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

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.

Online temperature estimation of Shell coal gasification process based on extended Kalman filter

Obtaining the temperature inside the gasifier of a Shell coal gasification process(SCGP)in real-time is very important for safe process operation.However,this temperature cannot be measured directly due to the harsh operating condition.Estimating this temperature using the extended Kalman filter(EKF)based on a simplified mechanistic model is proposed in this paper.The gasifier is partitioned into three zones.The quench pipe and the transfer duct are seen as two additional zones.A simplified mechanistic model is developed in each zone and formulated as a state-space representation.The temperature in each zone is estimated by the EKF in real-time.The proposed method is applied to an industrial SCGP and the effectiveness of the estimated temperatures is verified by a process variable both qualitatively and quan-titatively.The prediction capability of the simplified mechanistic model is validated.The effectiveness of the proposed method is further verified by comparing it to a Kalman filter-based single-zone temperature estimation method.

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.

Nonlinear Control of an Induction Motor Using a Reduced-Order Extended Sliding Mode Observer for Rotor Flux and Speed Sensorless Estimation

This article proposes an innovative strategy to the problem of non-linear estimation of states for electrical machine systems. This method allows the estimation of variables that are difficult to access or that are simply impossible to measure. Thus, as compared with a full-order sliding mode observer, in order to reduce the execution time of the estimation, a reduced-order discrete-time Extended sliding mode observer is proposed for on-line estimation of rotor flux, speed and rotor resistance in an induction motor using a robust feedback linearization control. Simulations results on Matlab-Simulink environment for a 1.8 kW induction motor are presented to prove the effectiveness and high robustness of the proposed nonlinear control and observer against modeling uncertainty and measurement noise.

SURGE FORECAST FOR AERONAUTICAL ENGINES WITH EXTENDED KALMAN ESTIMATION

Abstract In this paper,the theory of extended Kalman estimation is applied to state estimate ofcompression system, for which a nonlinear model is developed by Greitzer.A criterion ofdetermining whether surge will occur in a turbine engine is presented.The combination ofstate estimation and the criterion of determining surge forms a surge prediction algorithm,which is the theoretical basis of designing a surge indicator for the turbine engine.

Model Predictive Direct Torque Control of Permanent Magnet Synchronous Motor (PMSM) with Online Parameter Estimation Based on Extended Kalman Filter

Aiming at the torque and flux ripples in the direct torque control and the time-varying parameters for permanent magnet synchronous motor (PMSM), a model predictive direct torque control with online parameter estimation based on the extended Kalman filter for PMSM is designed. By predicting the errors of torque and flux based on the model and the current states of the system, the optimal voltage vector is selected to minimize the error of torque and flux. The stator resistance and inductance are estimated online via EKF to reduce the effect of model error and the current estimation can reduce the error caused by measurement noise. The stability of the EKF is proved in theory. The simulation experiment results show the method can estimate the motor parameters, reduce the torque, and flux ripples and improve the performance of direct torque control for permanent magnet synchronous motor (PMSM).

Speed Sensorless Vector Control of Induction Motor Based on Reduced Order Extended Kalman Filter

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.

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.

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.

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.

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.

Remaining Useful Life Prediction of Li-Po Batteries in UAVs Using Extended Kalman Filter

The use of batteries in UAVs （unmanned aerial vehicles） has become common due to some advantages in comparison with internal combustion engines such as weight reduction and better power control. However, in these vehicles it is critical to monitor the RUL （remaining useful life） of the batteries. This information can be used, for instance, as a decision support tool to define which missions could be assigned to the UAV until the next battery recharge. This work presents a methodology to predict the RUL of Li-Po （Lithium-Polymer） batteries. The approach uses an extended Kalman filter and an exponential model for the degradation evolution. The proposed methodology uses time series of battery terminal voltages, assuming that the discharge occurs under a constant current condition. Different discharge current levels were considered.The results showed that the proposed methodology provides good results, despite its simplicity.

MULTISENSOR DISTRIBUTED EXTENDED KALMAN FILTERING ALGORITHM AND ITS APPLICATION TO RADAR/IR TARGET TRACKING

A multisensor distributed extended Kalman filtering algorithm is presented for nonlinear system, in which the dynamic equation of the system and the equations of sensor’s measurements are linearized in the global estimate and global prediction respectively and the suboptimal global estimate based on all available information can be reconstructed from the estimates computed by local sensors based solely on their own local information and transmitted to the data fusion center. An analysis of the properties of the algorithm presented here shows that the global estimate has higher precision than the local one and smaller linearization error than the existing method. Finally, an application of the algorithm to radar/IR tracking of a maneuvering target is illustrated. Simulation results show the effectiveness of the algorithm.

A Model-calibration Approach to Using Complete Auxiliary Information from Stratified Sampling Survey Data

In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator（or GREG）.

On a Novel Extended Lomax Distribution with Asymmetric Properties and Its Statistical Applications

In this article,we highlight a new three-parameter heavy-tailed lifetime distribution that aims to extend the modeling possibilities of the Lomax distribution.It is called the extended Lomax distribution.The considered distribution naturally appears as the distribution of a transformation of a random variable following the logweighted power distribution recently introduced for percentage or proportion data analysis purposes.As a result,its cumulative distribution has the same functional basis as that of the Lomax distribution,but with a novel special logarithmic term depending on several parameters.The modulation of this logarithmic term reveals new types of asymetrical shapes,implying a modeling horizon beyond that of the Lomax distribution.In the first part,we examine several of its mathematical properties,such as the shapes of the related probability and hazard rate functions;stochastic comparisons;manageable expansions for various moments;and quantile properties.In particular,based on the quantile functions,various actuarial measures are discussed.In the second part,the distribution’s applicability is investigated with the use of themaximumlikelihood estimationmethod.The behavior of the obtained parameter estimates is validated by a simulation work.Insurance claim data are analyzed.We show that the proposed distribution outperforms eight well-known distributions,including the Lomax distribution and several extended Lomax distributions.In addition,we demonstrate that it gives preferable inferences from these competitor distributions in terms of risk measures.

Dynamic Load Identification for Structures with Variable Stiffness Based on Extended Kalman Filter

We introduce the extended Kalman filter(EKF)method combined with the least square estimation to identify the unknown load acting on the time-varying structure and realize the tracking of the structural parameters of the time-varying system.Firstly,we propose the dynamic load identification method when the unknown parameters are stiffness coefficients.Then,a five-degree-of-freedom slowly-varying-stiffness structure is introduced to verify the effectiveness and the accuracy of the EKF method.The results show that the EKF method can accurately identify unknown loads and structural parameters simultaneously even considering noises in the input data.

A new extended H_∞ filter for discrete nonlinear systems

Nonlinear estimation problem is investigated in this paper. By extension of a linear H_∞estimation with corrector-predictor form to nonlinear cases, a new extended H_∞filter is proposed for time-varying discrete-time nonlinear systems. The new filter has a simple observer structure based on a local linearization model, and can be viewed as a general case of the extended Kalman filter (EKF). An example demonstrates that the new filter with a suitable-chosen prescribed H_∞bound performs better than the EKF.

Model-driven full system dynamics estimation of PMSM-driven chain shell magazine

Based on the system dynamic model, a full system dynamics estimation method is proposed for a chain shell magazine driven by a permanent magnet synchronous motor(PMSM). An adaptive extended state observer(AESO) is proposed to estimate the unmeasured states and disturbance, in which the model parameters are adjusted in real time. Theoretical analysis shows that the estimation errors of the disturbances and unmeasured states converge exponentially to zero, and the parameter estimation error can be obtained from the extended state. Then, based on the extended state of the AESO, a novel parameter estimation law is designed. Due to the convergence of AESO, the novel parameter estimation law is insensitive to controllers and excitation signal. Under persistent excitation(PE) condition, the estimated parameters will converge to a compact set around the actual parameter value. Without PE signal, the estimated parameters will converge to zero for the extended state. Simulation and experimental results show that the proposed method can accurately estimate the unmeasured states and disturbance of the chain shell magazine, and the estimated parameters will converge to the actual value without strictly continuous PE signals.

Robust design of sliding mode control for airship trajectory tracking with uncertainty and disturbance estimation

The robotic airship can provide a promising aerostatic platform for many potential applications.These applications require a precise autonomous trajectory tracking control for airship.Airship has a nonlinear and uncertain dynamics.It is prone to wind disturbances that offer a challenge for a trajectory tracking control design.This paper addresses the airship trajectory tracking problem having time varying reference path.A lumped parameter estimation approach under model uncertainties and wind disturbances is opted against distributed parameters.It uses extended Kalman filter(EKF)for uncertainty and disturbance estimation.The estimated parameters are used by sliding mode controller(SMC)for ultimate control of airship trajectory tracking.This comprehensive algorithm,EKF based SMC(ESMC),is used as a robust solution to track airship trajectory.The proposed estimator provides the estimates of wind disturbances as well as model uncertainty due to the mass matrix variations and aerodynamic model inaccuracies.The stability and convergence of the proposed method are investigated using the Lyapunov stability analysis.The simulation results show that the proposed method efficiently tracks the desired trajectory.The method solves the stability,convergence,and chattering problem of SMC under model uncertainties and wind disturbances.