Kalman Filter Method Research Articles

Adaptive Joint Sigma-Point Kalman Filtering for Lithium-Ion Battery Parameters and State-of-Charge Estimation

Precise modeling and state of charge (SoC) estimation of a lithium-ion battery (LIB) are crucial for the safety and longevity of battery systems in electric vehicles. Traditional methods often fail to adapt to the dynamic, nonlinear, and time-varying behavior of LIBs under different operating conditions. In this paper, an advanced joint estimation approach of the model parameters and SoC is proposed utilizing an enhanced Sigma Point Kalman Filter (SPKF). Based on the second-order equivalent circuit model (2RC-ECM), the proposed approach was compared to the two most widely used methods for simultaneously estimating the model parameters and SoC, including a hybrid recursive least square (RLS)-extended Kalman filter (EKF) method, and simple joint SPKF. The proposed adaptive joint SPKF (ASPKF) method addresses the limitations of both the RLS+EKF and simple joint SPKF, especially under dynamic operating conditions. By dynamically adjusting to changes in the battery’s characteristics, the method significantly enhances model accuracy and performance. The results demonstrate the robustness, computational efficiency, and reliability of the proposed ASPKF approach compared to traditional methods, making it an ideal solution for battery management systems (BMS) in modern EVs.

Adaptive MSSRCPF filtering based on constrained optimization and fading memory for SINS/GNSS integrated navigation

To address particle degeneracy and the challenge of selecting importance density functions in traditional particle filters for complex nonlinear systems, we propose an adaptive mixed-order spherical simplex-radial cubature particle filter algorithm based on constrained optimization and fading memory. This algorithm integrates constrained optimization, an adaptive fading memory strategy, adaptive adjustment of particle numbers and weights, and the advantages of mixed-order spherical simplex-radial cubature Kalman filtering. By designing the importance density function using a mixed-order integration method, the algorithm significantly improves filtering accuracy over traditional cubature Kalman filters while maintaining lower computational complexity than high-order cubature Kalman filter methods. The adaptive fading memory strategy dynamically adjusts the covariance matrix, enhancing sensitivity to current measurement information and reducing the influence of historical data. By dynamically adjusting the noise covariance matrix and constraining the ratio between the error covariance and measurement noise covariance, the algorithm improves the convergence speed and accuracy of state estimation. An adaptive particle number and weight adjustment strategy based on effective sample size and entropy regularization dynamically adjusts the number of particles to reduce computational complexity while ensuring filtering accuracy, and employs entropy regularization to suppress weight over-concentration, thereby reducing the impact of outliers on the filtering results. Simulation results demonstrate that in complex SINS/GNSS integrated navigation systems, especially under high-noise and nonlinear conditions, the proposed algorithm significantly improves positioning accuracy compared to the CPF method, with the maximum latitude error reduced by approximately 54.8%, the maximum longitude error reduced by approximately 40.5%, and the maximum altitude error reduced by approximately 68.3%. Compared to the FMCPF method, the proposed algorithm also shows clear advantages in positioning accuracy, convergence speed, and computational efficiency, validating its effectiveness and practicality in complex environments.

Multi-innovation adaptive Kalman filter algorithm for estimating the SOC of lithium-ion batteries based on singular value decomposition and Schmidt orthogonal transformation

The state of charge (SOC) of lithium battery is a key parameter for effective management of battery management systems (BMS). To address the problems of low precision, complex computation and poor robustness of traditional charging state estimation methods, an enhanced algorithm based on Unscented Kalman filter (UKF) is proposed. The singular value decomposition (SVD) method is adopted to ensure the normal operation of the Unscented Kalman Filter (UKF) algorithm even when the matrix P lacks positive semi-definiteness from a mathematical perspective. This enhancement significantly improves the theoretical robustness of UKF. Schmidt orthogonal transformation is concurrently used to reduce the computational complexity in the sampling point selection process, and the multi-innovation theory is combined with adaptive noise control to further improve the accuracy of SOC estimation. The algorithm is validated using the Urban Dynamometer Driving Schedule (UDDS) condition. The simulation results are excited using Singular value decomposition-multi-innovation adaptive Schmidt orthogonal unscented Kalman filter method (SVD-MIASOUKF). 0.95 % and 1.29 % of maximum errors are obtained at 25 °C and −10 °C, while the maximum errors are 2.46 %–2.99 % using SVD-UKF and UKF. The proposed approach shows faster convergence speed and higher estimation accuracy in comparison to traditional algorithms.

Using an ensemble Kalman filter method for a soil nitrogen transport model in the real rice field

The overuse of nitrogen fertilizer in rice field of China leads to nitrogen loss and serious water pollution, so it is vital to accurately predict soil nitrogen transport in rice field. But the prediction errors of soil nitrogen transport are great due to complex chemical and reactive conditions and uncertain parameters in real rice fields. In this study, a prediction model of soil nitrogen transport in a rice field was established via modifying the HYDRUS-1D source code, and a data assimilation method called the ensemble Kalman filtering (EnKF) was coupled, based on the observed NH4+-N and NO3–-N concentrations at different depths in a real rice field. Study results for two different protocols of assimilating observed NH4+-N and NO3–-N concentrations simultaneously and separately were compared. It indicated the predictions accuracy of NH4+-N and NO3–-N concentrations was improved significantly via the EnKF method, and the former protocol is better than the latter. Moreover, for the latter protocol, observations of NO3–-N concentrations were more efficient than NH4+-N to improve the predictions accuracy of NH4+-N and NO3–-N concentrations at different depths. Inversed parameters of urea hydrolysis, NH4+-N volatilization, soil adsorption of NH4+-N, nitrification and denitrification increased over time. On the whole, the inversed model parameters were more stable at deep soil than shallow soil, which were different at different depths. With soil depths increase, parameters of the NH4+-N adsorption and NO3–-N denitrification increased, while parameters of urea hydrolysis, NH4+-N volatilization and nitrification decreased. This study improved the model predictions accuracy and inversed the model parameters, revealing the mechanism of nitrogen loss in real rice fields, which can provide scientific basis to reduce serious environmental problems caused by the overuse of nitrogen fertilizer.

A Kalman Filtering Method on Time–Frequency Discrimination Analysis

A Kalman Filtering Method on Time–Frequency Discrimination Analysis

Investigation on the Seismic Damage and Identification of Lateral Stiffness for Ancient Timber Structures

ABSTRACTThis paper investigates the seismic damage and identification of lateral stiffness for ancient timber structures. Based on the shaking table test of a palace‐style timber structure, the lateral displacement responses, interstory equivalent lateral stiffness (IELS), and sensitivity of lateral displacement to degradation of IELS were analyzed to investigate the degradation and identification of IELS. The state and observation equations of a simplified mechanical model of the timber frame considering the friction slipping of the column base were predicted. Considering the noise disturbance in the test, the IELS of the model was identified by the partial least squares–singular value decomposition (PLS‐SVD) and extended Kalman filter (EKF) method. Results shown that the ratio of the IELS of the column frame layer to Ru‐Fu layer decreased as the seismic damage increased, and the peak lateral displacement was more sensitive to the damage of the column frame layer than the Ru‐Fu layer. Under nondamage conditions, the identification error of the IELS was about 10%, while the error ranged from 15% to 20% under damage conditions. Through the identification of the equivalent lateral stiffness of the Xi'an bell tower, it was validated that the hybrid method is effective in monitoring the IELS of ancient timber structures.

Design a novel algorithm for enhancing UWB positioning accuracy in GPS denied environments

Accurate indoor positioning is the key to the development of the Internet of Things and intelligent devices. In view of GPS-denied indoor environments, we propose to build the indoor local positioning system by using ultra-wide band (UWB) system. In order to enhance the localization accuracy of UWB system, we propose a novel algorithm which integrates the Maximum Correntropy Criterion (MCC) and unscented Kalman filter (UKF) method to reconstruct the measurement distance by using the maximum entropy principle to reduce the influence of outliers and unknown process noise on the smooth effect. Subsequently, the least square (LS) method is implemented to attain the target node (TN) initial position coordinates, and the Taylor algorithm is then performed to further optimize the localization results of the LS method. Lastly, the experimental investigation is conducted to assess the effectiveness and applicability of the developed method via the UWB system in indoor scenarios. The experimental outcomes demonstrate that the developed MCCUKF-LS method can achieve the lowest root mean square error (RMSE), and enhance the positioning accuracy of the TN compared with the LS, KF-LS, and UKF-LS methods. The overall average RMSE of MCCUKF-LS method is reduced by 45.7% contracted with the LS algorithm. The average error of x-, y- and z-axis orientation for the LS method is reduced from 0.074 m, 0.067 m, 0.098 m to 0.036 m, 0.034 m, 0.044 m, and the achieved accuracy in the orientation of the three axes is increased by 51.4%, 49.3% and 55.1% respectively, which reveals that the designed fusion technique is capable of enhancing the positioning accuracy of the TN effectively, providing a new positioning methodology and reference for indoor positioning in GPS-denied environments.

Study on vehicle state and tire–road friction coefficient estimation based on maximum correntropy generalized high-degree cubature Kalman filter

To cope with the challenges of inadequate precision and weak robustness of tire–road friction coefficient (TRFC) and vehicle state estimation under mixed Gaussian noise circumstances, this research puts forward a method combining maximum correntropy criterion (MCC) and generalized high-degree cubature Kalman filter (GHCKF). A coupled lateral and longitudinal vehicle model and the Dugoff tire model are established. The vehicle mass is estimated using the recursive least squares approach based on a forgetting factor (FFRLS). Low-cost onboard sensors are utilized to design observers for vehicle state and TRFC. The observers’ effectiveness is tested by Carsim/Simulink co-simulation tests under the conditions of sine steering input and steering wheel angle step input. The research results indicate that in handling mixed Gaussian noise environments, maximum correntropy generalized high-degree cubature Kalman filter (MCGHCKF) method outperforms maximum correntropy cubature Kalman filter (MCCKF), GHCKF, and cubature Kalman filter (CKF) methods concerning robustness and estimation accuracy, providing stable and reliable support for systems of vehicle active safety control.

Estimation of SOC for Li-ion battery-powered three-wheeled electric vehicle using machine learning methods

Abstract The Battery Management System (BMS) serves as the heart of the electric vehicle system, in which estimating the state of charge (SOC) is the crucial part of the BMS to ensure the durability, reliability, and sustainability of the battery pack. Due to its nonlinear characteristics, accurately estimating the SOC for a slow degradation of the charge is highly cumbersome. The literature provides a series of machine learning algorithms (MLA) to estimate and predict the SOC of lithium-ion (Li-ion) battery systems for electric vehicle (EV) applications. The literature has proposed various MLA, coulomb counting, and different Kalman filter methods to address this challenge and estimate the SOC of Li-ion battery systems for EV applications. This research looks at the differences and similarities between the coulomb counting method, the unscented Kalman filter method, and a number of machine learning algorithms. These include linear regression, polynomial linear regression, support vector regression, decision trees, random forests, artificial neural networks (ANN), and long short-term memory (LSTM). The goal is to assess the MLAs' accuracy in estimating battery SOC. Analyzing model errors optimizes the battery's performance parameter. We identify ANN and LSTM as the two most efficient methods for accurate SOC estimation in an EV-operated BMS system by evaluating the performance indices of the aforementioned machine learning methodologies. Once again, the LSTM model for SOC estimation has proven to be highly accurate in analyzing the discrepancy between the actual and predicted traveling ranges of the designed prototype. We design a MATLAB/SIMULINK EV powertrain by collecting realtime data from the Li-ion battery pack, analyzing the SOC variation data, and using the previously mentioned MLA in the Python platform to estimate the SOC and its accuracy. It highlights the effectiveness of advanced MLAs in improving SOC estimation, thereby enhancing the performance and reliability of EV battery systems.

Wavelet denoising analysis on vacuum-process monitoring signals of aerospace vacuum vessel structures

Abstract The monitoring of micro-defects or external actions induced vacuum degradation in aerospace vacuum vessels is an important challenge. A vacuum-process monitoring method based on quasi-distributed fiber Bragg grating (FBG) sensing technology is proposed. Due to the influence of environmental noise and vacuum pump operation noise, the raw signals measured by FBG sensors contain a large amount of noises, which affects the measurement accuracy and data analysis. Therefore, the wavelet threshold (WT) denoising method is proposed to analyze the influence of noises on the monitoring signals measured by two different kinds of FBG sensors. The evaluation of the monitoring signals after denoising indicates that the proposed method can effectively remove the noise and significantly improve signal quality. The highest signal-to-noise ratio of the processed signals can reach 37.61 dB and the mean square error is 3.68 × 10−7, while retaining the key features of the original signal. The proposed WT denoising method demonstrates better performance and feasibility compared with moving average filtering and Kalman filtering methods. The study provides critical supports for improving the performance and reliability of the vacuum vessel monitoring system.

State of Charge Estimation of Lithium-Ion Batteries Based on Fractional-Order Model with Mul-ti-Innovations Dual Cubature Kalman Filter Method

An accurate estimation of the lithium battery’s state of charge (SOC) is critical. The article proposes a dual fractional order multi-innovations cubature Kalman filter (DFOMICKF) algorithm for estimating lithium battery SOC. The algorithm adopts the idea of multiple time scales, where one of the FOMICKF is used to identify the circuit model parameters online in the macro time scale. Another FOMICKF is used to estimate the SOC in the micro time scale, and the circuit parameters updated online in real-time are passed into the estimation of the SOC filter to form an online joint estimation method of SOC and circuit parameters. Finally, multiple algorithms of DFOMICKF, FOMICKF, FOCKF, and CKF are compared and experimented under different working conditions to compare and analyze the estimated SOC errors. It is verified that the proposed algorithm can solve the problems of inaccuracy, poor convergence, and poor robustness of the traditional Kalman filtering algorithm for estimating SOC, which has good research value.

Parameter-input estimation of RC thermal models of buildings using unscented Kalman filter and nonlinear least square method

Effective building energy management (e.g. temperature control strategies) necessitates reliable and computationally efficient building thermal models. One type of them is the resistor–capacitor (RC) model. However, estimating model parameters and inputs (e.g. solar heat gain) simultaneously is challenging, especially when some of the temperature states are missing due to instrumentation limitations and/or sensor malfunctions. The present study utilizes unscented Kalman filter (UKF) and nonlinear least squares (NLSs) methods for parameters and input estimation of RC models with possible unavailable temperature states. The estimation procedure, mathematical operations and result analysis are presented in detail. To evaluate the capability of the method, two case studies were conducted. The first case study involved a simple, made-up RC model with known parameters, inputs and states, while the second case study used monitored data from a single detached house. The capability of the method was evaluated by comparing the estimated parameters, inputs and states to the corresponding true values in both study cases. The performance evaluation shows that the proposed method can effectively estimate RC model parameters and inputs, even with certain missing states. The proposed method can be employed for timely online updating of RC model parameters to improve response prediction.

Enhanced Kalman filter methods for end pose measurement of parallel kinematic machine considering the error sensitivity

For robust accuracy, this paper proposes a parallel measurement method for parallel kinematic machine (PKM) combining indirect measurement using grating ruler with direct measurement using monocular vision. However, due to differing error sensitivity of two methods, the general Kalman filter (KF) cannot integrate them under the assumption of equal data weighting. Therefore, a novel Enhanced KF data fusion method designed to account for varying data sensitivities is developed.The paper first outlines the principles of parallel measurement approach for PKMs, followed by modeling the error sensitivities associated with each measurement source. Subsequently, an enhanced KF data fusion model is developed, treating these sensitivities as noise, and validated. Compared to the conventional KF method, the root mean squared (RMS) position error is significantly reduced from 0.569 mm to 0.293 mm. This enhanced KF method presents an innovative approach to multi-source data fusion, tailored to the error characteristics of different measurement sources.

Research on Vehicle Stability Control Based on a Union Disturbance Observer and Improved Adaptive Unscented Kalman Filter

This paper considers external disturbances imposed on vehicle systems. Based on a vehicle dynamics model of the vehicle with three degrees of freedom (3-DOFs), a union disturbance observer (UDO) composed of a nonlinear disturbance observer (NDO) and an extended state observer (ESO) was designed to obtain external disturbances and unmodeled items. Meanwhile, an improved adaptive unscented Kalman filter (iAUKF) with anti-disturbance and anti-noise properties is proposed, based on the UDO and the unscented Kalman filter (UKF) method, to evaluate the sideslip angle of vehicle systems. Finally, a vehicle yaw stability controller was designed based on UDO and the global fast terminal sliding mode control (GFTSMC) method. The results of co-simulation demonstrated that the proposed UDO was effectively able to observe external disturbances and unmodeled items. The proposed iAUKF, which considers external disturbances, not only achieves adaptive updating and adjustment of filtering parameters under different sensor noise intensities but can also resist external disturbances, improving the estimation accuracy and robustness of the UKF. In the anti-disturbance performance test, the maximum estimation error of the sideslip angle of the iAUKF under the three working conditions was less than 0.1°, 0.02°, and 0.5°, respectively. Based on the UDO and the GFTSMC, a vehicle yaw stability controller is described, which improves the accuracy of control and the robustness of the vehicle’s stability control system and greatly strengthens the driving safety of the vehicle.

Power Forecast of Renewable Energy Power Plant Based on Kalman Filter Method

At present, the prediction accuracy of water power plant is poor. In order to improve the prediction accuracy of water power plant. Firstly, the regression sliding model is obtained by analyzing the power sequence of the water power plant, and the regression sliding model is regarded as Kalman filter method. Then, the equation value is obtained by the state equation of Kalman filter method, and the power generation is predicted by Kalman filter method. In the follow-up case analysis, the evaluation index of the China Energy Bureau is used to evaluate the prediction accuracy of power generation. The MATLAB prediction results show that the proposed method in this paper can get better results and higher prediction accuracy.

Research on precise lithium battery state of charge estimation method based on CALSE-LSTM model and pelican algorithm

This paper presents an innovative fusion model called “CALSE-LSTM,” which integrates Convolutional Neural Networks (CNNs), Long Short-Term Memory Networks (LSTMs), self-attention mechanisms, and squeeze-and-excitation attention mechanisms to optimize the estimation accuracy of the State of Charge (SoC). The model incorporates battery historical data as input and employs a dual-attention mechanism based on CNN-LSTM to extract diverse features from the input data, thereby enhancing the model's ability to learn hidden information. To further improve model performance, we fine-tune the model parameters using the Pelican algorithm. Experiments conducted under Urban Dynamometer Driving Schedule (UDDS) conditions show that the CALSE-LSTM model achieves a Root Mean Squared Error (RMSE) of only 1.73 % in lithium battery SoC estimation, significantly better than GRU, LSTM, and CNN-LSTM models, reducing errors by 31.9 %, 31.3 %, and 15 %, respectively. Ablation experiments further confirm the effectiveness of the dual-attention mechanism and its potential to improve SoC estimation performance. Additionally, we validate the learning efficiency of CALSE-LSTM by comparing model training time with the number of iterations. Finally, in the comparative experiment with the Kalman filtering method, the model in this paper significantly improved its performance by incorporating power consumption as an additional feature input. This further verifies the accuracy of CALSE-LSTM in estimating the State of Charge (SoC) of lithium batteries.

Pressurized Water reactor power level control: A nonlinear generalized predictive control with extended Kalman filter method

Reactor power level control is an effective way to achieve load tracking of Pressurized Water Reactor (PWR) in a nuclear power station. A novel Nonlinear Generalized Predictive Control with Extended Kalman Filter (NGPC + EKF) is proposed to solve the problem that discrete predictive model mismatch in noisy environment. In this paper, an NGPC controller is developed to realize the reactor load tracking, and an EKF is used to estimate reactor states and suppress noise. Finally, the control methods of PID, MPC, NGPC and NGPC + EKF are compared by two simulation experiments, load tracking experiment and step response experiment. The load tracking experiment results show that NGPC + EKF method obtains better noise suppression ability and tracking effect. In the step response experiment, the proposed NGPC + EKF scheme is also proved to have better step response performance than others.

Deep learning‐based location prediction in VANET

AbstractIn recent years, Vehicular Ad‐hoc Network (VANET) has become an essential component of intelligent transportation systems that, along with the previous systems such as traffic condition, accident alert, automatic parking, and cruise control, use the communication of vehicle to vehicle and vehicle to the roadside unit to facilitate road transportation. Several challenges hinder efforts to improve traffic conditions and reduce traffic fatalities through VANET. A critical challenge is achieving highly accurate and reliable vehicle localization within the VANET. Additionally, the frequent unavailability of Global Positioning System (GPS), particularly in tunnels and parking lots, presents another significant obstacle. Traditional methods like Dead Reckoning offer low accuracy and reliability due to accumulating errors. Similarly, GPS positioning, map matching with mobile phone location services, and other existing solutions struggle with accuracy and economic feasibility. In this article, two Kalman filter approaches are used based on signal statistical information and the other learning‐based networks, including traditional neural network, deep neural network and LSTM (long short‐term memory) to locate the car. The prediction error of car position with root mean square measures. The squared error and distance prediction error are evaluated. It is shown that in terms of prediction time and processing time of vehicle localization, all the vehicle localization methods are efficient in terms of response time for localization, and Kalman filter methods, traditional neural network and deep neural network are faster than LSTM method. Also, in terms of localization error, Kalman filter works better than learning‐based methods, and in learning‐based methods, both deep neural network and LSTM methods perform better than traditional neural network in terms of localization error.

Hybrid six sigma based on recursive kalman filter and weibull distribution to estimate the lifespan of Bulb LEDs

The durability of LED bulbs ensures that the lights can operate for a long time without needing to be replaced or maintained too often. The brightness of high-power LED bulbs provides a strong and efficient light source, saves energy, and has a long lifespan. The traditional method of testing LED bulb life span has limitations such as long testing time, limited accuracy, high cost, inability to predict accurately, and failure to respond quickly. Therefore, the development of new and improved testing methods is necessary to effectively and accurately evaluate and ensure the durability of LED bulbs. This research paper proposes a hybrid Six Sigma method based on the recursive Kalman filter and Weibull distribution to estimate the lifespan of Bulb LEDs. The goal of the new method for evaluating LED bulb life is to provide accurate, reliable, and multi-dimensional information about the life of LED lamps, meeting the requirements of accuracy, diversity, time-saving, resources, credibility, and the ability to evaluate from a variety of perspectives. As a result of the research, the recursive Kalman filter method has strengths such as high accuracy, flexibility, saving computational resources, the ability to handle inaccurate data, and scalability. When applied to LED bulb life assessment, it provides an accurate and reliable estimate of LED lamp life. Research results on longevity testing were reduced from 1650 h to 710 h. The end-of-life test time is 710 h, and the aging time per life test cycle is 135 h. The cost of life testing is reduced from 2100.17 USD to 410.12 USD. This LED bulb lifespan testing method can be applied to similar types of LED products to improve the company's productivity and business efficiency.

Prediction of IGBT Gate Oxide Layer's Performance Degradation Based on MultiScaleFormer Network.

Insulated gate bipolar transistors (IGBTs) are widely used in power electronic devices, and their health prediction problems have attracted much attention in the field of power electronic equipment health management. The performance degradation of IGBT gate oxide is one of the most important failure modes. In order to analyze this failure mechanism and the ease of implementation of a monitoring circuit, the gate leakage current of IGBTs was selected as the fault precursor parameter for the degradation of their gate oxide performance, and feature selection and fusion were carried out by using time domain characteristic analysis, grayscale correlation, Mahalanobis distance, Kalman filter, and other methods. Thus, a health indicator was obtained to characterize the degradation of IGBT performance, which was used to indicate the degree of aging of the IGBT gate oxide layer. In this paper, we propose an improved degradation prediction model called MultiScaleFormer, inspired by advanced design ideas of the iTransformer network architecture, combined with the health parameters of IGBTs to construct a degradation prediction model for the IGBT gate oxide layer. MultiScaleFormer showed the highest fitting accuracy compared with the Long Short-Term Memory (LSTM), Convolutional Neural Network (CNN), Support Vector Regression (SVR), Gaussian Process Regression (GPR), CNN-LSTM, and Transformer models in our experiment. The mean absolute error (MAE) of the MultiScaleFormer prediction was as low as 0.0087. Extraction of the health indicator and the construction and verification of the degradation prediction model were carried out on the dataset released by the NASA-Ames Laboratory. These results demonstrate the feasibility of the gate leakage current as a fault precursor parameter for IGBT gate oxide failure, and the feasibility and accuracy of the MultiScaleFormer prediction model for IGBT performance degradation.