Extended Kalman Filter Algorithm Research Articles

An Improved Comprehensive Learning - Particle Swarm Optimization - Extended Kalman Filtering Method for the Online High-Precision State of Charge and Model Parameter Co-Estimation of Lithium-Ion Batteries

The precise assessment of the state of charge (SOC) of lithium-ion batteries (LIBs) is critical in battery management systems. This work offers a comprehensive learning particle swarm optimization (CLPSO) and extended Kalman filter (EKF) technique to forecast the SOC of LIBs in order to obtain an accurate SOC estimate for power batteries. Firstly, to address the challenge of identifying various parameters of the battery model, the bilinear transformation technique is employed to determine the parameters of the second-order RC equivalent circuit model. Secondly, to improve the fitness values for the conventional PSO algorithm, which is prone to entering local optimality, a learning strategy () is added to the particle velocity update method. The optimized PSO and EKF algorithms are integrated to perform online prediction of the SOC of LIBs. The experimental results demonstrate that under the conditions of the Beijing Bus Dynamic Stress Test (BBDST), Dynamic Stress Test (DST), and Hybrid Pulse Power Characterization Test (HPPC), the parameter identification inaccuracy of CLPSO is restricted to 1%. After multi-metric evaluation, the maximum error and mean absolute error of the CLPSO-EKF algorithm in SOC estimation are 0.32% and 0.0652%, respectively, demonstrating a higher robustness and accuracy advantage over other versions.

A hierarchical adaptive extended Kalman filter algorithm for lithium-ion battery state of charge estimation

A hierarchical adaptive extended Kalman filter algorithm for lithium-ion battery state of charge estimation

An Adaptive Double Extended Kalman Filter Algorithm Based on Incremental Change Rate for Co-estimation of Battery SOC and Capacity

The battery state of charge (SOC) and capacity are important state management indicators of the battery management system, and their estimation accuracy directly affects the safety of power battery use and the driver’s driving experience. Since the increment change rate of the estimated variable can reflect the changing trend of the estimated variable, an extended Kalman filter algorithm based on the increment change rate is proposed in this paper, on this basis, an adaptive double-extended Kalman filter algorithm based on incremental change rate is constructed for the co-estimation of SOC and capacity of batteries. The tests under various operating conditions show that the target algorithm proposed in this paper has greater advantages over the traditional adaptive double-extended Kalman filter algorithm, and the maximum absolute error value (MAE) and root mean square error (RMSE) of the target algorithm can be reduced by 36.3% and 74.4% (SOC), 95.5% and 97.6% (capacity) compared with the traditional adaptive double-extended Kalman filter algorithm under DST operating conditions; The MAE and RMSE of the target algorithm can be reduced by 79.1% and 92.3% (SOC), 95.4% and 96.2% (capacity) under BBDST operating conditions.

State of charge estimation of lithium-ion battery based on extended Kalman filter algorithm

Due to excellent power and energy density, low self-discharge and long life, lithium-ion battery plays an important role in many fields. Directed against the complexity of above noises and the strong sensitivity of the common Kalman filter algorithm to noises, the state of charge estimation of lithium-ion battery based on extended Kalman filter algorithm is investigated in this paper. Based on the second-order resistor-capacitance equivalent circuit model, the battery model parameters are identified using the MATLAB/Simulink software. A battery parameter test platform is built to test the charge-discharge efficiency, open-circuit voltage and state of charge relationship curve, internal resistance and capacitance of the individual battery are tested. The simulation and experimental results of terminal voltage for lithium-ion battery is compared to verify the effectiveness of this method. In addition, the general applicability of state of charge estimation algorithm for the battery pack is explored. The ampere-hour integral method combined with the battery modeling is used to estimate the state of charge of lithium-ion battery. The comparison of extended Kalman filter algorithm between experimental results and simulation estimated results is obtained to verify the accuracy. The extended Kalman filter algorithm proposed in this study not only establishes the theoretical basis for the condition monitoring but also provides the safe guarantee for the engineering application of lithium-ion battery.

A High-Precision Insulation Inspection Method Based on the Double-Arm Unbalanced Bridge for Electric Ships

In order to ensure the safe navigation of electric ships, it is especially important to detect the insulation status between the ship’s high-voltage system and the ship’s hull in real time. In this paper, a real-time insulation resistance (IR) detection method based on the double-arm unbalanced bridge method was proposed for the problem that the IR calculation results of electric ships have large errors. The detection principle was described, and an experimental test platform was built. The influence law of each branch resistance and voltage on the IR measurement error in this circuit was studied to provide a reference for the parameter selection of the double-arm unbalanced bridge and the effect of temperature on the measurement results was also considered. Besides, the Extended Kalman filtering (EKF) algorithm was used to reduce the influence of voltage fluctuation on the insulation detection error. The results show that the insulation testing method could accurately measure the IR, and the insulation testing error was less than 2.4%, and the error was about 0.18% after processing with the EKF algorithm. This proves that this paper improves the measurement accuracy of IR from three aspects: circuit design of insulation testing, bridge parameter selection and filtering algorithm.

A Low-cost Inertial Rail Track Positioning Technology Based on Distributed Optical System Assistance

The low-cost MEMS inertial system is difficult to achieve high-precision measurement for path track, which decreases accuracy of output. Aiming at this problem, a distributed optical track assisted the low-cost inertial system scheme is proposed in this paper. Firstly, the positional relationship of the sub-modules is pre-calibrated on the test track. Secondly, the position and speed are calculated by processing the time difference of the photoelectric interruption. In this system, the low-cost MEMS inertial system is used to measure the attitude, speed, and position information. Subsequently, the data of the inertial system and the optical system are fused by the extended Kalman filter algorithm. To verify the feasibility of the scheme, a short rail speed measurement experimental platform is built in an indoor environment. Compared with the low-cost gyroscope, the result shows that the error divergence assisted by the optical system can be effectively suppressed. The positioning accuracy can reach the centimeter level in the results of the experiment.

High-Precision State of Charge Estimation of Urban-Road-Condition Lithium-Ion Batteries Based on Optimized High-Order Term Compensation-Adaptive Extended Kalman Filtering

It is significant to improve the accuracy of estimating the state of charge (SOC) of lithium-ion batteries under different working conditions on urban roads. In this study, an improved second-order polarized equivalent circuit (SO-PEC) modeling method is proposed. Accuracy test using segmented parallel exponential fitting parameter identification method. Online parameter identification using recursive least squares with variable forgetting factors(VFFRLS). An optimized higher-order term compensation-adaptive extended Kalman filter (HTC-AEKF) is proposed in the process of estimating SOC. The algorithm incorporates a noise-adaptive algorithm that introduces noise covariance into the recursive process in real-time to reduce the impact of process noise and observation noise on the accuracy of SOC estimation. Multiple iterations are performed for some of the processes in the extended Kalman filter(EKF) to compensate for the accuracy impact of missing higher-order terms in the linearization process. Model validation results show over 98% accuracy. The results after comparing with the EKF algorithm show a 4.1% improvement in SOC estimation accuracy under Hybrid Pulse Power Characterization(HPPC) working conditions. 2.7% improvement in accuracy in Dynamic Stress Test(DST) working conditions. 2.1% improvement in Beijing Bus Dynamic Stress Test(BBDST) working conditions. The superiority of the algorithm is demonstrated.

Security-Ensured State of Charge Estimation of Lithium-Ion Batteries Subject to Malicious Attacks

This paper is concerned with the secure estimation problem of the state of charge (SOC) for Lithium-ion batteries subject to deception attacks. A second-order resistor-capacitor (RC) equivalent circuit model (ECM), whose parameters are identified by means of the extended Kalman filter algorithm, is applied to characterize the static and dynamic behaviors of a Lithium-ion battery. With the aid of the polynomial-function fitting technique, the nonlinear relationship between the open circuit voltage and SOC of the ECM is established. The deception attacks launched by the malicious adversary are taken into consideration during the data transmission from the voltage/current sensor to the estimator. By employing the Lyapunov stability theory, a second-order RC-ECM-based nonlinear observer is designed in the presence of deception attacks. In addition, sufficient conditions are derived to guarantee the uniform boundedness of the estimation error and the estimator gain matrix is implicitly parameterized by solving finite linear matrix inequalities with certain constraints. Finally, the effectiveness of the proposed estimation method is verified through the experiments under the Dynamic Stress Test and Federal Urban Driving Schedule driving cycle.

Three-axis high-accuracy spacecraft attitude estimation via sequential extended Kalman filtering of single-axis magnetometer measurements

Magnetometer is a highly advantageous sensor for determining a spacecraft’s attitude. This article provides a solution to the problem of spacecraft attitude estimation using magnetometer measurements only. To ensure full observability of spacecraft attitude states, it is necessary to use at least two types of sensors. Consequently, utilizing a single sensor, such as the magnetometer, poses a significant challenge for any attitude estimation algorithm, including the extended Kalman filter (EKF). Moreover, implementing the EKF algorithm, or any other attitude estimation algorithm, is computationally intensive. To address these issues, an algorithm has been developed that estimates spacecraft attitude angles and attitude rates using a sequential extended Kalman filter (SEKF). This algorithm offers numerous benefits over those found in the literature such as high accuracy, low computational resource requirements, the ability to converge even with large initial attitude and angular velocity estimation errors, and the ability to function even if two of the three measurement channels of the magnetometer are not functioning. With these benefits, the developed SEKF algorithm is capable of operating in all spacecraft operational modes, delivering accurate performance and computation time. In spite of measurements with large noise values, the high accuracy achieved by the SEKF algorithm enables the magnetometer to serve as the sole source of attitude information, even if one or two magnetometer measurement channels are not functioning.

State of Charge and State of Health Estimation of Lithium-Ion Battery Packs With Inconsistent Internal Parameters Using Dual Extended Kalman Filter

Abstract The internal battery parameters of the lithium-ion battery energy storage system may be inconsistent due to different aging degrees during the operation, and the thermal effect can also threaten the safety of the system. In this paper, based on the second-order resistor–capacitor equivalent circuit model and the dual extended Kalman filter (DEKF) algorithm, an electrical simulation model of a LIB pack with inconsistent parameters considering the thermal effect is established, in which state of charge (SOC) and state of health (SOH) are estimated using DEKF, while the temperature is calculated by a thermal module. The simulation results show that the DEKF algorithm has a good effect on battery state and parameter estimation, with the root-mean-square error of voltage is lower than 0.01 V and SOC mean absolute error (MAE) is below 1.50%, while SOH error is 3.37%. In addition, the thermal module can provide an accurate estimation of the inconsistent temperature rise of the battery pack, and the MAE between the model-calculated temperature and the experiment is no more than 6.60%. The results provide the basic data for the scale-up of the electrothermal co-simulation model of the LIB energy storage system.

Double Extended Kalman Filter Algorithm Based on Weighted Multi-Innovation and Weighted Maximum Correlation Entropy Criterion for Co-Estimation of Battery SOC and Capacity.

Most of the traditional extended Kalman filter algorithms for the co-estimation of SOC and capacity of lithium-ion batteries are designed based on the minimum mean square error (MMSE) criterion, which may show superior performance in Gaussian noise scenes. However, due to the complexity of the battery operating environment, it is likely to face non-Gaussian noise (especially outlier noise), at which time the performance of the traditional extended Kalman filter algorithms will be seriously weakened. To solve the above problems, this paper first proposes a double extended Kalman filter algorithm based on weighted multi-innovation and weighted maximum correlation entropy (WMI-WMCC-DEKF) for the co-estimation of battery SOC and capacity. In this paper, the performance of the target algorithm is verified and compared by generating different types of noise from three noise models: weak Gaussian mixture noise, strong Gaussian mixture noise, and outlier noise. The maximum absolute error value (MAE) and root mean square error value (RMSE) of the WMI-WMCC-DEKF algorithm can achieve the highest performance improvement of 69.3 and 84.2% (SOC), 61.3, and 94.2% (capacity), respectively. The experimental results fully prove that the target algorithm has excellent performance against three kinds of noises.

Online estimations for electrical and mechanical parameters of the induction motor by extended Kalman filter

In this study, a novel extended Kalman filter (EKF)-based observer is designed to increase the number of estimated states and parameters of the induction motor (IM). To perform the online estimations of stationary axis components of stator currents and rotor fluxes ([Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]) as well as rotor mechanical speed ([Formula: see text]), which are required for direct vector control (DVC) systems along with the load torque ([Formula: see text]), rotor resistance ([Formula: see text]), magnetizing inductance ([Formula: see text]), and the reciprocal of the total inertia of the system ([Formula: see text]), the proposed EKF uses the measured phase currents and voltages together with the measured rotor speed. To estimate all of the five states ([Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]) plus four parameters ([Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]), the proposed EKF-based observer does not include a switching operation nor a hybrid structure, which is a common approach in the literature for online state and parameter estimations of IMs and results in design complexity and computational load increase. In simulation studies, the estimation performance of the proposed EKF is tested and verified under the variations of [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] in DVC systems that perform the speed and position controls of IM. The obtained results confirm the satisfying tracking performances and thus better control achievements of the speed and position controlled IM drives in this paper. Moreover, the proposed EKF and the EKF without [Formula: see text]-estimation are compared in the position control system to demonstrate the importance of the [Formula: see text] estimation. In the comparison, nearly 10 times less mean square error (MSE) is obtained in the estimations of [Formula: see text], [Formula: see text], [Formula: see text], and the magnitude of the rotor flux for the proposed EKF. Finally, the proposed EKF algorithm is tested and verified in real-time experiments with a challenging speed reversal scenario causing nonlinear variations in both [Formula: see text] and [Formula: see text].

Soft Short-circuit Fault Diagnosis of the Lithium-ion Battery Pack Based on an Improved EKF Algorithm

Background: Lithium-ion batteries are widely used in new energy vehicles and energy storage systems due to their superior performance. However, lithium batteries are prone to safety problems in the use process, so the fault diagnosis technology of lithium batteries has attracted more attention. Objective: This study aimed to ensure the safety of lithium batteries and accurately and timely diagnose the soft short circuit (soft SC) fault of lithium battery. Methods: Aiming at the energy storage lithium battery pack, this study proposed a soft short-circuit fault diagnosis method for the lithium-ion battery pack based on the improved Extended Kalman Filter (EKF) algorithm. First, the 1st-order RC equivalent circuit model of normal battery and soft SC fault battery was established, and model parameters were identified using Recursive Least Squares with Forgetting Factor (FFRLS). Then, using the improved EKF, the state of charge (SOC) of a single cell was estimated, and the difference between the calculated SOC and the estimated SOC by the coulomb counting method was used to detect soft SC faults and compared them with the reference data. Finally, the SC resistance value indicated the severity of the fault. Results: The proposed method could accurately diagnose the soft short circuit fault, and the error was found to be lower than the traditional EKF algorithm. The estimation error was about 0.4% for the battery with slight failure and about 1.5% for the battery with serious failure. Conclusion: The experimental results showed that the improved EKF algorithm could estimate the SOC difference more accurately, and the effect of soft SC fault diagnosis was better. At the same time, it could quantitatively identify the size of the short circuit resistance, which is very helpful for the subsequent management of the battery system.

Joint estimation of SOC and SOH of lithium battery based on multi-time scale EKF-ASRCKF algorithm

To address the low accuracy of battery charged of state (SOC) estimation due to fixed model parameters and capacity, a joint multi-time scale estimation algorithm (EKF-ASRCKF) is proposed in this paper, which consists of the adaptive square root cubature Kalman filter (ASRCKF) algorithm and the extended Kalman filter (EKF) algorithm. Firstly, the model parameters and capacity on the macroscopic time scale are identified by the EKF algorithm; meanwhile, the battery capacity estimation results characterize the battery health of state (SOH). Then the ASRCKF algorithm estimates the SOC on the microscopic time scale. Finally, the experimental validation is carried out under the BBDST condition. The validation result indicates that the EKF-ASRCKF algorithm provides a good estimation of the model parameters and capacity, which further improves the estimation precision of the battery SOC.

Research on Sensorless Control of Built-in Permanent Magnet Synchronous Motor Based on Extended Kalman Filter Algorithm

The permanent magnet synchronous motor (PMSM) is a system of complex interior structure coupling and nonlinear, variable parameters. In order to track and observe the position and speed of PMSM in real time, the extended Kalman filter (EKF) algorithm is used in this paper to track the speed and position of the built-in PMSM. The influence of the Q and R covariance matrix on the observation effect is studied by using the control variable method of trial and error. The reliability of the EKF on the observation function of velocity position is verified by MATLAB simulation.

Attitude Calculation of Quadrotor UAV Based on Extended Kalman Filter and Complementary Filter

Quadrotor UAV obtain the attitude calculation result from inertial measurement unit (IMU), but IMU has the the problems of high noise and low precision, to solve the problems, this paper first introduces the extended Kalman filter (EKF) and complementary filter, and uses them to filter the output of the accelerometer and magnetic sensor. The effects of the two methods are compared by static testing and dynamic testing. The results show that both filtering methods can improve the precision of the attitude angle solutions, but the EKF algorithm performs better.

Nonlinear disturbance observer based multiple‐model adaptive explicit model predictive control for nonlinear MIMO system

AbstractIn this article, a nonlinear disturbance observer‐based multiple‐model adaptive explicit model predictive control (NDO‐MMAEMPC) scheme is developed for a nonlinear MIMO system with parametric uncertainty as well as an external disturbance. The proposed method manages external disturbances without affecting the degree of smoothness of the control signals. Further, to cope with the unknown system uncertainty, blending‐based adaptive identification schemes are used for the same class of systems. For each identification model, an explicit nonlinear model predictive controller is computed off‐line for the corresponding model in advance, which saves computation power during operation. The generated control inputs from the set of explicit controllers are being blended online using adaptive weight. An extended Kalman filter algorithm is employed for the estimation of the unavailable states of the nonlinear system. Using an aerodynamic laboratory setup, the effectiveness of the proposed control algorithm is verified.

Modal identification of building structures under unknown input conditions using extended Kalman filter and long-short term memory

Various system identification (SI) techniques have been developed to ensure the sufficient structural performance of buildings. Recently, attempts have been made to solve the problem of the excessive computational time required for operational modal analysis (OMA), which is involved in SI, by using the deep learning (DL) algorithm and to overcome the limited applicability to structural problems of extended Kalman filter (EKF)-based SI technology through the development of a method enabling SI under unknown input conditions by adding a term for the input load to the algorithm. Although DL-based OMA methods and EKF-based SI techniques under unknown input conditions are being developed in various forms, they still produce incomplete identification processes when extracting the identification parameters. The neural network of the developed DL-based OMA method fails to extract all modal parameters perfectly, and EKF-based SI techniques has the limitations of a heavy algorithm and an increased computational burden with an input load term added to the algorithm. Therefore, this study proposes an EKF-based long short-term memory (EKF-LSTM) method that can identify modal parameters. The proposed EKF-LSTM method applies modal-expanded dynamic governing equations to the EKF to identify the modal parameters, where the input load used in the EKF algorithm is estimated using the LSTM method. The EKF-LSTM method can identify all modal parameters using the EKF, which is highly applicable to structural problems. Because the proposed method estimates the input load through an already trained LSTM network, there is no problem with computational burden when estimating the input load. The proposed EKF-LSTM method was verified using a numerical model with three degrees of freedom, and its effectiveness was confirmed by utilizing a steel frame structure model with three floors.

ARWLS-AFEKE: SOC Estimation and Capacity Correction of Lithium Batteries Based on a Fusion Algorithm

Accuracy of battery charge status (SOC) estimation plays a significant role in the management of electric vehicle power batteries. However, recently, abrupt changes from SOC data often occurs in the actual operation of electric vehicles and some errors appear in the establishment of battery models and noise models, which give rise to the poorly adaptive and robust performance of traditional algorithms in the process of SOC estimation. The fusion algorithm proposed in this paper can effectively improve the accuracy of models and SOC estimation of lithium-ion batteries. Based on the second-order R-C network model, this method optimizes the accuracy of parameter identification by adopting the adaptive recursive weighted least square algorithm (ARWLS). In addition, the adaptive fading extended Kalman filter algorithm (AFEKF) is applied to estimate the SOC of lithium-ion batteries. Additionally, via introducing a fading factor, the optimal Kalman gain is updated in real-time, which can reduce the impact of data mutation on battery modeling. Compared with the offline AEKF algorithm and the EKF algorithm, the adaptive recursive weighted least square-adaptive fading extended Kalman filter (ARWLS-AFEKF) fusion algorithm had higher accuracy and adaptability, which can be adapted to the variable noise environment.

A comparative study of state of charge estimation methods of ultracapacitors for electric vehicles considering temperature characteristics

This paper systematically compares and evaluates three types SOC estimation methods for ultracapacitors (UCs) under different ambient temperatures. Firstly, based on the UC dynamic test data, the key parameters of Thevenin model are identified by genetic algorithm. Next, the polynomial fitting is employed to determine the relationship between parameters and ambient temperatures, and the temperature-varied model is established. At the same time, according to the extended Kalman filter (EKF), adaptive extended Kalman filter (AEKF) and unscented Kalman filter algorithm (UKF), three kinds UC SOC estimation methods are designed, which are suitable for different ambient temperatures. Then, the accuracy, robustness and self-correction ability of these SOC estimation methods are evaluated by using the urban dynamometer driving schedule test data at −10 °C, 10 °C, 25 °C and 40 °C. Finally, the results indicate that the AEKF algorithm is superior to the EKF and UKF, and its average absolute error and root mean square error are within 0.227 % and 0.318 % at different temperatures, respectively. In addition, the proposed temperature-varied model has a wider application.