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Keywords = derivative unscented Kalman filter

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27 pages, 9150 KB  
Article
Physics-Driven Hybrid Framework for Vehicle State Estimation Using Residual Learning and Adaptive UKF
by Peng Zhou, Yanbin Zhou, Xi Sun, Ziming Li, Mingpu Liu and Ping Han
Appl. Sci. 2026, 16(9), 4230; https://doi.org/10.3390/app16094230 - 26 Apr 2026
Viewed by 432
Abstract
Accurate estimation of vehicle sideslip angle and lateral velocity is essential for the stability control of Advanced Driver Assistance Systems (ADASs). Traditional physics-based observers often exhibit dynamic response distortions under stability-limit conditions due to unmodeled tire relaxation effects, while data-driven methods lack physical [...] Read more.
Accurate estimation of vehicle sideslip angle and lateral velocity is essential for the stability control of Advanced Driver Assistance Systems (ADASs). Traditional physics-based observers often exhibit dynamic response distortions under stability-limit conditions due to unmodeled tire relaxation effects, while data-driven methods lack physical interpretability. This paper proposes a Physics-Driven Hybrid Estimation Framework (PD-HEF) to bridge this gap. First, a nonlinear nominal model is constructed as a physical skeleton, and dynamic residual equations are derived to define learning targets. Second, a Spatio-Temporal Feature Coupled Residual Network is designed to capture time-domain phase lag and compensate for spatial nonlinear deviations. Furthermore, a hybrid unscented Kalman filter is developed to inject predicted residuals into the sigma-point evolution. A Dual-Layer Adaptive Mechanism is also introduced to regulate trust weights based on innovation statistics. Joint simulations demonstrate that the proposed framework reduces the root mean square error by over 60% compared to traditional observers while satisfying real-time constraints. Full article
(This article belongs to the Section Mechanical Engineering)
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32 pages, 2621 KB  
Article
State-Space Estimation in Discriminant Subspace: A Kalman Filtering Approach for Turbofan Engine RUL Prediction
by Uğur Yıldırım and Hüseyin Afșer
Machines 2026, 14(2), 226; https://doi.org/10.3390/machines14020226 - 14 Feb 2026
Viewed by 776
Abstract
Accurate remaining useful life (RUL) prediction of turbofan engines is critical for aviation safety and maintenance optimization; however, deep learning approaches often lack interpretability and require extensive training data. This study proposes a framework integrating Linear Discriminant Analysis (LDA) with Kalman filtering for [...] Read more.
Accurate remaining useful life (RUL) prediction of turbofan engines is critical for aviation safety and maintenance optimization; however, deep learning approaches often lack interpretability and require extensive training data. This study proposes a framework integrating Linear Discriminant Analysis (LDA) with Kalman filtering for turbofan engine prognostics. The methodology projects high-dimensional sensor measurements onto a two-dimensional LDA subspace, where degradation trajectories are tracked using state-space estimation, with RUL predictions derived from distances to learned critical failure boundaries. A health index-based classification scheme partitions engine states into three operational regions: Critical, Warning, and Healthy. Three Kalman filter variants—Linear Kalman Filter (LKF), Extended Kalman Filter (EKF), and Unscented Kalman Filter (UKF)—were compared against an Autoregressive (AR) baseline using the NASA C-MAPSS dataset. Using the Prognostics and Health Management 2008 asymmetric scoring function, UKF achieved the best performance with a Score of 552572, representing a 54.9% improvement over AR (1224299), indicating substantially fewer late predictions. While RMSE values remained comparable across methods (36–37 cycles), the Kalman filter variants demonstrated meaningful improvements in avoiding dangerous late predictions critical for safety-oriented maintenance scheduling. EKF also demonstrated substantial improvement with 36.1% Score reduction. Classification accuracy improved from 70.72% (AR) to 73.27% (UKF). The proposed LDA–Kalman framework provides a computationally efficient and geometrically interpretable alternative to deep learning methods for real-time engine health monitoring. Full article
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27 pages, 4240 KB  
Article
Robust State Estimation of Power System Based on Unscented Kalman Filter with Fractional-Order Adaptive Generalized Cross Correlation Entropy
by Yan Huang, Shangyong Wen, Hongyan Xin and Chaohui Xin
Mathematics 2026, 14(4), 642; https://doi.org/10.3390/math14040642 - 12 Feb 2026
Viewed by 592
Abstract
With the high penetration of power electronic devices, modern power systems exhibit complex fractional-order dynamic characteristics. Addressing this, along with the prevalent issues of multi-modal non-Gaussian noise, outliers, and sudden load changes, a fractional-order adaptive generalized cross correlation entropy unscented Kalman filter (FO-AGCCE-UKF) [...] Read more.
With the high penetration of power electronic devices, modern power systems exhibit complex fractional-order dynamic characteristics. Addressing this, along with the prevalent issues of multi-modal non-Gaussian noise, outliers, and sudden load changes, a fractional-order adaptive generalized cross correlation entropy unscented Kalman filter (FO-AGCCE-UKF) method is proposed in this paper. First, acknowledging that traditional integer-order models overlook the cumulative effects of historical states, a fractional-order (FO) discrete-time state-space model is constructed based on the Grünwald–Letnikov definition. This model accurately characterizes the long-memory and non-locality properties of power systems, thereby improving modeling accuracy during transient processes. Second, to mitigate the impact of non-Gaussian noise and outliers, the generalized cross correlation entropy (GCCE) criterion is adopted to replace the traditional mean square error (MSE) criterion. Combined with statistical linearization techniques, a novel recursive filtering framework is derived to enhance robustness against heavy-tailed noise. Furthermore, to address the time-varying and unknown statistical properties of process and measurement noise, an adaptive update mechanism for noise covariance matrices is introduced, which corrects noise parameters online based on innovation sequences. Simulation experiments and comparative analysis on multiple power systems of different scales demonstrate that the proposed method not only exhibits superior anti-interference capability in mixed-Gaussian noise environments but also achieves a faster convergence speed and higher tracking accuracy during dynamic events such as sudden load changes. Full article
(This article belongs to the Special Issue Fractional Order Systems and Its Applications)
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28 pages, 5821 KB  
Article
Four-Wheel Steering Control for Mining X-by-Wire Chassis Based on AUKF State Estimation
by Qiang Ji, Yueqi Bi, Mingrui Hao, Jiaran Li and Long Chen
World Electr. Veh. J. 2025, 16(12), 677; https://doi.org/10.3390/wevj16120677 - 17 Dec 2025
Cited by 1 | Viewed by 587
Abstract
To address the challenges to driving stability caused by large-curvature steering of wire-controlled mining vehicles in narrow tunnels, a fused four-wheel steering (4WS) control strategy based on real-time estimation of vehicle state parameters is proposed. A comprehensive longitudinal–lateral–yaw dynamics model for 4WS is [...] Read more.
To address the challenges to driving stability caused by large-curvature steering of wire-controlled mining vehicles in narrow tunnels, a fused four-wheel steering (4WS) control strategy based on real-time estimation of vehicle state parameters is proposed. A comprehensive longitudinal–lateral–yaw dynamics model for 4WS is established, and a comparative study is conducted on three control methods: proportional feedforward control, yaw rate feedback control, and fused control. Expressions for steady-state yaw rate gain under different control modes are derived, and the stability differences in 4WS characteristics among these strategies are thoroughly analyzed. To overcome the difficulty in directly acquiring state information for chassis steering control, a vehicle state parameter estimator based on the unscented Kalman filter (UKF) is designed. To enhance the robustness to noise and computational real-time performance of vehicle state estimation in complex environments, a method for real-time estimation of noise covariance matrices using innovative sequences is adopted, improving the estimation accuracy of the algorithm. To validate the effectiveness of the control strategies, a co-simulation platform integrating Carsim and Matlab/Simulink is developed to simulate the performance of the three 4WS control methods under step steering and sinusoidal steering input conditions. The results show that, under low-speed conditions, 4WS strategies increase the yaw rate by approximately 50% and reduce the turning radius by over 45%, significantly enhancing steering maneuverability. Under medium-high speed conditions, 4WS strategies decrease the yaw rate by up to 68% and increase the turning radius by 17–29%, effectively suppressing oversteering tendencies to comprehensively improve stability, with the integrated control strategy demonstrating the best performance. Under both test conditions, the fused feedforward and feedback control strategy reduces the steady-state yaw rate by approximately 12.7% and 48.7%, respectively, compared to other control strategies, demonstrating superior stability. Full article
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21 pages, 2478 KB  
Article
Road Adhesion Coefficient Estimation Method for Distributed Drive Electric Vehicles Based on SR-UKF
by Jinhui Li, Xinyu Wei and Hui Peng
Vehicles 2025, 7(4), 154; https://doi.org/10.3390/vehicles7040154 - 6 Dec 2025
Viewed by 1038
Abstract
To improve recognition accuracy, convergence speed, and numerical stability in estimating the road adhesion coefficient for distributed-drive electric vehicles, a nonlinear seven-degree-of-freedom vehicle dynamics model was developed based on a modified Dugoff tire model. Using the Unscented Kalman Filter (UKF) as a foundation, [...] Read more.
To improve recognition accuracy, convergence speed, and numerical stability in estimating the road adhesion coefficient for distributed-drive electric vehicles, a nonlinear seven-degree-of-freedom vehicle dynamics model was developed based on a modified Dugoff tire model. Using the Unscented Kalman Filter (UKF) as a foundation, a Square-Root Unscented Kalman Filter (SR-UKF) algorithm was derived through covariance-square-root processing and Singular Value Decomposition (SVD). A co-simulation platform was built with CarSim and Simulink, and a vehicle speed-following model was developed for simulation analysis. The results show that the SR-UKF algorithm for road identification consistently maintains matrix positive definiteness, ensures numerical stability, speeds up convergence, and fully utilizes measurement information. Simulations under various road conditions (high-adhesion, low-adhesion, split-μ, and opposite-μ) and driving scenarios demonstrate that, compared to the traditional UKF, the SR-UKF converges faster and provides higher estimation accuracy, enabling real-time, accurate estimation of the road adhesion coefficient across multiple scenarios. Final results confirm that the SR-UKF exhibits excellent estimation accuracy and robustness on low-adhesion surfaces, confirming its superiority under high-risk conditions. This offers a dependable basis for improving vehicle active safety. Full article
(This article belongs to the Topic Dynamics, Control and Simulation of Electric Vehicles)
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29 pages, 6001 KB  
Article
Vision-Based Geolocation of Moving Ground Targets Using Kalman Filtering with a Gimbal Camera on Board a UAV
by Jaemin Kim, Youngrun Kim, SuHyeon Kim, Hyeongjun Cho and Dongwon Jung
Aerospace 2025, 12(12), 1065; https://doi.org/10.3390/aerospace12121065 - 30 Nov 2025
Cited by 2 | Viewed by 2227
Abstract
Unmanned aerial vehicles (UAVs) are vital for surveillance missions requiring the geolocation of moving ground targets, yet small, resource-constrained platforms often lack integrated, robust systems that can handle disturbances such as wind, occlusions, and noise. This paper presents an integrated, end-to-end vision-based geolocation [...] Read more.
Unmanned aerial vehicles (UAVs) are vital for surveillance missions requiring the geolocation of moving ground targets, yet small, resource-constrained platforms often lack integrated, robust systems that can handle disturbances such as wind, occlusions, and noise. This paper presents an integrated, end-to-end vision-based geolocation pipeline specifically designed for embedded deployment on resource-constrained UAVs with gimbal cameras. Starting from a rough initial position estimate, pan/tilt angles are computed to orient the gimbal, and then a visual tracking module combining object detection (via Tiny-YOLO) and feedback control (using CSRT) centers the target in the frame. The target’s absolute position is derived from UAV inertial data and gimbal angles. To mitigate noisy or unavailable direct geolocation due to disturbances or visual lock loss, Kalman filtering is integrated with a unicycle-based motion model. Both an extended Kalman filter (EKF) and unscented Kalman filter (UKF) are evaluated and tuned in high-fidelity simulations, with the UKF demonstrating superior performance by reducing the 2D position RMSE by 33% compared to the EKF in occlusion scenarios. The system is implemented on embedded hardware and validated through real flight tests, establishing the operational capability of vision-based surveillance on small UAV platforms. Full article
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31 pages, 8852 KB  
Article
Real-Time Model–Data Fusion for Accurate Wellbore Pressure Prediction in HTHP Wells
by Shaozhe Huang, Zhengming Xu, Yachao Li, Taotao Gou, Ziqing Yuan, Jinan Shi and Honggeng Gao
Appl. Sci. 2025, 15(18), 9911; https://doi.org/10.3390/app15189911 - 10 Sep 2025
Cited by 2 | Viewed by 1213
Abstract
Accurate wellbore pressure management is critical for safety and efficiency in deep drilling, where narrow pressure windows and extreme high-temperature, high-pressure (HTHP) conditions exist. Current methods, including direct measurement and model-based prediction, face limitations such as sensor reliability issues and inaccurate lab-derived parameters. [...] Read more.
Accurate wellbore pressure management is critical for safety and efficiency in deep drilling, where narrow pressure windows and extreme high-temperature, high-pressure (HTHP) conditions exist. Current methods, including direct measurement and model-based prediction, face limitations such as sensor reliability issues and inaccurate lab-derived parameters. Data-driven AI methods lack interpretability and generalize poorly. This study proposes a model-data fusion approach to address these issues. It integrates mechanistic models with real-time data using the Unscented Kalman Filter (UKF) for real-time parameter correction. Friction correction factors are introduced to continuously update and optimize the estimation of frictional pressure drop. Validated with field data, the model demonstrates high accuracy, with absolute percentage errors below 5% and mean absolute errors (MAPE) below 1%. It also shows strong robustness, maintaining low MAPE (1.10–2.15%) despite significant variations in frictional pressure drop distribution. This method significantly enhances prediction reliability for safer ultra-deep drilling operations. Full article
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22 pages, 3531 KB  
Article
A Combination Positioning Method for Boom-Type Roadheaders Based on Binocular Vision and Inertial Navigation
by Jiameng Cheng, Dongjie Wang, Jiming Liu, Pengjiang Wang, Weixiong Zheng, Rui Li and Miao Wu
Machines 2025, 13(2), 128; https://doi.org/10.3390/machines13020128 - 8 Feb 2025
Cited by 2 | Viewed by 1228
Abstract
A positioning method for a roadheader based on fiber-optic strap-down inertial navigation and binocular vision is proposed to address the issue of low measurement accuracy of the mining machine position caused by single-sensor methods in underground coal mines. A vision system for the [...] Read more.
A positioning method for a roadheader based on fiber-optic strap-down inertial navigation and binocular vision is proposed to address the issue of low measurement accuracy of the mining machine position caused by single-sensor methods in underground coal mines. A vision system for the mining machine position is constructed based on the four-point target fixed on the body of the roadheader, and the position and attitude information of the roadheader are obtained by combining the inertial navigation on the body. To deal with the problem of position detection inaccuracies caused by the accumulation of errors in inertial navigation measurements over time and disturbances from body vibrations to the combined positioning system, an Adaptive Derivative Unscented Kalman Filtering (ADUKF) algorithm is proposed, which can suppress the impact of process variance uncertainties on the filtering. The simulation results demonstrate that, compared to the Unscented Kalman Filtering algorithm, the position errors in the three directions are reduced by 20%, 20.68%, and 28.57%, respectively. Experiments demonstrate that the method can compensate for the limitations of single-measurement methods and meet the positioning accuracy requirements for underground mining standards. Full article
(This article belongs to the Section Robotics, Mechatronics and Intelligent Machines)
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26 pages, 6434 KB  
Article
Motion and Inertia Estimation for Non-Cooperative Space Objects During Long-Term Occlusion Based on UKF-GP
by Rabiul Hasan Kabir and Xiaoli Bai
Sensors 2025, 25(3), 647; https://doi.org/10.3390/s25030647 - 22 Jan 2025
Cited by 2 | Viewed by 1809
Abstract
This study addresses the motion and inertia parameter estimation problem of a torque-free, tumbling, non-cooperative space object (target) under long-term occlusions. To solve this problem, we employ a data-driven Gaussian process (GP) to simulate sensor measurements. In particular, we implement the multi-output GP [...] Read more.
This study addresses the motion and inertia parameter estimation problem of a torque-free, tumbling, non-cooperative space object (target) under long-term occlusions. To solve this problem, we employ a data-driven Gaussian process (GP) to simulate sensor measurements. In particular, we implement the multi-output GP to predict the projection measurements of a stereo-camera system onboard a chaser spacecraft. A product kernel, consisting of two periodic kernels, is used in the GP models to capture the periodic trends from non-periodic projection data. The initial guesses for the periodicity hyper-parameters of the GP models are intelligently derived from fast Fourier transform (FFT) analysis of the projection data. Additionally, we propose an unscented Kalman filter–Gaussian process (UKF-GP) fusion algorithm for target motion and inertia parameter estimation. The predicted projections from the GP models and their derivatives are used as the pseudo-measurements for UKF-GP during long-term occlusion. Results from Monte Carlo (MC) simulations demonstrate that, for varying tumbling frequencies, the UKF-GP can accurately estimate the target’s motion variables over hundreds of seconds, a capability the conventional UKF algorithm lacks. Full article
(This article belongs to the Section Physical Sensors)
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29 pages, 11632 KB  
Article
An Improved Unscented Kalman Filter Applied to Positioning and Navigation of Autonomous Underwater Vehicles
by Jinchao Zhao, Ya Zhang, Shizhong Li, Jiaxuan Wang, Lingling Fang, Luoyin Ning, Jinghao Feng and Jianwu Zhang
Sensors 2025, 25(2), 551; https://doi.org/10.3390/s25020551 - 18 Jan 2025
Cited by 13 | Viewed by 5036
Abstract
To enhance the positioning accuracy of autonomous underwater vehicles (AUVs), a new adaptive filtering algorithm (RHAUKF) is proposed. The most widely used filtering algorithm is the traditional Unscented Kalman Filter or the Adaptive Robust UKF (ARUKF). Excessive noise interference may cause a decrease [...] Read more.
To enhance the positioning accuracy of autonomous underwater vehicles (AUVs), a new adaptive filtering algorithm (RHAUKF) is proposed. The most widely used filtering algorithm is the traditional Unscented Kalman Filter or the Adaptive Robust UKF (ARUKF). Excessive noise interference may cause a decrease in filtering accuracy and is highly likely to result in divergence by means of the traditional Unscented Kalman Filter, resulting in an increase in uncertainty factors during submersible mission execution. An estimation model for system noise, the adaptive Unscented Kalman Filter (UKF) algorithm was derived in light of the maximum likelihood criterion and optimized by applying the rolling-horizon estimation method, using the Newton–Raphson algorithm for the maximum likelihood estimation of noise statistics, and it was verified by simulation experiments using the Lie group inertial navigation error model. The results indicate that, compared with the UKF algorithm and the ARUKF, the improved algorithm reduces attitude angle errors by 45%, speed errors by 44%, and three-dimensional position errors by 47%. It can better cope with complex underwater environments, effectively address the problems of low filtering accuracy and even divergence, and improve the stability of submersibles. Full article
(This article belongs to the Section Navigation and Positioning)
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22 pages, 899 KB  
Article
Square Root Unscented Kalman Filter-Based Multiple-Model Fault Diagnosis of PEM Fuel Cells
by Abdulrahman Allam, Michael Mangold and Ping Zhang
Sensors 2025, 25(1), 29; https://doi.org/10.3390/s25010029 - 24 Dec 2024
Cited by 3 | Viewed by 2021
Abstract
Harsh operating conditions imposed by vehicular applications significantly limit the utilization of proton exchange membrane fuel cells (PEMFCs) in electric propulsion systems. Improper/poor management and supervision of rapidly varying current demands can lead to undesired electrochemical reactions and critical cell failures. Among other [...] Read more.
Harsh operating conditions imposed by vehicular applications significantly limit the utilization of proton exchange membrane fuel cells (PEMFCs) in electric propulsion systems. Improper/poor management and supervision of rapidly varying current demands can lead to undesired electrochemical reactions and critical cell failures. Among other failures, flooding and catalytic degradation are failure mechanisms that directly impact the composition of the membrane electrode assembly and can cause irreversible cell performance deterioration. Due to the functional significance and high manufacturing costs of the catalyst layer, monitoring internal fuel cell states is crucial. For this purpose, a diagnostic-oriented multi-scale PEMFC catalytic degradation model is developed which incorporates the failure effects of catalytic degradation on cell dynamics and global stack performance. Embedded to the multi-scale model is a square root unscented Kalman filter (SRUKF)-based multiple-model fault diagnosis scheme. In this approach, multiple models are used to estimate specific internal PEMFC system parameters, such as the mass transfer coefficient of the gas diffusion layer or the exchange current density, which are treated as additional system states. Online state estimates are provided by the SRUKF, which additionally propagates model-conditioned statistical information to update a Bayesian framework for model selection. The Bayesian model selection method carries fault indication signals that are interpreted by a derived decision logic to obtain reliable information on the current-operating system regime. The proposed diagnosis scheme is evaluated through simulations using the LA 92 and NEDC driving cycles. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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15 pages, 3062 KB  
Article
Robust Estimation of Lithium Battery State of Charge with Random Missing Current Measurement Data
by Xi Li, Zongsheng Zheng, Jinhao Meng and Qinling Wang
Electronics 2024, 13(22), 4436; https://doi.org/10.3390/electronics13224436 - 12 Nov 2024
Cited by 6 | Viewed by 1909
Abstract
The precise estimation of the state of charge (SOC) in lithium batteries is crucial for enhancing their operational lifespan. To address the issue of reduced accuracy in SOC estimation caused by the random missing values of lithium battery current measurements, a joint estimation [...] Read more.
The precise estimation of the state of charge (SOC) in lithium batteries is crucial for enhancing their operational lifespan. To address the issue of reduced accuracy in SOC estimation caused by the random missing values of lithium battery current measurements, a joint estimation method which combines recursive least squares with missing input data (MIDRLS) and the unscented Kalman filter (UKF) algorithm is proposed, called the MIDRLS-UKF algorithm. Firstly, the equivalent circuit model of a Thevenin battery is formulated. Then, the current imputation model is designed to interpolate the missing data, based on which the MIDRLS algorithm is derived by solving the unbiased estimation of the gradient of the objective function, thus realizing the online high-precision identification of the circuit model parameters. Furthermore, the proposed algorithm is combined with the UKF algorithm to facilitate the online precise estimation of SOC. The simulation results indicate a marked decrease in the SOC estimation error when employing the proposed joint algorithm, as opposed to the conventional forgetting factor recursive least squares (FFRLS) algorithm combined with the UKF joint estimation algorithm, which verifies the precision and effectiveness of the proposed joint algorithm. Full article
(This article belongs to the Special Issue Technology and Approaches of Battery Energy Storage System)
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23 pages, 7845 KB  
Article
Estimation of Lithium-Ion Battery SOC Based on IFFRLS-IMMUKF
by Xianguang Zhao, Tao Wang, Li Li and Yanqing Cheng
World Electr. Veh. J. 2024, 15(11), 494; https://doi.org/10.3390/wevj15110494 - 29 Oct 2024
Cited by 4 | Viewed by 2593
Abstract
The state of charge (SOC) is a characteristic parameter that indicates the remaining capacity of electric vehicle batteries. It plays a significant role in determining driving range, ensuring operational safety, and extending the service life of battery energy storage systems. Accurate SOC estimation [...] Read more.
The state of charge (SOC) is a characteristic parameter that indicates the remaining capacity of electric vehicle batteries. It plays a significant role in determining driving range, ensuring operational safety, and extending the service life of battery energy storage systems. Accurate SOC estimation can ensure the safety and reliability of vehicles. To tackle the challenge of precise SOC estimation in complex environments, this study introduces an improved forgetting factor recursive least squares (IFFRLS) method, which integrates the Golden Jackal optimization (GJO) algorithm with the traditional FFRLS method. This integration is grounded in the formulation of a lithium battery state equation derived from a second-order RC equivalent circuit model. Additionally, the research utilizes the interactive multiple model unscented Kalman filter (IMMUKF) algorithm for SOC estimation, with experimental validation conducted under various conditions, including hybrid pulse power characterization (HPPC), urban dynamometer driving schedule (UDDS), and real underwater scenarios. The experimental results demonstrate that the SOC estimation method of lithium batteries based on IFFRLS-IMMUKF exhibits high accuracy and a favorable temperature applicability range. Full article
(This article belongs to the Special Issue Intelligent Electric Vehicle Control, Testing and Evaluation)
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19 pages, 2355 KB  
Article
The Square-Root Unscented and the Square-Root Cubature Kalman Filters on Manifolds
by Joachim Clemens and Constantin Wellhausen
Sensors 2024, 24(20), 6622; https://doi.org/10.3390/s24206622 - 14 Oct 2024
Cited by 3 | Viewed by 2786
Abstract
Estimating the state of a system by fusing sensor data is a major prerequisite in many applications. When the state is time-variant, derivatives of the Kalman filter are a popular choice for solving that task. Two variants are the square-root unscented Kalman filter [...] Read more.
Estimating the state of a system by fusing sensor data is a major prerequisite in many applications. When the state is time-variant, derivatives of the Kalman filter are a popular choice for solving that task. Two variants are the square-root unscented Kalman filter (SRUKF) and the square-root cubature Kalman filter (SCKF). In contrast to the unscented Kalman filter (UKF) and the cubature Kalman filter (CKF), they do not operate on the covariance matrix but on its square root. In this work, we modify the SRUKF and the SCKF for use on manifolds. This is particularly relevant for many state estimation problems when, for example, an orientation is part of a state or a measurement. In contrast to other approaches, our solution is both generic and mathematically coherent. It has the same theoretical complexity as the UKF and CKF on manifolds, but we show that the practical implementation can be faster. Furthermore, it gains the improved numerical properties of the classical SRUKF and SCKF. We compare the SRUKF and the SCKF on manifolds to the UKF and the CKF on manifolds, using the example of odometry estimation for an autonomous car. It is demonstrated that all algorithms have the same localization performance, but our SRUKF and SCKF have lower computational demands. Full article
(This article belongs to the Section Vehicular Sensing)
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14 pages, 11769 KB  
Article
Research on Longitudinal Control of Electric Vehicle Platoons Based on Robust UKF–MPC
by Jiading Bao, Zishan Lin, Hui Jing, Huanqin Feng, Xiaoyuan Zhang and Ziqiang Luo
Sustainability 2024, 16(19), 8648; https://doi.org/10.3390/su16198648 - 6 Oct 2024
Cited by 6 | Viewed by 2053
Abstract
In a V2V communication environment, the control of electric vehicle platoons faces issues such as random communication delays, packet loss, and external disturbances, which affect sustainable transportation systems. In order to solve these problems and promote the development of sustainable transportation, a longitudinal [...] Read more.
In a V2V communication environment, the control of electric vehicle platoons faces issues such as random communication delays, packet loss, and external disturbances, which affect sustainable transportation systems. In order to solve these problems and promote the development of sustainable transportation, a longitudinal control algorithm for the platoon based on robust Unscented Kalman Filter (UKF) and Model Predictive Control (MPC) is designed. First, a longitudinal kinematic model of the vehicle platoon is constructed, and discrete state–space equations are established. The robust UKF algorithm is derived by enhancing the UKF algorithm with Huber-M estimation. This enhanced algorithm is then used to estimate the state information of the leading vehicle. Based on the vehicle state information obtained from the robust UKF estimation, feedback correction and compensation are added to the MPC algorithm to design the robust UKF–MPC longitudinal controller. Finally, the effectiveness of the proposed controller is verified through CarSim/Simulink joint simulation. The simulation results show that in the presence of communication delay and data loss, the robust UKF–MPC controller outperforms the MPC and UKF–MPC controllers in terms of MSE and IAE metrics for vehicle spacing error and acceleration tracking error and exhibits stronger robustness and stability. Full article
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