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
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
To deal with the adverse influence of model failures on Kalman filtering （KF） estimation, it is necessary to investigate the generalized reliability theory, including the model failure detection and identification m...To deal with the adverse influence of model failures on Kalman filtering （KF） estimation, it is necessary to investigate the generalized reliability theory, including the model failure detection and identification method as well as the separability and reliability theories. Although the generalized reliability theory for the least square has been discussed for many decades, the generalized reliability theory of KF is not widely discussed. Compared with the least square, KF includes not only the measurement model, but also the dynamic model. In KF, the predicted value of the state parameters from the dynamic model is considered as pseudomeasurements and combined with the observed measurements to compose the form of the least square. According to the reliability of the least square, the generalized reliability of KF is derived. Then, the dynamic model failure of precise point positioning is simulated to demonstrate the usage of the generalized reliability theory. The results show that the adverse influence of the dynamic model failure is more severe than that of the measurement model. Moreover, it is recommended that the model failure identification should always be used even if the overall model test passes. It is shown that the derived generalized reliability measures are suitable for the generalized KF estimation.展开更多
The standalone Global Positioning System (GPS) does not meet the higher accuracy requirements needed for approach and landing phase of an aircraft. To meet the Category-I Precision Approach (CAT-I PA) requirements of ...The standalone Global Positioning System (GPS) does not meet the higher accuracy requirements needed for approach and landing phase of an aircraft. To meet the Category-I Precision Approach (CAT-I PA) requirements of civil aviation, satellite based augmentation system (SBAS) has been planned by various countries including USA, Europe, Japan and India. The Indian SBAS is named as GPS Aided Geo Augmented Navigation (GAGAN). The GAGAN network consists of several dual frequency GPS receivers located at various airports around the Indian subcontinent. The ionospheric delay, which is a function of the total electron content (TEC), is one of the main sources of error affecting GPS/SBAS accuracy. A dual frequency GPS receiver can be used to estimate the TEC. However, line-of-sight TEC derived from dual frequency GPS data is corrupted by the instrumental biases of the GPS receiver and satellites. The estimation of receiver instrumental bias is particularly important for obtaining accurate estimates of ionospheric delay. In this paper, two prominent techniques based on Kalman filter and Self-Calibration Of pseudo Range Error (SCORE) algorithm are used for estimation of instrumental biases. The estimated instrumental bias and TEC results for the GPS Aided Geo Augmented Navigation (GAGAN) station at Hyderabad (78.47°E, 17.45°N), India are presented.展开更多
Based on a uniform linear array, a new widely linear unscented Kalman filter-based constant modulus algorithm (WL-UKF-CMA) for blind adaptive beamforming is proposed. The new algorithm is designed according to the con...Based on a uniform linear array, a new widely linear unscented Kalman filter-based constant modulus algorithm (WL-UKF-CMA) for blind adaptive beamforming is proposed. The new algorithm is designed according to the constant modulus criterion and takes full advantage of the noncircular property of the signal of interest (SOI), significantly increasing the output signal-to interference-plus-noise ratio (SINR), enhancing the convergence speed and decreasing the steady-state misadjustment. Since it requires no known training data, the proposed algorithm saves a large amount of the available spectrum. Theoretical analysis and simulation results are presented to demonstrate its superiority over the conventional linear least mean square-based CMA (L-LMS-CMA), the conventional linear recursive least square-based CMA (L-RLS-CMA), WL-LMS-CMA, WL-RLS-CMA and L-UKF-CMA.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.
基金supported by the National Natural Science Foundation of China (41074010)the National Science and Technology Planning Projects (2012BAC25B01)+1 种基金the Knowledge Innovation Program of the Chinese Academy of Sciences (KZCX2-EW-QN605)the President Fund of University of Chinese Academy of Sciences
文摘To deal with the adverse influence of model failures on Kalman filtering （KF） estimation, it is necessary to investigate the generalized reliability theory, including the model failure detection and identification method as well as the separability and reliability theories. Although the generalized reliability theory for the least square has been discussed for many decades, the generalized reliability theory of KF is not widely discussed. Compared with the least square, KF includes not only the measurement model, but also the dynamic model. In KF, the predicted value of the state parameters from the dynamic model is considered as pseudomeasurements and combined with the observed measurements to compose the form of the least square. According to the reliability of the least square, the generalized reliability of KF is derived. Then, the dynamic model failure of precise point positioning is simulated to demonstrate the usage of the generalized reliability theory. The results show that the adverse influence of the dynamic model failure is more severe than that of the measurement model. Moreover, it is recommended that the model failure identification should always be used even if the overall model test passes. It is shown that the derived generalized reliability measures are suitable for the generalized KF estimation.
文摘The standalone Global Positioning System (GPS) does not meet the higher accuracy requirements needed for approach and landing phase of an aircraft. To meet the Category-I Precision Approach (CAT-I PA) requirements of civil aviation, satellite based augmentation system (SBAS) has been planned by various countries including USA, Europe, Japan and India. The Indian SBAS is named as GPS Aided Geo Augmented Navigation (GAGAN). The GAGAN network consists of several dual frequency GPS receivers located at various airports around the Indian subcontinent. The ionospheric delay, which is a function of the total electron content (TEC), is one of the main sources of error affecting GPS/SBAS accuracy. A dual frequency GPS receiver can be used to estimate the TEC. However, line-of-sight TEC derived from dual frequency GPS data is corrupted by the instrumental biases of the GPS receiver and satellites. The estimation of receiver instrumental bias is particularly important for obtaining accurate estimates of ionospheric delay. In this paper, two prominent techniques based on Kalman filter and Self-Calibration Of pseudo Range Error (SCORE) algorithm are used for estimation of instrumental biases. The estimated instrumental bias and TEC results for the GPS Aided Geo Augmented Navigation (GAGAN) station at Hyderabad (78.47°E, 17.45°N), India are presented.
基金supported by the National Natural Science Foundation of China(61573113)the Harbin Science and Technology Innovation Talents(Excellent Discipline Leader)Research Fund(2014RFXXJ074)the National Scholarship([2016]3100)
文摘Based on a uniform linear array, a new widely linear unscented Kalman filter-based constant modulus algorithm (WL-UKF-CMA) for blind adaptive beamforming is proposed. The new algorithm is designed according to the constant modulus criterion and takes full advantage of the noncircular property of the signal of interest (SOI), significantly increasing the output signal-to interference-plus-noise ratio (SINR), enhancing the convergence speed and decreasing the steady-state misadjustment. Since it requires no known training data, the proposed algorithm saves a large amount of the available spectrum. Theoretical analysis and simulation results are presented to demonstrate its superiority over the conventional linear least mean square-based CMA (L-LMS-CMA), the conventional linear recursive least square-based CMA (L-RLS-CMA), WL-LMS-CMA, WL-RLS-CMA and L-UKF-CMA.
