The work proposes a distributed Kalman filtering(KF)algorithm to track a time-varying unknown signal process for a stochastic regression model over network systems in a cooperative way.We provide the stability analysi...The work proposes a distributed Kalman filtering(KF)algorithm to track a time-varying unknown signal process for a stochastic regression model over network systems in a cooperative way.We provide the stability analysis of the proposed distributed KF algorithm without independent and stationary signal assumptions,which implies that the theoretical results are able to be applied to stochastic feedback systems.Note that the main difficulty of stability analysis lies in analyzing the properties of the product of non-independent and non-stationary random matrices involved in the error equation.We employ analysis techniques such as stochastic Lyapunov function,stability theory of stochastic systems,and algebraic graph theory to deal with the above issue.The stochastic spatio-temporal cooperative information condition shows the cooperative property of multiple sensors that even though any local sensor cannot track the time-varying unknown signal,the distributed KF algorithm can be utilized to finish the filtering task in a cooperative way.At last,we illustrate the property of the proposed distributed KF algorithm by a simulation example.展开更多
Using similar single-difference methodology(SSDM) to solve the deformation values of the monitoring points, there is unstability of the deformation information series, at sometimes.In order to overcome this shortcomin...Using similar single-difference methodology(SSDM) to solve the deformation values of the monitoring points, there is unstability of the deformation information series, at sometimes.In order to overcome this shortcoming, Kalman filtering algorithm for this series is established,and its correctness and validity are verified with the test data obtained on the movable platform in plane. The results show that Kalman filtering can improve the correctness, reliability and stability of the deformation information series.展开更多
A wireless sensor network mobile target tracking algorithm(ISO-EKF)based on improved snake optimization algorithm(ISO)is proposed to address the difficulty of estimating initial values when using extended Kalman filte...A wireless sensor network mobile target tracking algorithm(ISO-EKF)based on improved snake optimization algorithm(ISO)is proposed to address the difficulty of estimating initial values when using extended Kalman filtering to solve the state of nonlinear mobile target tracking.First,the steps of extended Kalman filtering(EKF)are introduced.Second,the ISO is used to adjust the parameters of the EKF in real time to adapt to the current motion state of the mobile target.Finally,the effectiveness of the algorithm is demonstrated through filtering and tracking using the constant velocity circular motion model(CM).Under the specified conditions,the position and velocity mean square error curves are compared among the snake optimizer(SO)-EKF algorithm,EKF algorithm,and the proposed algorithm.The comparison shows that the proposed algorithm reduces the root mean square error of position by 52%and 41%compared to the SOEKF algorithm and EKF algorithm,respectively.展开更多
Solar radio burst(SRB)is one of the main natural interference sources of Global Positioning System(GPS)signals and can reduce the signal-to-noise ratio(SNR),directly affecting the tracking performance of GPS receivers...Solar radio burst(SRB)is one of the main natural interference sources of Global Positioning System(GPS)signals and can reduce the signal-to-noise ratio(SNR),directly affecting the tracking performance of GPS receivers.In this paper,a tracking algorithm based on the adaptive Kalman filter(AKF)with carrier-to-noise ratio estimation is proposed and compared with the conventional second-order phase-locked loop tracking algo-rithms and the improved Sage-Husa adaptive Kalman filter(SHAKF)algorithm.It is discovered that when the SRBs occur,the improved SHAKF and the AKF with carrier-to-noise ratio estimation enable stable tracking to loop signals.The conven-tional second-order phase-locked loop tracking algorithms fail to track the receiver signal.The standard deviation of the carrier phase error of the AKF with carrier-to-noise ratio estimation out-performs 50.51%of the improved SHAKF algorithm,showing less fluctuation and better stability.The proposed algorithm is proven to show more excellent adaptability in the severe envi-ronment caused by the SRB occurrence and has better tracking performance.展开更多
[目的/意义]针对温室温湿度预测中多传感器数据融合可靠性低、传统模型忽略温湿度动态耦合,以及参数调优依赖人工经验等问题。[方法]首先,对传统卡尔曼(Kalman)滤波算法实施改进,通过动态调整过程噪声协方差和观测噪声协方差,结合新息...[目的/意义]针对温室温湿度预测中多传感器数据融合可靠性低、传统模型忽略温湿度动态耦合,以及参数调优依赖人工经验等问题。[方法]首先,对传统卡尔曼(Kalman)滤波算法实施改进,通过动态调整过程噪声协方差和观测噪声协方差,结合新息方差动态分配多传感器权重。其次,针对温湿度的强耦合性及其协同控制的需求,构建多输出长短期记忆-注意力机制(Long Short-Term Memory-Attention,LSTM-Attention)模型,以温湿度协同预测为目标,引入注意力机制自适应加权关键环境因子,并采用灰狼优化算法(Grey Wolf Optimizer,GWO)自动对超参数进行寻优。[结果和讨论]提出的自适应卡尔曼滤波算法在多点温湿度融合中的平均绝对偏差分别为1.59℃和8.64%,比传统卡尔曼滤波算法分别降低1.24%、8.57%。以该算法融合结果作为模型训练集,模型在温湿度预测中决定系数R2分别达到98.2%和99.3%,比传统Kalman提升4.7%和4.3%。GWO-LSTM-Atten⁃tion模型的温湿度预测均方根误差分别为0.7768℃和2.0564%,比LSTM、LSTM-Attention时间序列预测模型分别降低15.6%、6.6%,湿度分别降低29.2%、5.7%。[结论]提出的自适应卡尔曼融合算法能够有效抑制异常值影响,可在非平稳环境变化下实现多传感器数据可靠融合。在温室多环境因子预测中,GWO-LSTM-Attention模型温湿度预测值在未来可作为控制温室环境的重要参考,进而实现对温室环境的实时调控。展开更多
Aim To analyze the traditional hierarchical Kalman filtering fusion algorithm theoretically and point out that the traditional Kalman filtering fusion algorithm is complex and can not improve the tracking precision we...Aim To analyze the traditional hierarchical Kalman filtering fusion algorithm theoretically and point out that the traditional Kalman filtering fusion algorithm is complex and can not improve the tracking precision well, even it is impractical, and to propose the weighting average fusion algorithm. Methods The theoretical analysis and Monte Carlo simulation methods were ed to compare the traditional fusion algorithm with the new one,and the comparison of the root mean square error statistics values of the two algorithms was made. Results The hierarchical fusion algorithm is not better than the weighting average fusion and feedback weighting average algorithm The weighting filtering fusion algorithm is simple in principle, less in data, faster in processing and better in tolerance.Conclusion The weighting hierarchical fusion algorithm is suitable for the defective sensors.The feedback of the fusion result to the single sersor can enhance the single sensorr's precision. especially once one sensor has great deviation and low accuracy or has some deviation of sample period and is asynchronous to other sensors.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
In the normal operation condition, a conventional square-root cubature Kalman filter （SRCKF） gives sufficiently good estimation results. However, if the measurements are not reliable, the SRCKF may give inaccurate r...In the normal operation condition, a conventional square-root cubature Kalman filter （SRCKF） gives sufficiently good estimation results. However, if the measurements are not reliable, the SRCKF may give inaccurate results and diverges by time. This study introduces an adaptive SRCKF algorithm with the filter gain correction for the case of measurement malfunctions. By proposing a switching criterion, an optimal filter is selected from the adaptive and conventional SRCKF according to the measurement quality. A subsystem soft fault detection algorithm is built with the filter residual. Utilizing a clear subsystem fault coefficient, the faulty subsystem is isolated as a result of the system reconstruction. In order to improve the performance of the multi-sensor system, a hybrid fusion algorithm is presented based on the adaptive SRCKF. The state and error covariance matrix are also predicted by the priori fusion estimates, and are updated by the predicted and estimated information of subsystems. The proposed algorithms were applied to the vessel dynamic positioning system simulation. They were compared with normal SRCKF and local estimation weighted fusion algorithm. The simulation results show that the presented adaptive SRCKF improves the robustness of subsystem filtering, and the hybrid fusion algorithm has the better performance. The simulation verifies the effectiveness of the proposed algorithms.展开更多
This paper proposes an adaptive unscented Kalman filter algorithm(ARUKF)to implement fault estimation for the dynamics of high⁃speed train(HST)with measurement uncertainty and time⁃varying noise with unknown statistic...This paper proposes an adaptive unscented Kalman filter algorithm(ARUKF)to implement fault estimation for the dynamics of high⁃speed train(HST)with measurement uncertainty and time⁃varying noise with unknown statistics.Firstly,regarding the actuator and sensor fault as the auxiliary variables of the dynamics of HST,an augmented system is established,and the fault estimation problem for dynamics of HST is formulated as the state estimation of the augmented system.Then,considering the measurement uncertainties,a robust lower bound is proposed to modify the update of the UKF to decrease the influence of measurement uncertainty on the filtering accuracy.Further,considering the unknown time⁃varying noise of the dynamics of HST,an adaptive UKF algorithm based on moving window is proposed to estimate the time⁃varying noise so that accurate concurrent actuator and sensor fault estimations of dynamics of HST is implemented.Finally,a five-car model of HST is given to show the effectiveness of this method.展开更多
基金supported in part by Sichuan Science and Technology Program under Grant No.2025ZNSFSC151in part by the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No.XDA27030201+1 种基金the Natural Science Foundation of China under Grant No.U21B6001in part by the Natural Science Foundation of Tianjin under Grant No.24JCQNJC01930.
文摘The work proposes a distributed Kalman filtering(KF)algorithm to track a time-varying unknown signal process for a stochastic regression model over network systems in a cooperative way.We provide the stability analysis of the proposed distributed KF algorithm without independent and stationary signal assumptions,which implies that the theoretical results are able to be applied to stochastic feedback systems.Note that the main difficulty of stability analysis lies in analyzing the properties of the product of non-independent and non-stationary random matrices involved in the error equation.We employ analysis techniques such as stochastic Lyapunov function,stability theory of stochastic systems,and algebraic graph theory to deal with the above issue.The stochastic spatio-temporal cooperative information condition shows the cooperative property of multiple sensors that even though any local sensor cannot track the time-varying unknown signal,the distributed KF algorithm can be utilized to finish the filtering task in a cooperative way.At last,we illustrate the property of the proposed distributed KF algorithm by a simulation example.
文摘Using similar single-difference methodology(SSDM) to solve the deformation values of the monitoring points, there is unstability of the deformation information series, at sometimes.In order to overcome this shortcoming, Kalman filtering algorithm for this series is established,and its correctness and validity are verified with the test data obtained on the movable platform in plane. The results show that Kalman filtering can improve the correctness, reliability and stability of the deformation information series.
基金supported by National Natural Science Foundation of China (Nos.62265010,62061024)Gansu Province Science and Technology Plan (No.23YFGA0062)Gansu Province Innovation Fund (No.2022A-215)。
文摘A wireless sensor network mobile target tracking algorithm(ISO-EKF)based on improved snake optimization algorithm(ISO)is proposed to address the difficulty of estimating initial values when using extended Kalman filtering to solve the state of nonlinear mobile target tracking.First,the steps of extended Kalman filtering(EKF)are introduced.Second,the ISO is used to adjust the parameters of the EKF in real time to adapt to the current motion state of the mobile target.Finally,the effectiveness of the algorithm is demonstrated through filtering and tracking using the constant velocity circular motion model(CM).Under the specified conditions,the position and velocity mean square error curves are compared among the snake optimizer(SO)-EKF algorithm,EKF algorithm,and the proposed algorithm.The comparison shows that the proposed algorithm reduces the root mean square error of position by 52%and 41%compared to the SOEKF algorithm and EKF algorithm,respectively.
基金supported by the Foundation of Key Laboratory of Micro-inertial Instrument and Advanced Navigation Technology,Ministry of Education,Chinathe National Natural Science Foundation of China (61873064)
文摘Solar radio burst(SRB)is one of the main natural interference sources of Global Positioning System(GPS)signals and can reduce the signal-to-noise ratio(SNR),directly affecting the tracking performance of GPS receivers.In this paper,a tracking algorithm based on the adaptive Kalman filter(AKF)with carrier-to-noise ratio estimation is proposed and compared with the conventional second-order phase-locked loop tracking algo-rithms and the improved Sage-Husa adaptive Kalman filter(SHAKF)algorithm.It is discovered that when the SRBs occur,the improved SHAKF and the AKF with carrier-to-noise ratio estimation enable stable tracking to loop signals.The conven-tional second-order phase-locked loop tracking algorithms fail to track the receiver signal.The standard deviation of the carrier phase error of the AKF with carrier-to-noise ratio estimation out-performs 50.51%of the improved SHAKF algorithm,showing less fluctuation and better stability.The proposed algorithm is proven to show more excellent adaptability in the severe envi-ronment caused by the SRB occurrence and has better tracking performance.
文摘[目的/意义]针对温室温湿度预测中多传感器数据融合可靠性低、传统模型忽略温湿度动态耦合,以及参数调优依赖人工经验等问题。[方法]首先,对传统卡尔曼(Kalman)滤波算法实施改进,通过动态调整过程噪声协方差和观测噪声协方差,结合新息方差动态分配多传感器权重。其次,针对温湿度的强耦合性及其协同控制的需求,构建多输出长短期记忆-注意力机制(Long Short-Term Memory-Attention,LSTM-Attention)模型,以温湿度协同预测为目标,引入注意力机制自适应加权关键环境因子,并采用灰狼优化算法(Grey Wolf Optimizer,GWO)自动对超参数进行寻优。[结果和讨论]提出的自适应卡尔曼滤波算法在多点温湿度融合中的平均绝对偏差分别为1.59℃和8.64%,比传统卡尔曼滤波算法分别降低1.24%、8.57%。以该算法融合结果作为模型训练集,模型在温湿度预测中决定系数R2分别达到98.2%和99.3%,比传统Kalman提升4.7%和4.3%。GWO-LSTM-Atten⁃tion模型的温湿度预测均方根误差分别为0.7768℃和2.0564%,比LSTM、LSTM-Attention时间序列预测模型分别降低15.6%、6.6%,湿度分别降低29.2%、5.7%。[结论]提出的自适应卡尔曼融合算法能够有效抑制异常值影响,可在非平稳环境变化下实现多传感器数据可靠融合。在温室多环境因子预测中,GWO-LSTM-Attention模型温湿度预测值在未来可作为控制温室环境的重要参考,进而实现对温室环境的实时调控。
文摘Aim To analyze the traditional hierarchical Kalman filtering fusion algorithm theoretically and point out that the traditional Kalman filtering fusion algorithm is complex and can not improve the tracking precision well, even it is impractical, and to propose the weighting average fusion algorithm. Methods The theoretical analysis and Monte Carlo simulation methods were ed to compare the traditional fusion algorithm with the new one,and the comparison of the root mean square error statistics values of the two algorithms was made. Results The hierarchical fusion algorithm is not better than the weighting average fusion and feedback weighting average algorithm The weighting filtering fusion algorithm is simple in principle, less in data, faster in processing and better in tolerance.Conclusion The weighting hierarchical fusion algorithm is suitable for the defective sensors.The feedback of the fusion result to the single sersor can enhance the single sensorr's precision. especially once one sensor has great deviation and low accuracy or has some deviation of sample period and is asynchronous to other sensors.
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 Natural Science Foundation of China （50979017, NSFC60775060） the National High Technology Ship Research Project of China （GJCB09001）
文摘In the normal operation condition, a conventional square-root cubature Kalman filter （SRCKF） gives sufficiently good estimation results. However, if the measurements are not reliable, the SRCKF may give inaccurate results and diverges by time. This study introduces an adaptive SRCKF algorithm with the filter gain correction for the case of measurement malfunctions. By proposing a switching criterion, an optimal filter is selected from the adaptive and conventional SRCKF according to the measurement quality. A subsystem soft fault detection algorithm is built with the filter residual. Utilizing a clear subsystem fault coefficient, the faulty subsystem is isolated as a result of the system reconstruction. In order to improve the performance of the multi-sensor system, a hybrid fusion algorithm is presented based on the adaptive SRCKF. The state and error covariance matrix are also predicted by the priori fusion estimates, and are updated by the predicted and estimated information of subsystems. The proposed algorithms were applied to the vessel dynamic positioning system simulation. They were compared with normal SRCKF and local estimation weighted fusion algorithm. The simulation results show that the presented adaptive SRCKF improves the robustness of subsystem filtering, and the hybrid fusion algorithm has the better performance. The simulation verifies the effectiveness of the proposed algorithms.
基金the Department of Education of Liaoning Province(Grant No.JDL2020020)the Changzhou Applied Basic Research Program(Grant No.CJ2020007).
文摘This paper proposes an adaptive unscented Kalman filter algorithm(ARUKF)to implement fault estimation for the dynamics of high⁃speed train(HST)with measurement uncertainty and time⁃varying noise with unknown statistics.Firstly,regarding the actuator and sensor fault as the auxiliary variables of the dynamics of HST,an augmented system is established,and the fault estimation problem for dynamics of HST is formulated as the state estimation of the augmented system.Then,considering the measurement uncertainties,a robust lower bound is proposed to modify the update of the UKF to decrease the influence of measurement uncertainty on the filtering accuracy.Further,considering the unknown time⁃varying noise of the dynamics of HST,an adaptive UKF algorithm based on moving window is proposed to estimate the time⁃varying noise so that accurate concurrent actuator and sensor fault estimations of dynamics of HST is implemented.Finally,a five-car model of HST is given to show the effectiveness of this method.
