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 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
To precisely determine the integrated orbit of the Chinese manned spacecraft mission, a smoother and Bayesian filter based technique for optimum semi-codeless tracking of the P（Y） code on dual-frequency GPS signals ...To precisely determine the integrated orbit of the Chinese manned spacecraft mission, a smoother and Bayesian filter based technique for optimum semi-codeless tracking of the P（Y） code on dual-frequency GPS signals has been advanced. This signal processing technique has been proven effective and robust for affording access to dual-frequency GPS signals. This paper introduces the signal dynamics and measurement models, describes the W o D bit estimation method, and corrects the mistakes of direct estimation of W bit in current semi-codeless tracking. Median filter is chosen as a smoother to find the best measurements at the current time among the history and current information. The Bayesian filter is used to track the L2 P（Y） code phase and L2 carrier phase recursively.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
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
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
The Bayesian probabilistic approach is proposed to estimate the process noise and measurement noise parameters for a Kalman filter. With state vectors and covariance matrices estimated by the Kalman filter, the likeho...The Bayesian probabilistic approach is proposed to estimate the process noise and measurement noise parameters for a Kalman filter. With state vectors and covariance matrices estimated by the Kalman filter, the likehood of the measurements can be constructed as a function of the process noise and measurement noise parameters. By maximizing the likelihood function with respect to these noise parameters, the optimal values can be obtained. Furthermore, the Bayesian probabilistic approach allows the associated uncertainty to be quantified. Examples using a single-degree-of-freedom system and a ten-story building illustrate the proposed method. The effect on the performance of the Kalman filter due to the selection of the process noise and measurement noise parameters was demonstrated. The optimal values of the noise parameters were found to be close to the actual values in the sense that the actual parameters were in the region with significant probability density. Through these examples, the Bayesian approach was shown to have the capability to provide accurate estimates of the noise parameters of the Kalman filter, and hence for state estimation.展开更多
The online diagnosis for aircraft system has always been a difficult problem. This is due to time evolution of system change, uncertainty of sensor measurements, and real-time requirement of diagnostic inference. To a...The online diagnosis for aircraft system has always been a difficult problem. This is due to time evolution of system change, uncertainty of sensor measurements, and real-time requirement of diagnostic inference. To address this problem, two dynamic Bayesian network(DBN) approaches are proposed. One approach prunes the DBN of system, and then uses particle filter(PF) for this pruned DBN(PDBN) to perform online diagnosis. The problem is that estimates from a PF tend to have high variance for small sample sets. Using large sample sets is computationally expensive. The other approach compiles the PDBN into a dynamic arithmetic circuit(DAC) using an offline procedure that is applied only once, and then uses this circuit to provide online diagnosis recursively. This approach leads to the most computational consumption in the offline procedure. The experimental results show that the DAC, compared with the PF for PDBN, not only provides more reliable online diagnosis, but also offers much faster inference.展开更多
A novel statistical method based on particle filtering is presented for multiple vehicle acoustic signals separation problem in wireless sensor network. The particle filtering method is able to deal with non-Gaussian ...A novel statistical method based on particle filtering is presented for multiple vehicle acoustic signals separation problem in wireless sensor network. The particle filtering method is able to deal with non-Gaussian and nonlinear models and non-stationary sources. Using some instantaneously mixed observations of several real-world vehicle acoustic signals, the proposed statistical method is compared with a conventional non-stationary Blind Source Separation algorithm and attractive simulation results are achieved. Moreover, considering the natural convenience to transmit particles between sensor nodes, the algorithm based on particle filtering is believed to have potential to enable the task of multiple vehicles recognition collaboratively performed by sensor nodes in distributed wireless sensor network.展开更多
This paper investigates the problem of state estimation for discrete-time stochastic linear systems, where additional knowledge on the unknown inputs is available at an aggregate level and the knowledge on the missing...This paper investigates the problem of state estimation for discrete-time stochastic linear systems, where additional knowledge on the unknown inputs is available at an aggregate level and the knowledge on the missing measurements can be described by a known stochastic distribution. Firstly, the available knowledge on the unknown inputs and the state equation is used to form the prior distribution of the state vector at each time step. Secondly, to obtain an analytically tractable likelihood function, the effect of missing measurements is broken down into a systematic part and a random part, and the latter is modeled as part of the observation noise. Then, a recursive filter is obtained based on Bayesian inference. Finally, a numerical example is provided to evaluate the performance of the proposed methods.展开更多
Along with the wide application of e-mail nowadays, many spam e-mails flood into people’s email-boxes and cause catastrophes to their study and life. In anti-spam e-mails campaign, we depend on not only legal measure...Along with the wide application of e-mail nowadays, many spam e-mails flood into people’s email-boxes and cause catastrophes to their study and life. In anti-spam e-mails campaign, we depend on not only legal measures but also technological approaches. The Bayesian classifier provides a simple and effective approach to discriminate classification. This paper presents a new improved Bayesian-based anti-spam e-mail filter. We adopt a way of attribute selection based on word entropy, use vector weights which are represented by word frequency, and deduce its corresponding formula. It is proved that our filter improves total performances apparently in our experiment.展开更多
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.
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.
基金supported by the National Natural Science Foundation of China(Grant No.40374054).
文摘To precisely determine the integrated orbit of the Chinese manned spacecraft mission, a smoother and Bayesian filter based technique for optimum semi-codeless tracking of the P（Y） code on dual-frequency GPS signals has been advanced. This signal processing technique has been proven effective and robust for affording access to dual-frequency GPS signals. This paper introduces the signal dynamics and measurement models, describes the W o D bit estimation method, and corrects the mistakes of direct estimation of W bit in current semi-codeless tracking. Median filter is chosen as a smoother to find the best measurements at the current time among the history and current information. The Bayesian filter is used to track the L2 P（Y） code phase and L2 carrier phase recursively.
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.
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.
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Fundo para o Desenvolvimento das Ciências e da Tecnologia (FDCT) Under Grant No. 052/2005/A
文摘The Bayesian probabilistic approach is proposed to estimate the process noise and measurement noise parameters for a Kalman filter. With state vectors and covariance matrices estimated by the Kalman filter, the likehood of the measurements can be constructed as a function of the process noise and measurement noise parameters. By maximizing the likelihood function with respect to these noise parameters, the optimal values can be obtained. Furthermore, the Bayesian probabilistic approach allows the associated uncertainty to be quantified. Examples using a single-degree-of-freedom system and a ten-story building illustrate the proposed method. The effect on the performance of the Kalman filter due to the selection of the process noise and measurement noise parameters was demonstrated. The optimal values of the noise parameters were found to be close to the actual values in the sense that the actual parameters were in the region with significant probability density. Through these examples, the Bayesian approach was shown to have the capability to provide accurate estimates of the noise parameters of the Kalman filter, and hence for state estimation.
基金Projects(2010ZD11007,20100751010)supported by Aeronautical Science Foundation of China
文摘The online diagnosis for aircraft system has always been a difficult problem. This is due to time evolution of system change, uncertainty of sensor measurements, and real-time requirement of diagnostic inference. To address this problem, two dynamic Bayesian network(DBN) approaches are proposed. One approach prunes the DBN of system, and then uses particle filter(PF) for this pruned DBN(PDBN) to perform online diagnosis. The problem is that estimates from a PF tend to have high variance for small sample sets. Using large sample sets is computationally expensive. The other approach compiles the PDBN into a dynamic arithmetic circuit(DAC) using an offline procedure that is applied only once, and then uses this circuit to provide online diagnosis recursively. This approach leads to the most computational consumption in the offline procedure. The experimental results show that the DAC, compared with the PF for PDBN, not only provides more reliable online diagnosis, but also offers much faster inference.
基金the National "863" High Technology Development Program (2006AA01Z216)the MajorResearch Program of the Science and Technology Commission of Shanghai Municipality of China (054SGA1001).
文摘A novel statistical method based on particle filtering is presented for multiple vehicle acoustic signals separation problem in wireless sensor network. The particle filtering method is able to deal with non-Gaussian and nonlinear models and non-stationary sources. Using some instantaneously mixed observations of several real-world vehicle acoustic signals, the proposed statistical method is compared with a conventional non-stationary Blind Source Separation algorithm and attractive simulation results are achieved. Moreover, considering the natural convenience to transmit particles between sensor nodes, the algorithm based on particle filtering is believed to have potential to enable the task of multiple vehicles recognition collaboratively performed by sensor nodes in distributed wireless sensor network.
基金jointly funded by UK Engineering and Physical Sciences Research Council(EPSRC)and BAE System(EP/H501401/1)
文摘This paper investigates the problem of state estimation for discrete-time stochastic linear systems, where additional knowledge on the unknown inputs is available at an aggregate level and the knowledge on the missing measurements can be described by a known stochastic distribution. Firstly, the available knowledge on the unknown inputs and the state equation is used to form the prior distribution of the state vector at each time step. Secondly, to obtain an analytically tractable likelihood function, the effect of missing measurements is broken down into a systematic part and a random part, and the latter is modeled as part of the observation noise. Then, a recursive filter is obtained based on Bayesian inference. Finally, a numerical example is provided to evaluate the performance of the proposed methods.
文摘Along with the wide application of e-mail nowadays, many spam e-mails flood into people’s email-boxes and cause catastrophes to their study and life. In anti-spam e-mails campaign, we depend on not only legal measures but also technological approaches. The Bayesian classifier provides a simple and effective approach to discriminate classification. This paper presents a new improved Bayesian-based anti-spam e-mail filter. We adopt a way of attribute selection based on word entropy, use vector weights which are represented by word frequency, and deduce its corresponding formula. It is proved that our filter improves total performances apparently in our experiment.
