Vertical Tire Forces Estimation of Multi-Axle Trucks Based on an Adaptive Treble Extend Kalman Filter

Vertical tire forces are essential for vehicle modelling and dynamic control.However,an evaluation of the vertical tire forces on a multi-axle truck is difficult to accomplish.The current methods require a large amount of experimental data and many sensors owing to the wide variation of the parameters and the over-constraint.To simplify the design process and reduce the demand of the sensors,this paper presents a practical approach to estimating the vertical tire forces of a multi-axle truck for dynamic control.The estimation system is based on a novel vertical force model and a proposed adaptive treble extend Kalman filter(ATEKF).To adapt to the widely varying parameters,a sliding mode update is designed to make the ATEKF adaptive,and together with the use of an initial setting update and a vertical tire force adjustment,the overall system becomes more robust.In particular,the model aims to eliminate the effects of the over-constraint and the uneven weight distribution.The results show that the ATEKF method achieves an excellent performance in a vertical force evaluation,and its performance is better than that of the treble extend Kalman filter.

WSN Mobile Target Tracking Based on Improved Snake-Extended Kalman Filtering Algorithm

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.

Improved Adaptive Iterated Extended Kalman Filter for GNSS/INS/UWB-Integrated Fixed-Point Positioning

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.

FPGA Implementation of Extended Kalman Filter for Parameters Estimation of Railway Wheelset

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.

Notes on Convergence and Modeling for the Extended Kalman Filter

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.

Unscented extended Kalman filter for target tracking

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 nonlinearity 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.

Dual Extended Kalman Filter for Combined Estimation of Vehicle State and Road Friction

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.

Extended Kalman Filter-based localization algorithm by edge computing in Wireless Sensor Networks

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.

Unknown Input Extended Kalman Filter and Applications in Nonlinear Fault Diagnosis

未知输入观察员是为线性系统的柔韧的故障诊断的最著名的策略之一，但是非线性的案例上的研究不是足够的。在另一方面，当非线性的确定的系统的一个观察员最近被导出，扩大 Kalman 过滤器(EKF ) 在非线性的评价，和它的集中是著名的。由联合 EKF 和未知输入 Kalman 过滤器，我们建议一个柔韧的非线性的评估者把未知输入称为 EKF (UIEKF ) 并且用线性矩阵不平等(LMI ) 在一些温和条件下面作为一个非线性的柔韧的观察员证明它的集中。一个三坦克的系统的模拟“ DTS200 ”，在工艺程序的控制的一个基准，基于 UIEKF 与不确定性，和故障诊断为非线性的系统作为一个观察员表明 UIEKF 的坚韧性和有效性被发现成功。

Extended Kalman filtering-based channel estimation for space-time coded MIMO-OFDM systems

时空编码了系统作为未来宽带的一个答案被认为无线通讯系统的多重输入的多重产量的直角的频率部门 multiplexing (MIMO-OFDM ) 。这份报纸建议扩大 Kalman 基于过滤器(基于 EKF ) 为时空的隧道评价方法编码了 MIMO-OFDM 系统。建议方法能利用飞行员符号和一个扩大 Kalman 过滤器没有隧道统计的任何优先的知识，估计隧道。与最少比较，平方(LS ) 和最少意味着平方(LMS ) 方法，基于 EKF 的途径在理论有更好的表演。计算机模拟证明建议方法超过 LS 和 LMS 方法。因此，它能以计算复杂性的谦虚成本为戏剧的系统性能提供改进。

Time-domain identification of dynamic properties of layered soil by using extended Kalman filter and recorded seismic data

A novel time-domain identification technique is developed for the seismic response analysis of soil-structurc interaction. A two-degree-of-freedom (2DOF) model with eight lumped parameters is adopted to model the frequencydependent 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 arc applied in the EKF procedure. A realistic identification cxamplc 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 for use in other similar soil conditions. Ifa universal database that covers information related to most soil conditions is developed in the future, engineers could conveniently perform time history analyses of soil-structural interaction.

Maneuvering Target Tracking Algorithm Based on Muti-paramter Sequential Extended Kalman Filter

Based on the information theory,the performance of maneuvering target tracking can be improved by increasing the input information( observation vector).In this paper,the estimations of radial acceleration and radial velocity obtained in the signal processing are introduced into the measurement vector by coordinate transformation.In order to solve the problem of high nonlinearity of the radial acceleration,radial velocity and the state vector,a new algorithm of multi-parameter sequential extended Kalman filter( MSEKF) is proposed.The tracking performance of this algorithm is tested and compared with the other tracking algorithms.It is shown that the proposed algorithm outperforms these algorithms in strong and weak maneuvering environments.

Application of Extended Kalman Filter to the Modeling of Electric Arc Furnace for Power Quality Issue

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.

Federal extended Kalman filter based on reconstructed observation in incomplete observations

In the estimation and identification of nonlinear system state,aiming at the adverse effect of observation missing randomly caused by detection probability of used sensor which is less than 1,a novel federal extended Kalman filter( FEKF) based on reconstructed observation in incomplete observations( ROIO) is proposed in this paper. On the basis of multi-sensor observation sets,the observation is exchanged at different times to construct a new observation set. Based on each observation set,an extended Kalman filter algorithm is used to estimate the state of the target,and then the federal filtering algorithm is used to solve the state estimation based on the multi-sensor observation data. The effect of the sensor probing probability on the filtering result and the effect of the number of sensors on the filtering result are obtained by the simulation experiment,respectively. The simulation results demonstrate effectiveness of the proposed algorithm.

Analysis of SDEs Applied to SEIR Epidemic Models by Extended Kalman Filter Method

A disease transmission model of SEIR type is discussed in a stochastic point of view. We start by formulating the SEIR epidemic model in form of a system of nonlinear differential equations and then change it to a system of nonlinear stochastic differential equations (SDEs). The numerical simulation of the resulting SDEs is done by Euler-Maruyama scheme and the parameters are estimated by adaptive Markov chain Monte Carlo and extended Kalman filter methods. The stochastic results are discussed and it is observed that with the SDE type of modeling, the parameters are also identifiable.

A Robust Extended Kalman Filter for Speed-Sensorless Control of a Linearized and Decoupled PMSM Drive

This paper uses a robust feedback linearization strategy in order to assure a good dynamic performance, stability and a decoupling of the currents for Permanent Magnet Synchronous Motor (PMSM) in a rotating reference frame (d, q). However this control requires the knowledge of certain variables (speed, torque, position) that are difficult to access or its sensors require the additional mounting space, reduce the reliability in harsh environments and increase the cost of motor. And also a stator resistance variation can induce a performance degradation of the system. Thus a sixth-order Discrete-time Extended Kalman Filter approach is proposed for on-line estimation of speed, rotor position, load torque and stator resistance in a PMSM. The interesting simulations results obtained on a PMSM subjected to the load disturbance show very well the effectiveness and good performance of the proposed nonlinear feedback control and Extended Kalman Filter algorithm for the estimation in the presence of parameter variation and measurement noise.

Design and Digital Implementation of Controller for PMSM Using Extended Kalman Filter

A novel digital implementation of speed controller for a Permanent Magnet Synchronous Motor (PMSM) with disturbance rejection using conventional observer combined with Extended Kalman Filter (EKF) is proposed. First, the EKF is constructed to achieve a precise estimation of the speed and current from the noisy measurement. Second, a proportional integral derivative (PID) controller is developed based on Linear Quadratic Regulator (LQR) to achieve speed command tracking performance. Then, an observer is designed and its error is utilized to provide load disturbance compensation. The proposed method greatly enhances the PMSM performance by reducing the control signal variation as well as the disturbance. The speed control performance is significantly improved compared to the case when we have an observer acting alone. The simulation results for the speed response and variation of the states when the PMSM is subjected to the load disturbance are presented. The results verify the effectiveness of the proposed method.

Kernel Entropy Based Extended Kalman Filter for GPS Navigation Processing

This paper investigates the kernel entropy based extended Kalman filter(EKF)as the navigation processor for the Global Navigation Satellite Systems(GNSS),such as the Global Positioning System(GPS).The algorithm is effective for dealing with non-Gaussian errors or heavy-tailed(or impulsive)interference errors,such as the multipath.The kernel minimum error entropy(MEE)and maximum correntropy criterion(MCC)based filtering for satellite navigation system is involved for dealing with non-Gaussian errors or heavy-tailed interference errors or outliers of the GPS.The standard EKF method is derived based on minimization of mean square error(MSE)and is optimal only under Gaussian assumption in case the system models are precisely established.The GPS navigation algorithm based on kernel entropy related principles,including the MEE criterion and the MCC will be performed,which is utilized not only for the time-varying adaptation but the outlier type of interference errors.The kernel entropy based design is a new approach using information from higher-order signal statistics.In information theoretic learning(ITL),the entropy principle based measure uses information from higher-order signal statistics and captures more statistical information as compared to MSE.To improve the performance under non-Gaussian environments,the proposed filter which adopts the MEE/MCC as the optimization criterion instead of using the minimum mean square error(MMSE)is utilized for mitigation of the heavy-tailed type of multipath errors.Performance assessment will be carried out to show the effectiveness of the proposed approach for positioning improvement in GPS navigation processing.

Adaptive Extended Kalman Filtering for Bearings-Only Targets Tracking Problem

An adaptive extended Kalman filtering (AEKF) is proposed for nonlinear control systems. For bearingsonly targets tracking problem, we present an adaptive extended Kalman filter which suits a nonlinear observation model and a linear dynamical model. Simulation results have shown that the adaptive extended Kalman filter for the passivetracking problem performs better than the original extended Kalman filter (EKF).