Adaptive Extended Kalman Filter Algorithm Research Articles

State-of-charge estimation of lithium-ion battery: Joint long short-term memory network and adaptive extended Kalman filter online estimation algorithm

With the widespread use of lithium-ion batteries, estimating the State of Charge (SOC) has been one of the most critical tasks in the battery management system (BMS). In this paper, a joint long short-term memory recurrent neural network (LSTM-RNN) and adaptive extended Kalman filter (AEKF) algorithm is proposed to achieve accurate SOC estimation. The proposed algorithm generates an initial SOC estimation value through a trained LSTM-RNN with a sliding time window signal sequence as input. The initial estimation value is then used as a feedback input to the AEKF. The results show that only a 30-s time series as the input of the LSTM-RNN can achieve satisfactory estimation results. Compared with traditional adaptive extended Kalman filter and unscented Kalman filter (UKF), the proposed algorithm has a better performance of estimation accuracy under various discharging conditions, especially when applied at low temperatures. Finally, the SOC estimation results under four operating conditions and various temperatures show that the maximum error is less than 2.5 %, in particular, the root mean square error (RMSE) and the mean absolute error (MAE) are below 1.01 % and 0.64 %. The proposed algorithm is an effective SOC estimation method with good robustness and high estimation accuracy.

A novel multi-factor fuzzy membership function - adaptive extended Kalman filter algorithm for the state of charge and energy joint estimation of electric-vehicle lithium-ion batteries

In view of the unmeasurable state parameters of electric-vehicle lithium-ion batteries, this paper investigates a novel multi-factor fuzzy membership function - adaptive extended Kalman filter (MFMF-AEKF) algorithm for the online joint estimation of the state of charge and energy. Strong nonlinear characteristics of model parameters are characterized by considering multiple processing factors of electrochemical and diffusion effects for lithium-ion batteries and constructing an optimized multifactor coupling model. In the proposed MFMF-AEKF method, multi-space-scale factors are introduced to realize the numerical analysis of the multi-factor coupled model parameters and state estimation under dynamic working conditions of electric-vehicle lithium-ion batteries. The proposed MFMF-AEKF algorithm estimates the state of charge (SOC) with the overall best mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE), and maximum error (ME) values of 1.822 %, 4.322 %, 1.947 %, and 2.954 %, respectively, under challenging working conditions. And The MAE, MAPE, RMSE, and ME values for the state of energy (SOE) are 0.617 %, 1.711 %, 0.695 %, and 1.011 %, respectively. Both state estimation results are better than the traditional method. The proposed MFMF-AEKF algorithm has higher estimation accuracy which provides a feasible estimation algorithm for the joint SOC and SOE of lithium-ion batteries.

Leveraging digital twins for fault diagnosis in autonomous ships

Autonomous ships are vulnerable to a spectrum of potential faults, including propeller damage, shaft-line failures, and electrical supply disruptions. Swift fault detection is critical to minimize the potentially catastrophic consequences of these issues. In this paper, we introduce an innovative digital twin-based method for diagnosing faults in autonomous ships. Our digital twin system collects data from the ship’s sensor array, conducts comprehensive analysis, computes fault parameters, and provides real-time visualizations of the findings. To achieve this, we utilize the ship’s dynamical model and employ a novel adaptive extended Kalman filter (AEKF) algorithm to estimate the severity of these faults. We evaluate the effectiveness of this approach through numerical simulations and practical implementation in an autonomous surface vehicle called the Otter, developed by Maritime Robotics. The experimental results, which consider both normal and faulty ship propulsion systems, underscore the significant potential of this novel approach to improve ship condition monitoring during operational activities.

A fast convergence strategy based on gray wolf optimization algorithm for co-estimation of battery state of charge and capacity

Under the same initial noise covariance, the extended Kalman filter (EKF) algorithm and the adaptive extended Kalman filter (AEKF) algorithm show different convergence rates in the battery state estimation experiments. It can be concluded from the experimental results that the convergence rate of the EKF algorithm is usually faster than that of the AEKF algorithm, but the estimation accuracy of the AEKF algorithm is usually better than that of the EKF algorithm. In response to this issue, this article proposes a fast convergence strategy based on the grey Wolf optimization (GWO) algorithm for the co-estimation of battery SOC and capacity. Based on battery parameter identification, the proposed algorithm utilizes the GWO to optimize the initial noise covariance of the EKF algorithm. Then, the EKF algorithm with optimized initial noise covariance is used to quickly pull the SOC estimation results into a stable region and switch to the AEKF algorithm to jointly estimate the SOC and capacity of the battery. Through data validation under different working conditions, it is shown that the proposed target algorithm has a much faster convergence ability than the comparison algorithm, and the proposed algorithm also exhibits excellent robustness under different initialization errors and temperatures.

State of charge estimation for lithium-ion battery based on adaptive extended Kalman filter with improved residual covariance matrix estimator

The accurate estimation of the state of charge (SOC) in lithium-ion batteries plays a pivotal role in battery management systems. This paper proposes an improved adaptive extended Kalman filter (IAEKF) algorithm for more precise SOC estimation. Initially, a novel characteristic parameter is introduced to assess the suitability of the forgetting factor in the adaptive forgetting factor recursive least squares (AFFRLS) algorithm. This evaluation aims to improve the accuracy of recognizing the parameters of the battery model. Additionally, an even function with adjustable parameters is constructed to solve the appropriate value for the forgetting factor. Subsequently, the correlation coefficients of the residual series at different moments are approximated by mathematical transformations that link the inner products of the column vectors in the constructed residual matrix to the calculation of the correlation coefficients. By comparing it with optimized thresholds using particle swarm optimization, one can adjust the sliding window length to enhance the estimation accuracy of IAEKF. The experimental results confirm that IAEKF achieves superior estimation accuracy and robustness compared to other AEKF algorithms, and the accuracy of AFFRLS parameter identification is higher than that of recursive least squares, thereby substantiating the effectiveness of the proposed algorithms.

Ultrasonic- and IMU-Based High-Precision UAV Localization for the Low-Cost Autonomous Inspection in Oil and Gas Pressure Vessels

With the increasing demands for unmanned aerial vehicle (UAV) based autonomous inspections in the oil and gas industry, one of the challenging issues for 3D UAV positioning has emerged due to the satellite signal blocking. Considering the existing characteristics of the ultrasonic based technique, such as the low cost, extremely lightweight and high positioning accuracy, it can be promising as the potential solution. Nevertheless, the low position update rate and vulnerable positioning performance to the changing environment still limit its applications on UAV. Therefore, in this article, an ultrasonic and inertial measurement unit (IMU) based localisation algorithm and low cost UAV autonomous inspection system are presented. With the incorporation of the IMU, the position update rate, accuracy and stability of the algorithm can all be significantly improved. This is done by the adaptively estimated noise covariance matrices through the proposed adaptive extended Kalman filter (AEKF) algorithm and the added weighting factors. Followed by, an additional virtual observation process is presented to overcome the unavailability of the observation information for further performance improvement. Finally, extensive numerical results and field tests demonstrate that the proposed algorithm and system can achieve the high update rate, reliable, accurate and precision UAV positioning in oil and gas pressure vessels and are feasible for the UAV autonomous inspection in these environments.

An Improved Multi-Timescale AEKF–AUKF Joint Algorithm for State-of-Charge Estimation of Lithium-Ion Batteries

State-of-charge (SoC) estimation is one of the core functions of battery energy management systems. An accurate SoC estimation can guarantee the safe and reliable operation of the batteries system. In order to overcome the practical problems of low accuracy, noise uncertainty, poor robustness, and adaptability in parameter identification and SoC estimation of lithium-ion batteries, this paper proposes a joint estimation method based on the adaptive extended Kalman filter (AEKF) algorithm and the adaptive unscented Kalman filter (AUKF) algorithm in multiple time scales for 18,650 ternary lithium-ion batteries. Based on the slowly varying characteristics of lithium-ion batteries’ parameters and the quickly varying characteristics of the SoC parameter, firstly, the AEKF algorithm was used to online identify the parameters of the model of batteries with a macroscopic time scale. Secondly, the identified parameters were applied to the AUKF algorithm for SoC estimation of lithium-ion batteries with a microscopic time scale. Finally, the comparative simulation experiments were implemented, and the experimental results show the proposed joint algorithm has higher accuracy, adaptivity, robustness, and self-correction capability compared with the conventional algorithm.

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 improved proportional control forgetting factor recursive least square-Monte Carlo adaptive extended Kalman filtering algorithm for high-precision state-of-charge estimation of lithium-ion batteries

An improved proportional control forgetting factor recursive least square-Monte Carlo adaptive extended Kalman filtering algorithm for high-precision state-of-charge estimation of lithium-ion batteries

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.

State of charge estimation of ternary lithium-ion batteries at variable ambient temperatures

Among the factors that affect lithium-ion batteries, ambient temperature has a great influence on the charge and discharge rate, general battery performance, and storage capacity of the battery, hence accurate state of charge (SOC) estimation over a wide range of temperatures is essential and necessary. In this paper, a Second-order Thevenin equivalent circuit model is established with ambient temperature compensation over varying ambient temperature conditions. An improved Fixed Range Forgetting Factor-Adaptive Extended Kalman Filtering (FRFF-AEKF) algorithm with the Saga-Husa Adaptive filter (SHAF) is proposed for the accurate estimation of SOC at variable ambient temperature. The temperatures −10°C, 10 °C, 25 °C, and 40 °C are set to depict low, normal, and high ambient temperatures in which lithium-ion batteries in electric vehicles (EVs) and most electronic devices usually operate. Tests conducted include the hybrid pulse power characterization (HPPC) for obtaining data required for parameterization, and for SOC estimation and verification, the Beijing Bus Dynamic stress (BBDST). The object of the tests was a ternary lithium-ion battery representing those used in electric vehicles (EVs). To improve adaptability, reduced noise, and achieve faster convergence with increased accuracy, the range of forgetting factor is fixed between a variable range of 0.997–1. To verify the performance of the proposed algorithm under varying conditions and different ambient temperatures, the SOC estimation result was compared with that of the adaptive extended Kalman filtering (AEKF) algorithm. The results show that the proposed improved algorithm implemented with the established Second-order Thevenin equivalent model has a 1.1 % better estimation accuracy compared to the results of the AEKF algorithm. This confirms that the proposed method can achieve accurate SOC estimation and is adaptive to variable ambient temperatures.

Digital Twin-Driven Fault Diagnosis for Autonomous Surface Vehicles

This paper presents a digital twin-driven fault diagnosis approach based on a graphical model and an adaptive extended Kalman filter algorithm for autonomous surface vehicles. In contrast with the traditional adaptive Kalman filter algorithm, where the fault parameters are treated as extended state variables, the newly proposed adaptive extended Kalman filter algorithm estimates the magnitude of the faults by calculating the parameter estimation gains directly from the sensor systems. To this end, the algorithm utilizes data from a global navigation satellite system receiver assuming the persistence of excitation conditions on the control inputs. The algorithm is tested in the Otter, an autonomous surface vehicle developed by Maritime Robotics, in which one of its propellers is faulty. Technically, the digital twin receives real-time data from the sensor system, estimates the magnitude of the actuator faults, and visualizes the results in a web-based application using JavaScript with Three.js library and Mapbox for real-world 3D map generation. Information regarding the magnitude of the faults is important for fault-tolerant control. Simulation and experimental results show the proposed approach is able to detect and estimate the actuator faults accurately.

Research on UWB Indoor Positioning Algorithm under the Influence of Human Occlusion and Spatial NLOS

Ultra-wideband (UWB) time-of-flight (TOF)-based ranging information in a non-line-of-sight (NLOS) environment can display significant forward errors, which directly affect positioning performance. NLOS has been a major factor limiting the improvement of UWB positioning accuracy and its application in complex scenarios. Therefore, in order to weaken the influence of the indoor complex environment on the NLOS environment of UWB and to further improve the performance of positioning, in this paper, we first analyze the factors and characteristics of NLOS formation in an indoor environment. The NLOS is divided into fixed NLOS influenced by spatial structure and dynamic random NLOS influenced by human occlusion. Then, the anchor LOS/NLOS information map is established by making full use of indoor spatial a priori information. On this basis, a robust adaptive extended Kalman filtering algorithm based on the anchor LOS/NLOS information map is designed, which is not only effectively able to exclude the influence of spatial NLOS, but can also optimize the random error. The proposed algorithm was validated in different experimental scenarios. The experimental results show that the positioning accuracy is better than 0.32 m in complex indoor NLOS environments.

A Novel Multi-Constraint Peak Power Prediction Method Combined with Online Model Parameter Identification and State-of-Charge Co-Estimation of Lithium-Ion Batteries

The accuracy of the peak power is influenced by the accurate battery model, the results of the parameter identification, and the state of charge (SOC). First, to accurately predict the peak power of lithium-ion batteries, this paper proposes an improved Thevenin model to describe the operating state of lithium-ion batteries by introducing model noise into the Thevenin model. Second, to achieve accurate online parameter identification, a Forgetting Factor Recursive Extended Least Squares (FFRELS) method is proposed to identify the parameters of the improved model. To optimize the effect of noise on SOC estimation, an improved adaptive extended Kalman filtering (AEKF) algorithm is proposed. Finally, to obtain higher accuracy of peak power estimation, a multi-constrained peak power prediction method based on state-recursive estimation is used in this paper. Experimental results show that the maximum error of the FFRELS algorithm under different working conditions is 34.35 mV, and the SOC estimation error of the improved AEKF algorithm is less than 0.53%. The improved multi-constraint peak power estimation algorithm has high estimation accuracy under two complex working conditions, and can accurately predict the power input and output capability of the battery.

Sensorless control of marine permanent magnet synchronous propulsion motor based on adaptive extended Kalman filter

Gross error interference or noise statistical deviation is the main factor that leads to the accuracy deterioration of extended Kalman filter (EKF) in estimating the speed and rotor position of ship propulsion permanent magnet synchronous motor (PMSM). In this paper, an adaptive extended Kalman filter (AEKF) algorithm based on innovation sequence is proposed. In the proposed method, gross error interference is first added to EKF to analyze its influence on the observation accuracy. Then, the weighting coefficient is set in the calculation of innovation covariance. By adjusting the weight of the innovation covariance matrix at the adjacent time, the innovation covariance difference is calculated and then used in the calculation of Kalman gain. The observation performance comparison between AEKF and EKF strategies is conducted with subject to gross error interference and noise statistics deviate. Simulation and experimental results demonstrate that the proposed AEKF has stronger robustness and higher prediction accuracy of speed and rotor position.

Comprehensive co-estimation of lithium-ion battery state of charge, state of energy, state of power, maximum available capacity, and maximum available energy

In developing an efficient battery management system (BMS), accurate battery state estimation is always required. However, the trade-off between computational efficiency and accuracy of state estimation is hard to maintain. This work proposes the comprehensive co-estimation method for battery states, maximum available capacity, and maximum available energy estimation. The existing correlation between different battery states is effectively utilized to achieve high accuracy and reduce the computational burden. A combined state of charge (SOC) and state of energy (SOE) estimation using the dual forgetting factor adaptive extended Kalman filter (DFFAEKF) algorithm and experimental quantitative relations between SOC and SOE are utilized to estimate the SOC and SOE. Due to low computational cost and simplicity, the multiple constraints model-based SOP estimation using the Rint model is employed. The maximum available capacity and maximum available energy estimation are performed using a new sliding window-approximate weighted total least square (SW-AWTLS) algorithm. The performance of the proposed co-estimation method is validated by two different chemistry battery cells under dynamic load profiles at different operating temperatures. Moreover, the comparison with other existing co-estimation methods is also conducted, whose results indicate the superior accuracy of the proposed comprehensive co-estimation method.

A Continuous PDR and GNSS Fusing Algorithm for Smartphone Positioning

Pedestrian dead reckoning (PDR), used in state-of-the-art smartphones, calculates pedestrian positions by using built-in inertial sensors. However, the complex and changeable usage modes of smartphones have been obstructing the development of PDR in the field of gait detection. Since the measurement of the sensor is affected by noise, position errors will emerge, needing to be corrected periodically via external measurements. To this end, an optimization-based PDR (OBPDR) method for smartphones is proposed in this study. First, an improved finite state machine (IFSM) gait detection method is designed, which can improve the gait recognition rate and stability compared with the traditional peak detection method. Second, the step detection algorithm proposed in this paper is combined with a heading estimation to obtain the PDR dynamic model. Finally, the measurements of GNSS are fused to the PDR model, based on an adaptive extended Kalman filter (AEKF) algorithm, which can enhance the adaptability of the system to the environment in order to reduce the cumulative errors of PDR. Experiments are carried out to evaluate the performance of the proposed method. The results indicate that compared with the gait detection method, based on peak detection, and the integrated positioning method, based on an extended Kalman filter, the proposed method boasts favorable robustness and a high gait recognition rate, the recognition accuracy being kept between 97.5% and 98.5%; the average position error decreased by more than 67.25%.

State of charge estimation for lithium-ion batteries based on fractional order multiscale algorithm

The accuracy of state of charge (SoC) plays a critical role in lithium-ion batteries management system, whereas it gradually reduces as ohmic internal resistance growing and maximum available capacity decreasing with battery aging, which is still an open and challenging problem in SoC estimation. To tackle this issue, a multi-scale estimation algorithm is proposed by incorporating fractional order adaptive extended Kalman filter and variable forgetting factor recursive least square (FOAEKF-VFFRLS). Firstly, in order to describe the physicochemical reactions inside battery accurately, a fractional order model of lithium-ion battery with its discrete form is introduced, and the resistor-capacitor (RC) values as well as the order of capacitors are obtained by employing ant colony algorithm (ACA). Secondly, for enhancing SoC estimation accuracy, a fractional order adaptive extended Kalman filter algorithm (FOAEKF) is proposed to continuously modify the noise statistical characteristics while utilizing observation data information. Thirdly, to predict ohmic internal resistance and maximum available capacity for battery, a variable forgetting factor recursive least square algorithm (VFFRLS) is established based on the fact that forgetting factor determined by individual data error would be suddenly changes in the case of inaccurate or perturbed data. Besides, to further improve the accuracy of SoC estimation, a multi-scale estimation approach is proposed in light of the slow variation of battery internal resistance and the fast change of SoC. Finally, through comparative experiments, it is proved that the proposed approach has comprehensive strengths. First, the minimum root mean square error (RMSE) of SoC estimation error is controlled within 0.52 %. Second, terminal voltage error is kept small while limiting SoC errors within narrow ranges. Third, favorable robustness in terms of SoC estimation is achieved despite SoC initial value is mis-initialized.

A dual‐rate sampled multiple innovation adaptive extended Kalman filter algorithm for state of charge estimation

A dual‐rate sampled multiple innovation adaptive extended Kalman filter algorithm for state of charge estimation

Adaptive particle filter for state estimation with application to non‐linear system

Particle filtering (PF) has certain application value, but the disadvantage is that there is a phenomenon of particle degradation. In order to reduce the impact of this problem, this paper presents a new adaptive PF approach to improve the estimate accuracy. From the perspective of selecting an appropriate important density functions, in this filter, the particles are first updated using the Spherical Simplex Unscented Kalman Filter algorithm, and then the particles are updated using the Adaptive Extended Kalman filter algorithm. Simultaneously, from the perspective of improving the resampling method, a new resampling technique based on the random resampling method has been designed and fused to this filter. The comparison and analysis of two simulation schemes have been conducted to assess the performance of the designed filtering algorithm. The simulation results show the effectiveness of the proposed approach.