Dual Extended Kalman Filter Research Articles

Co-Estimating State of Charge and Capacity of Automotive Lithium-Ion Batteries Under Deep Degradation Using Multiple Estimators

Since battery systems typically account for over 40% of the cost of an electric vehicle, their mid-life replacements are exceptional. Therefore, the battery’s lifespan must exceed that of the vehicle. To ensure long-term and safe use, accurate state-of-charge (SOC) estimation must be maintained throughout the battery’s lifespan. This requires appropriate updates to parameters, such as capacity, in the battery model. In this context, dual extended Kalman filters, which simultaneously estimate both states and parameters, have gained interest. While existing reports on simultaneous estimators seemed promising, our study found that they performed well under low levels of battery aging but encountered issues at higher levels. Accurately reflecting the actual physicochemical changes of the parameters in aging cells is challenging for two reasons: the limited number of measurements of terminal voltage available for numerous parameters, and the weak observability of the capacity. Therefore, we combined the simultaneous estimator with a capacity estimator operated separately during charging and a sequential estimator specialized for an enhanced self-correcting model, achieving SOC accuracy within 5% even when the SOH decreased by 30%. However, there is still much work to be carried out to implement sequential estimators in battery management systems operating in real time with limited computational resources.

Multi-interest adaptive unscented Kalman filter based on improved matrix decomposition methods for lithium-ion battery state of charge estimation

Accurately predicting the state of charge (SOC) is crucial to improving Li-ion battery performance. However, available model-based estimation approaches still face challenges in handling model uncertainty and measurement noise effects on parameter identification. Besides, the widely used unscented Kalman filter (UKF) algorithm has limitations in electric vehicles as it requires the error covariance matrix to maintain positive definiteness, limiting its applicability under certain conditions. This study introduces the bias-compensated forgetting factor recursive least squares (BCFFRLS) method for parameter estimation within the second-order RC equivalent circuit model specific to the INR18650-20R battery. Furthermore, we propose a novel algorithm named the optimization multi-interest adaptive unscented Kalman filter (O-MIAUKF). This algorithm is designed to address stability and robustness issues with traditional UKF encounters in dynamic environments. Experimental validation demonstrates that the O-MIAUKF algorithm excels in maintaining strong stability and robustness in various working conditions, accurately estimating SOC even with a non-positive covariance matrix. The SOC estimation error remains stable at 0.8 %, which is lower than that of the current Extended Kalman Filter (EKF), UKF, and Dual Extended Kalman Filter (DEKF).

Research on state-of-charge estimation of lithium-ion batteries based on an improved gas-liquid dynamics model

Improving the accuracy of state of charge (SOC) is beneficial for the safety and service life of batteries. The battery analysis model has become one of the research hotspots due to its clear physical significance and visibility of parameters. Based on analytical modeling methods, an improved gas-liquid dynamics (GLD) model of the lithium-ion battery (LIB) is proposed, which excels in simulating lithium-ion diffusion behavior and terminal voltage rebound characteristics under the open circuit state of LIBs. The parameter mapping relationships between the LIB and GLD model are improved and estimation equations of SOC, terminal voltage, and open circuit voltage are deduced according to GLD state equations. Based on these estimation equations and dual extended Kalman filter, an efficient real-time SOC estimation method for LIBs is developed. The performance of SOC estimation method is verified by LIBs data sampled by onboard BMS under five working conditions. Results show that the proposed method has strong robustness of the initial error of SOC = ±20 % which is eliminated within 15 s, and has a reliable performance of SOC estimation against the current and terminal voltage noises.

Online Multi-Parameter Observation of IPM Machine With Reconstructed Nonlinear Small-Signal Model Based on Dual EKF

Flux nonlinearity due to cross-coupling saturation is critical for interior permanent magnet (IPM) machine control. To obtain accurate parameters in real-time, this paper proposes a novel reconstructed nonlinear small-signal model which simplifies the observability analysis and design of the observer. Compared with traditional methods, the observability of the reconstructed small-signal model shows that all resistance and inductance parameters are observable under entire operation region. The flux cross-coupling saturation is also well considered. A Dual-Extended-Kalman-Filter (DEKF) based observer for the reconstructed model is introduced to achieve fast parameters convergence. The effectiveness of the proposed observer is experimentally evaluated with a 60kW IPM machine and verified by finite element analysis (FEA).

Estimation of Lateral Velocity and Cornering Stiffness in Vehicle Dynamics Based on Multi-Source Information Fusion

<div>To address the challenge of directly measuring essential dynamic parameters of vehicles, this article introduces a multi-source information fusion estimation method. Using the intelligent front camera (IFC) sensor to analyze lane line polynomial information and a kinematic model, the vehicle’s lateral velocity and sideslip angle can be determined without extra sensor expenses. After evaluating the strengths and weaknesses of the two aforementioned lateral velocity estimation techniques, a fusion estimation approach for lateral velocity is proposed. This approach extracts the vehicle’s lateral dynamic characteristics to calculate the fusion allocation coefficient. Subsequently, the outcomes from the two lateral velocity estimation techniques are merged, ensuring rapid convergence under steady-state conditions and precise tracking in dynamic scenarios. In addition, we introduce a tire parameter online adaptive module (TPOAM) to continually update essential tire parameters such as cornering stiffnesses, with its effectiveness demonstrated through DLC and slalom simulation tests. Using a dual extended Kalman filter (DEKF) observer, the article allows for joint estimation of vehicle states and tire parameters. Ultimately, we offer a cost-effective estimation method of vital dynamic vehicle parameters to support the motion control module in autonomous driving.</div>

Electrochemical Model-Based State-Space Approach for Real-Time Parameter Estimation of Lithium-Ion Batteries

Lithium-ion batteries are widely used in various applications, including electric vehicles and renewable energy storage systems, due to their high energy density, long cycle life, and low self-discharge rate. Accurate estimation of battery state of charge (SOC) and state of health (SOH) is crucial for their safe and efficient operation.In this study, we propose a model-based state-space solver for real-time monitoring of lithium-ion batteries under various operating conditions. The state-space model simplifies a single-particle model and enables simulations considering the current state of the battery using a Kalman filter. The model includes a one-dimensional Single Particle Model with Electrolyte (SPMe) and uses eigenfunction expansion to solve the mass conservation equation for the electrolyte phase. The final form of the state-space model for the solid and electrolyte phase includes a voltage equation using lithium-ion concentration. The proposed solver was validated by comparing it with the SPMe solver, and the results agree well.To achieve on-line updating of the battery model parameters, we propose a multi-scale parameter adaptive method based on dual Kalman filters for estimating the SPMe model parameters. The fast time-varying parameters are separated from the slowly time-varying parameters, and then each group is estimated by a different Kalman filter with a different time constant. This method enables the estimation of both the SOC and all parameters, including the SPMe model parameters. Additionally, we provide a parameter adjustment method for dual extended Kalman filters when estimating multiple parameters.The proposed method reduces the influence of the initial state error on the algorithm and improves its robustness. Experimental results demonstrate that the accuracy of the algorithm is improved by separating the fast and slow parameters and estimating them with different Kalman filters. The proposed solver can be used with Kalman filters and the like in an onboard environment due to its fast calculation speed. Figure 1

Sensor fault‐tolerant control for an internal combustion engine

SummaryThis research presents the design of a fault‐tolerant system based on a dual extended Kalman filter (DEKF) and a bank of two high‐gain observers to ensure the continuous operation of an internal combustion engine (ICE) despite total and partial faults in the mass airflow (MAF) sensor, temperature sensor, and pressure sensor. The DEKF aims to estimate the air mass flow rate () through the throttle valve. The DEKF uses the temperature and pressure measured in the intake manifold to accurately estimate the (), a failure in any of both sensors will not allow the correct functioning of the DEKF. Therefore, a bank of two high‐gain observers is proposed to estimate the pressure and temperature from only one measure. Observer 1 estimates the temperature and pressure from the pressure, and Observer 2 uses the temperature for estimating pressure and temperature. Hence, if the temperature or pressure sensors fail, the estimated temperature or pressure will replace the ill‐measure signal. The results show the effectiveness of the proposed fault‐tolerant system in the case of one sensor or multiple sensor faults.

Research on state-parameter estimation of unmanned Tractor—A hybrid method of DEKF and ARBFNN

Unmanned tractor relies on multi-sensor information collection to obtain the current state or parameters. However, when driving in complex field, it will inevitably suffer from the uneven ground, the impact of crop straw and clods et al., which usually poses considerable challenges for multi-sensor to obtain stable and accurate value of states and parameters to realize tractor automatic lane guidance control. Therefore, a novel state and parameter estimation method by mixing the dual extended Kalman filter (DEKF) technology and adaptive radial basis function neural network (ARBFNN) technology is proposed in this paper. Firstly, DEKF technique is applied to estimate key states and initial model time-varying parameters–front/rear axle cornering stiffnesses at the same time. Then, in order to further improve the accuracy of estimation value of front/rear axle cornering stiffnesses during the automatic lane guidance control process, an ARBFNN technology is investigated by taking the heading error, lateral error and initial estimation value of front/rear axle cornering stiffnesses from DEKF as inputs to approach ideal estimation value. Finally, results of automatic lane guidance control scenarios from both simulation and hardware-in-loop (HIL) implementation show that the proposed hybrid estimated method of DEKF and ARBFNN can robustly obtain satisfactory estimation value and automatic lane guidance control performance for tractor when the control system is characterized by both time-varying model parameters and uncertain external energy-bounded disturbance. A comparative study is also conducted to investigate cases to show its effectiveness when the hybrid DEKF-ARBFNN state and parameter estimation method is used and when it is not.

Estimation of wheelset equivalent conicity using the dual extended Kalman filter

This paper presents the implementation of the dual extended Kalman filter (DEKF) to estimate wheelset equivalent conicity, an accurate understanding of which can facilitate the implementation of an effective model-based estimator. The estimator is developed to identify the wheelset equivalent conicity of high-speed railway vehicles while negotiating a curve. The designed DEKF estimator employs two discrete-time extended Kalman filters combining state and parameter estimators in parallel. This estimator uses easily available measurements from acceleration sensors measuring at axle boxes and a rate gyroscope measuring bogie frame yaw velocity. Two tests, including linearized and actual wheel-rail geometry, are carried out at a speed of 250 km/h with stochastic and deterministic track features using multibody simulations, SIMPACK. The results with acceptable estimation errors for both track conditions indicate adequate performance and reliability of the designed DEKF estimator. They demonstrate the feasibility of utilizing this DEKF method in rail vehicle applications as the knowledge of time-varying parameters is not only important in achieving an effective estimator for vehicle control but also useful for vehicle condition monitoring.

Estimation of the Wetting Efficiency of an Evaporator by a Dual Extended Kalman Filter

This work presents the development of a Dual Extended Kalman Filter (DEKF) used to calculate the parameter known as wetting efficiency of a falling film evaporator. The wetting efficiency refers to the part of the tube that is in contact with the falling film. This parameter depends on different factors as the type of surface, physical properties of the fluid, and mainly the mass flow rate. The knowledge of the value of this parameter gives information about the lack or the abundance of the mass flow rate of the falling film. The evaporator consists of 13 tubes, in which the wetting efficiency of the first tube is estimated using the experimental outlet temperature of the fluid flowing inside the tubes. The results show that the predicted temperature for the first tube matches adequately the measured temperature. Alternatively, the wetting efficiency and the overall heat transfer coefficient were estimated together as a single parameter. The results show that both approaches can be used to estimate the unknown evaporator parameters, however, estimating the wetting efficiency gives more system information because it determines the lack of fluid on the tubes.

Rotor Asymmetry Detection in Wound Rotor Induction Motor Using Kalman Filter Variants and Investigations on Their Robustness: An Experimental Implementation

This paper analyzes the performance of Kalman filter-based estimators for robust filtering and rotor asymmetry detection in wound rotor induction machines (WRIMs) using real-time data. Filter models were designed based on an extended model of WRIMs. The detection of rotor asymmetry was achieved by estimating the states of rotor resistance and speed using four filters. The sensitivity of the parameters under healthy and asymmetry conditions was thoroughly analyzed and categorized as low, medium, and high sensitivity parameters. Robust model-based estimators were designed to minimize the probability of false alarms. The performance analysis demonstrated that the dual unscented Kalman filter (DUKF) outperformed other Kalman filters such as the extended Kalman filter (EKF), dual extended Kalman filter (DEKF), and unscented Kalman filter (UKF) for state estimation of WRIM.

Combined Estimation of Vehicle Dynamic State and Inertial Parameter for Electric Vehicles Based on Dual Central Difference Kalman Filter Method

Distributed drive electric vehicles (DDEVs) possess great advantages in the viewpoint of fuel consumption, environment protection and traffic mobility. Whereas the effects of inertial parameter variation in DDEV control system become much more pronounced due to the drastic reduction of vehicle weights and body size, and inertial parameter has seldom been tackled and systematically estimated. This paper presents a dual central difference Kalman filter (DCDKF) where two Kalman filters run in parallel to simultaneously estimate vehicle different dynamic states and inertial parameters, such as vehicle sideslip angle, vehicle mass, vehicle yaw moment of inertia, the distance from the front axle to centre of gravity. The proposed estimation method only integrates and utilizes real-time measurements of hub torque information and other in-vehicle sensors from standard DDEVs. The four-wheel nonlinear vehicle dynamics estimation model considering payload variations, Pacejka tire model, wheel and motor dynamics model is developed, the observability of the DCDKF observer is analysed and derived via Lie derivative and differential geometry theory. To address system nonlinearities in vehicle dynamics estimation, the DCDKF and dual extended Kalman filter (DEKF) are also investigated and compared. Simulation with various maneuvers are carried out to verify the effectiveness of the proposed method using Matlab/Simulink-Carsim®. The results show that the proposed DCDKF method can effectively estimate vehicle dynamic states and inertial parameters despite the existence of payload variations and variable driving conditions. This research provides a boot-strapping procedure which can performs optimal estimation to estimate simultaneously vehicle system state and inertial parameter with high accuracy and real-time ability.

Temperature sensor-free parameter and state joint estimation for battery pack in electric vehicles

Model based state estimation methods rely heavily on a relatively stable open-circuit-voltage (OCV)-state-of-charge (SOC) curve which is described as temperature dependent in traditional definition. However, the temperature of not every cell can be measured accurately in EVs, which restricts their application. To decouple the influences of temperature on battery characteristics, this paper proposes a new method to describe the relation between OCV and SOC, which simplifies a traditional four-dimensional mapping between temperature, aging, OCV and SOC into a temperature-independent three-dimensional mapping. These newly-defined capacity and OCV-SOC curve are independent of battery temperature, which are verified based on a large number of test data under different temperatures and aging conditions. A cooperative estimation of model parameters and state based on dual extended Kalman filter (DEKF) algorithm for a battery pack is developed by building a parameter database of noise characteristics into DEKF algorithm. Battery experimental and hardware-in-the-loop platform is built to verify the performances of the proposed method for battery management systems (BMSs) in all climate EVs. The results indicate that the proposed method can accurately estimate battery SOC with the error within 3 % after fast convergence regardless of battery initial SOC and capacity degradation.

Multistate joint estimation of ultracapacitor based on trans-scale dual extended Kalman filter

Accurate ultracapacitor state of charge (SOC) estimation directly affects safety, durability and reliability of hybrid energy storage system. For that, this paper presents a multistate joint estimation method of ultracapacitor based on trans-scale dual extended Kalman filter to predict SOC and model parameters in real-time. Firstly, an ultracapacitor model is established by using experimental data. Then, the model is combined with two Kalman filters, one of which is used to estimate SOC, and another one is applied to achieve trans-scale update the model parameters. Finally, the effectiveness of the method is verified in the urban dynamometer driving schedule at different temperatures. The validation results show that the mean absolute errors of voltage, SOC and capacity estimation are within 0.49 mV, 0.63% and 0.04 Ah, respectively. Moreover, compared with the other two traditional SOC estimation methods, whose results show that the proposed algorithm has higher estimation accuracy and more stable convergence ability.

Enhanced multi-state estimation methods for lithium-ion batteries considering temperature uncertainties

Due to their high energy density and minimal emissions, lithium-ion batteries are frequently employed in electric vehicles (EVs). Accurate estimation of the micro-parameters, state of charge (SOC), and state of health (SOH) are a few primary monitoring functions of the battery management system (BMS) to increase the battery's efficiency and safety under various operating conditions. This paper proposes a SOC and SOH co-estimation method by adopting an ensemble empirical mode decomposition method with adaptive noise and an autoencoder (EEMDA) to extract, decompose, and reconstruct the full-scale charging voltage and current data for a dual extended Kalman filter (DEKF) with multi-parameter and time-scale updates for accurate estimation based on a variable forgetting factor limited memory recursive least squares (VFF-LMRLS) method. The VFF-LMRLS method is used to solve the data saturation phenomenon and identify the battery's characteristic micro-parameters based on a proposed dynamic migration second-order resistor-capacitor equivalent circuit model under different operating states. Battery tests are conducted at temperatures ranging from −10 to 50 °C under complex working conditions. Using the VFF-LMRLS method, the effects of different temperatures on the micro-parameters are discussed. The SOC and SOH results of the proposed EEMDA-DEKF method based on the dynamic migration battery model show that the mean absolute error and root mean square error metrics have the least values of 0.0233% and 0.0252%, which signify an optimal performance improvement of 93.26% and 93.66%, respectively, compared to the conventional DEKF method. Based on the experimental results and analyses, the proposed method has a high degree of accuracy and robustness, which makes it feasible for battery monitoring and prognostic BMS applications.

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.

An Enhanced Fusion Algorithm With Empirical Thermoelectric Models for Sensorless Temperature Estimation of Li-ion Battery Cells

An enhanced dual extended Kalman filter method is presented in this article for estimating and tracking the state-of-temperature of lithium-ion battery cells. A simple but effective dynamic and measurement empirical fit models are proposed and utilized to estimate the state-of-temperature concurrently with the state-of-charge. The proposed dual estimator improves the estimation accuracy of the temperature state by accounting for the variations in the state-of-charge. To test the performance of the proposed estimation method, two independent lithium-ion battery cell datasets were used to derive the empirical models and run the estimation algorithm. The obtained results show a promising performance of the estimation method in terms of the high estimation accuracy even in the case when the measurement contains high-magnitude noise or when the estimation algorithm is inaccurately initialized. The proposed models and the estimation algorithm are derived and experimentally tested in this article.

Prognostics of Lithium-Ion batteries using knowledge-constrained machine learning and Kalman filtering

• Propose a knowledge-constrained machine learning method for batteries prognostics • Propose a data-driven stochastic model for battery degradation • Employ an ANN-based DEKF method to capture the dynamics of lithium-ion batteries • Validate the proposed approach using NASA dataset for battery prognostics Accurately predicting the remaining useful life (RUL) of lithium-ion rechargeable batteries remains challenging as the battery capacity degrades in a stochastic manner given the internal complex electrochemical reactions of the battery and the external operational/environmental conditions. In this work, a knowledge-constrained machine learning framework is developed to learn the stochastic degradation of battery performance over working cycles for health prognostics of Lithium-Ion batteries. An artificial neural network (ANN) model is first trained and synchronized using a Dual Extended Kalman Filter (DEKF) to obtain critical health information of Lithium-Ion batteries. With the obtained health information, a knowledge-constrained machine learning method (KcML) is then developed to predict the stochastic degradation of the battery capacity in operation. Specifically, prior knowledge in battery capacity fade can be formulated as extra constraints to facilitate the development of machine learning models with improved fidelity level for battery capacity predictions. A dataset published by NASA is utilized to demonstrate the effectiveness of the proposed knowledge-constrained machine learning approach.

State and covariance estimation of a semi-batch reactor for bioprocess applications

In this work, extended Kalman filter (EKF) and moving horizon estimation (MHE)-based approaches are introduced and applied to a Galacto-oligosaccharides (GOS) bioprocess system considering a recently developed enzymatic model. Using this model, plant data is simulated by varying the kinetic parameters and applying white noise to the resulting output. In terms of EKF applications, both the canonical and parametric (Dual EKF) formulations have their covariances specified using a modified direct optimization (DO) algorithm to reduce estimation error. This work also outlines the development and application of a novel Parameter-based Moving Horizon Estimation (P-MHE) approach and directly compares it to traditional MHE formulations. The proposed P-MHE method reduces both the estimation error and computational time of traditional MHE approaches. When compared to EKF-based approaches, P-MHE can compete in terms of estimation error while exhibiting excellent robustness characteristics such as guaranteed feasibility. Despite the increased computational time of P-MHE when compared to the EKF formulations, state estimates can be obtained in under 3 seconds once a measurement arrives, allowing this algorithm to be applied to real-time process monitoring and other process systems.

A three-time-scale dual extended Kalman filtering for parameter and state estimation of Li-ion battery

Estimation of battery state and parameters play an important role in electric vehicle battery management system (BMS). Second-order RC model is applied, the initial parameters of battery model are determined by experiments. Data points of open circuit voltage and state of charge (OCV-SOC) are determined by experiment. Different function forms are used to fit the OCV-SOC discrete points, and the function form with great fitting effect is selected as the OCV-SOC fitting form. Dual extended Kalman filter which is divided into Parameter filter and state filter is applied. Battery state in state filter is a fast-time-varying parameter, The battery model parameters in parameter filter are divided into two parts. the battery model parameters are classified according to the influence of each parameter on the terminal voltage. A longer sampling time is applied to the parameters that have a strong impact on the terminal voltage, and a longest sampling time is applied to the parameters that have a weak impact on the terminal voltage. The time-scale classification method is validated both quantitatively and qualitatively. Compared with the previous methods, the three-time-scale classification method can reduce the number of parameter updates.