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.

Proactive traffic responsive control based on state-space neural network and extended Kalman filter

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.

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.

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.

Unknown Input Extended Kalman Filter and Applications in Nonlinear Fault Diagnosis

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.

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.

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.

Galerkin-based extended Kalman filter with application to CO2 removal system

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.

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

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.

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.

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.

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.

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.

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.