scholarly journals Structural Stiffness Identification Based on the Extended Kalman Filter Research

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Fenggang Wang ◽  
Xianzhang Ling ◽  
Xun Xu ◽  
Feng Zhang
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
State Equation ◽  
The State ◽  
Physical Parameters ◽  
Structural Stiffness ◽  
Structural Dynamic ◽  
Discrete State ◽  
Response Acquisition ◽  
Shear Structure

For the response acquisition of the structure section measuring points, the method of identifying the structural stiffness parameters is developed by using the extended Kalman filter. The state equation of structural system parameter is a nonlinear equation. Dispersing the structural dynamic equation by using Newmark-βmethod, the state transition matrix of discrete state equation is deduced and the solution of discrete state equation is simplified. The numerical simulation shows that the error of structural recognition doesnot exceed 5% when the noise level is 3%. It meets the requirements of the error limit of the engineering structure, which indicates that the derivation described in this paper has the robustness for the structural stiffness recognition. Shear structure parameter identification examples illustrate its applicability, and the method can also be used to identify physical parameters of large structure.

scholarly journals Tracking of pendulum using particle filter with residual resampling

2018 ◽  
Vol 7 (2.7) ◽  
pp. 12
Author(s):  
Penumarty Hiranmayi ◽  
Kola Sai Gowtham ◽  
S Koteswara Rao ◽  
V Gopi Tilak
Keyword(s):  
Monte Carlo ◽  
Kalman Filter ◽  
Particle Filter ◽  
Extended Kalman Filter ◽  
Horizontal Direction ◽  
Bayesian Filtering ◽  
Discrete State ◽  
Harmonic Motion ◽  
Simple Pendulum ◽  
Importance Resampling

The phenomenon of simple harmonic motion is more vigilantly explained using a simple pendulum. The angular motion of a pendulum is linear in nature. But the analysis of the motion along the horizontal direction is non-linear. To estimate this, several algorithms like the Kalman filter, Extended Kalman Filter etc. are adopted. Here in this paper, Particle filter is chosen which is a method to form Monte Carlo approximations to the solutions of Bayesian filtering equations. Sequential importance resampling based Particle filters are used where the filtering distributions are multi-nodal or consist of discrete state components since under these circumstances the Bayesian approximations do not always work well.

scholarly journals Estimation of lithium-ion battery state-of-charge using an extended kalman filter

2021 ◽  
Vol 10 (4) ◽  
pp. 1759-1768
Author(s):  
Mouhssine Lagraoui ◽  
Ali Nejmi ◽  
Hassan Rayhane ◽  
Abderrahim Taouni
Keyword(s):  
Kalman Filter ◽  
Lithium Ion Battery ◽  
Extended Kalman Filter ◽  
Lithium Ion ◽  
The State ◽  
Operating Conditions ◽  
State Of Charge ◽  
Ohmic Loss ◽  
Battery Management System ◽  
Transfer Resistance

The main goal of a battery management system (BMS) is to estimate parameters descriptive of the battery pack operating conditions in real-time. One of the most critical aspects of BMS systems is estimating the battery's state of charge (SOC). However, in the case of a lithium-ion battery, it is not easy to provide an accurate estimate of the state of charge. In the present paper we propose a mechanism based on an extended kalman filter (EKF) to improve the state-of-charge estimation accuracy on lithium-ion cells. The paper covers the cell modeling and the system parameters identification requirements, the experimental tests, and results analysis. We first established a mathematical model representing the dynamics of a cell. We adopted a model that comprehends terms that describe the dynamic parameters like SOC, open-circuit voltage, transfer resistance, ohmic loss, diffusion capacitance, and resistance. Then, we performed the appropriate battery discharge tests to identify the parameters of the model. Finally, the EKF filter applied to the cell test data has shown high precision in SOC estimation, even in a noisy system.

scholarly journals Angular velocity fusion of the microelectromechanical system inertial measurement unit array based on extended Kalman filter with correlated system noises

2020 ◽  
pp. 002029402091770
Author(s):  
Li Xing ◽  
Xiaowei Tu ◽  
Weixing Qian ◽  
Yang Jin ◽  
Pei Qi
Keyword(s):  
Kalman Filter ◽  
Angular Velocity ◽  
Extended Kalman Filter ◽  
Inertial Measurement Unit ◽  
Angular Rate ◽  
The State ◽  
Measurement Unit ◽  
Fusion Method ◽  
Microelectromechanical System ◽  
Inertial Measurement

The paper proposes an angular velocity fusion method of the microelectromechanical system inertial measurement unit array based on the extended Kalman filter with correlated system noises. In the proposed method, an adaptive model of the angular velocity is built according to the motion characteristics of the vehicles and it is regarded as the state equation to estimate the angular velocity. The signal model of gyroscopes and accelerometers in the microelectromechanical system inertial measurement unit array is used as the measurement equation to fuse and estimate the angular velocity. Due to the correlation of the state and measurement noises in the presented fusion model, the traditional extended Kalman filter equations are optimized, so as to accurately and reliably estimate the angular velocity. By simulating angular rates in different motion modes, such as constant and change-in-time angular rates, it is verified that the proposed method can reliably estimate angular rates, even when the angular rate has been out of the microelectromechanical system gyroscope measurement range. And results show that, compared with the traditional angular rate fusion method of microelectromechanical system inertial measurement unit array, it can estimate angular rates more accurately. Moreover, in the kinematic vehicle experiments, the performance advantage of the proposed method is also verified and the angular rate estimation accuracy can be increased by about 1.5 times compared to the traditional method.

A filter with a guaranteed asymptotic performance

1993 ◽  
Vol 441 (1911) ◽  
pp. 33-57
Keyword(s):  
Kalman Filter ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Extended Kalman Filter ◽  
Noise Level ◽  
Low Noise ◽  
The State ◽  
Optimal Probability ◽  
Expected Values

In the case of low noise levels the optimal probability density function summarizing the available information about the state of a system can be accurately approximated by the product of a gaussian function and a linear function. The approximation preserves the ability to estimate to an accuracy of O ( λ -2 ) the expected value of any twice continuously differentiable function defined on the state space. The parameter λ depends on the noise level. If the noise level in the system is low then λ is large. A new filtering method based on this approximation is described. The approximating function is updated recursively as the system evolves with time, and as new measurements of the system state are obtained. The updates preserve the ability to estimate the expected values of functions to an accuracy of O ( λ -2 ). The new filter does not store previous measurements or previous approximations to the optimal probability density function. The new filter is called the asymptotic filter, because the definition of the filter and the analysis of its properties are based on the theory of asymptotic expansion of integrals of Laplace type. An analysis of the state propagation equations shows that the asymptotic filter performs better than a particular widely used suboptimal approximation to the optimal filter, the extended Kalman filter. The extended Kalman filter does not, in general, preserve the ability to estimate expected values to an accuracy of O ( λ -2 ). The computational cost of the asymptotic filter is comparable to that of the iterated extended Kalman filter.

scholarly journals Performance and stochastic stability of the adaptive fading extended Kalman filter with the matrix forgetting factor

2016 ◽  
Vol 14 (1) ◽  
pp. 934-945
Author(s):  
Cenker Biçer ◽  
Levent Özbek ◽  
Hasan Erbay
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Extended Kalman Filter ◽  
Stochastic Systems ◽  
Estimation Error ◽  
The State ◽  
Forgetting Factor ◽  
The Matrix ◽  
Stochastic Framework ◽  
Theoretical Results

AbstractIn this paper, the stability of the adaptive fading extended Kalman filter with the matrix forgetting factor when applied to the state estimation problem with noise terms in the non–linear discrete–time stochastic systems has been analysed. The analysis is conducted in a similar manner to the standard extended Kalman filter’s stability analysis based on stochastic framework. The theoretical results show that under certain conditions on the initial estimation error and the noise terms, the estimation error remains bounded and the state estimation is stable.The importance of the theoretical results and the contribution to estimation performance of the adaptation method are demonstrated interactively with the standard extended Kalman filter in the simulation part.

The State of Charge Estimation of Lithium Battery in Electric Vehicle Based on Extended Kalman Filter

2014 ◽  
Vol 953-954 ◽  
pp. 796-799
Author(s):  
Huan Huan Sun ◽  
Jun Bi ◽  
Sai Shao
Keyword(s):  
Kalman Filter ◽  
Electric Vehicle ◽  
Extended Kalman Filter ◽  
Nonlinear Problems ◽  
Least Square Method ◽  
State Equation ◽  
State Of Charge ◽  
Least Square ◽  
Accurate Estimation ◽  
Battery State Of Charge

Accurate estimation of battery state of charge (SOC) is important to ensure operation of electric vehicle. Since a nonlinear feature exists in battery system and extended kalman filter algorithm performs well in solving nonlinear problems, the paper proposes an EKF-based method for estimating SOC. In order to obtain the accurate estimation of SOC, this paper is based on composite battery model that is a combination of three battery models. The parameters are identified using the least square method. Then a state equation and an output equation are identified. All experimental data are collected from operating EV in Beijing. The results of the experiment show  that the relative error of estimation of state of charge is reasonable, which proves this method has good estimation performance.

scholarly journals Research on the State of Charge of Lithium-Ion Battery Based on the Fractional Order Model

Energies ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 6307
Author(s):  
Lin Su ◽  
Guangxu Zhou ◽  
Dairong Hu ◽  
Yuan Liu ◽  
Yunhai Zhu
Keyword(s):  
Kalman Filter ◽  
Fractional Order ◽  
Colored Noise ◽  
Unscented Kalman Filter ◽  
The State ◽  
State Of Charge ◽  
Accurate Estimation ◽  
Order Model ◽  
Discrete State ◽  
Fractional Order Model

Accurate estimation of the state of charge (SOC) of lithium batteries is paramount to ensuring consistent battery pack operation. To improve SOC estimation accuracy and suppress colored noise in the system, a fractional order model based on an unscented Kalman filter and an H-infinity filter (FOUHIF) estimation algorithm was proposed. Firstly, the discrete state equation of a lithium battery was derived, as per the theory of fractional calculus. Then, the HPPC experiment and the PSO algorithm were used to identify the internal parameters of the second order RC and fractional order models, respectively. As discovered during working tests, the parameters identified via the fractional order model proved to be more accurate. Furthermore, the feasibility of using the FOUHIF algorithm was evaluated under the conditions of NEDC and UDDS, with obvious colored noise. Compared with the fractional order unscented Kalman filter (FOUKF) and integer order unscented Kalman filter (UKF) algorithms, the FOUHIF algorithm showed significant improvement in both the accuracy and robustness of the estimation, with maximum errors of 1.86% and 1.61% under the two working conditions, and a terminal voltage prediction error of no more than 5.29 mV.

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