Dual Extended Kalman Filter Research Articles

A Remaining Discharge Energy Prediction Method for Lithium-Ion Battery Pack Considering SOC and Parameter Inconsistency

The remaining discharge energy prediction of the battery pack is an important function of a battery management system. One of the key factors contributing to the inaccuracy of battery pack remaining discharge energy prediction is the inconsistency of the state and model parameters. For a batch of lithium-ion batteries with nickel cobalt aluminum oxide cathode material, after analyzing the characteristics of battery model parameter inconsistency, a “specific and difference” model considering state of charge and R0 inconsistency is established. The dual time-scale dual extended Kalman filter algorithm is proposed to estimate the state of charge and R0 of each cell in the battery pack, and the remaining discharge energy prediction algorithm of the battery pack is established. The effectiveness of the state estimation and remaining discharge energy prediction algorithm is verified. The results show that the state of charge estimation error of each cell is less than 1%, and the remaining discharge energy prediction error of the battery pack is less than 1% over the entire discharge cycle. The main reason which causes the difference between the “specific and difference” and “mean and difference” models is the nonlinearity of the battery’s state of charge - open circuit voltage curve. When the nonlinearity is serious, the “specific and difference” model has higher precision.

An On-Board Model-Based Condition Monitoring for Lithium-Ion Batteries

A model-based condition monitoring for lithium-ion (Li-ion) batteries involves estimating critical model parameters (e.g., capacity and impedance) and operational states [e.g., state of charge (SOC) and state of health]. This is important to design high-performance and safety-critical battery systems. Moreover, the tuning parameters of the condition monitoring algorithms significantly influence the performance of the algorithms. This paper proposes a real-time model-based condition monitoring for Li-ion batteries based on a real-time second-order resistor–capacitor electrical circuit battery model. The proposed method consists of an extended Kalman filter based online parameter identification and a smooth variable structure filter based state estimation. The two filters are systematically integrated to cooperate with each other and named hybrid filter (HF). Furthermore, a proposed particle swarm optimization based tuning parameter optimization is employed to find the optimal tuning parameters of the HF. The proposed method is compared with the dual extended Kalman filter (DEKF) via simulations and validated by experiments using a low-priced microcontroller. The results show that the proposed method can effectively choose the tuning parameters and has less computational complexity and higher accuracy of the SOC and capacity estimation than those of the conventional DEKF. Therefore, the proposed HF can be suitable for use in real-time embedded battery management system applications.

Integrated control of active steering and braking systems with tyre forces and cornering stiffness estimation

A model-based integrated controller for active steering and active braking systems is proposed to enhance vehicle handling and stability. A hierarchical scheme is adopted, including vehicle layer based on model predictive control (MPC), actuator layer, and observer layer. The MPC controller adopts a predictive model with the lateral force of front axle and yaw moment as inputs, which leaves the nonlinearity and coupling of tyre forces to be solved by the tyre force allocation algorithm in actuator layer, leading to more precise control action. In order to maintain satisfactory control performance with respect to the variation of tyre character, a dual extended Kalman filter (DEKF) is designed in the observer layer to estimate tyre forces and cornering stiffness. The observed results are used to reduce the mismatch of the reference models in vehicle layer and actuator layer. The effectiveness of the proposed controller is demonstrated by simulations in CarSim environment.

State of charge estimation for LiFePO4 battery via dual extended kalman filter and charging voltage curve

The state-of-charge (SOC) estimation method currently ignores the measurement error caused by the Battery Management System (BMS). In this paper, the characteristic of LiFePO4 battery is deeply studied to explore the relationship between open-circuit-voltage (OCV) and SOC. By the analysis of the characteristic of the curve, the results show that the curve does not change with the battery aging by the capacity correction. Meanwhile, the feature of the charging voltage curve is also analyzed. It is pointed out that the ohmic internal resistance and capacity can be obtained by the transformation of the charging voltage curve, which reduces the workload of the dual extended kalman filter (DEKF) algorithm. Based on the DEKF algorithm, the SOC under constant current and dynamic discharge conditions are estimated. The results show that the estimation error is within 3%. The influence of battery voltage and current measurement noise on the estimation accuracy of the SOC is then analyzed. It is found that the measurement noise increases the SOC estimation deviation. Finally, the open circuit voltage in measurement equation is replaced by the charging voltage. And a new method of combining DEKF algorithm and charging voltage curve for SOC estimation is proposed. The results of the experiments under constant current and dynamic discharge conditions show that the proposed method can eliminate the measurement noise and ensure the accuracy of SOC estimation.

Sequential state prediction and parameter estimation with constrained dual extended Kalman filter for building zone thermal responses

This article introduces a parameter estimation and state prediction technique called constrained dual Extended Kalman Filter (EKF) that can be used in model prediction controls (MPC) and fault detection and diagnostics (FDD) in building systems. The proposed method is an improvement over the existing nonlinear filter-based methods such as the joint EKF or Unscented Kalman Filter, which is widely adopted in previous building controls research. Case studies using both simulation and real measurements are conducted to demonstrate the proposed algorithm when used for a building thermal zone. Data from parametric simulations are used to test the thermal model's ability to capture parameter variations. Measured data from five identical offices is collected to test the performance of parameter estimates and state predictions under real-life operation. Overall, the proposed algorithm is 25% faster than a conventional EKF with improved numerical stability. It can also help mitigate numerical instabilities seen in previous EKF research. The reduced thermal model used in this paper is also capable of detecting most of the parametric changes to the thermal zone and providing reliable temperature predictions.

Estimation of Lithium-Ion Battery State of Charge for Electric Vehicles Based on Dual Extended Kalman Filter

State of Charge (SOC) estimation accuracy and robustness is significant to battery energy management, safety in use and residual cycle life. However, model parameters strongly depend on the battery status such as current rate, temperature and cycle times. In the research, Dual Extended Kalman Filter (DEKF) is used to reduce the influence of measurement and system noise and provide an accurate and robust solution by estimating both the battery states and the model parameters. In addition, a novel Open Circuit Voltage (OCV) curve acquisition method is presented to eliminate the affection of temperature and keep cycle times in consider. The validation is carried out by bench testing. Results show that the algorithm can be fast convergent in 60 seconds and stable keeping error below 3% in different current rate, temperature and cycle times.

Comparative study of methods for integrated model identification and state of charge estimation of lithium-ion battery

Model-based observers appeal to both research and industry utilization due to the high accuracy and robustness. To further improve the robustness to dynamic work conditions and battery ageing, the online model identification is integrated to the state estimation, giving rise to the co-estimation methods. This paper systematically compares three types of co-estimation methods for the online state of charge of lithium-ion battery. This first method is dual extended Kalman filter which uses two parallel filters for co-estimation. The second method is a typical data-model fusion method which uses recursive least squares for model identification and extended Kalman filter for state estimation. Meanwhile, a noise compensating method based on recursive total least squares and Rayleigh quotient minimization is exploited for online model identification, which is further designed in conjunction with the extended Kalman filter to estimate the state of charge. Simulation and experimental studies are carried out to compare the performances of three methods in terms of the accuracy, convergence property, and noise immunity. The computing cost and tuning effort are further discussed to give insights to the application prospective of different methods.

An Extended Kalman Filter and Back Propagation Neural Network Algorithm Positioning Method Based on Anti-lock Brake Sensor and Global Navigation Satellite System Information.

Telematics box (T-Box) chip-level Global Navigation Satellite System (GNSS) receiver modules usually suffer from GNSS information failure or noise in urban environments. In order to resolve this issue, this paper presents a real-time positioning method for Extended Kalman Filter (EKF) and Back Propagation Neural Network (BPNN) algorithms based on Antilock Brake System (ABS) sensor and GNSS information. Experiments were performed using an assembly in the vehicle with a T-Box. The T-Box firstly use automotive kinematical Pre-EKF to fuse the four wheel speed, yaw rate and steering wheel angle data from the ABS sensor to obtain a more accurate vehicle speed and heading angle velocity. In order to reduce the noise of the GNSS information, After-EKF fusion vehicle speed, heading angle velocity and GNSS data were used and low-noise positioning data were obtained. The heading angle speed error is extracted as target and part of low-noise positioning data were used as input for training a BPNN model. When the positioning is invalid, the well-trained BPNN corrected heading angle velocity output and vehicle speed add the synthesized relative displacement to the previous absolute position to realize a new position. With the data of high-precision real-time kinematic differential positioning equipment as the reference, the use of the dual EKF can reduce the noise range of GNSS information and concentrate good-positioning signals of the road within 5 m (i.e. the positioning status is valid). When the GNSS information was shielded (making the positioning status invalid), and the previous data was regarded as a training sample, it is found that the vehicle achieved 15 minutes position without GNSS information on the recycling line. The results indicated this new position method can reduce the vehicle positioning noise when GNSS information is valid and determine the position during long periods of invalid GNSS information.

Concurrent Real-Time Estimation of State of Health and Maximum Available Power in Lithium-Sulfur Batteries

Lithium-sulfur (Li-S) batteries are an emerging energy storage technology with higher performance than lithium-ion batteries in terms of specific capacity and energy density. However, several scientific and technological gaps need to be filled before Li-S batteries will penetrate the market at a large scale. One such gap, which is tackled in this paper, is represented by the estimation of state-of-health (SOH). Li-S batteries exhibit a complex behaviour due to their inherent mechanisms, which requires a special tailoring of the already literature-available state-of-charge (SOC) and SOH estimation algorithms. In this work, a model of SOH based on capacity fade and power fade has been proposed and incorporated in a state estimator using dual extended Kalman filters has been used to simultaneously estimate Li-S SOC and SOH. The dual extended Kalman filter’s internal estimates of equivalent circuit network parameters have also been used to the estimate maximum available power of the battery at any specified instant. The proposed estimators have been successfully applied to both fresh and aged Li-S pouch cells, showing that they can accurately track accurately the battery SOC, SOH, and power, providing that initial conditions are suitable. However, the estimation of the Li-S battery cells’ capacity fade is shown to be more complex, because the practical available capacity varies highly with the applied current rates and the dynamics of the mission profile.

Dual estimation based vocal tract shape computation

This paper presents a new method for direct estimation of vocal tract shape from the speech signal. The method computes cross-sectional areas of uniform-length cylindrical tubes comprising the vocal tract. Cross-sectional areas are calculated from reflection coefficients at tube junctions whose values depend on the areas of adjoining tubes. A new state space representation of the speech production system has been formulated in which reflection coefficients are parameters. The state space model has been constructed using state equations of the glottal flow signal and vocal tract formulated from Liljencrants–Fant model and concatenated tube model respectively. Dual extended Kalman filtering algorithm has been used for estimation of unknown parameters of the system. The estimated reflection coefficients are then used to compute cross-sectional areas of the vocal tract. The performance of proposed technique has been compared to an existing shape estimation method proposed by Wakita. For both synthesized and natural speech signals, the performance of proposed method has been found to be comparable to the existing one. Nevertheless, the Kalman filter algorithm used in proposed method has provisions to tune measurement noise covariance which can be adjusted based on the noise level in speech. Therefore, the performance of proposed method has been seen to be comparatively more robust to noise than the existing technique.

Revisiting the dual extended Kalman filter for battery state-of-charge and state-of-health estimation: A use-case life cycle analysis

Abstract One of the most discussed topics in battery research is the state-of-charge (SOC) and state-of-health (SOH) determination of traction batteries. Unfortunately, neither is directly measurable and both must be derived from sensor signals using model-based algorithms. These signals can be noisy and erroneous, leading to an inaccurate estimate and, hence, to a limitation of usable battery capacity. A popular approach tackling these difficulties is the dual extended Kalman filter (DEKF). It consists of two extended Kalman filters (EKFs), that synchronously estimate both the battery states and parameters. An analysis of the reliability of the DEKF estimation against realistically fading battery parameters is still a widely discussed subject. This work investigates the DEKF performance from a high-level perspective, involving different load dynamics and SOH stages. A numerical optimization-based approach for the crucial filter parameterization is employed. We show that the DEKF partly improves the accuracy of the SOC estimation compared to the simple EKF over battery lifetime within the operational limits of an automotive application. However, capacity and internal resistance estimation becomes unreliable and partly diverges from the reference under constant and realistic load scenarios coupled with advanced degradation. As a consequence, a downstream use of both parameters in a SOC or SOH estimation is hampered over the battery lifetime. Extensions are needed to improve reliability and enable employment in real-world applications.

Successive-approximation algorithm for estimating capacity of Li-ion batteries

This paper proposes a capacity estimation algorithm for Li-ion batteries (LIBs) using the successive approximation method. Model-based capacity estimation method can be applied to a variety of current profiles because the capacity is calculated from state of charge (SOC) estimated accurately using the functional relationship between open circuit voltage (OCV) and the SOC. However, with aging, the OCV-SOC table changes, which worsens the estimation accuracy. Therefore, additional experiments are necessary to compensate the errors whenever the capacity should be identified. To overcome this restriction, this paper proposes an algorithm for estimating both the capacity and the corresponding OCV-SOC table based on the preliminary OCV-SOC tables obtained from other batteries. The capacity and the table are updated successively based on the prior capacity estimate. This work proposes two algorithms for voltage characteristics: OCV measurement and SOC estimation cases. The former uses the measured OCV to calculate the SOCs directly, while the latter estimates the SOCs using a dual extended Kalman filter (DEKF). Aging data from five LIB packs are analyzed, and the capacity estimation errors are less than 2.2% for the OCV measurement case and 3.06% until 20% loss of capacity estimate for SOC estimation case.

Estimation of the Diesel Particulate Filter Soot Load Based on an Equivalent Circuit Model

In order to estimate the diesel particulate filter (DPF) soot load and improve the accuracy of regeneration timing, a novel method based on an equivalent circuit model is proposed based on the electric-fluid analogy. This proposed method can reduce the impact of the engine transient operation on the soot load, accurately calculate the flow resistance, and improve the estimation accuracy of the soot load. Firstly, the least square method is used to identify the flow resistance based on the World Harmonized Transient Cycle (WHTC) test data, and the relationship between flow resistance, exhaust temperature and soot load is established. Secondly, the online estimation of the soot load is achieved by using the dual extended Kalman filter (DEKF). The results show that this method has good convergence and robustness with the maximal absolute error of 0.2 g/L at regeneration timing, which can meet engineering requirements. Additionally, this method can estimate the soot load under engine transient operating conditions and avoids a large number of experimental tests, extensive calibration and the analysis of complex chemical reactions required in traditional methods.

Extended Kalman filter for fouling detection in thermal power plant reheater

A model based on-line foul monitoring approach for a power plant reheater is proposed. Dual Extended Kalman Filter (DEKF) is designed to estimate the model parameters that influence fouling. Based on the estimated parameters the performance index (Cleanliness Factor) is obtained to retrieve the extent of fouling on reheater. The simulation and experimental validation using power plant data shows the efficacy of DEKF over conventional Joint-EKF (JEKF) in estimating the model parameters. The outcome of the work will assist in soot blow scheduling for reheater by perceiving the fall in cleanliness factor and will also help in analysing its impact on heat transfer efficiency.

Lithium-Ion Battery Online Rapid State-of-Power Estimation under Multiple Constraints

The paper aims to realize a rapid online estimation of the state-of-power (SOP) with multiple constraints of a lithium-ion battery. Firstly, based on the improved first-order resistance-capacitance (RC) model with one-state hysteresis, a linear state-space battery model is built; then, using the dual extended Kalman filtering (DEKF) method, the battery parameters and states, including open-circuit voltage (OCV), are estimated. Secondly, by employing the estimated OCV as the observed value to build the second dual Kalman filters, the battery SOC is estimated. Thirdly, a novel rapid-calculating peak power/SOP method with multiple constraints is proposed in which, according to the bisection judgment method, the battery’s peak state is determined; then, one or two instantaneous peak powers are used to determine the peak power during T seconds. In addition, in the battery operating process, the actual constraint that the battery is under is analyzed specifically. Finally, three simplified versions of the Federal Urban Driving Schedule (SFUDS) with inserted pulse experiments are conducted to verify the effectiveness and accuracy of the proposed online SOP estimation method.

Hardware-in-the-Loop Platform for Assessing Battery State Estimators in Electric Vehicles

The development of new algorithms for the management and state estimation of lithium-ion batteries requires their verification and performance assessment using different approaches and tools. This paper aims at presenting an advanced hardware in the loop platform that uses an accurate model of the battery to test the functionalities of battery management systems (BMSs) in electric vehicles. The developed platform sends the simulated battery data directly to the BMS under test via a communication link, ensuring the safety of the tests. As a case study, the platform has been used to test two promising battery state estimators, the adaptive mix algorithm and the dual extended Kalman filter, implemented on a field-programmable gate array-based BMS. The results show the importance of the assessment of these algorithms under different load profiles and conditions of the battery, thus highlighting the capabilities of the proposed platform to simulate many different situations in which the estimators will work in the target application.

A framework of quality prediction in multivariable process based on nonlinear dynamical analysis

Real-time prediction of process quality is the key factor for guaranteeing product performance. Static modeling method could not consider the impact of noise variables on quality characteristics, which will easily lead quality problem for instability. This paper proposes a dynamic quality modeling and prediction approach for multivariable process using nonlinear dynamical analysis. The quality state model for any time of process is regarded as an evolution product obtained from the adjacent previous moment. Dual extended Kalman filter algorithm is introduced to real-time adjust the quality prediction model, which refers to the weights and the centers in radial basis function network. So the dynamic adaptive neural network is proposed to predict the following state of quality. Finally, a case about crack prediction of continuous casting slab is conducted to illustrate the feasibility of proposed approach, result shows that it could accurately track the nonlinear dynamic continuous casting process.

Target torque estimation for gearshift in dual clutch transmission with uncertain parameters

The target torque of engaging clutches during gearshift is a key factor that affects the dynamic response of powertrains equipped with the dual clutch transmissions (DCT). This paper investigates a method to estimate the target torque of engaging clutches under conditions where engine torque and measurement signals contain white noise and some vehicle parameters (the radius of wheel and rolling friction coefficient) are uncertain. To compute the target torque accurately, the state of system should be estimated when the uncertain parameters exist. The vehicle powertrain is modeled as the 3DOF system when one clutch is closed and the 4DOF system when two clutches are open, while the measured signals include speeds of the engine, transmission, and vehicle (rotational speed of wheels). In addition to traditional extended Kalman filter (EKF), both the joint extended Kalman filter (JEKF) and dual extended Kalman filter (DEKF) are used to estimate the target torque. The simulation results show that DEKF and JEKF provide much higher accuracy in the estimation of target torque than EKF when some parameters of the model are uncertain, so as to produce a better ride performance of the transmission during gearshift, i.e. reduction of power interruption and compressed shifting time. Furthermore, the DEKF provides higher accuracy than the JEKF in estimating uncertain parameters.

Dual EKF-Based State and Parameter Estimator for a LiFePO4 Battery Cell

This work presents the design of a dual extended Kalman filter (EKF) as a state/parameter estimator suitable for adaptive state-of-charge (SoC) estimation of an automotive lithium–iron–phosphate (LiFePO₄) cell. The design of both estimators is based on an experimentally identified, lumped-parameter equivalent battery electrical circuit model. In the proposed estimation scheme, the parameter estimator has been used to adapt the SoC EKF-based estimator, which may be sensitive to nonlinear map errors of battery parameters. A suitable weighting scheme has also been proposed to achieve a smooth transition between the parameter estimator-based adaptation and internal model within the SoC estimator. The effectiveness of the proposed SoC and parameter estimators, as well as the combined dual estimator, has been verified through computer simulations on the developed battery model subject to New European Driving Cycle (NEDC) related operating regimes.

Real-Time Estimation of Temperature Distribution for Cylindrical Lithium-Ion Batteries Under Boundary Cooling

This paper presents a real-time estimation method for the temperature distribution of cylindrical batteries under boundary air cooling. A space-/time-separation-based analytical model is developed using Karhunen–Loeve decomposition and Galerkin's method. The model parameters can be identified and optimized using data-based approaches. The developed analytical model demonstrates the robustness to variation of thermal parameters. However, the change of boundary cooling will significantly degrade the performance of the developed analytical model. For the known boundary cooling, the compensation model for cooling effects can be derived to improve the modeling performance. For the unknown boundary cooling in real practice, a dual-extended Kalman filter can be used to simultaneously estimate coupled parameters and convection coefficient in the compensation model. The proposed method can achieve satisfactory performance in the battery duty-cycle experiments.