Unscented Kalman Filter Approach Research Articles

State of health estimation of lithium-ion battery using dual adaptive unscented Kalman filter and Coulomb counting approach

Several charging and discharging processes of lithium-ion batteries (LIBs) can lead to a battery fading and degradation effect. This may cause sudden faults, leakages, and explosions. As a result, it is highly important to estimate the state of health (SoH) of the battery to avoid any battery problems. This article proposes a novel hybrid dual adaptive unscented Kalman filter (DAUKF)-Coulomb counting approach (CCA) to efficiently state of charge (SoC) and SoH estimation of LIBs. The Gazelle optimization algorithm (GOA) is utilized in identifying LIB model parameters under various SoC conditions. It is used for minimizing the integral squared error between measured and estimated battery voltages. The battery model includes loading, fading, and various dynamic conditions. The GOA-based model has better results than other models by >8 %. The proposed hybrid DAUKF-CCA is compared with the dual adaptive extended Kalman filter (DAEKF)-CCA and other multiple algorithms. The fitness function consists of integral squared error between estimated and measured SoC of LIBs. The simulation results of the DAUKF-CCA are verified by a comparison with the measurement results performed using commercial Panasonic LiBs. The SoC results using the DAUKF-CCA are very close to the measurement results and the error is <1 %. The proposed DAUKF-CCA can ensure that the SoC and SoH estimation of LIBs is efficiently achieved.

An adaptive unscented Kalman filter approach to secure state estimation for wireless sensor networks

AbstractWireless sensor networks are vulnerable to false data injection attacks, which may mislead the state estimation. To solve this problem, this paper presents a chi‐square test‐based adaptive secure state estimation (CTASSE) algorithm for state estimation and attack detection. Taking advantage of Kalman filters, attack signal together with process noise or measurement noise are described as total white Gaussian noise with uncertain covariance matrix. The chi‐square test method is used in the adaptation of the total noise covariance and attack detection. Then, a standard adaptive unscented Kalman filter (UKF) is used for the state estimation. Finally, simulation results show that the proposed CTASSE algorithm performs better than other UKFs in state estimation and is also effective in real‐time attack detection.

Identification of linear and nonlinear flutter derivatives of bridge decks by unscented Kalman filter approach from free vibration or stochastic buffeting response

This study presents an unscented Kalman filter (UKF) approach for identification of linear or nonlinear flutter derivatives (FDs) of bridge decks from free vibration or buffeting response time history. The nonlinear FDs, which are dependent on torsional vibration amplitude, are represented in polynomial functions of torsional displacement. The augmented state variables of the two degrees of freedom (2DOF) bridge deck system, which include bridge deck motions and unknown FDs, are estimated simultaneously with the UKF approach based on response measurement data. Firstly, the steady-state vortex-induced vibration and flutter of a streamlined bridge deck section are used to illustrate the performance of UKF approach in extracting nonlinear FDs. The equivalent linear FDs are also identified from the same response data which reveals the deficiency of the linear model. Secondly, the stochastic buffeting responses of the bridge deck contributed from two modal responses with linear FDs are generated, and the performance of UKF approach with unknown excitations is examined. It is pointed out that the buffeting response must be separated into two modal response components, such that the unknown buffeting force excitations can be modeled as white noise processes, and the UKF approach offers satisfactory identification of FDs.

An Adaptive and Robust UKF Approach Based on Gaussian Process Regression-Aided Variational Bayesian

In this study, both adaptive and robust one is proposed, considering that the properties of a classic unscented Kalman filter (UKF) can be degraded severely by the outliers measured in the contamination distribution and the effects of time-varying noise. An adaptive and robust UKF approach on Gaussian process regression- assisted Variational Bayesian is proposed. The Variable Bayesian (VB) method is used to statistically approximate the time-varying noise due to the strong nonlinearity and inaccuracy of the system model. At the same time, Gaussian Process Regression (GPR) has the advantage of machine learning. The observation information trained by the GPR model performs real-time prediction of the sliding window. Based on the above two points, the output source of the measurement information is estimated to realize the robustness of the filter measurement update. When the noise is uncertain and there are outliers in the measurement information, simulation and SINS/GPS integrated navigation of actual tests were performed, respectively. The test outcomes indicate that the algorithm has better nonlinear estimation performance than the traditional method, the effectiveness of the filtering algorithm proposed is verified.

A motion capture algorithm based on inertia-Kinect sensors for lower body elements and step length estimation

Motion capture is a process that movements of living organisms like human or objects are captured and the results are processed for the desired applications. These applications are in rehabilitation, sports, film industry and etc. There are many techniques and instruments for motion capture that optical camera systems are the most accurate ones. But these cameras are high cost and limited to labs. Some sensors like Inertial Measurement Units (IMU) and recently, Kinect cameras have been considered by many researchers because these are low cost and easy to use. But problems like bias, accumulated error and occlusion make them look for improvements. Fusion algorithms are one of the best methods that help to use from each sensor’s strengths. The purpose of this work is design and implementation of an efficient algorithm for estimation of lower limbs joints 3D positions and step length. Orientation quaternions are considered as estimation states. An algorithm was developed with gradient descent and unscented Kalman filter approach based on IMUs and Kinect’s measurements. The IMUs’ data consist of three mutually orthogonal gyroscopes, three mutually orthogonal accelerometers, and a three-axis magnetometer. In this algorithm bias and magnetic distortions have been compensated in parallel structure. The resulted errors have been reported with respect to VICON optical camera system. The results obtained from an experimental test, show up to 60 percent improvement on Kinect in joints 3D positions estimation and the algorithm improves step length estimation error of Kinect from 7.8 cm to 0.03 cm.

Prognostic-oriented Fuel Cell Catalyst Aging Modeling and Its Application to Health-Monitoring and Prognostics of a PEM Fuel Cell

Today, poor long-term performance and durability combined with high production and maintenance costs remain the main obstacles for the commercialization of the polymer electrolyte membrane (PEM) fuel cells (PEMFCs). While on-line diagnosis and operating condition optimization play an important role in addressing the durability issue of the fuel cell, health-monitoring and prognosis (or PHM) techniques are of equally great significance in terms of scheduling condition-based maintenance (CBM) to minimize repair and maintenance costs, the associated operational disruptions, and also the risk of unscheduled downtime for the fuel cell systems.The two essential components of a PHM scheme for a general engineering system are 1) an accurate aging model that is capable of capturing the system’s gradual health deterioration, and 2) an algorithm for damage estimation and prognostics. In this paper, a physics-based, prognostic-oriented fuel cell catalyst degradation model is developed to characterize the relationship between the operating conditions and the degradation rate of the electro-chemical surface area (ECSA). The model complexity is kept minimal for on-line prognostic purpose. An unscented Kalman filter (UKF) approach is then proposed for the purpose of damage tracking and remaining useful life prediction of a PEMFC.

Uncertainty in model-based treatment decision support: Applied to aortic valve stenosis.

Patient outcome in trans‐aortic valve implantation (TAVI) therapy partly relies on a patient's haemodynamic properties that cannot be determined from current diagnostic methods alone. In this study, we predict changes in haemodynamic parameters (as a part of patient outcome) after valve replacement treatment in aortic stenosis patients. A framework to incorporate uncertainty in patient‐specific model predictions for decision support is presented. A 0D lumped parameter model including the left ventricle, a stenotic valve and systemic circulatory system has been developed, based on models published earlier. The unscented Kalman filter (UKF) is used to optimize model input parameters to fit measured data pre‐intervention. After optimization, the valve treatment is simulated by significantly reducing valve resistance. Uncertain model parameters are then propagated using a polynomial chaos expansion approach. To test the proposed framework, three in silico test cases are developed with clinically feasible measurements. Quality and availability of simulated measured patient data are decreased in each case. The UKF approach is compared to a Monte Carlo Markov Chain (MCMC) approach, a well‐known approach in modelling predictions with uncertainty. Both methods show increased confidence intervals as measurement quality decreases. By considering three in silico test‐cases we were able to show that the proposed framework is able to incorporate optimization uncertainty in model predictions and is faster and the MCMC approach, although it is more sensitive to noise in flow measurements. To conclude, this work shows that the proposed framework is ready to be applied to real patient data.

The gravity estimation with square-root unscented Kalman filter in the cold atom gravimeter

In the atomic gravimeter, the interference fringe is obtained by scanning the chirp rate of the Raman lasers to compensate for the gravity induced Doppler frequency shift and then the gravitational acceleration can be obtained by extracting the phase of the atomic interference fringe. The phase of the interference fringe is proportional to the chirp rate, therefore the accurate estimation of the chirp rate is the key issue to obtain accurate gravitational acceleration. In practice, the model for estimating the chirp rate is not perfect, and there is system state error. In this paper, we propose a square root unscented Kalman filter (SR-UKF) approach for estimating gravitational acceleration, which can take the system state error into account. The experiments on simulated and real data are performed to demonstrate the feasibility and effectiveness of the SR-UKF method, which can provide an alternative approach for the gravity estimation. In addition, it can be combined with the tidal model for gravity estimation, and can also be used for real-time gravity measurement.

Online estimation ofinertial parameter for lightweight electric vehicle using dual unscented Kalman filter approach

Accurate knowledge of vehicle inertial parameters (e.g. vehicle mass and yaw moment of inertia) is essential to manage vehicle potential trajectories and improve vehicle active safety. For lightweight electric vehicles (LEVs), whose control performance of dynamics system can be substantially affected due to the drastic reduction of vehicle weights and body size, such knowledge is even more critical. This study proposes a dual unscented Kalman filter (DUKF) approach, where two UKFs run in parallel to simultaneously estimate vehicle states and parameters such as vehicle velocity, vehicle sideslip angle, and inertial parameters. The proposed method only utilises real-time measurements from torque information of in-wheel motor and sensors in a standard car. The four-wheel non-linear vehicle dynamics model considering payload variations is developed, local observability of the DUKF observer is analysed and derived via differential geometry theory. To address the non-linearities in vehicle dynamics, the DUKF and dual extended Kalman filter (DEKF) are also presented and compared. Simulations with various manoeuvres are carried out using the platform of MATLAB/Simulink-Carsim®. Simulation results of MATLAB/Simulink-Carsim® show that the proposed DUKF method can effectively estimate inertial parameters of LEV under different payloads. Moreover, the investigation reveals that the proposed DUKF approach has better performance of estimating vehicle inertial parameters compared with the DEKF method.

Improving the Reliability of Probabilistic Multi-Step-Ahead Flood Forecasting by Fusing Unscented Kalman Filter with Recurrent Neural Network

It is fundamentally challenging to quantify the uncertainty of data-driven flood forecasting. This study introduces a general framework for probabilistic flood forecasting conditional on point forecasts. We adopt an unscented Kalman filter (UKF) post-processing technique to model the point forecasts made by a recurrent neural network and their corresponding observations. The methodology is tested by using a long-term 6-h timescale inflow series of the Three Gorges Reservoir in China. The main merits of the proposed approach lie in: first, overcoming the under-prediction phenomena in data-driven flood forecasting; second, alleviating the uncertainty encountered in data-driven flood forecasting. Two commonly used artificial neural networks, a recurrent and a static neural network, were used to make the point forecasts. Then the UKF approach driven by the point forecasts demonstrated its competency in increasing the reliability of probabilistic flood forecasts significantly, where predictive distributions encountered in multi-step-ahead flood forecasts were effectively reduced to small ranges. The results demonstrated that the UKF plus recurrent neural network approach could suitably extract the complex non-linear dependence structure between the model’s outputs and observed inflows and overcome the systematic error so that model reliability as well as forecast accuracy for future horizons could be significantly improved.

Battery Management System With State-of-Charge and Opportunistic State-of-Health for a Miniaturized Satellite

The lifespan of a satellite is primarily dependent on its battery performance. Thus, proper management and monitoring of the battery is important. Most miniaturized satellites of cubeSat and nanosatellite primarily rely on battery voltage readings for monitoring and seldom provide battery health status in a satellite. As the voltage readings can be affected by satellite operating conditions such as temperature and battery lifespan, it can give unreliable readings that might jeopardize satellite operation. The availability of the battery health status can prevent unexpected battery failures and provide useful insights into the planning of satellite operations. In this article, the battery management system of a satellite with state-of-charge (SOC) and state-of-health (SOH) monitoring is presented. For SOC estimation, a scaled unscented Kalman filter (UKF) is proposed. When compared to the existing UKF approach, it requires fewer sigma points and the positive weights used in the scaled unscented transform ensure the positive semidefiniteness of the covariance matrix leading to the improved numerical stability of the filter. Conversely, SOH monitoring is achieved by taking advantage of the opportunity arising from the satellite operations. The battery parameters are extracted without artificially injecting charge and discharge pulses. To validate the performance of the BMS, the experimental prelaunch tests and the actual in-flight data of the VELOX-II satellite is used as an example. From the results, the SOC estimation error is approximately 1% and the SOH estimation is consistent with the manufacturer's datasheet.

Two-dimensional temperature distribution estimation for a cross-flow planar solid oxide fuel cell stack

The uniform temperature distribution of a cross-flow planar solid oxide fuel cell (SOFC) stack plays an essential role in stack thermal safety and electrical property. However, because of the strict requirements in stack sealing struture, it is hard to acquire the temperature inside the stack using thermal detection devices within an acceptable cost. Therefore, accurately estimating the two-dimensional (2-D) temperature distribution of the cross-flow stack is crucial for its thermal management. In this paper, Firstly, a 2-D mechanism model of a cross-flow planar SOFC stack is established. The stack is divided into 5*5 nodes along the gas flow directions, which can reflect the stack states with moderate computational burden. Then, experimental test data is utilized to modify and validate the stack model, guaranteeing the model accuracy as well as the reliability of model-based state estimator design. Finally, easily-measured stack inputs and outputs are selected, and a temperature distribution estimator combined with unscented kalman filter (UFK) approach is developed to achieve accurate and fast temperature distribution estimation of a cross-flow SOFC stack. Simulation results demonstrate that the UKF-based temperature distribution estimator can precisely and quickly achieve the temperature distribution estimation of the cross-flow stack under both static state and dynamic state changes and is applicable to cross-flow stacks with different size or cell number as well, the maximum estimated absolute error is less than 0.15 K with an absolute error rate of 0.015%, which indicates the developed estimator has good estimation performances.

Experiments on State and Unmeasured-Parameter Estimation of Two Degree-of-Freedom System for Precise Control Based on JAUKF

We herein present system parameter estimation using the joint adaptive unscented Kalman filter and state estimation approach for a two degree-of-freedom (2-DOF) mechanical system. The unscented Kalman filter (UKF) is applied broadly in diverse engineering fields to estimate the state of the dynamic system and improve the control precision by reducing measurement noise. One aspect of parameter identification is that unmeasured parameter estimation is important in designing and maintaining the system performance with a suitable controller. This is because changes in the system parameters estimated will occur owing to external shock and deterioration in operation. State estimation has been studied thoroughly and developed widely, but not in terms of parameter estimation. Parameter estimation is important because system parameters can be altered owing to wear and tear, large disturbance, or exposure to extreme temperatures. It is difficult to disassemble and measure the parameter when it changes; hence, computational estimation is a solution. The proposed method simultaneously estimates the states as well as the parameters of custom-made 2-DOF mechanical system that is a nonlinear dynamical system. The adaptive rules in the estimation process are considered based on the moving average window method to address the effects of unexpected noise in the sensor measurements. The experimental results are analyzed to demonstrate the effectiveness of the proposed method for estimating the states and parameters. This method demonstrates better performance compared to using the joint-UKF in terms of convergence time, accuracy, and robustness to noise.

Online state of charge estimation of Li-ion battery based on an improved unscented Kalman filter approach

• State equations are derived from the battery equivalent circuit model. • Improved unscented Kalman filter approach composed of model adaptive and noise adaptive was introduced. • Experiment of sensitivity analysis was designed. • The experimental results revealed the effectiveness of the purposed approach. An improved unscented Kalman filter approach is proposed to enhance online state of charge estimation in terms of both accuracy and robustness. The goal is to address the drawback associated with the unscented Kalman filter in terms of its requirement for an accurate model and a priori noise statistics. Firstly, Li-ion battery modelling and offline parameter identification is performed. Secondly, a sensitivity analysis experiment is designed to verify which model parameter has the greatest influence on state of charge estimation accuracy, in order to provide an appropriate parameter for the model adaptive algorithm. Thirdly, an improved unscented Kalman filter approach, composed of a model adaptive algorithm and a noise adaptive algorithm, is introduced. Finally, the results are discussed, which reveal that the proposed approach’s estimation error is less than 1.79% with acceptable robustness and time complexity.

A multi-model probability SOC fusion estimation approach using an improved adaptive unscented Kalman filter technique

Abstract Battery model is crucial for the accurate estimation of the state of charge (SOC) in a battery management system of electric vehicles. However, differences exist within optimal battery models corresponding to different types of batteries. Even for the same type of battery, the corresponding optimal battery model may vary with the change of the battery status. To solve the problem, this paper proposes a multi-model probability fusion estimation (MMPFE) method to realize an accurate description of battery characteristics and a precise SOC estimation. An improved adaptive unscented Kalman filter (AUKF) approach is developed for measurement noise variance online update based on the idea of orthogonality between residual and innovation during the SOC estimation. Finally, the proposed MMPFE method was verified by experiments using LiFeO4 and LiMnO2 batteries, respectively. Results indicate that when a voltage drift of +3 mV was applied on the LiFeO4 battery under UDDS condition and an initial SOC error was applied on LiMnO2 battery under FUDS condition at different temperatures, the proposed method still can estimated the precise SOC. Comparing with the results obtained by the other methods under the same conditions, the method presented in the paper shows a higher SOC estimation accuracy and better robustness.

An Adaptive Square Root Unscented Kalman Filter Approach for State of Charge Estimation of Lithium-Ion Batteries

An accurate state of charge (SOC) estimation is of great importance for the battery management systems of electric vehicles. To improve the accuracy and robustness of SOC estimation, lithium-ion battery SOC is estimated using an adaptive square root unscented Kalman filter (ASRUKF) method. The square roots of the variance matrices of the SOC and noise can be calculated directly by the ASRUKF algorithm, which ensures the symmetry and nonnegative definiteness of the matrices. The process values and measurement noise covariance can be adaptively adjusted, which greatly improves the accuracy, stability, and self-adaptability of the filter. The effectiveness of the proposed method has been verified through experiments under different operating conditions. The obtained results were compared with those of extended Kalman filter (EKF) and unscented Kalman filter (UKF) , which indicates that the ASRUKF method provides better accuracy, robustness and convergence in the estimation of battery SOC for electric vehicles. The proposed method has a mean SOC estimation error of 0.5% and a maximum SOC estimation error of 0.8%. These errors are lower than those of other methods.

A wavelet transform-adaptive unscented Kalman filter approach for state of charge estimation of LiFePo4 battery

Summary LiFePo4 battery is widely used in electric vehicles; however, its flatness and hysteresis of the open-circuit voltage curve pose a big challenge to precise state of charge (SOC) estimation. The issue is discussed and addressed in this paper. First, a cell model with hysteresis is built to describe real-time dynamic characteristics of the LiFePo4 battery. Second, the model parameters and SOC are estimated independently to avoid the possibility of cross interference between them. For model identification, an adaptive unscented Kalman filter (AUKF) algorithm is used to identify the cell parameters as they change slowly. While SOC could change rapidly, wavelet transform AUKF algorithm is put forward to estimate SOC. In the novel algorithm, the measurement noise can be estimated and updated online. Finally, the performance of the proposed method is verified under dynamic current condition. The experimental results show that estimated value based on the proposed method is more accurate than unscented Kalman filter-based method and AUKF-based algorithm. Meanwhile, the proposed estimator also has the merits of fast convergence and good robustness against the initialization uncertainty.

Study of Wind Turbine Fault Diagnosis Based on Unscented Kalman Filter and SCADA Data

Effective wind turbine fault diagnostic algorithms are crucial for wind turbine intelligent condition monitoring. An unscented Kalman filter approach is proposed to successfully detect and isolate two types of gearbox failures of a wind turbine in this paper. The state space models are defined for the unscented Kalman filter model by a detailed wind turbine nonlinear systematic principle analysis. The three failure modes being studied are gearbox damage, lubrication oil leakage and pitch failure. The results show that unscented Kalman filter model has special response to online input parameters under different fault conditions. Such property makes it effective on fault identification. It also shows that properly defining unscented Kalman filter state space vectors and control vectors are crucial for improving its sensitivity to different failures. Online fault detection capability of this approach is then proved on SCADA data. The developed unsented Kalman filter model provides an effective way for wind turbine fault detection using supervisory control and data acquisition data. This is essential for further intelligent WT condition monitoring.

Inferring nonlinear lateral flow immunoassay state-space models via an unscented Kalman filter

This paper is concerned with the problem of learning structure of the lateral flow immunoassay (LFIA) devices via short but available time series of the experiment measurement. The model for the LFIA is considered as a nonlinear state-space model that includes equations describing both the biochemical reaction process of LFIA system and the observation output. Especially, the time-delays occurring among the biochemical reactions are considered in the established model. Furthermore, we utilize the unscented Kalman filter (UKF) algorithm to simultaneously identify not only the states but also the parameters of the improved state-space model by using short but high-dimensional experiment data in terms of images. It is shown via experiment results that the UKF approach is particularly suitable for modelling the LFIA devices. The identified model with time-delay is of great significance for the quantitative analysis of LFIA in both the accurate prediction of the dynamic process of the concentration distribution of the antigens/antibodies and the performance optimization of the LFIA devices.

A Direct and Non-Singular UKF Approach Using Euler Angle Kinematics for Integrated Navigation Systems.

This paper presents a direct and non-singular approach based on an unscented Kalman filter (UKF) for the integration of strapdown inertial navigation systems (SINSs) with the aid of velocity. The state vector includes velocity and Euler angles, and the system model contains Euler angle kinematics equations. The measured velocity in the body frame is used as the filter measurement. The quaternion nonlinear equality constraint is eliminated, and the cross-noise problem is overcome. The filter model is simple and easy to apply without linearization. Data fusion is performed by an UKF, which directly estimates and outputs the navigation information. There is no need to process navigation computation and error correction separately because the navigation computation is completed synchronously during the filter time updating. In addition, the singularities are avoided with the help of the dual-Euler method. The performance of the proposed approach is verified by road test data from a land vehicle equipped with an odometer aided SINS, and a singularity turntable test is conducted using three-axis turntable test data. The results show that the proposed approach can achieve higher navigation accuracy than the commonly-used indirect approach, and the singularities can be efficiently removed as the result of dual-Euler method.