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.

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.

Two-step measurement update for extended Kalman filtering

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.

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.

Distributed Estimation of Oscillations in Power Systems: An Extended Kalman Filtering Approach

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.

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 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.

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.

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-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.

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.

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.

Estimation of Quaternion Motion for GPS-Based Attitude Determination Using the Extended Kalman Filter

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.

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).

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.

Time-varying parameters estimation with adaptive neural network EKF for missile-dual control system

In this paper, a filtering method is presented to estimate time-varying parameters of a missile dual control system with tail fins and reaction jets as control variables. In this method, the long-short-term memory(LSTM) neural network is nested into the extended Kalman filter(EKF) to modify the Kalman gain such that the filtering performance is improved in the presence of large model uncertainties. To avoid the unstable network output caused by the abrupt changes of system states,an adaptive correction factor is introduced to correct the network output online. In the process of training the network, a multi-gradient descent learning mode is proposed to better fit the internal state of the system, and a rolling training is used to implement an online prediction logic. Based on the Lyapunov second method, we discuss the stability of the system, the result shows that when the training error of neural network is sufficiently small, the system is asymptotically stable. With its application to the estimation of time-varying parameters of a missile dual control system, the LSTM-EKF shows better filtering performance than the EKF and adaptive EKF(AEKF) when there exist large uncertainties in the system model.

On extended state Kalman filter-based identification algorithm for aerodynamic parameters

In this paper, the problem of time-varying aerodynamic parameters identification under measurement noises is studied. By analyzing the key aerodynamic parameters that affect the aircraft control system, a system model with extended states for identifying equivalent aerodynamic parameters is established, and error parameters are extended to the system state, avoiding the difficulty caused by the unknown dynamic in the system. Furthermore, an identification algorithm based on extended state Kalman filter is designed, and it is proved that the algorithm has quasi-consistency, thus, the estimation error can be evaluated in real time. Finally, the simulation results under typical flight scenarios show that the designed algorithm can accurately identify aerodynamic parameters, and has desired convergence speed and convergence precision.

Airship aerodynamic model estimation using unscented Kalman filter

An airship model is made-up of aerostatic,aerodynamic,dynamic,and propulsive forces and torques.Besides others,the computation of aerodynamic forces and torques is difficult.Usually,wind tunnel experimentation and potential flow theory are used for their calculations.However,the limitations of these methods pose difficulties in their accurate calculation.In this work,an online estimation scheme based on unscented Kalman filter(UKF)is proposed for their calculation.The proposed method introduces six auxiliary states for the complete aerodynamic model.UKF uses an extended model and provides an estimate of a complete state vector along with auxiliary states.The proposed method uses the minimum auxiliary state variables for the approximation of the complete aerodynamic model that makes it computationally less intensive.UKF estimation performance is evaluated by developing a nonlinear simulation environment for University of Engineering and Technology,Taxila(UETT)airship.Estimator performance is validated by performing the error analysis based on estimation error and 2-σ uncertainty bound.For the same problem,the extended Kalman filter(EKF)is also implemented and its results are compared with UKF.The simulation results show that UKF successfully estimates the forces and torques due to the aerodynamic model with small estimation error and the comparative analysis with EKF shows that UKF improves the estimation results and also it is more suitable for the under-consideration problem.

Modified switched IMM estimator based on autoregressive extended Viterbi method for maneuvering target tracking

In this paper, a new approach of maneuvering target tracking algorithm based on the autoregressive extended Viterbi(AREV) model is proposed. In contrast to weakness of traditional constant velocity(CV) and constant acceleration(CA) models to noise effect reduction, the autoregressive(AR) part of the new model which changes the structure of state space equations is proposed. Also using a dynamic form of the state transition matrix leads to improving the rate of convergence and decreasing the noise effects. Since AR will impose the load of overmodeling to the computations, the extended Viterbi(EV) method is incorporated to AR in two cases of EV1 and EV2. According to most probable paths in the interacting multiple model(IMM) during nonmaneuvering and maneuvering parts of estimation, EV1 and EV2 respectively can decrease load of overmodeling computations and improve the AR performance. This new method is coupled with proposed detection schemes for maneuver occurrence and termination as well as for switching initializations. Appropriate design parameter values are derived for the detection schemes of maneuver occurrences and terminations. Finally, simulations demonstrate that the performance of the proposed model is better than the other older linear and also nonlinear algorithms in constant velocity motions and also in various types of maneuvers.