithm is illustrated through simulation scenario of multi-sensor multi-target tracking.
基金Supported by the National Natural Science Foundation of China(No.61976080)the Science and Technology Key Project of Science and TechnologyDepartment of Henan Province(No.212102310298)+1 种基金the Academic Degrees&Graduate Education Reform Project of Henan Province(No.2021SJGLX195Y)the Innovation and Quality Improvement Project for Graduate Education of Henan University(No.SYL20010101)。
文摘A novel variational Bayesian inference based on adaptive cubature Kalman filter(VBACKF)algorithm is proposed for the problem of state estimation in a target tracking system with time-varying measurement noise and random measurement losses.Firstly,the Inverse-Wishart(IW)distribution is chosen to model the covariance matrix of time-varying measurement noise in the cubature Kalman filter framework.Secondly,the Bernoulli random variable is introduced as the judgement factor of the measurement losses,and the Beta distribution is selected as the conjugate prior distribution of measurement loss probability to ensure that the posterior distribution and prior distribution have the same function form.Finally,the joint posterior probability density function of the estimated variables is approximately decoupled by the variational Bayesian inference,and the fixed-point iteration approach is used to update the estimated variables.The simulation results show that the proposed VBACKF algorithm considers the comprehensive effects of system nonlinearity,time-varying measurement noise and unknown measurement loss probability,moreover,effectively improves the accuracy of target state estimation in complex scene.
基金supported by the Fundamental Research Funds for the Central Universities(xzy022020045)the National Natural Science Foundation of China(61976175)。
文摘Traditional cubature Kalman filter(CKF)is a preferable tool for the inertial navigation system(INS)/global positioning system(GPS)integration under Gaussian noises.The CKF,however,may provide a significantly biased estimate when the INS/GPS system suffers from complex non-Gaussian disturbances.To address this issue,a robust nonlinear Kalman filter referred to as cubature Kalman filter under minimum error entropy with fiducial points(MEEF-CKF)is proposed.The MEEF-CKF behaves a strong robustness against complex nonGaussian noises by operating several major steps,i.e.,regression model construction,robust state estimation and free parameters optimization.More concretely,a regression model is constructed with the consideration of residual error caused by linearizing a nonlinear function at the first step.The MEEF-CKF is then developed by solving an optimization problem based on minimum error entropy with fiducial points(MEEF)under the framework of the regression model.In the MEEF-CKF,a novel optimization approach is provided for the purpose of determining free parameters adaptively.In addition,the computational complexity and convergence analyses of the MEEF-CKF are conducted for demonstrating the calculational burden and convergence characteristic.The enhanced robustness of the MEEF-CKF is demonstrated by Monte Carlo simulations on the application of a target tracking with INS/GPS integration under complex nonGaussian noises.
基金Supported by the National Natural Science Foundation of China(No.61300214)the Science and Technology Innovation Team Support Plan of Education Department of Henan Province(13IRTSTHN021)+1 种基金the Post-doctoral Science Foundation of China(No.2014M551999)the Funding Scheme of Young Key Teacher of Henan Province Universities(No.2013GGJS-026)
文摘Aiming at the adverse effect caused by observation noise on system state estimation precision,a novel distributed cubature Kalman filter(CKF) based on observation bootstrap sampling is proposed.Firstly,combining with the extraction and utilization of the latest observation information and the prior statistical information from observation noise modeling,an observation bootstrap sampling strategy is designed.The objective is to deal with the adverse influence of observation uncertainty by increasing observations information.Secondly,the strategy is dynamically introduced into the cubature Kalman filter,and the distributed fusion framework of filtering realization is constructed.Better filtering precision is obtained by promoting observation reliability without increasing the hardware cost of observation system.Theory analysis and simulation results show the proposed algorithm feasibility and effectiveness.
基金Supported by the National High Technology Research and Development Program of China(2010AA09Z104)the Fundamental Research Funds of the Zhejiang University(2014FZA5020)
文摘Mobile robot systems performing simultaneous localization and mapping(SLAM) are generally plagued by non-Gaussian noise.To improve both accuracy and robustness under non-Gaussian measurement noise,a robust SLAM algorithm is proposed.It is based on the square-root cubature Kalman filter equipped with a Huber' s generalized maximum likelihood estimator(GM-estimator).In particular,the square-root cubature rule is applied to propagate the robot state vector and covariance matrix in the time update,the measurement update and the new landmark initialization stages of the SLAM.Moreover,gain weight matrices with respect to the measurement residuals are calculated by utilizing Huber' s technique in the measurement update step.The measurement outliers are suppressed by lower Kalman gains as merging into the system.The proposed algorithm can achieve better performance under the condition of non-Gaussian measurement noise in comparison with benchmark algorithms.The simulation results demonstrate the advantages of the proposed SLAM algorithm.
基金supported by the Ministry of Science and Technology,Taiwan[Grant No.MOST 108-2221-E-019-013]。
文摘This paper evaluates the state estimation performance for processing nonlinear/non-Gaussian systems using the cubature particle lter(CPF),which is an estimation algorithm that combines the cubature Kalman lter(CKF)and the particle lter(PF).The CPF is essentially a realization of PF where the third-degree cubature rule based on numerical integration method is adopted to approximate the proposal distribution.It is benecial where the CKF is used to generate the importance density function in the PF framework for effectively resolving the nonlinear/non-Gaussian problems.Based on the spherical-radial transformation to generate an even number of equally weighted cubature points,the CKF uses cubature points with the same weights through the spherical-radial integration rule and employs an analytical probability density function(pdf)to capture the mean and covariance of the posterior distribution using the total probability theorem and subsequently uses the measurement to update with Bayes’rule.It is capable of acquiring a maximum a posteriori probability estimate of the nonlinear system,and thus the importance density function can be used to approximate the true posterior density distribution.In Bayesian ltering,the nonlinear lter performs well when all conditional densities are assumed Gaussian.When applied to the nonlinear/non-Gaussian distribution systems,the CPF algorithm can remarkably improve the estimation accuracy as compared to the other particle lterbased approaches,such as the extended particle lter(EPF),and unscented particle lter(UPF),and also the Kalman lter(KF)-type approaches,such as the extended Kalman lter(EKF),unscented Kalman lter(UKF)and CKF.Two illustrative examples are presented showing that the CPF achieves better performance as compared to the other approaches.