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
A space-time coded multiple-input multiple-output orthogonal frequency-division multiplexing （MIMO-OFDM） system is considered as a solution to the future wideband wireless communication system. This paper proposes a...A space-time coded multiple-input multiple-output orthogonal frequency-division multiplexing （MIMO-OFDM） system is considered as a solution to the future wideband wireless communication system. This paper proposes an extended Kalman filtering-based （EKF-based） channel estimation method for space-time coded MIMO-OFDM systems. The proposed method can exploit pilot symbols and an extended Kalman filter to estimate channel without any prior knowledge of channel statistics. In comparison with the least square （LS） and the least mean square （LMS） methods, the EKF-based approach has a better performance in theory. Computer simulations demonstrate the proposed method outperforms the LS and LMS methods. Therefore it can offer draznatic system performance improvement at a modest cost of computational complexity.展开更多
The nonlinear filtering for a class of discrete-time stochastic dynamic systems whose measurement equations contain linear (or universal linearizable) components and nonlinear components which are mutually statistical...The nonlinear filtering for a class of discrete-time stochastic dynamic systems whose measurement equations contain linear (or universal linearizable) components and nonlinear components which are mutually statistical independent is investigated. A two-step measurement update is proposed for the filtering of the systems. The first-step update is a linear (or universal linearization) measurement correction which introduces an intermediate estimate, while the second-step nonlinear linearization update produces the final posterior estimate based on the first-step estimate. Since the first measurement correction is a linear or universal linearization update, it provides an accurate linearization reference point for the second nonlinear measurement update. Two simulation examples show superiority of the new estimation method.展开更多
In this paper,an efficient model structure composed of a second-order resistance-capacitance network and a simply analytical open circuit voltage versus state of charge(SOC) map is applied to characterize the voltage ...In this paper,an efficient model structure composed of a second-order resistance-capacitance network and a simply analytical open circuit voltage versus state of charge(SOC) map is applied to characterize the voltage behavior of a lithium iron phosphate battery for electric vehicles(EVs).As a result,the overpotentials of the battery can be depicted using a second-order circuit network and the model parameterization can be realized under any battery loading profile,without a special characterization experiment.In order to ensure good robustness,extended Kalman filtering is adopted to recursively implement the calibration process.The linearization involved in the calibration algorithm is realized through recurrent derivatives in a recursive form.Validation results show that the recursively calibrated battery model can accurately delineate the battery voltage behavior under two different transient power operating conditions.A comparison with a first-order model indicates that the recursively calibrated second-order model has a comparable accuracy in a major part of the battery SOC range and a better performance when the SOC is relatively low.展开更多
To provide stable and accurate position information of control points in a complex coastal environment,an adaptive iterated extended Kalman filter(AIEKF)for fixed-point positioning integrating global navigation satell...To provide stable and accurate position information of control points in a complex coastal environment,an adaptive iterated extended Kalman filter(AIEKF)for fixed-point positioning integrating global navigation satellite system,inertial navigation system,and ultra wide band(UWB)is proposed.In thismethod,the switched global navigation satellite system(GNSS)and UWB measurement are used as the measurement of the proposed filter.For the data fusion filter,the expectation-maximization(EM)based IEKF is used as the forward filter,then,the Rauch-Tung-Striebel smoother for IEKF filter’s result smoothing.Tests illustrate that the proposed AIEKF is able to provide an accurate estimation.展开更多
It is necessary to know the status of adhesion conditions between wheel and rail for efficient accelerating and decelerating of railroad vehicle.The proper estimation of adhesion conditions and their real-time impleme...It is necessary to know the status of adhesion conditions between wheel and rail for efficient accelerating and decelerating of railroad vehicle.The proper estimation of adhesion conditions and their real-time implementation is considered a challenge for scholars.In this paper,the development of simulation model of extended Kalman filter(EKF)in MATLAB/Simulink is presented to estimate various railway wheelset parameters in different contact conditions of track.Due to concurrent in nature,the Xilinx®System-on-Chip Zynq Field Programmable Gate Array(FPGA)device is chosen to check the onboard estimation ofwheel-rail interaction parameters by using the National Instruments(NI)myRIO®development board.The NImyRIO®development board is flexible to deal with nonlinearities,uncertain changes,and fastchanging dynamics in real-time occurring in wheel-rail contact conditions during vehicle operation.The simulated dataset of the railway nonlinear wheelsetmodel is tested on FPGA-based EKF with different track conditions and with accelerating and decelerating operations of the vehicle.The proposed model-based estimation of railway wheelset parameters is synthesized on FPGA and its simulation is carried out for functional verification on FPGA.The obtained simulation results are aligned with the simulation results obtained through MATLAB.To the best of our knowledge,this is the first time study that presents the implementation of a model-based estimation of railway wheelset parameters on FPGA and its functional verification.The functional behavior of the FPGA-based estimator shows that these results are the addition of current knowledge in the field of the railway.展开更多
The goal of this work is to provide an understanding of estimation technology for both linear and nonlinear dynamical systems.A critical analysis of both the Kalman filter(KF)and the extended Kalman filter(EKF)will be...The goal of this work is to provide an understanding of estimation technology for both linear and nonlinear dynamical systems.A critical analysis of both the Kalman filter(KF)and the extended Kalman filter(EKF)will be provided,along with examples to illustrate some important issues related to filtering convergence due to system modeling.A conceptual explanation of the topic with illustrative examples provided in the paper can help the readers capture the essential principles and avoid making mistakes while implementing the algorithms.Adding fictitious process noise to the system model assumed by the filter designers for convergence assurance is being investigated.A comparison of estimation accuracy with linear and nonlinear measurements is made.Parameter identification by the state estimation method through the augmentation of the state vector is also discussed.The intended readers of this article may include researchers,working engineers,or engineering students.This article can serve as a better understanding of the topic as well as a further connection to probability,stochastic process,and system theory.The lesson learned enables the readers to interpret the theory and algorithms appropriately and precisely implement the computer codes that nicely match the estimation algorithms related to the mathematical equations.This is especially helpful for those readers with less experience or background in optimal estimation theory,as it provides a solid foundation for further study on the theory and applications of the topic.展开更多
Online estimation of electromechanical oscillation parameters provides essential information to prevent system instability and blackout and helps to identify event categories and locations.We formulate the problem as ...Online estimation of electromechanical oscillation parameters provides essential information to prevent system instability and blackout and helps to identify event categories and locations.We formulate the problem as a state space model and employ the extended Kalman filter to estimate oscillation frequencies and damping factors directly based on data from phasor measurement units.Due to considerations of communication burdens and privacy concerns,a fully distributed algorithm is proposed using diffusion extended Kalman filter.The effectiveness of proposed algorithms is confirmed by both simulated and real data collected during events in State Grid Jiangsu Electric Power Company.展开更多
The state-space neural network and extended Kalman filter model is used to directly predict the optimal timing plan that corresponds to futuristic traffic conditions in real time with the purposes of avoiding the lagg...The state-space neural network and extended Kalman filter model is used to directly predict the optimal timing plan that corresponds to futuristic traffic conditions in real time with the purposes of avoiding the lagging of the signal timing plans to traffic conditions. Utilizing the traffic conditions in current and former intervals, the network topology of the state-space neural network （SSNN）, which is derived from the geometry of urban arterial routes, is used to predict the optimal timing plan corresponding to the traffic conditions in the next time interval. In order to improve the effectiveness of the SSNN, the extended Kalman filter （EKF） is proposed to train the SSNN instead of conventional approaches. Raw traffic data of the Guangzhou Road, Nanjing and the optimal signal timing plan generated by a multi-objective optimization genetic algorithm are applied to test the performance of the proposed model. The results indicate that compared with the SSNN and the BP neural network, the proposed model can closely match the optimal timing plans in futuristic states with higher efficiency.展开更多
A speed sensorless vector control system of induction motor with estimated rotor speed and rotor flux using a new reduced order extended Kalman filter is proposed. With this method, two rotor flux components are sele...A speed sensorless vector control system of induction motor with estimated rotor speed and rotor flux using a new reduced order extended Kalman filter is proposed. With this method, two rotor flux components are selected as the state variables, and the rotor speed as an estimated parameter is regarded as an augmented state variable. The algorithm with reduced order decreases the computational complexity and makes the proposed estimator feasible to be implemented in real time. The simulation results show high accuracy of the estimation algorithm and good performance of speed control, and verify the usefulness of the proposed algorithm.展开更多
This study investigates how the events of deception attacks are distributed during the fusion of multi-sensor nonlinear systems.First,a deception attack with limited energy(DALE)is introduced under the framework of di...This study investigates how the events of deception attacks are distributed during the fusion of multi-sensor nonlinear systems.First,a deception attack with limited energy(DALE)is introduced under the framework of distributed extended Kalman consensus filtering(DEKCF).Next,a hypothesis testing-based mechanism to detect the abnormal data generated by DALE,in the presence of the error term caused by the linearization of the nonlinear system,is established.Once the DALE is detected,a new rectification strategy can be triggered to recalibrate the abnormal data,restoring it to its normal state.Then,an attack-resilient DEKCF(AR-DEKCF)algorithm is proposed,and its fusion estimation errors are demonstrated to satisfy the mean square exponential boundedness performance,under appropriate conditions.Finally,the effectiveness of the AR-DEKCF algorithm is confirmed through simulations involving multi-unmanned aerial vehicle(multi-UAV)tracking problems.展开更多
A new method of unscented extended Kalman filter （UEKF） for nonlinear system is presented. This new method is a combination of the unscented transformation and the extended Kalman filter （EKF）. The extended Kalman...A new method of unscented extended Kalman filter （UEKF） for nonlinear system is presented. This new method is a combination of the unscented transformation and the extended Kalman filter （EKF）. The extended Kalman filter is similar to that in a conventional EKF. However, in every running step of the EKF the unscented transformation is running, the deterministic sample is caught by unscented transformation, then posterior mean of non- lineadty is caught by propagating, but the posterior covariance of nonlinearity is caught by linearizing. The accuracy of new method is a little better than that of the unscented Kalman filter （UKF）, however, the computational time of the UEKF is much less than that of the UKF.展开更多
Vehicle state and tire-road adhesion are of great use and importance to vehicle active safety control systems. However, it is always not easy to obtain the information with high accuracy and low expense. Recently, man...Vehicle state and tire-road adhesion are of great use and importance to vehicle active safety control systems. However, it is always not easy to obtain the information with high accuracy and low expense. Recently, many estimation methods have been put forward to solve such problems, in which Kalman filter becomes one of the most popular techniques. Nevertheless, the use of complicated model always leads to poor real-time estimation while the role of road friction coefficient is often ignored. For the purpose of enhancing the real time performance of the algorithm and pursuing precise estimation of vehicle states, a model-based estimator is proposed to conduct combined estimation of vehicle states and road friction coefficients. The estimator is designed based on a three-DOF vehicle model coupled with the Highway Safety Research Institute（HSRI） tire model; the dual extended Kalman filter （DEKF） technique is employed, which can be regarded as two extended Kalman filters operating and communicating simultaneously. Effectiveness of the estimation is firstly examined by comparing the outputs of the estimator with the responses of the vehicle model in CarSim under three typical road adhesion conditions（high-friction, low-friction, and joint-friction）. On this basis, driving simulator experiments are carried out to further investigate the practical application of the estimator. Numerical results from CarSim and driving simulator both demonstrate that the estimator designed is capable of estimating the vehicle states and road friction coefficient with reasonable accuracy. The DEKF-based estimator proposed provides the essential information for the vehicle active control system with low expense and decent precision, and offers the possibility of real car application in future.展开更多
The Extended Kalman Filter(EKF)has received abundant attention with the growing demands for robotic localization.The EKF algorithm is more realistic in non-linear systems,which has an autonomous white noise in both th...The Extended Kalman Filter(EKF)has received abundant attention with the growing demands for robotic localization.The EKF algorithm is more realistic in non-linear systems,which has an autonomous white noise in both the system and the estimation model.Also,in the field of engineering,most systems are non-linear.Therefore,the EKF attracts more attention than the Kalman Filter(KF).In this paper,we propose an EKF-based localization algorithm by edge computing,and a mobile robot is used to update its location concerning the landmark.This localization algorithm aims to achieve a high level of accuracy and wider coverage.The proposed algorithm is helpful for the research related to the use of EKF localization algorithms.Simulation results demonstrate that,under the situations presented in the paper,the proposed localization algorithm is more accurate compared with the current state-of-the-art localization algorithms.展开更多
Unknown input observer is one of the most famous strategies for robust fault diagnosis of linear systems, but studies on nonlinear cases are not sufficient. On the other hand, the extended Kalman filter （EKF） is wel...Unknown input observer is one of the most famous strategies for robust fault diagnosis of linear systems, but studies on nonlinear cases are not sufficient. On the other hand, the extended Kalman filter （EKF） is wellknown in nonlinear estimation, and its convergence as an observer of nonlinear deterministic system has been derived recently. By combining the EKF and the unknown input Kalman filter, we propose a robust nonlinear estimator called unknown input EKF （UIEKF） and prove its convergence as a nonlinear robust observer under some mild conditions using linear matrix inequality （LMI）. Simulation of a three-tank system “DTS200”, a benchmark in process control, demonstrates the robustness and effectiveness of the UIEKF as an observer for nonlinear systems with uncertainty, and the fault diagnosis based on the UIEKF is found successful.展开更多
A novel time-domain identification technique is developed for the seismic response analysis of soil-structure interaction.A two-degree-of-freedom (2DOF) model with eight lumped parameters is adopted to model the frequ...A novel time-domain identification technique is developed for the seismic response analysis of soil-structure interaction.A two-degree-of-freedom (2DOF) model with eight lumped parameters is adopted to model the frequency- dependent behavior of soils.For layered soil,the equivalent eight parameters of the 2DOF model are identified by the extended Kalman filter (EKF) method using recorded seismic data.The polynomial approximations for derivation of state estimators are applied in the EKF procedure.A realistic identification example is given for the layered-soil of a building site in Anchorage,Alaska in the United States.Results of the example demonstrate the feasibility and practicality of the proposed identification technique.The 2DOF soil model and the identification technique can be used for nonlinear response analysis of soil-structure interaction in the time-domain for layered or complex soil conditions.The identified parameters can be stored in a database tor use in other similar soil conditions,lfa universal database that covers information related to most soil conditions is developed in the thture,engineers could conveniently perform time history analyses of soil-structural interaction.展开更多
The carbon dioxide removal system is the most critical system for controlling CO2 mass concentration in long-term manned spacecraft.In order to ensure the controlling CO2 mass concentration in the cabin within the all...The carbon dioxide removal system is the most critical system for controlling CO2 mass concentration in long-term manned spacecraft.In order to ensure the controlling CO2 mass concentration in the cabin within the allowable range,the state of CO2 removal system needs to be estimated in real time.In this paper,the mathematical model is firstly established that describes the actual system conditions and then the Galerkin-based extended Kalman filter algorithm is proposed for the estimation of the state of CO2.This method transforms partial differential equation to ordinary differential equation by using Galerkin approaching method,and then carries out the state estimation by using extended Kalman filter.Simulation experiments were performed with the qualification of the actual manned space mission.The simulation results show that the proposed method can effectively estimate the system state while avoiding the problem of dimensional explosion,and has strong robustness regarding measurement noise.Thus,this method can establish a basis for system fault diagnosis and fault positioning.展开更多
Electric arc furnaces(EAFs)represent one of the most disturbing loads in the subtransmission or transmission electric power systems.Therefore,it is necessary to build a practical model to descript the behavior of EAF ...Electric arc furnaces(EAFs)represent one of the most disturbing loads in the subtransmission or transmission electric power systems.Therefore,it is necessary to build a practical model to descript the behavior of EAF in the simulation of power system for power quality issues.This paper deals with the modeling of EAF based on the combination of extended Kalman filter to identify the parameter of arc current and the power balance equation to obtain the dynamic,multi-valued u-i characteristics of EAF load.The whole EAF systems are simulated by means of power system blockset in Matlab to validate the proposed EAF model.This model can also be used to assess the impact of the new plant or highly varying nonlinear loads that exhibit chaos in power systems.展开更多
In this paper,the Global Positioning System(GPS)interferometer provides the preliminarily computed quaternions,which are then employed as the measurement of the extended Kalman filter(EKF)for the attitude determinatio...In this paper,the Global Positioning System(GPS)interferometer provides the preliminarily computed quaternions,which are then employed as the measurement of the extended Kalman filter(EKF)for the attitude determination system.The estimated quaternion elements from the EKF output with noticeably improved precision can be converted to the Euler angles for navigation applications.The aim of the study is twofold.Firstly,the GPS-based computed quaternion vector is utilized to avoid the singularity problem.Secondly,the quaternion estimator based on the EKF is adopted to improve the estimation accuracy.Determination of the unknown baseline vector between the antennas sits at the heart of GPS-based attitude determination.Although utilization of the carrier phase observables enables the relative positioning to achieve centimeter level accuracy,however,the quaternion elements derived from the GPS interferometer are inherently noisy.This is due to the fact that the baseline vectors estimated by the least-squares method are based on the raw double-differenced measurements.Construction of the transformation matrix is accessible according to the estimate of baseline vectors and thereafter the computed quaternion elements can be derived.Using the Euler angle method,the process becomes meaningless when the angles are at 90where the singularity problem occurs.A good alternative is the quaternion approach,which possesses advantages over the equivalent Euler angle based transformation since they apply to all attitudes.Simulation results on the attitude estimation performance based on the proposed method will be presented and compared to the conventional method.The results presented in this paper elucidate the superiority of proposed algorithm.展开更多
This paper presents a more accurate battery state of charge(SOC)and state of health(SOH)estimation method.A lithium battery is represented by a nonlinear two-order resistance-capacitance equivalent circuit model.The m...This paper presents a more accurate battery state of charge(SOC)and state of health(SOH)estimation method.A lithium battery is represented by a nonlinear two-order resistance-capacitance equivalent circuit model.The model parameters are estimated by searching least square error optimization algorithm.Precisely defined by this method,the model parameters allow to accurately determine the capacity of the battery,which in turn allows to specify the SOC prediction value used as a basis for the SOH value.Application of the extended Kalman filter(EKF)removes the need of prior known initial SOC,and applying the fuzzy logic helps to eliminate the measurement and process noise.Simulation results obtained during the urban dynamometer driving schedule(UDDS)test show that the maximum error in estimation of the battery SOC is 0.66%.Battery capacity is estimate by offline updated Kalman filter,and then SOH will be predicted.The maximum error in estimation of the battery capacity is 1.55%.展开更多
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Project supported by the National Natural Science Foundation of China （Grant No.60572157）, and the National High- Technology Research and Development Program of China （Grant No.2003AA123310）
文摘A space-time coded multiple-input multiple-output orthogonal frequency-division multiplexing （MIMO-OFDM） system is considered as a solution to the future wideband wireless communication system. This paper proposes an extended Kalman filtering-based （EKF-based） channel estimation method for space-time coded MIMO-OFDM systems. The proposed method can exploit pilot symbols and an extended Kalman filter to estimate channel without any prior knowledge of channel statistics. In comparison with the least square （LS） and the least mean square （LMS） methods, the EKF-based approach has a better performance in theory. Computer simulations demonstrate the proposed method outperforms the LS and LMS methods. Therefore it can offer draznatic system performance improvement at a modest cost of computational complexity.
文摘The nonlinear filtering for a class of discrete-time stochastic dynamic systems whose measurement equations contain linear (or universal linearizable) components and nonlinear components which are mutually statistical independent is investigated. A two-step measurement update is proposed for the filtering of the systems. The first-step update is a linear (or universal linearization) measurement correction which introduces an intermediate estimate, while the second-step nonlinear linearization update produces the final posterior estimate based on the first-step estimate. Since the first measurement correction is a linear or universal linearization update, it provides an accurate linearization reference point for the second nonlinear measurement update. Two simulation examples show superiority of the new estimation method.
基金Project (No. 61004092) supported by the National Natural ScienceFoundation of China
文摘In this paper,an efficient model structure composed of a second-order resistance-capacitance network and a simply analytical open circuit voltage versus state of charge(SOC) map is applied to characterize the voltage behavior of a lithium iron phosphate battery for electric vehicles(EVs).As a result,the overpotentials of the battery can be depicted using a second-order circuit network and the model parameterization can be realized under any battery loading profile,without a special characterization experiment.In order to ensure good robustness,extended Kalman filtering is adopted to recursively implement the calibration process.The linearization involved in the calibration algorithm is realized through recurrent derivatives in a recursive form.Validation results show that the recursively calibrated battery model can accurately delineate the battery voltage behavior under two different transient power operating conditions.A comparison with a first-order model indicates that the recursively calibrated second-order model has a comparable accuracy in a major part of the battery SOC range and a better performance when the SOC is relatively low.
基金supported in part by the Shandong Natural Science Foundation under Grant ZR2020MF067.
文摘To provide stable and accurate position information of control points in a complex coastal environment,an adaptive iterated extended Kalman filter(AIEKF)for fixed-point positioning integrating global navigation satellite system,inertial navigation system,and ultra wide band(UWB)is proposed.In thismethod,the switched global navigation satellite system(GNSS)and UWB measurement are used as the measurement of the proposed filter.For the data fusion filter,the expectation-maximization(EM)based IEKF is used as the forward filter,then,the Rauch-Tung-Striebel smoother for IEKF filter’s result smoothing.Tests illustrate that the proposed AIEKF is able to provide an accurate estimation.
文摘It is necessary to know the status of adhesion conditions between wheel and rail for efficient accelerating and decelerating of railroad vehicle.The proper estimation of adhesion conditions and their real-time implementation is considered a challenge for scholars.In this paper,the development of simulation model of extended Kalman filter(EKF)in MATLAB/Simulink is presented to estimate various railway wheelset parameters in different contact conditions of track.Due to concurrent in nature,the Xilinx®System-on-Chip Zynq Field Programmable Gate Array(FPGA)device is chosen to check the onboard estimation ofwheel-rail interaction parameters by using the National Instruments(NI)myRIO®development board.The NImyRIO®development board is flexible to deal with nonlinearities,uncertain changes,and fastchanging dynamics in real-time occurring in wheel-rail contact conditions during vehicle operation.The simulated dataset of the railway nonlinear wheelsetmodel is tested on FPGA-based EKF with different track conditions and with accelerating and decelerating operations of the vehicle.The proposed model-based estimation of railway wheelset parameters is synthesized on FPGA and its simulation is carried out for functional verification on FPGA.The obtained simulation results are aligned with the simulation results obtained through MATLAB.To the best of our knowledge,this is the first time study that presents the implementation of a model-based estimation of railway wheelset parameters on FPGA and its functional verification.The functional behavior of the FPGA-based estimator shows that these results are the addition of current knowledge in the field of the railway.
基金supported by the Ministry of Science and Technology,Taiwan(Grant Number MOST 110-2221-E-019-042).
文摘The goal of this work is to provide an understanding of estimation technology for both linear and nonlinear dynamical systems.A critical analysis of both the Kalman filter(KF)and the extended Kalman filter(EKF)will be provided,along with examples to illustrate some important issues related to filtering convergence due to system modeling.A conceptual explanation of the topic with illustrative examples provided in the paper can help the readers capture the essential principles and avoid making mistakes while implementing the algorithms.Adding fictitious process noise to the system model assumed by the filter designers for convergence assurance is being investigated.A comparison of estimation accuracy with linear and nonlinear measurements is made.Parameter identification by the state estimation method through the augmentation of the state vector is also discussed.The intended readers of this article may include researchers,working engineers,or engineering students.This article can serve as a better understanding of the topic as well as a further connection to probability,stochastic process,and system theory.The lesson learned enables the readers to interpret the theory and algorithms appropriately and precisely implement the computer codes that nicely match the estimation algorithms related to the mathematical equations.This is especially helpful for those readers with less experience or background in optimal estimation theory,as it provides a solid foundation for further study on the theory and applications of the topic.
基金This work is supported by the Science and Technology Project of State Grid Corporation(No.5455HJ160007).
文摘Online estimation of electromechanical oscillation parameters provides essential information to prevent system instability and blackout and helps to identify event categories and locations.We formulate the problem as a state space model and employ the extended Kalman filter to estimate oscillation frequencies and damping factors directly based on data from phasor measurement units.Due to considerations of communication burdens and privacy concerns,a fully distributed algorithm is proposed using diffusion extended Kalman filter.The effectiveness of proposed algorithms is confirmed by both simulated and real data collected during events in State Grid Jiangsu Electric Power Company.
基金The National Natural Science Foundation of China (No.50422283)the Soft Science Research Project of Ministry of Housing and Urban-Rural Development of China (No.2008-K5-14)
文摘The state-space neural network and extended Kalman filter model is used to directly predict the optimal timing plan that corresponds to futuristic traffic conditions in real time with the purposes of avoiding the lagging of the signal timing plans to traffic conditions. Utilizing the traffic conditions in current and former intervals, the network topology of the state-space neural network （SSNN）, which is derived from the geometry of urban arterial routes, is used to predict the optimal timing plan corresponding to the traffic conditions in the next time interval. In order to improve the effectiveness of the SSNN, the extended Kalman filter （EKF） is proposed to train the SSNN instead of conventional approaches. Raw traffic data of the Guangzhou Road, Nanjing and the optimal signal timing plan generated by a multi-objective optimization genetic algorithm are applied to test the performance of the proposed model. The results indicate that compared with the SSNN and the BP neural network, the proposed model can closely match the optimal timing plans in futuristic states with higher efficiency.
文摘A speed sensorless vector control system of induction motor with estimated rotor speed and rotor flux using a new reduced order extended Kalman filter is proposed. With this method, two rotor flux components are selected as the state variables, and the rotor speed as an estimated parameter is regarded as an augmented state variable. The algorithm with reduced order decreases the computational complexity and makes the proposed estimator feasible to be implemented in real time. The simulation results show high accuracy of the estimation algorithm and good performance of speed control, and verify the usefulness of the proposed algorithm.
基金supported by the National Natural Science Foundation of China(Nos.62103283 and 12371308)。
文摘This study investigates how the events of deception attacks are distributed during the fusion of multi-sensor nonlinear systems.First,a deception attack with limited energy(DALE)is introduced under the framework of distributed extended Kalman consensus filtering(DEKCF).Next,a hypothesis testing-based mechanism to detect the abnormal data generated by DALE,in the presence of the error term caused by the linearization of the nonlinear system,is established.Once the DALE is detected,a new rectification strategy can be triggered to recalibrate the abnormal data,restoring it to its normal state.Then,an attack-resilient DEKCF(AR-DEKCF)algorithm is proposed,and its fusion estimation errors are demonstrated to satisfy the mean square exponential boundedness performance,under appropriate conditions.Finally,the effectiveness of the AR-DEKCF algorithm is confirmed through simulations involving multi-unmanned aerial vehicle(multi-UAV)tracking problems.
文摘A new method of unscented extended Kalman filter （UEKF） for nonlinear system is presented. This new method is a combination of the unscented transformation and the extended Kalman filter （EKF）. The extended Kalman filter is similar to that in a conventional EKF. However, in every running step of the EKF the unscented transformation is running, the deterministic sample is caught by unscented transformation, then posterior mean of non- lineadty is caught by propagating, but the posterior covariance of nonlinearity is caught by linearizing. The accuracy of new method is a little better than that of the unscented Kalman filter （UKF）, however, the computational time of the UEKF is much less than that of the UKF.
基金supported by National Natural Science Foundation of China(Grant Nos. 51075176, 51105165)
文摘Vehicle state and tire-road adhesion are of great use and importance to vehicle active safety control systems. However, it is always not easy to obtain the information with high accuracy and low expense. Recently, many estimation methods have been put forward to solve such problems, in which Kalman filter becomes one of the most popular techniques. Nevertheless, the use of complicated model always leads to poor real-time estimation while the role of road friction coefficient is often ignored. For the purpose of enhancing the real time performance of the algorithm and pursuing precise estimation of vehicle states, a model-based estimator is proposed to conduct combined estimation of vehicle states and road friction coefficients. The estimator is designed based on a three-DOF vehicle model coupled with the Highway Safety Research Institute（HSRI） tire model; the dual extended Kalman filter （DEKF） technique is employed, which can be regarded as two extended Kalman filters operating and communicating simultaneously. Effectiveness of the estimation is firstly examined by comparing the outputs of the estimator with the responses of the vehicle model in CarSim under three typical road adhesion conditions（high-friction, low-friction, and joint-friction）. On this basis, driving simulator experiments are carried out to further investigate the practical application of the estimator. Numerical results from CarSim and driving simulator both demonstrate that the estimator designed is capable of estimating the vehicle states and road friction coefficient with reasonable accuracy. The DEKF-based estimator proposed provides the essential information for the vehicle active control system with low expense and decent precision, and offers the possibility of real car application in future.
基金The work of J.-H.Lee was supported by the Cross-Ministry Giga KOREA Project grant funded by the Korea Government(MSIT)(No.GK20P0400,Development of Mobile Edge Computing Platform Technology for URLLC Services).
文摘The Extended Kalman Filter(EKF)has received abundant attention with the growing demands for robotic localization.The EKF algorithm is more realistic in non-linear systems,which has an autonomous white noise in both the system and the estimation model.Also,in the field of engineering,most systems are non-linear.Therefore,the EKF attracts more attention than the Kalman Filter(KF).In this paper,we propose an EKF-based localization algorithm by edge computing,and a mobile robot is used to update its location concerning the landmark.This localization algorithm aims to achieve a high level of accuracy and wider coverage.The proposed algorithm is helpful for the research related to the use of EKF localization algorithms.Simulation results demonstrate that,under the situations presented in the paper,the proposed localization algorithm is more accurate compared with the current state-of-the-art localization algorithms.
基金Supported by the National Natural Science Foundation of China (No. 60234010, 60574084)the Field Bus Technology & Automation Key Lab of Beijing at North China and the National 973 Program of China (No. 2002CB312200).
文摘Unknown input observer is one of the most famous strategies for robust fault diagnosis of linear systems, but studies on nonlinear cases are not sufficient. On the other hand, the extended Kalman filter （EKF） is wellknown in nonlinear estimation, and its convergence as an observer of nonlinear deterministic system has been derived recently. By combining the EKF and the unknown input Kalman filter, we propose a robust nonlinear estimator called unknown input EKF （UIEKF） and prove its convergence as a nonlinear robust observer under some mild conditions using linear matrix inequality （LMI）. Simulation of a three-tank system “DTS200”, a benchmark in process control, demonstrates the robustness and effectiveness of the UIEKF as an observer for nonlinear systems with uncertainty, and the fault diagnosis based on the UIEKF is found successful.
文摘A novel time-domain identification technique is developed for the seismic response analysis of soil-structure interaction.A two-degree-of-freedom (2DOF) model with eight lumped parameters is adopted to model the frequency- dependent behavior of soils.For layered soil,the equivalent eight parameters of the 2DOF model are identified by the extended Kalman filter (EKF) method using recorded seismic data.The polynomial approximations for derivation of state estimators are applied in the EKF procedure.A realistic identification example is given for the layered-soil of a building site in Anchorage,Alaska in the United States.Results of the example demonstrate the feasibility and practicality of the proposed identification technique.The 2DOF soil model and the identification technique can be used for nonlinear response analysis of soil-structure interaction in the time-domain for layered or complex soil conditions.The identified parameters can be stored in a database tor use in other similar soil conditions,lfa universal database that covers information related to most soil conditions is developed in the thture,engineers could conveniently perform time history analyses of soil-structural interaction.
基金Project(050403)supported by Pre-research Project in the Manned Space Filed of China。
文摘The carbon dioxide removal system is the most critical system for controlling CO2 mass concentration in long-term manned spacecraft.In order to ensure the controlling CO2 mass concentration in the cabin within the allowable range,the state of CO2 removal system needs to be estimated in real time.In this paper,the mathematical model is firstly established that describes the actual system conditions and then the Galerkin-based extended Kalman filter algorithm is proposed for the estimation of the state of CO2.This method transforms partial differential equation to ordinary differential equation by using Galerkin approaching method,and then carries out the state estimation by using extended Kalman filter.Simulation experiments were performed with the qualification of the actual manned space mission.The simulation results show that the proposed method can effectively estimate the system state while avoiding the problem of dimensional explosion,and has strong robustness regarding measurement noise.Thus,this method can establish a basis for system fault diagnosis and fault positioning.
文摘Electric arc furnaces(EAFs)represent one of the most disturbing loads in the subtransmission or transmission electric power systems.Therefore,it is necessary to build a practical model to descript the behavior of EAF in the simulation of power system for power quality issues.This paper deals with the modeling of EAF based on the combination of extended Kalman filter to identify the parameter of arc current and the power balance equation to obtain the dynamic,multi-valued u-i characteristics of EAF load.The whole EAF systems are simulated by means of power system blockset in Matlab to validate the proposed EAF model.This model can also be used to assess the impact of the new plant or highly varying nonlinear loads that exhibit chaos in power systems.
基金the Ministry of Science and Technology of the Republic of China[Grant No.MOST 108-2221-E-019-013].
文摘In this paper,the Global Positioning System(GPS)interferometer provides the preliminarily computed quaternions,which are then employed as the measurement of the extended Kalman filter(EKF)for the attitude determination system.The estimated quaternion elements from the EKF output with noticeably improved precision can be converted to the Euler angles for navigation applications.The aim of the study is twofold.Firstly,the GPS-based computed quaternion vector is utilized to avoid the singularity problem.Secondly,the quaternion estimator based on the EKF is adopted to improve the estimation accuracy.Determination of the unknown baseline vector between the antennas sits at the heart of GPS-based attitude determination.Although utilization of the carrier phase observables enables the relative positioning to achieve centimeter level accuracy,however,the quaternion elements derived from the GPS interferometer are inherently noisy.This is due to the fact that the baseline vectors estimated by the least-squares method are based on the raw double-differenced measurements.Construction of the transformation matrix is accessible according to the estimate of baseline vectors and thereafter the computed quaternion elements can be derived.Using the Euler angle method,the process becomes meaningless when the angles are at 90where the singularity problem occurs.A good alternative is the quaternion approach,which possesses advantages over the equivalent Euler angle based transformation since they apply to all attitudes.Simulation results on the attitude estimation performance based on the proposed method will be presented and compared to the conventional method.The results presented in this paper elucidate the superiority of proposed algorithm.
基金Open Fund Project of State Key Laboratory of Large Electric Transmission Systems and Equipment Technology(No.SKLLDJ042017005)。
文摘This paper presents a more accurate battery state of charge(SOC)and state of health(SOH)estimation method.A lithium battery is represented by a nonlinear two-order resistance-capacitance equivalent circuit model.The model parameters are estimated by searching least square error optimization algorithm.Precisely defined by this method,the model parameters allow to accurately determine the capacity of the battery,which in turn allows to specify the SOC prediction value used as a basis for the SOH value.Application of the extended Kalman filter(EKF)removes the need of prior known initial SOC,and applying the fuzzy logic helps to eliminate the measurement and process noise.Simulation results obtained during the urban dynamometer driving schedule(UDDS)test show that the maximum error in estimation of the battery SOC is 0.66%.Battery capacity is estimate by offline updated Kalman filter,and then SOH will be predicted.The maximum error in estimation of the battery capacity is 1.55%.
