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Keywords = enhanced extended Kalman filter

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21 pages, 1573 KiB  
Review
A Novel Real-Time Battery State Estimation Using Data-Driven Prognostics and Health Management
by Juliano Pimentel, Alistair A. McEwan and Hong Qing Yu
Appl. Sci. 2025, 15(15), 8538; https://doi.org/10.3390/app15158538 (registering DOI) - 31 Jul 2025
Abstract
This paper presents a novel data-driven framework for real-time State of Charge (SOC) estimation in lithium-ion battery systems using a data-driven Prognostics and Health Management (PHM) approach. The method leverages an optimized bidirectional Long Short-Term Memory (Bi-LSTM) network, trained with enhanced datasets filtered [...] Read more.
This paper presents a novel data-driven framework for real-time State of Charge (SOC) estimation in lithium-ion battery systems using a data-driven Prognostics and Health Management (PHM) approach. The method leverages an optimized bidirectional Long Short-Term Memory (Bi-LSTM) network, trained with enhanced datasets filtered via exponentially weighted moving averages (EWMAs) and refined through SHAP-based feature attribution. Compared against a Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) across ten diverse drive cycles, the proposed model consistently achieved superior performance, with mean absolute errors (MAEs) as low as 0.40%, outperforming EKF (0.66%) and UKF (1.36%). The Bi-LSTM model also demonstrated higher R2 values (up to 0.9999) and narrower 95% confidence intervals, confirming its precision and robustness. Real-time implementation on embedded platforms yielded inference times of 1.3–2.2 s, validating its deployability for edge applications. The framework’s model-free nature makes it adaptable to other nonlinear, time-dependent systems beyond battery SOC estimation. Full article
(This article belongs to the Special Issue Design and Applications of Real-Time Embedded Systems)
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26 pages, 8468 KiB  
Article
An Autonomous Localization Vest System Based on Advanced Adaptive PDR with Binocular Vision Assistance
by Tianqi Tian, Yanzhu Hu, Xinghao Zhao, Hui Zhao, Yingjian Wang and Zhen Liang
Micromachines 2025, 16(8), 890; https://doi.org/10.3390/mi16080890 (registering DOI) - 30 Jul 2025
Abstract
Despite significant advancements in indoor navigation technology over recent decades, it still faces challenges due to excessive dependency on external infrastructure and unreliable positioning in complex environments. This paper proposes an autonomous localization system that integrates advanced adaptive pedestrian dead reckoning (APDR) and [...] Read more.
Despite significant advancements in indoor navigation technology over recent decades, it still faces challenges due to excessive dependency on external infrastructure and unreliable positioning in complex environments. This paper proposes an autonomous localization system that integrates advanced adaptive pedestrian dead reckoning (APDR) and binocular vision, designed to provide a low-cost, high-reliability, and high-precision solution for rescuers. By analyzing the characteristics of measurement data from various body parts, the chest is identified as the optimal placement for sensors. A chest-mounted advanced APDR method based on dynamic step segmentation detection and adaptive step length estimation has been developed. Furthermore, step length features are innovatively integrated into the visual tracking algorithm to constrain errors. Visual data is fused with dead reckoning data through an extended Kalman filter (EKF), which notably enhances the reliability and accuracy of the positioning system. A wearable autonomous localization vest system was designed and tested in indoor corridors, underground parking lots, and tunnel environments. Results show that the system decreases the average positioning error by 45.14% and endpoint error by 38.6% when compared to visual–inertial odometry (VIO). This low-cost, wearable solution effectively meets the autonomous positioning needs of rescuers in disaster scenarios. Full article
(This article belongs to the Special Issue Artificial Intelligence for Micro Inertial Sensors)
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30 pages, 20494 KiB  
Article
Research on INS/GNSS Integrated Navigation Algorithm for Autonomous Vehicles Based on Pseudo-Range Single Point Positioning
by Zhongchao Liang, Kunfeng He, Zijian Wang, Haobin Yang and Junqiang Zheng
Electronics 2025, 14(15), 3048; https://doi.org/10.3390/electronics14153048 - 30 Jul 2025
Abstract
This study proposes an enhanced integration framework for the global navigation satellite system (GNSS) and inertial navigation system (INS). The framework combines real-time differential GNSS corrections with an adaptive extended Kalman filter (EKF) to address positional accuracy and system robustness challenges in practical [...] Read more.
This study proposes an enhanced integration framework for the global navigation satellite system (GNSS) and inertial navigation system (INS). The framework combines real-time differential GNSS corrections with an adaptive extended Kalman filter (EKF) to address positional accuracy and system robustness challenges in practical navigation scenarios. The proposed method dynamically compensates for positioning inaccuracies and sensor drift by integrating differential GNSS corrections to reduce errors and employing an adaptive EKF to address temporal synchronization discrepancies and misalignment angle deviations. Simulation and experimental results demonstrate that the framework keeps horizontal positioning error within 2 m and achieves a maximum accuracy improvement of 4.2 m compared to conventional single-point positioning. This low-cost solution ensures robust performance for practical autonomous navigation scenarios. Full article
(This article belongs to the Section Systems & Control Engineering)
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23 pages, 5173 KiB  
Article
Improvement of Cooperative Localization for Heterogeneous Mobile Robots
by Efe Oğuzhan Karcı, Ahmet Mustafa Kangal and Sinan Öncü
Drones 2025, 9(7), 507; https://doi.org/10.3390/drones9070507 - 19 Jul 2025
Viewed by 324
Abstract
This research focuses on enhancing cooperative localization for heterogeneous mobile robots composed of a quadcopter and an unmanned ground vehicle. The study employs sensor fusion techniques, particularly the Extended Kalman Filter, to fuse data from various sensors, including GPSs, IMUs, and cameras. By [...] Read more.
This research focuses on enhancing cooperative localization for heterogeneous mobile robots composed of a quadcopter and an unmanned ground vehicle. The study employs sensor fusion techniques, particularly the Extended Kalman Filter, to fuse data from various sensors, including GPSs, IMUs, and cameras. By integrating these sensors and optimizing fusion strategies, the research aims to improve the precision and reliability of cooperative localization in complex and dynamic environments. The primary objective is to develop a practical framework for cooperative localization that addresses the challenges posed by the differences in mobility and sensing capabilities among heterogeneous robots. Sensor fusion is used to compensate for the limitations of individual sensors, providing more accurate and robust localization results. Moreover, a comparative analysis of different sensor combinations and fusion strategies helps to identify the optimal configuration for each robot. This research focuses on the improvement of cooperative localization, path planning, and collaborative tasks for heterogeneous robots. The findings have broad applications in fields such as autonomous transportation, agricultural operation, and disaster response, where the cooperation of diverse robotic platforms is crucial for mission success. Full article
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19 pages, 2969 KiB  
Article
Damage Detection for Offshore Wind Turbines Subjected to Non-Stationary Ambient Excitations: A Noise-Robust Algorithm Using Partial Measurements
by Ning Yang, Peng Huang, Hongning Ye, Wuhua Zeng, Yusen Liu, Juhuan Zheng and En Lin
Energies 2025, 18(14), 3644; https://doi.org/10.3390/en18143644 - 10 Jul 2025
Viewed by 238
Abstract
Reliable damage detection in operational offshore wind turbines (OWTs) remains challenging due to the inherent non-stationarity of environmental excitations and signal degradation from noise-contaminated partial measurements. To address these limitations, this study proposes a robust damage detection method for OWTs under non-stationary ambient [...] Read more.
Reliable damage detection in operational offshore wind turbines (OWTs) remains challenging due to the inherent non-stationarity of environmental excitations and signal degradation from noise-contaminated partial measurements. To address these limitations, this study proposes a robust damage detection method for OWTs under non-stationary ambient excitations using partial measurements with strong noise resistance. The method is first developed for a scenario with known non-stationary ambient excitations. By reformulating the time-domain equation of motion in terms of non-stationary cross-correlation functions, structural stiffness parameters are estimated using partially measured acceleration responses through the extended Kalman filter (EKF). To account for the more common case of unknown excitations, the method is enhanced via the extended Kalman filter under unknown input (EKF-UI). This improved approach enables the simultaneous identification of the physical parameters of OWTs and unknown non-stationary ambient excitations through the data fusion of partial acceleration and displacement responses. The proposed method is validated through two numerical cases: a frame structure subjected to known non-stationary ground excitation, followed by an OWT tower under unknown non-stationary wind and wave excitations using limited measurements. The numerical results confirm the method’s capability to accurately identify structural damage even under significant noise contamination, demonstrating its practical potential for OWTs’ damage detection applications. Full article
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22 pages, 3432 KiB  
Article
Tracking Accuracy Evaluation of Autonomous Agricultural Tractors via Rear Three-Point Hitch Estimation Using a Hybrid Model of EKF Transformer
by Eun-Kuk Kim, Tae-Ho Han, Jun-Ho Lee, Cheol-Woo Han and Ryu-Gap Lim
Agriculture 2025, 15(14), 1475; https://doi.org/10.3390/agriculture15141475 - 9 Jul 2025
Viewed by 325
Abstract
The objective of this study was to improve measurement accuracy in the evaluation of autonomous agricultural tractor performance by addressing external disturbances, such as sensor installation errors, vibrations, and heading-induced bias that occur during the measurement of the conventional rear three-point hitch (Rear [...] Read more.
The objective of this study was to improve measurement accuracy in the evaluation of autonomous agricultural tractor performance by addressing external disturbances, such as sensor installation errors, vibrations, and heading-induced bias that occur during the measurement of the conventional rear three-point hitch (Rear 3-Point) system. To mitigate these disturbances, the measurement point was relocated to the cab, where external interference is comparatively minimal. However, in compliance with the ISO 12188 standard, the Rear 3-Point system must be used as the reference measurement point. Therefore, its coordinates were indirectly estimated using an extended Kalman filter (EKF) and artificial intelligence (AI)-based techniques. A hybrid model was developed in which a transformer-based AI model was trained using the Rear 3-Point coordinates predicted by EKF as the ground truth. While traditional time-series models, such as LSTM and GRU, show limitations in predicting nonlinear data, the application of an attention mechanism was found to enhance prediction performance by effectively learning temporal dependencies and vibration patterns. The experimental results show that the EKF-based estimation achieved a precision of RMSE 1.6 mm, a maximum error of 12.6 mm, and a maximum standard deviation of 3.9 mm compared to actual measurements. From the perspective of experimental design, the proposed hybrid model was able to predict the trajectory of the autonomous agricultural tractor with significantly reduced external disturbances when compared to the actual measured Rear 3-Point coordinates, while also complying with the ISO 12188 standard. These findings suggest that the proposed approach provides an effective and integrated solution for developing high-precision autonomous agricultural systems. Full article
(This article belongs to the Special Issue Soil-Machine Systems and Its Related Digital Technologies Application)
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19 pages, 4219 KiB  
Article
Schur Complement Optimized Iterative EKF for Visual–Inertial Odometry in Autonomous Vehicles
by Guo Ma, Cong Li, Hui Jing, Bing Kuang, Ming Li, Xiang Wang and Guangyu Jia
Machines 2025, 13(7), 582; https://doi.org/10.3390/machines13070582 - 4 Jul 2025
Viewed by 232
Abstract
Accuracy and nonlinear processing capabilities are critical to the positioning and navigation of autonomous vehicles in visual–inertial odometry (VIO). Existing filtering-based VIO methods struggle to deal with strongly nonlinear systems and often exhibit low precision. To this end, this paper proposes a VIO [...] Read more.
Accuracy and nonlinear processing capabilities are critical to the positioning and navigation of autonomous vehicles in visual–inertial odometry (VIO). Existing filtering-based VIO methods struggle to deal with strongly nonlinear systems and often exhibit low precision. To this end, this paper proposes a VIO method based on the Schur complement and Iterated Extended Kalman Filtering (IEKF). The algorithm first enhances ORB (Oriented FAST and Rotated BRIEF) features using Multi-Layer Perceptron (MLP) and Transformer architectures to improve feature robustness. It then integrates visual information and Inertial Measurement Unit (IMU) data through IEKF, constructing a complete residual model. The Schur complement is applied during covariance updates to compress the state dimension, improving computational efficiency and significantly enhancing the system’s ability to handle nonlinearities while maintaining real-time performance. Compared to traditional Extended Kalman Filtering (EKF), the proposed method demonstrates stronger stability and accuracy in high-dynamic scenarios. The experimental results show that the algorithm achieves superior state estimation performance on several typical visual–inertial datasets, demonstrating excellent accuracy and robustness. Full article
(This article belongs to the Topic Advances in Mobile Robotics Navigation, 2nd Volume)
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18 pages, 2791 KiB  
Article
Deterministic Data Assimilation in Thermal-Hydraulic Analysis: Application to Natural Circulation Loops
by Lanxin Gong, Changhong Peng and Qingyu Huang
J. Nucl. Eng. 2025, 6(3), 23; https://doi.org/10.3390/jne6030023 - 3 Jul 2025
Viewed by 290
Abstract
Recent advances in high-fidelity modeling, numerical computing, and data science have spurred interest in model-data integration for nuclear reactor applications. While machine learning often prioritizes data-driven predictions, this study focuses on data assimilation (DA) to synergize physical models with measured data, aiming to [...] Read more.
Recent advances in high-fidelity modeling, numerical computing, and data science have spurred interest in model-data integration for nuclear reactor applications. While machine learning often prioritizes data-driven predictions, this study focuses on data assimilation (DA) to synergize physical models with measured data, aiming to enhance predictive accuracy and reduce uncertainties. We implemented deterministic DA methods—Kalman filter (KF) and three-dimensional variational (3D-VAR)—in a one-dimensional single-phase natural circulation loop and extended 3D-VAR to RELAP5, a system code for two-phase loop analysis. Unlike surrogate-based or model-reduction strategies, our approach leverages full-model propagation without relying on computationally intensive sampling. The results demonstrate that KF and 3D-VAR exhibit robustness against varied noise types, intensities, and distributions, achieving significant uncertainty reduction in state variables and parameter estimation. The framework’s adaptability is further validated under oceanic conditions, suggesting its potential to augment baseline models beyond conventional extrapolation boundaries. These findings highlight DA’s capacity to improve model calibration, safety margin quantification, and reactor field reconstruction. By integrating high-fidelity simulations with real-world data corrections, the study establishes a scalable pathway to enhance the reliability of nuclear system predictions, emphasizing DA’s role in bridging theoretical models and operational demands without compromising computational efficiency. Full article
(This article belongs to the Special Issue Advances in Thermal Hydraulics of Nuclear Power Plants)
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39 pages, 2307 KiB  
Article
Modeling of Energy Management System for Fully Autonomous Vessels with Hybrid Renewable Energy Systems Using Nonlinear Model Predictive Control via Grey Wolf Optimization Algorithm
by Harriet Laryea and Andrea Schiffauerova
J. Mar. Sci. Eng. 2025, 13(7), 1293; https://doi.org/10.3390/jmse13071293 - 30 Jun 2025
Viewed by 305
Abstract
This study presents a multi-objective predictive energy management system (EMS) for optimizing hybrid renewable energy systems (HRES) in autonomous marine vessels. The objective is to minimize fuel consumption and emissions while maximizing renewable energy usage and pure-electric sailing durations. The EMS combines nonlinear [...] Read more.
This study presents a multi-objective predictive energy management system (EMS) for optimizing hybrid renewable energy systems (HRES) in autonomous marine vessels. The objective is to minimize fuel consumption and emissions while maximizing renewable energy usage and pure-electric sailing durations. The EMS combines nonlinear model predictive control (NMPC) with metaheuristic optimizers—Grey Wolf Optimization (GWO) and Genetic Algorithm (GA)—and is benchmarked against a conventional rule-based (RB) method. The HRES architecture comprises photovoltaic arrays, vertical-axis wind turbines (VAWTs), diesel engines, generators, and a battery storage system. A ship dynamics model was used to represent propulsion power under realistic sea conditions. Simulations were conducted using real-world operational and environmental datasets, with state prediction enhanced by an Extended Kalman Filter (EKF). Performance is evaluated using marine-relevant indicators—fuel consumption; emissions; battery state of charge (SOC); and emission cost—and validated using standard regression metrics. The NMPC-GWO algorithm consistently outperformed both NMPC-GA and RB approaches, achieving high prediction accuracy and greater energy efficiency. These results confirm the reliability and optimization capability of predictive EMS frameworks in reducing emissions and operational costs in autonomous maritime operations. Full article
(This article belongs to the Special Issue Advancements in Hybrid Power Systems for Marine Applications)
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19 pages, 3878 KiB  
Article
An Enhanced Error-Adaptive Extended-State Kalman Filter Model Predictive Controller for Supercritical Power Plants
by Gang Chen, Shan Hua, Changhao Fan, Chun Wang, Shuchong Wang and Li Sun
Algorithms 2025, 18(7), 387; https://doi.org/10.3390/a18070387 - 26 Jun 2025
Viewed by 301
Abstract
This study introduces an Enhanced Error-Adaptive Extended-State Kalman Filter Model Predictive Control (EEA-ESKF-MPC) method to tackle strong coupling and inertia in supercritical power plants. By enhancing the ESKF-MPC framework with a mechanism that dynamically adjusts error weights based on real-time deviations and employs [...] Read more.
This study introduces an Enhanced Error-Adaptive Extended-State Kalman Filter Model Predictive Control (EEA-ESKF-MPC) method to tackle strong coupling and inertia in supercritical power plants. By enhancing the ESKF-MPC framework with a mechanism that dynamically adjusts error weights based on real-time deviations and employs exponential smoothing, alongside a BP neural network for thermal unit simulation, the approach achieves superior performance. Simulations show reductions in the Integrated Absolute Error (IAE) for load and temperature by 3.05% and 2.46%, respectively, with a modest 0.43% pressure IAE increase compared to ESKF-MPC. Command disturbance tests and real condition tracking experiments, utilizing data from a 350 MW supercritical unit, reinforce the method’s effectiveness, highlighting its exceptional dynamic performance and precise tracking of operational parameter changes under multivariable coupling conditions, offering a scalable solution for modern power systems. Full article
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
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16 pages, 3317 KiB  
Article
A Novel Structural Vibration Sensing Approach Based on a Miniaturized Inertial Measurement Unit
by Liyuan Yu, Zhilei Qiao, Shichao Xing, Yipeng Wu and Hongli Ji
Sensors 2025, 25(13), 3958; https://doi.org/10.3390/s25133958 - 25 Jun 2025
Viewed by 273
Abstract
Active or semi-active vibration control systems require real-time vibration information from controlled structures as feedback. However, integrating vibration sensors into some controlled structures remains a challenge due to factors such as mass and signal lines. This issue is particularly prominent in attachment structures [...] Read more.
Active or semi-active vibration control systems require real-time vibration information from controlled structures as feedback. However, integrating vibration sensors into some controlled structures remains a challenge due to factors such as mass and signal lines. This issue is particularly prominent in attachment structures located far from the spacecraft, such as robotic arms and solar panels. This paper presents a miniaturized autonomous inertial sensor that can be easily attached to the controlled structure to acquire vibration data and wirelessly transmit the data. We also establish the relationship between cantilevered structural vibration and the inertial acceleration or angular velocity directly measured by the sensor. Consequently, the feedback information for the control system can be calculated by the processor in real-time. This autonomous inertial sensor consists of an inertial measurement unit (IMU) named BMI088 and a common wireless communication unit. An improved Extended Kalman Filter (EKF) algorithm is employed to enhance the quality of the sensing data in practical environments. The experimental results validated the theoretical model, indicating that the miniaturized inertial sensor effectively captures the bending vibration characteristics of the controlled structure. Full article
(This article belongs to the Special Issue Advanced Inertial Sensors: Advances, Challenges and Applications)
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19 pages, 55351 KiB  
Article
Improving UAV Remote Sensing Photogrammetry Accuracy Under Navigation Interference Using Anomaly Detection and Data Fusion
by Chen Meng, Haoyang Yang, Cuicui Jiang, Qinglei Hu and Dongyu Li
Remote Sens. 2025, 17(13), 2176; https://doi.org/10.3390/rs17132176 - 25 Jun 2025
Viewed by 381
Abstract
Accurate and robust navigation is fundamental to Unmanned Aerial Vehicle (UAV) remote sensing operations. However, the susceptibility of UAV navigation sensors to diverse interference and malicious attacks can severely degrade positioning accuracy and compromise mission integrity. Addressing these vulnerabilities, this paper presents an [...] Read more.
Accurate and robust navigation is fundamental to Unmanned Aerial Vehicle (UAV) remote sensing operations. However, the susceptibility of UAV navigation sensors to diverse interference and malicious attacks can severely degrade positioning accuracy and compromise mission integrity. Addressing these vulnerabilities, this paper presents an integrated framework combining sensor anomaly detection with a Dynamic Adaptive Extended Kalman Filter (DAEKF) and federated filtering algorithms to bolster navigation resilience and accuracy for UAV remote sensing. Specifically, mathematical models for prevalent UAV sensor attacks were established. The proposed framework employs adaptive thresholding and residual consistency checks for the real-time identification and isolation of anomalous sensor measurements. Based on these detection outcomes, the DAEKF dynamically adjusts its sensor fusion strategies and noise covariance matrices. To further enhance the fault tolerance, a federated filtering architecture was implemented, utilizing adaptively weighted sub-filters based on assessed trustworthiness to effectively isolate faults. The efficacy of this framework was validated through rigorous experiments that involved real-world flight data and software-defined radio (SDR)-based Global Positioning System (GPS) spoofing, alongside simulated attacks. The results demonstrate exceptional performance, where the average anomaly detection accuracy exceeded 99% and the precision surpassed 98%. Notably, when benchmarked against traditional methods, the proposed system reduced navigation errors by a factor of approximately 2-3 under attack scenarios, which substantially enhanced the operational stability of the UAVs in challenging environments. Full article
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18 pages, 1319 KiB  
Article
Autonomous Orbit Determination of LLO Satellite Using DRO–LLO Links and Lunar Laser Ranging
by Shixu Chen, Shuanglin Li, Jinghui Pu, Yingjie Xu and Wenbin Wang
Aerospace 2025, 12(7), 576; https://doi.org/10.3390/aerospace12070576 - 25 Jun 2025
Viewed by 369
Abstract
A stable and high-precision autonomous orbit determination scheme for a Low Lunar Orbit (LLO) spacecraft is proposed, leveraging satellite-to-satellite tracking (SST) measurement data and lunar laser ranging data. One satellite orbits around the LLO, while the other satellite orbits around the Distant Retrograde [...] Read more.
A stable and high-precision autonomous orbit determination scheme for a Low Lunar Orbit (LLO) spacecraft is proposed, leveraging satellite-to-satellite tracking (SST) measurement data and lunar laser ranging data. One satellite orbits around the LLO, while the other satellite orbits around the Distant Retrograde Orbit (DRO). An inter-satellite ranging link is established between the two satellites, while the LLO satellite conducts laser ranging with a Corner Cube Reflector (CCR) on the lunar surface. Both inter-satellite ranging data and lunar laser ranging data are acquired through measurements. By integrating these data with orbital dynamics and employing the Extended Kalman Filter (EKF) method, the position and velocity states of the two formation satellites are estimated. This orbit determination scheme operates independently of ground measurement and control stations, achieving a high degree of autonomy. Simulation results demonstrate that the position accuracy of the LLO satellite can reach 0.1 m, and that of the DRO satellite can reach 10 m. Compared to the autonomous orbit determination scheme relying solely on SST measurement data, this proposed scheme exhibits several advantages, including shorter convergence time, higher convergence accuracy, and enhanced robustness of the navigation system against initial orbit errors and orbital dynamic model errors. It can provide a valuable engineering reference for the autonomous navigation of lunar-orbiting satellites. Full article
(This article belongs to the Special Issue Precise Orbit Determination of the Spacecraft)
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21 pages, 3026 KiB  
Article
Adaptive Multi-Timescale Particle Filter for Nonlinear State Estimation in Wastewater Treatment: A Bayesian Fusion Approach with Entropy-Driven Feature Extraction
by Xiaolong Chen, Hongfeng Zhang, Cora Un In Wong and Zhengchun Song
Processes 2025, 13(7), 2005; https://doi.org/10.3390/pr13072005 - 25 Jun 2025
Cited by 1 | Viewed by 375
Abstract
We propose an adaptive multi-timescale particle filter (AMTS-PF) for nonlinear state estimation in wastewater treatment plants (WWTPs) to address multi-scale temporal dynamics. The AMTS-PF decouples the problem into minute-level state updates and hour-level parameter refinements, integrating adaptive noise tuning, multi-scale entropy-driven feature extraction, [...] Read more.
We propose an adaptive multi-timescale particle filter (AMTS-PF) for nonlinear state estimation in wastewater treatment plants (WWTPs) to address multi-scale temporal dynamics. The AMTS-PF decouples the problem into minute-level state updates and hour-level parameter refinements, integrating adaptive noise tuning, multi-scale entropy-driven feature extraction, and dual-timescale particle weighting. It dynamically adjusts noise covariances via Bayesian fusion and uses wavelet-based entropy analysis for adaptive resampling. The method interfaces seamlessly with existing WWTP control systems, providing real-time state estimates and refined parameters. Implemented on a heterogeneous computing architecture, it combines edge-level parallelism and cloud-based inference. Experimental validation shows superior performance over extended Kalman filters and single-timescale particle filters in handling nonlinearities and time-varying dynamics. The proposed AMTS-PF significantly enhances the accuracy of state estimation in WWTPs compared to traditional methods. Specifically, during the 14-day evaluation period using the Benchmark Simulation Model No. 1 (BSM1), the AMTS-PF achieved a root mean square error (RMSE) of 54.3 mg/L for heterotroph biomass (XH) estimation, which is a 37% reduction compared to the standard particle filter (PF) with an RMSE of 68.9 mg/L. For readily biodegradable substrate (Ss) and particulate products (Xp), the AMTS-PF also demonstrated superior performance with RMSE values of 7.2 mg/L and 9.8 mg/L, respectively, representing improvements of 24% and 21% over the PF. In terms of slow parameters, the AMTS-PF showed a 37% reduction in RMSE for the maximum heterotrophic growth rate (μH) estimation compared to the PF. These results highlight the effectiveness of the AMTS-PF in handling the multi-scale temporal dynamics and nonlinearities inherent in WWTPs. This work advances the state-of-the-art in WWTP monitoring by unifying multi-scale temporal modeling with adaptive Bayesian estimation, offering a practical solution for improving operational efficiency and process reliability. Full article
(This article belongs to the Special Issue Processes Development for Wastewater Treatment)
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22 pages, 7195 KiB  
Article
Bayesian Optimization-Based State-of-Charge Estimation with Temperature Drift Compensation for Lithium-Ion Batteries
by Zhen-Rong Yuan, Ke-Feng Huang, Cai-Hua Xu, Jun-Chao Zou and Jun Yan
Batteries 2025, 11(7), 243; https://doi.org/10.3390/batteries11070243 - 24 Jun 2025
Viewed by 684
Abstract
With the widespread application of electric vehicles and electrical energy storage systems, the accurate monitoring of lithium battery states has become crucial for ensuring safety and improving efficiency in terms of the applications. For this reason, this study proposes an algorithm focusing on [...] Read more.
With the widespread application of electric vehicles and electrical energy storage systems, the accurate monitoring of lithium battery states has become crucial for ensuring safety and improving efficiency in terms of the applications. For this reason, this study proposes an algorithm focusing on Bayesian optimization-based adaptive extended Kalman filter (BO-AEKF) to enhance the numerical accuracy and stability of state-of-charge (SOC) estimation for lithium batteries under various operating conditions. By comparing with traditional methods, the proposed algorithm, introducing a temperature-adaptive mechanism and a dynamic parameter updating strategy, can effectively address the estimation limitations under severe temperature variations and initial SOC uncertainties. Experimental results demonstrate that the proposed algorithm exhibits superior estimation performance at different temperatures, including −10 °C, 0 °C, 25 °C, and 50 °C; particularly under dynamic operating conditions, the maximum error (MAX) and root mean square error (RMSE) are reduced by 51.9% and 74.5%, respectively, compared to the extended Kalman filter (EKF) and adaptive extended Kalman filter (AEKF) algorithms. Furthermore, the BO-AEKF achieves rapid convergence even with unknown initial SOC values, demonstrating its robustness and adaptability. These findings provide more reliable technical support for the development of battery management systems, making them suitable for state estimation in electric vehicles and renewable energy storage systems. Full article
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