In this paper,an advanced satellite navigation filter design,referred to as the Variational Bayesian Maximum Correntropy Extended Kalman Filter(VBMCEKF),is introduced to enhance robustness and adaptability in scenario...In this paper,an advanced satellite navigation filter design,referred to as the Variational Bayesian Maximum Correntropy Extended Kalman Filter(VBMCEKF),is introduced to enhance robustness and adaptability in scenarios with non-Gaussian noise and heavy-tailed outliers.The proposed design modifies the extended Kalman filter(EKF)for the global navigation satellite system(GNSS),integrating the maximum correntropy criterion(MCC)and the variational Bayesian(VB)method.This adaptive algorithm effectively reduces non-line-of-sight(NLOS)reception contamination and improves estimation accuracy,particularly in time-varying GNSS measurements.Experimental results show that the proposed method significantly outperforms conventional approaches in estimation accuracy under heavy-tailed outliers and non-Gaussian noise.By combining MCC with VB approximation for real-time noise covariance estimation using fixed-point iteration,the VBMCEKF achieves superior filtering performance in challenging GNSS conditions.The method’s adaptability and precision make it ideal for improving satellite navigation performance in stochastic environments.展开更多
A modified unscented particle filtering scheme for nonlinear tracking is proposed, in view of the potential drawbacks （such as, particle impoverishment and numerical sensitivity in calculating the prior） of the conv...A modified unscented particle filtering scheme for nonlinear tracking is proposed, in view of the potential drawbacks （such as, particle impoverishment and numerical sensitivity in calculating the prior） of the conventional unscented particle filter （UPF） confronted in practice. Specifically, a different derivation of the importance weight is presented in detail. The proposed method can avoid the calculation of the prior and reduce the effects of the impoverishment problem caused by sampling from the proposal distribution, Simulations have been performed using two illustrative examples and results have been provided to demonstrate the validity of the modified UPF as well as its improved performance over the conventional one.展开更多
This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades o...This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date,one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective,which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics(e.g., mean and covariance) conditioned on a system's measurement data.This article offers a systematic introduction to the Bayesian state estimation framework and reviews various Kalman filtering(KF)techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation to more complicated problems such as simultaneous state and parameter/input estimation.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
We propose a technique based on the natural gradient method for variational lower bound maximization for a variational Bayesian Kalman filter.The natural gradient approach is applied to the Kullback-Leibler divergence...We propose a technique based on the natural gradient method for variational lower bound maximization for a variational Bayesian Kalman filter.The natural gradient approach is applied to the Kullback-Leibler divergence between the parameterized variational distribution and the posterior density of interest.Using a Gaussian assumption for the parametrized variational distribution,we obtain a closed-form iterative procedure for the Kullback-Leibler divergence minimization,producing estimates of the variational hyper-parameters of state estimation and the associated error covariance.Simulation results in both a Doppler radar tracking scenario and a bearing-only tracking scenario are presented,showing that the proposed natural gradient method outperforms existing methods which are based on other linearization techniques in terms of tracking accuracy.展开更多
Bayesian estimation theory provides a general approach for the state estimate of linear or nonlinear and Gaussian or non-Gaussian systems. In this study, we first explore two Bayesian-based methods： ensemble adjustme...Bayesian estimation theory provides a general approach for the state estimate of linear or nonlinear and Gaussian or non-Gaussian systems. In this study, we first explore two Bayesian-based methods： ensemble adjustment Kalman filter（EAKF） and sequential importance resampling particle filter（SIR-PF）, using a well-known nonlinear and non-Gaussian model（Lorenz ＇63 model）. The EAKF, which is a deterministic scheme of the ensemble Kalman filter（En KF）, performs better than the classical（stochastic） En KF in a general framework. Comparison between the SIR-PF and the EAKF reveals that the former outperforms the latter if ensemble size is so large that can avoid the filter degeneracy, and vice versa. The impact of the probability density functions and effective ensemble sizes on assimilation performances are also explored. On the basis of comparisons between the SIR-PF and the EAKF, a mixture filter, called ensemble adjustment Kalman particle filter（EAKPF）, is proposed to combine their both merits. Similar to the ensemble Kalman particle filter, which combines the stochastic En KF and SIR-PF analysis schemes with a tuning parameter, the new mixture filter essentially provides a continuous interpolation between the EAKF and SIR-PF. The same Lorenz ＇63 model is used as a testbed, showing that the EAKPF is able to overcome filter degeneracy while maintaining the non-Gaussian nature, and performs better than the EAKF given limited ensemble size.展开更多
In this paper, distributed Kalman filter design is studied for linear dynamics with unknown measurement noise variance, which modeled by Wishart distribution. To solve the problem in a multi-agent network, a distribut...In this paper, distributed Kalman filter design is studied for linear dynamics with unknown measurement noise variance, which modeled by Wishart distribution. To solve the problem in a multi-agent network, a distributed adaptive Kalman filter is proposed with the help of variational Bayesian, where the posterior distribution of joint state and noise variance is approximated by a free-form distribution. The con vergence of the proposed algorithm is proved in two main steps: n oise statistics is estimated, where each age nt only use its local information in variational Bayesian expectation (VB-E) step, and state is estimated by a consensus algorithm in variational Bayesian maximum (VB-M) step. Finally, a distributed target tracking problem is investigated with simulations for illustration.展开更多
This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise.Based on the cubature Kalman filter,we propose a new nonlinear filtering algorithm that employs ...This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise.Based on the cubature Kalman filter,we propose a new nonlinear filtering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise.The system states and the statistics of skew t noise distribution,including the shape matrix,the scale matrix,and the degree of freedom(DOF)are estimated jointly by employing variational Bayesian(VB)inference.The proposed method is validated in a target tracking example.Results of the simulation indicate that the proposed nonlinear filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.展开更多
In the real sound environment, the observation data are usually contaminated by additional background noise of arbitrary distribution type. In order to estimate several evaluation quantities for specific signal based ...In the real sound environment, the observation data are usually contaminated by additional background noise of arbitrary distribution type. In order to estimate several evaluation quantities for specific signal based on the observed noisy data, it is fundamental to estimate the fluctuating wave form of the specific signal. On the other hand, the observation data are very often measured in a digital level form at discrete times. This is because some signal processing methods by utilizing a digital computer are indispensable for extracting exactly various kinds of statistical evaluation for the specific signal based on the quantized level data. In this study, a Bayesian filter matched to the complicated sound environment system is derived. First, in the real situation where the sound environment system is affected by background noise of arbitrary probability distribution, a stochastic system model with quantized observation is established. Next, two types of the recursive algorithm of Bayesian filter to estimate the unknown specific signal are theoretically proposed in the quantized level form. Finally, the effectiveness of the proposed theory is experimentally confirmed by applying it to the estimation problem of real sound environment.展开更多
Data is always a crucial issue of concern especially during its prediction and computation in digital revolution.This paper exactly helps in providing efficient learning mechanism for accurate predictability and reduc...Data is always a crucial issue of concern especially during its prediction and computation in digital revolution.This paper exactly helps in providing efficient learning mechanism for accurate predictability and reducing redundant data communication.It also discusses the Bayesian analysis that finds the conditional probability of at least two parametric based predictions for the data.The paper presents a method for improving the performance of Bayesian classification using the combination of Kalman Filter and K-means.The method is applied on a small dataset just for establishing the fact that the proposed algorithm can reduce the time for computing the clusters from data.The proposed Bayesian learning probabilistic model is used to check the statistical noise and other inaccuracies using unknown variables.This scenario is being implemented using efficient machine learning algorithm to perpetuate the Bayesian probabilistic approach.It also demonstrates the generative function forKalman-filer based prediction model and its observations.This paper implements the algorithm using open source platform of Python and efficiently integrates all different modules to piece of code via Common Platform Enumeration(CPE)for Python.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
A distributed bearing-only target tracking algorithm based on variational Bayesian inference(VBI)under random measurement anomalies is proposed for the problem of adverse effect of random measurement anomalies on the ...A distributed bearing-only target tracking algorithm based on variational Bayesian inference(VBI)under random measurement anomalies is proposed for the problem of adverse effect of random measurement anomalies on the state estimation accuracy of moving targets in bearing-only tracking scenarios.Firstly,the measurement information of each sensor is complemented by using triangulation under the distributed framework.Secondly,the Student-t distribution is selected to model the measurement likelihood probability density function,and the joint posteriori probability density function of the estimated variables is approximately decoupled by VBI.Finally,the estimation results of each local filter are sent to the fusion center and fed back to each local filter.The simulation results show that the proposed distributed bearing-only target tracking algorithm based on VBI in the presence of abnormal measurement noise comprehensively considers the influence of system nonlinearity and random anomaly of measurement noise,and has higher estimation accuracy and robustness than other existing algorithms in the above scenarios.展开更多
基金supported by the National Science and Technology Council,Taiwan under grants NSTC 111-2221-E-019-047 and NSTC 112-2221-E-019-030.
文摘In this paper,an advanced satellite navigation filter design,referred to as the Variational Bayesian Maximum Correntropy Extended Kalman Filter(VBMCEKF),is introduced to enhance robustness and adaptability in scenarios with non-Gaussian noise and heavy-tailed outliers.The proposed design modifies the extended Kalman filter(EKF)for the global navigation satellite system(GNSS),integrating the maximum correntropy criterion(MCC)and the variational Bayesian(VB)method.This adaptive algorithm effectively reduces non-line-of-sight(NLOS)reception contamination and improves estimation accuracy,particularly in time-varying GNSS measurements.Experimental results show that the proposed method significantly outperforms conventional approaches in estimation accuracy under heavy-tailed outliers and non-Gaussian noise.By combining MCC with VB approximation for real-time noise covariance estimation using fixed-point iteration,the VBMCEKF achieves superior filtering performance in challenging GNSS conditions.The method’s adaptability and precision make it ideal for improving satellite navigation performance in stochastic environments.
文摘A modified unscented particle filtering scheme for nonlinear tracking is proposed, in view of the potential drawbacks （such as, particle impoverishment and numerical sensitivity in calculating the prior） of the conventional unscented particle filter （UPF） confronted in practice. Specifically, a different derivation of the importance weight is presented in detail. The proposed method can avoid the calculation of the prior and reduce the effects of the impoverishment problem caused by sampling from the proposal distribution, Simulations have been performed using two illustrative examples and results have been provided to demonstrate the validity of the modified UPF as well as its improved performance over the conventional one.
文摘This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To date,one of the most promising and popular approaches is to view and address the problem from a Bayesian probabilistic perspective,which enables estimation of the unknown state variables by tracking their probabilistic distribution or statistics(e.g., mean and covariance) conditioned on a system's measurement data.This article offers a systematic introduction to the Bayesian state estimation framework and reviews various Kalman filtering(KF)techniques, progressively from the standard KF for linear systems to extended KF, unscented KF and ensemble KF for nonlinear systems. It also overviews other prominent or emerging Bayesian estimation methods including Gaussian filtering, Gaussian-sum filtering, particle filtering and moving horizon estimation and extends the discussion of state estimation to more complicated problems such as simultaneous state and parameter/input estimation.
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.
基金co-supported by the National Natural Science Foundation of China(Nos.61790552 and 61976080)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University,China(No.CX201915)。
文摘We propose a technique based on the natural gradient method for variational lower bound maximization for a variational Bayesian Kalman filter.The natural gradient approach is applied to the Kullback-Leibler divergence between the parameterized variational distribution and the posterior density of interest.Using a Gaussian assumption for the parametrized variational distribution,we obtain a closed-form iterative procedure for the Kullback-Leibler divergence minimization,producing estimates of the variational hyper-parameters of state estimation and the associated error covariance.Simulation results in both a Doppler radar tracking scenario and a bearing-only tracking scenario are presented,showing that the proposed natural gradient method outperforms existing methods which are based on other linearization techniques in terms of tracking accuracy.
基金The National Natural Science Foundation of China under contract Nos 41276029 and 41321004the Project of State Key Laboratory of Satellite Ocean Environment Dynamics,Second Institute of Oceanography under contract No.SOEDZZ1404the National Basic Research Program(973 Program)of China under contract No.2013CB430302
文摘Bayesian estimation theory provides a general approach for the state estimate of linear or nonlinear and Gaussian or non-Gaussian systems. In this study, we first explore two Bayesian-based methods： ensemble adjustment Kalman filter（EAKF） and sequential importance resampling particle filter（SIR-PF）, using a well-known nonlinear and non-Gaussian model（Lorenz ＇63 model）. The EAKF, which is a deterministic scheme of the ensemble Kalman filter（En KF）, performs better than the classical（stochastic） En KF in a general framework. Comparison between the SIR-PF and the EAKF reveals that the former outperforms the latter if ensemble size is so large that can avoid the filter degeneracy, and vice versa. The impact of the probability density functions and effective ensemble sizes on assimilation performances are also explored. On the basis of comparisons between the SIR-PF and the EAKF, a mixture filter, called ensemble adjustment Kalman particle filter（EAKPF）, is proposed to combine their both merits. Similar to the ensemble Kalman particle filter, which combines the stochastic En KF and SIR-PF analysis schemes with a tuning parameter, the new mixture filter essentially provides a continuous interpolation between the EAKF and SIR-PF. The same Lorenz ＇63 model is used as a testbed, showing that the EAKPF is able to overcome filter degeneracy while maintaining the non-Gaussian nature, and performs better than the EAKF given limited ensemble size.
基金National Natural Science Foundation of China (Nos. 61733018, 61573344).
文摘In this paper, distributed Kalman filter design is studied for linear dynamics with unknown measurement noise variance, which modeled by Wishart distribution. To solve the problem in a multi-agent network, a distributed adaptive Kalman filter is proposed with the help of variational Bayesian, where the posterior distribution of joint state and noise variance is approximated by a free-form distribution. The con vergence of the proposed algorithm is proved in two main steps: n oise statistics is estimated, where each age nt only use its local information in variational Bayesian expectation (VB-E) step, and state is estimated by a consensus algorithm in variational Bayesian maximum (VB-M) step. Finally, a distributed target tracking problem is investigated with simulations for illustration.
基金This work was supported in part by National Natural Science Foundation of China under Grants 62103167 and 61833007in part by the Natural Science Foundation of Jiangsu Province under Grant BK20210451.
文摘This paper is focused on the state estimation problem for nonlinear systems with unknown statistics of measurement noise.Based on the cubature Kalman filter,we propose a new nonlinear filtering algorithm that employs a skew t distribution to characterize the asymmetry of the measurement noise.The system states and the statistics of skew t noise distribution,including the shape matrix,the scale matrix,and the degree of freedom(DOF)are estimated jointly by employing variational Bayesian(VB)inference.The proposed method is validated in a target tracking example.Results of the simulation indicate that the proposed nonlinear filter can perform satisfactorily in the presence of unknown statistics of measurement noise and outperform than the existing state-of-the-art nonlinear filters.
文摘In the real sound environment, the observation data are usually contaminated by additional background noise of arbitrary distribution type. In order to estimate several evaluation quantities for specific signal based on the observed noisy data, it is fundamental to estimate the fluctuating wave form of the specific signal. On the other hand, the observation data are very often measured in a digital level form at discrete times. This is because some signal processing methods by utilizing a digital computer are indispensable for extracting exactly various kinds of statistical evaluation for the specific signal based on the quantized level data. In this study, a Bayesian filter matched to the complicated sound environment system is derived. First, in the real situation where the sound environment system is affected by background noise of arbitrary probability distribution, a stochastic system model with quantized observation is established. Next, two types of the recursive algorithm of Bayesian filter to estimate the unknown specific signal are theoretically proposed in the quantized level form. Finally, the effectiveness of the proposed theory is experimentally confirmed by applying it to the estimation problem of real sound environment.
文摘Data is always a crucial issue of concern especially during its prediction and computation in digital revolution.This paper exactly helps in providing efficient learning mechanism for accurate predictability and reducing redundant data communication.It also discusses the Bayesian analysis that finds the conditional probability of at least two parametric based predictions for the data.The paper presents a method for improving the performance of Bayesian classification using the combination of Kalman Filter and K-means.The method is applied on a small dataset just for establishing the fact that the proposed algorithm can reduce the time for computing the clusters from data.The proposed Bayesian learning probabilistic model is used to check the statistical noise and other inaccuracies using unknown variables.This scenario is being implemented using efficient machine learning algorithm to perpetuate the Bayesian probabilistic approach.It also demonstrates the generative function forKalman-filer based prediction model and its observations.This paper implements the algorithm using open source platform of Python and efficiently integrates all different modules to piece of code via Common Platform Enumeration(CPE)for Python.
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 Science and Technology Key Project of Science and Technology Department of Henan Province(No.252102211041)the Key Research and Development Projects of Henan Province(No.231111212500).
文摘A distributed bearing-only target tracking algorithm based on variational Bayesian inference(VBI)under random measurement anomalies is proposed for the problem of adverse effect of random measurement anomalies on the state estimation accuracy of moving targets in bearing-only tracking scenarios.Firstly,the measurement information of each sensor is complemented by using triangulation under the distributed framework.Secondly,the Student-t distribution is selected to model the measurement likelihood probability density function,and the joint posteriori probability density function of the estimated variables is approximately decoupled by VBI.Finally,the estimation results of each local filter are sent to the fusion center and fed back to each local filter.The simulation results show that the proposed distributed bearing-only target tracking algorithm based on VBI in the presence of abnormal measurement noise comprehensively considers the influence of system nonlinearity and random anomaly of measurement noise,and has higher estimation accuracy and robustness than other existing algorithms in the above scenarios.
