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
Engineering tests can yield inaccurate data due to instrument errors,human factors,and environmental interference,introducing uncertainty in numerical model updating.This study employs the probability-box(p-box)method...Engineering tests can yield inaccurate data due to instrument errors,human factors,and environmental interference,introducing uncertainty in numerical model updating.This study employs the probability-box(p-box)method for representing observational uncertainty and develops a two-step approximate Bayesian computation(ABC)framework using time-series data.Within the ABC framework,Euclidean and Bhattacharyya distances are employed as uncertainty quantification metrics to delineate approximate likelihood functions in the initial and subsequent steps,respectively.A novel variational Bayesian Monte Carlo method is introduced to efficiently apply the ABC framework amidst observational uncertainty,resulting in rapid convergence and accurate parameter estimation with minimal iterations.The efficacy of the proposed updating strategy is validated by its application to a shear frame model excited by seismic wave and an aviation pump force sensor for thermal output analysis.The results affirm the efficiency,robustness,and practical applicability of the proposed method.展开更多
Future 6G communications will open up opportunities for innovative applications,including Cyber-Physical Systems,edge computing,supporting Industry 5.0,and digital agriculture.While automation is creating efficiencies...Future 6G communications will open up opportunities for innovative applications,including Cyber-Physical Systems,edge computing,supporting Industry 5.0,and digital agriculture.While automation is creating efficiencies,it can also create new cyber threats,such as vulnerabilities in trust and malicious node injection.Denialof-Service(DoS)attacks can stop many forms of operations by overwhelming networks and systems with data noise.Current anomaly detection methods require extensive software changes and only detect static threats.Data collection is important for being accurate,but it is often a slow,tedious,and sometimes inefficient process.This paper proposes a new wavelet transformassisted Bayesian deep learning based probabilistic(WT-BDLP)approach tomitigate malicious data injection attacks in 6G edge networks.The proposed approach combines outlier detection based on a Bayesian learning conditional variational autoencoder(Bay-LCVariAE)and traffic pattern analysis based on continuous wavelet transform(CWT).The Bay-LCVariAE framework allows for probabilistic modelling of generative features to facilitate capturing how features of interest change over time,spatially,and for recognition of anomalies.Similarly,CWT allows emphasizing the multi-resolution spectral analysis and permits temporally relevant frequency pattern recognition.Experimental testing showed that the flexibility of the Bayesian probabilistic framework offers a vast improvement in anomaly detection accuracy over existing methods,with a maximum accuracy of 98.21%recognizing anomalies.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
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
Simultaneous localization and mapping(SLAM)has been applied across a wide range of areas from robotics to automatic pilot.Most of the SLAM algorithms are based on the assumption that the noise is timeinvariant Gaussia...Simultaneous localization and mapping(SLAM)has been applied across a wide range of areas from robotics to automatic pilot.Most of the SLAM algorithms are based on the assumption that the noise is timeinvariant Gaussian distribution.In some cases,this assumption no longer holds and the performance of the traditional SLAM algorithms declines.In this paper,we present a robust SLAM algorithm based on variational Bayes method by modelling the observation noise as inverse-Wishart distribution with "harmonic mean".Besides,cubature integration is utilized to solve the problem of nonlinear system.The proposed algorithm can effectively solve the problem of filtering divergence for traditional filtering algorithm when suffering the time-variant observation noise,especially for heavy-tai led noise.To validate the algorithm,we compare it with other t raditional filtering algorithms.The results show the effectiveness of the algorithm.展开更多
In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first proposed for the variational Bayesian on Lie group, and then extended to the manifold that...In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first proposed for the variational Bayesian on Lie group, and then extended to the manifold that is approximated by Lie groups. Then the convergence of the proposed algorithm with respect to the manifold metric is proved in two iterative processes： variational Bayesian expectation （VB-F） step and variational Bayesian maximum （VB-M） step. Moreover, the effective of different metrics for Bayesian analysis is discussed.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
This paper investigates the navigational performance of Global Positioning System(GPS)using the variational Bayesian(VB)based robust filter with interacting multiple model(IMM)adaptation as the navigation processor.Th...This paper investigates the navigational performance of Global Positioning System(GPS)using the variational Bayesian(VB)based robust filter with interacting multiple model(IMM)adaptation as the navigation processor.The performance of the state estimation for GPS navigation processing using the family ofKalman filter(KF)may be degraded due to the fact that in practical situations the statistics of measurement noise might change.In the proposed algorithm,the adaptivity is achieved by estimating the timevarying noise covariance matrices based onVB learning using the probabilistic approach,where in each update step,both the system state and time-varying measurement noise were recognized as random variables to be estimated.The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning.One of the two major classical adaptive Kalman filter(AKF)approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate(MMAE).The IMM algorithm uses two or more filters to process in parallel,where each filter corresponds to a different dynamic or measurement model.The robust Huber’s M-estimation-based extended Kalman filter(HEKF)algorithm integrates both merits of the Huber M-estimation methodology and EKF.The robustness is enhanced by modifying the filter update based on Huber’s M-estimation method in the filtering framework.The proposed algorithm,referred to as the interactive multi-model based variational Bayesian HEKF(IMM-VBHEKF),provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors,such as the multipath effect.Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.展开更多
Prediction intervals(PIs)for industrial time series can provide useful guidance for workers.Given that the failure of industrial sensors may cause the missing point in inputs,the existing kernel dynamic Bayesian netwo...Prediction intervals(PIs)for industrial time series can provide useful guidance for workers.Given that the failure of industrial sensors may cause the missing point in inputs,the existing kernel dynamic Bayesian networks(KDBN),serving as an effective method for PIs construction,suffer from high computational load using the stochastic algorithm for inference.This study proposes a variational inference method for the KDBN for the purpose of fast inference,which avoids the timeconsuming stochastic sampling.The proposed algorithm contains two stages.The first stage involves the inference of the missing inputs by using a local linearization based variational inference,and based on the computed posterior distributions over the missing inputs the second stage sees a Gaussian approximation for probability over the nodes in future time slices.To verify the effectiveness of the proposed method,a synthetic dataset and a practical dataset of generation flow of blast furnace gas(BFG)are employed with different ratios of missing inputs.The experimental results indicate that the proposed method can provide reliable PIs for the generation flow of BFG and it exhibits shorter computing time than the stochastic based one.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
Aimed at the problem that the state estimation in the measurement update of the simultaneous localization and mapping(SLAM)method is incorrect or even not convergent because of the non-Gaussian measurement noise,outli...Aimed at the problem that the state estimation in the measurement update of the simultaneous localization and mapping(SLAM)method is incorrect or even not convergent because of the non-Gaussian measurement noise,outliers,or unknown and time-varying noise statistical characteristics,a robust SLAM method based on the improved variational Bayesian adaptive Kalman filtering(IVBAKF)is proposed.First,the measurement noise covariance is estimated using the variable Bayesian adaptive filtering algorithm.Then,the estimated covariance matrix is robustly processed through the weight function constructed in the form of a reweighted average.Finally,the system updates are iterated multiple times to further gradually correct the state estimation error.Furthermore,to observe features at different depths,a feature measurement model containing depth parameters is constructed.Experimental results show that when the measurement noise does not obey the Gaussian distribution and there are outliers in the measurement information,compared with the variational Bayesian adaptive SLAM method,the positioning accuracy of the proposed method is improved by 17.23%,20.46%,and 17.76%,which has better applicability and robustness to environmental disturbance.展开更多
An algorithm is presented for image prior combinations based blind deconvolution and applied to astronomical images.Using a hierarchical Bayesian framework, the unknown original image and all required algorithmic para...An algorithm is presented for image prior combinations based blind deconvolution and applied to astronomical images.Using a hierarchical Bayesian framework, the unknown original image and all required algorithmic parameters are estimated simultaneously. Through utilization of variational Bayesian analysis,approximations of the posterior distributions on each unknown are obtained by minimizing the Kullback-Leibler(KL) distance, thus providing uncertainties of the estimates during the restoration process. Experimental results on both synthetic images and real astronomical images demonstrate that the proposed approaches compare favorably to other state-of-the-art reconstruction methods.展开更多
Efficient estimation of line spectral from quantized samples is of significant importance in information theory and signal processing,e.g.,channel estimation in energy efficient massive MIMO systems and direction of a...Efficient estimation of line spectral from quantized samples is of significant importance in information theory and signal processing,e.g.,channel estimation in energy efficient massive MIMO systems and direction of arrival estimation.The goal of this paper is to recover the line spectral as well as its corresponding parameters including the model order,frequencies and amplitudes from heavily quantized samples.To this end,we propose an efficient gridless Bayesian algorithm named VALSE-EP,which is a combination of the high resolution and low complexity gridless variational line spectral estimation(VALSE)and expectation propagation(EP).The basic idea of VALSE-EP is to iteratively approximate the challenging quantized model of line spectral estimation as a sequence of simple pseudo unquantized models,where VALSE is applied.Moreover,to obtain a benchmark of the performance of the proposed algorithm,the Cram′er Rao bound(CRB)is derived.Finally,numerical experiments on both synthetic and real data are performed,demonstrating the near CRB performance of the proposed VALSE-EP for line spectral estimation from quantized samples.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
Aiming at the problem of filtering precision degradation caused by the random outliers of process noise and measurement noise in multi-target tracking(MTT) system,a new Gaussian-Student’s t mixture distribution proba...Aiming at the problem of filtering precision degradation caused by the random outliers of process noise and measurement noise in multi-target tracking(MTT) system,a new Gaussian-Student’s t mixture distribution probability hypothesis density(PHD) robust filtering algorithm based on variational Bayesian inference(GST-vbPHD) is proposed.Firstly,since it can accurately describe the heavy-tailed characteristics of noise with outliers,Gaussian-Student’s t mixture distribution is employed to model process noise and measurement noise respectively.Then Bernoulli random variable is introduced to correct the likelihood distribution of the mixture probability,leading hierarchical Gaussian distribution constructed by the Gaussian-Student’s t mixture distribution suitable to model non-stationary noise.Finally,the approximate solutions including target weights,measurement noise covariance and state estimation error covariance are obtained according to variational Bayesian inference approach.The simulation results show that,in the heavy-tailed noise environment,the proposed algorithm leads to strong improvements over the traditional PHD filter and the Student’s t distribution PHD filter.展开更多
Geochemical survey data are essential across Earth Science disciplines but are often affected by noise,which can obscure important geological signals and compromise subsequent prediction and interpretation.Quantifying...Geochemical survey data are essential across Earth Science disciplines but are often affected by noise,which can obscure important geological signals and compromise subsequent prediction and interpretation.Quantifying prediction uncertainty is hence crucial for robust geoscientific decision-making.This study proposes a novel deep learning framework,the Spatially Constrained Variational Autoencoder(SC-VAE),for denoising geochemical survey data with integrated uncertainty quantification.The SC-VAE incorporates spatial regularization,which enforces spatial coherence by modeling inter-sample relationships directly within the latent space.The performance of the SC-VAE was systematically evaluated against a standard Variational Autoencoder(VAE)using geochemical data from the gold polymetallic district in the northwestern part of Sichuan Province,China.Both models were optimized using Bayesian optimization,with objective functions specifically designed to maintain essential geostatistical characteristics.Evaluation metrics include variogram analysis,quantitative measures of spatial interpolation accuracy,visual assessment of denoised maps,and statistical analysis of data distributions,as well as decomposition of uncertainties.Results show that the SC-VAE achieves superior noise suppression and better preservation of spatial structure compared to the standard VAE,as demonstrated by a significant reduction in the variogram nugget effect and an increased partial sill.The SC-VAE produces denoised maps with clearer anomaly delineation and more regularized data distributions,effectively mitigating outliers and reducing kurtosis.Additionally,it delivers improved interpolation accuracy and spatially explicit uncertainty estimates,facilitating more reliable and interpretable assessments of prediction confidence.The SC-VAE framework thus provides a robust,geostatistically informed solution for enhancing the quality and interpretability of geochemical data,with broad applicability in mineral exploration,environmental geochemistry,and other Earth Science domains.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.
基金supported by the National Natural Science Foundation of China(Grant No.U23B20105).
文摘Engineering tests can yield inaccurate data due to instrument errors,human factors,and environmental interference,introducing uncertainty in numerical model updating.This study employs the probability-box(p-box)method for representing observational uncertainty and develops a two-step approximate Bayesian computation(ABC)framework using time-series data.Within the ABC framework,Euclidean and Bhattacharyya distances are employed as uncertainty quantification metrics to delineate approximate likelihood functions in the initial and subsequent steps,respectively.A novel variational Bayesian Monte Carlo method is introduced to efficiently apply the ABC framework amidst observational uncertainty,resulting in rapid convergence and accurate parameter estimation with minimal iterations.The efficacy of the proposed updating strategy is validated by its application to a shear frame model excited by seismic wave and an aviation pump force sensor for thermal output analysis.The results affirm the efficiency,robustness,and practical applicability of the proposed method.
文摘Future 6G communications will open up opportunities for innovative applications,including Cyber-Physical Systems,edge computing,supporting Industry 5.0,and digital agriculture.While automation is creating efficiencies,it can also create new cyber threats,such as vulnerabilities in trust and malicious node injection.Denialof-Service(DoS)attacks can stop many forms of operations by overwhelming networks and systems with data noise.Current anomaly detection methods require extensive software changes and only detect static threats.Data collection is important for being accurate,but it is often a slow,tedious,and sometimes inefficient process.This paper proposes a new wavelet transformassisted Bayesian deep learning based probabilistic(WT-BDLP)approach tomitigate malicious data injection attacks in 6G edge networks.The proposed approach combines outlier detection based on a Bayesian learning conditional variational autoencoder(Bay-LCVariAE)and traffic pattern analysis based on continuous wavelet transform(CWT).The Bay-LCVariAE framework allows for probabilistic modelling of generative features to facilitate capturing how features of interest change over time,spatially,and for recognition of anomalies.Similarly,CWT allows emphasizing the multi-resolution spectral analysis and permits temporally relevant frequency pattern recognition.Experimental testing showed that the flexibility of the Bayesian probabilistic framework offers a vast improvement in anomaly detection accuracy over existing methods,with a maximum accuracy of 98.21%recognizing anomalies.
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.
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the National Natural Science Foundation of China(No.61803260)。
文摘Simultaneous localization and mapping(SLAM)has been applied across a wide range of areas from robotics to automatic pilot.Most of the SLAM algorithms are based on the assumption that the noise is timeinvariant Gaussian distribution.In some cases,this assumption no longer holds and the performance of the traditional SLAM algorithms declines.In this paper,we present a robust SLAM algorithm based on variational Bayes method by modelling the observation noise as inverse-Wishart distribution with "harmonic mean".Besides,cubature integration is utilized to solve the problem of nonlinear system.The proposed algorithm can effectively solve the problem of filtering divergence for traditional filtering algorithm when suffering the time-variant observation noise,especially for heavy-tai led noise.To validate the algorithm,we compare it with other t raditional filtering algorithms.The results show the effectiveness of the algorithm.
基金This work was supported by the National Key Research and Development Program of China （No. 2016YF-B0901900） and the National Natural Science Foundation of China （Nos. 61733018, 61333001, 61573344）.
文摘In this paper, variational inference is studied on manifolds with certain metrics. To solve the problem, the analysis is first proposed for the variational Bayesian on Lie group, and then extended to the manifold that is approximated by Lie groups. Then the convergence of the proposed algorithm with respect to the manifold metric is proved in two iterative processes： variational Bayesian expectation （VB-F） step and variational Bayesian maximum （VB-M） step. Moreover, the effective of different metrics for Bayesian analysis is discussed.
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This work has been partially supported by the Ministry of Science and Technology,Taiwan[Grant Numbers MOST 108-2221-E-019-013 and MOST 109-2221-E-019-010].
文摘This paper investigates the navigational performance of Global Positioning System(GPS)using the variational Bayesian(VB)based robust filter with interacting multiple model(IMM)adaptation as the navigation processor.The performance of the state estimation for GPS navigation processing using the family ofKalman filter(KF)may be degraded due to the fact that in practical situations the statistics of measurement noise might change.In the proposed algorithm,the adaptivity is achieved by estimating the timevarying noise covariance matrices based onVB learning using the probabilistic approach,where in each update step,both the system state and time-varying measurement noise were recognized as random variables to be estimated.The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning.One of the two major classical adaptive Kalman filter(AKF)approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate(MMAE).The IMM algorithm uses two or more filters to process in parallel,where each filter corresponds to a different dynamic or measurement model.The robust Huber’s M-estimation-based extended Kalman filter(HEKF)algorithm integrates both merits of the Huber M-estimation methodology and EKF.The robustness is enhanced by modifying the filter update based on Huber’s M-estimation method in the filtering framework.The proposed algorithm,referred to as the interactive multi-model based variational Bayesian HEKF(IMM-VBHEKF),provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors,such as the multipath effect.Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.
基金supported by the National Key Research andDevelopment Program of China(2017YFA0700300)the National Natural Sciences Foundation of China(61533005,61703071,61603069)。
文摘Prediction intervals(PIs)for industrial time series can provide useful guidance for workers.Given that the failure of industrial sensors may cause the missing point in inputs,the existing kernel dynamic Bayesian networks(KDBN),serving as an effective method for PIs construction,suffer from high computational load using the stochastic algorithm for inference.This study proposes a variational inference method for the KDBN for the purpose of fast inference,which avoids the timeconsuming stochastic sampling.The proposed algorithm contains two stages.The first stage involves the inference of the missing inputs by using a local linearization based variational inference,and based on the computed posterior distributions over the missing inputs the second stage sees a Gaussian approximation for probability over the nodes in future time slices.To verify the effectiveness of the proposed method,a synthetic dataset and a practical dataset of generation flow of blast furnace gas(BFG)are employed with different ratios of missing inputs.The experimental results indicate that the proposed method can provide reliable PIs for the generation flow of BFG and it exhibits shorter computing time than the stochastic based one.
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.
基金Primary Research and Development Plan of Jiangsu Province(No.BE2022389)Jiangsu Province Agricultural Science and Technology Independent Innovation Fund Project(No.CX(22)3091)the National Natural Science Foundation of China(No.61773113)。
文摘Aimed at the problem that the state estimation in the measurement update of the simultaneous localization and mapping(SLAM)method is incorrect or even not convergent because of the non-Gaussian measurement noise,outliers,or unknown and time-varying noise statistical characteristics,a robust SLAM method based on the improved variational Bayesian adaptive Kalman filtering(IVBAKF)is proposed.First,the measurement noise covariance is estimated using the variable Bayesian adaptive filtering algorithm.Then,the estimated covariance matrix is robustly processed through the weight function constructed in the form of a reweighted average.Finally,the system updates are iterated multiple times to further gradually correct the state estimation error.Furthermore,to observe features at different depths,a feature measurement model containing depth parameters is constructed.Experimental results show that when the measurement noise does not obey the Gaussian distribution and there are outliers in the measurement information,compared with the variational Bayesian adaptive SLAM method,the positioning accuracy of the proposed method is improved by 17.23%,20.46%,and 17.76%,which has better applicability and robustness to environmental disturbance.
文摘An algorithm is presented for image prior combinations based blind deconvolution and applied to astronomical images.Using a hierarchical Bayesian framework, the unknown original image and all required algorithmic parameters are estimated simultaneously. Through utilization of variational Bayesian analysis,approximations of the posterior distributions on each unknown are obtained by minimizing the Kullback-Leibler(KL) distance, thus providing uncertainties of the estimates during the restoration process. Experimental results on both synthetic images and real astronomical images demonstrate that the proposed approaches compare favorably to other state-of-the-art reconstruction methods.
基金supported by National Natural Science Foundation of China(No.61901415)。
文摘Efficient estimation of line spectral from quantized samples is of significant importance in information theory and signal processing,e.g.,channel estimation in energy efficient massive MIMO systems and direction of arrival estimation.The goal of this paper is to recover the line spectral as well as its corresponding parameters including the model order,frequencies and amplitudes from heavily quantized samples.To this end,we propose an efficient gridless Bayesian algorithm named VALSE-EP,which is a combination of the high resolution and low complexity gridless variational line spectral estimation(VALSE)and expectation propagation(EP).The basic idea of VALSE-EP is to iteratively approximate the challenging quantized model of line spectral estimation as a sequence of simple pseudo unquantized models,where VALSE is applied.Moreover,to obtain a benchmark of the performance of the proposed algorithm,the Cram′er Rao bound(CRB)is derived.Finally,numerical experiments on both synthetic and real data are performed,demonstrating the near CRB performance of the proposed VALSE-EP for line spectral estimation from quantized samples.
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 National Natural Science Foundation of China(No.61976080)the Science and Technology Key Project of Science and Technology Department of Henan Province(No.212102310298)the Innovation and Quality Improvement Project for Graduate Education of Henan University(No.SYL20010101)。
文摘Aiming at the problem of filtering precision degradation caused by the random outliers of process noise and measurement noise in multi-target tracking(MTT) system,a new Gaussian-Student’s t mixture distribution probability hypothesis density(PHD) robust filtering algorithm based on variational Bayesian inference(GST-vbPHD) is proposed.Firstly,since it can accurately describe the heavy-tailed characteristics of noise with outliers,Gaussian-Student’s t mixture distribution is employed to model process noise and measurement noise respectively.Then Bernoulli random variable is introduced to correct the likelihood distribution of the mixture probability,leading hierarchical Gaussian distribution constructed by the Gaussian-Student’s t mixture distribution suitable to model non-stationary noise.Finally,the approximate solutions including target weights,measurement noise covariance and state estimation error covariance are obtained according to variational Bayesian inference approach.The simulation results show that,in the heavy-tailed noise environment,the proposed algorithm leads to strong improvements over the traditional PHD filter and the Student’s t distribution PHD filter.
基金supported by the National Natural Science Foundation of China(Nos.42530801,42425208)the Natural Science Foundation of Hubei Province(China)(No.2023AFA001)+1 种基金the MOST Special Fund from State Key Laboratory of Geological Processes and Mineral Resources,China University of Geosciences(No.MSFGPMR2025-401)the China Scholarship Council(No.202306410181)。
文摘Geochemical survey data are essential across Earth Science disciplines but are often affected by noise,which can obscure important geological signals and compromise subsequent prediction and interpretation.Quantifying prediction uncertainty is hence crucial for robust geoscientific decision-making.This study proposes a novel deep learning framework,the Spatially Constrained Variational Autoencoder(SC-VAE),for denoising geochemical survey data with integrated uncertainty quantification.The SC-VAE incorporates spatial regularization,which enforces spatial coherence by modeling inter-sample relationships directly within the latent space.The performance of the SC-VAE was systematically evaluated against a standard Variational Autoencoder(VAE)using geochemical data from the gold polymetallic district in the northwestern part of Sichuan Province,China.Both models were optimized using Bayesian optimization,with objective functions specifically designed to maintain essential geostatistical characteristics.Evaluation metrics include variogram analysis,quantitative measures of spatial interpolation accuracy,visual assessment of denoised maps,and statistical analysis of data distributions,as well as decomposition of uncertainties.Results show that the SC-VAE achieves superior noise suppression and better preservation of spatial structure compared to the standard VAE,as demonstrated by a significant reduction in the variogram nugget effect and an increased partial sill.The SC-VAE produces denoised maps with clearer anomaly delineation and more regularized data distributions,effectively mitigating outliers and reducing kurtosis.Additionally,it delivers improved interpolation accuracy and spatially explicit uncertainty estimates,facilitating more reliable and interpretable assessments of prediction confidence.The SC-VAE framework thus provides a robust,geostatistically informed solution for enhancing the quality and interpretability of geochemical data,with broad applicability in mineral exploration,environmental geochemistry,and other Earth Science domains.
