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Search Results (857)

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Keywords = Extended Kalman Filter (EKF)

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21 pages, 3410 KB  
Article
Advanced Approach for State-of-Charge Estimation Accounting for Battery Aging
by Woongchul Choi, Younggill Son and Jiwon Kwon
Batteries 2026, 12(5), 182; https://doi.org/10.3390/batteries12050182 - 20 May 2026
Abstract
Accurate battery state-of-charge (SOC) estimation is a core function of battery management systems (BMSs) for electric vehicles (EVs), as it directly affects energy management, safety, and reliability. However, battery aging significantly degrades the accuracy of conventional SOC estimation methods by causing capacity loss, [...] Read more.
Accurate battery state-of-charge (SOC) estimation is a core function of battery management systems (BMSs) for electric vehicles (EVs), as it directly affects energy management, safety, and reliability. However, battery aging significantly degrades the accuracy of conventional SOC estimation methods by causing capacity loss, increased internal resistance, and changes in voltage response characteristics. To address these issues, this study proposes an aging-aware SOC estimation method that combines an equivalent-circuit model (ECM) with an extended Kalman filter (EKF). In the proposed framework, aging effects are explicitly incorporated by using offline-identified SOH-dependent model parameters, including effective capacity, RC parameters, and SOC–OCV characteristics, and scheduling these parameters within the EKF prediction and correction process according to the available SOH information. Furthermore, the performance of the proposed method is experimentally validated under an Urban Dynamometer Driving Schedule (UDDS) using cylindrical lithium-ion cells with large current fluctuations. The experimental results demonstrate that the proposed aging-aware EKF maintains stable SOC estimation performance not only in the initial battery state but also throughout the gradual aging process and up to the end of battery life. These results demonstrate the potential of SOH-scheduled, aging-aware EKF-based SOC estimation to improve SOC accuracy in aged batteries under the investigated laboratory and dynamic load conditions. Full article
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31 pages, 1926 KB  
Article
Nonlinear State Estimation with Deep Learning for Financial Forecasting: An EKF-LSTM Hybrid Approach with Cross-Market Evidence
by Chunxia Tian, Yirong Bai, Roengchai Tansuchat and Songsak Sriboonchitta
Economies 2026, 14(5), 184; https://doi.org/10.3390/economies14050184 - 16 May 2026
Viewed by 192
Abstract
Predicting financial stock returns remains challenging due to their inherent nonlinearity, non-stationarity, and sensitivity to market microstructure noise. Existing approaches typically rely on either econometric filtering techniques or deep learning models in isolation, limiting their ability to jointly capture latent dynamics and complex [...] Read more.
Predicting financial stock returns remains challenging due to their inherent nonlinearity, non-stationarity, and sensitivity to market microstructure noise. Existing approaches typically rely on either econometric filtering techniques or deep learning models in isolation, limiting their ability to jointly capture latent dynamics and complex temporal dependencies. This study proposes a hybrid Extended Kalman Filter–Long Short-Term Memory (EKF–LSTM) framework that integrates nonlinear state-space filtering with deep sequential learning. The EKF component performs nonlinear state estimation and denoises to extract latent signals from noisy observations, while the LSTM network models nonlinear temporal dependencies in the filtered series. The proposed framework is evaluated using data from multiple international markets, including China, the United States, and Europe, providing cross-market evidence of model robustness. Empirical results show that the EKF–LSTM model consistently outperforms benchmark models (ARIMA, standalone EKF, LSTM, and GRU) across standard statistical metrics, including RMSE, MAE, and mean directional accuracy (MDA). In addition, the model delivers economically meaningful improvements under a long-only trading strategy, achieving higher risk-adjusted returns and lower maximum drawdowns relative to benchmark strategies. Diebold–Mariano tests further confirm that these performance gains are statistically significant. Overall, the findings demonstrate that integrating nonlinear state-space filtering with deep learning provides a robust and effective framework for financial time-series forecasting. However, the results should be interpreted with caution due to the limited sample size and the simplifying assumptions underlying the trading strategy. Full article
(This article belongs to the Special Issue Modeling and Forecasting of Financial Markets)
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17 pages, 1611 KB  
Article
Symmetry-Aware Vehicle State Estimation Using a Chaotic-Gradient-Optimized Extended Kalman Filter
by Qianyu Cheng, Wenguang Liu, Xi Liu, Huajun Che and Bei Ding
Symmetry 2026, 18(5), 847; https://doi.org/10.3390/sym18050847 (registering DOI) - 15 May 2026
Viewed by 103
Abstract
To address the uncertainty of the measurement noise covariance matrix in vehicle state estimation, this paper proposes a symmetry-aware extended Kalman filter optimized by a chaotic-gradient strategy. The symmetry-aware concept is introduced from the approximate mirror symmetry of vehicle lateral dynamics under left [...] Read more.
To address the uncertainty of the measurement noise covariance matrix in vehicle state estimation, this paper proposes a symmetry-aware extended Kalman filter optimized by a chaotic-gradient strategy. The symmetry-aware concept is introduced from the approximate mirror symmetry of vehicle lateral dynamics under left and right steering excitations. Under identical road adhesion and vehicle operating conditions, the yaw-rate and sideslip-angle responses should exhibit balanced statistical characteristics for positive and negative lateral motions. However, a fixed measurement noise covariance matrix may break this balance and lead to direction-dependent estimation bias or delayed convergence. To improve the statistical consistency of the estimation process, the proposed method adaptively tunes the measurement noise covariance matrix according to the innovation covariance mismatch. A chaotic search mechanism is first used to enhance global exploration, and a variable-step gradient method is then applied to refine the local optimal solution. Through the iterative combination of chaotic traversal and gradient-based refinement, the proposed observer improves the balance between model prediction and measurement correction under stochastic disturbances. The effectiveness of the proposed method is verified through CarSim and MATLAB/Simulink co-simulation. The results show that, compared with EKF, UKF, and AEKF benchmark observers, the proposed CG_EKF provides more accurate estimation of vehicle yaw rate and sideslip angle. Full article
(This article belongs to the Section Engineering and Materials)
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26 pages, 1923 KB  
Article
Sensorless Control of Compressor Motor Considering Inverter Nonlinearities and Parameter Estimation
by Tunahan Sapmaz and Ahmet Faruk Bakan
Energies 2026, 19(10), 2374; https://doi.org/10.3390/en19102374 - 15 May 2026
Viewed by 128
Abstract
In this study, parameter estimation-assisted sensorless control methods are proposed for compressor motors. As sensorless control strategies, rotating high-frequency injection (RHFI), pulsating high-frequency injection (RHFI), and an adaptive-gain sliding mode observer (AG-SMO) are employed. During startup, HFI-based methods are utilized, whereas AG-SMO is [...] Read more.
In this study, parameter estimation-assisted sensorless control methods are proposed for compressor motors. As sensorless control strategies, rotating high-frequency injection (RHFI), pulsating high-frequency injection (RHFI), and an adaptive-gain sliding mode observer (AG-SMO) are employed. During startup, HFI-based methods are utilized, whereas AG-SMO is activated under steady-state operating conditions. To mitigate parameter variations and inverter nonlinearities, Adaline Neural Network (ANN), Recursive Least Squares (RLS), and Extended Kalman Filter (EKF) algorithms are integrated for the real-time estimation of stator resistance and dead-time voltage. The proposed framework is validated through both simulation and experimental studies on a 30 W, 20 V interior permanent magnet motor commonly used in compressor applications. The results demonstrate that sensorless control algorithms alone provide robust operation, while the incorporation of parameter estimation effectively eliminates stability issues and ensures reliable transitions from low to high speeds. Comparative analysis reveals that ANN has a simple structure, RLS achieves faster convergence, and EKF provides smoother estimates under noisy conditions. Overall, the integration of sensorless control algorithms with ANN/RLS/EKF-based parameter estimation and dead-time compensation offers a cost-effective and reliable solution for high-performance compressor applications. Full article
35 pages, 24919 KB  
Article
High-Precision and Efficient Calibration of Robot Polishing Systems Using an Adaptive Residual EKF Optimized by MIPO
by Lei Wang, Yuqi Yao, Shouxin Ruan, Hainan Li, Xinming Zhang, Yiwen Zhang, Zihao Zang and Zhenglei Yu
Sensors 2026, 26(10), 3087; https://doi.org/10.3390/s26103087 - 13 May 2026
Viewed by 408
Abstract
This paper proposes an adaptive residual extended Kalman filter method optimized by a multi-strategy improved parrot optimization algorithm (MIPO-ARKEKF) to improve the kinematic parameter calibration accuracy and efficiency of robotic polishing systems. To address the limitations of the standard extended Kalman filter (EKF), [...] Read more.
This paper proposes an adaptive residual extended Kalman filter method optimized by a multi-strategy improved parrot optimization algorithm (MIPO-ARKEKF) to improve the kinematic parameter calibration accuracy and efficiency of robotic polishing systems. To address the limitations of the standard extended Kalman filter (EKF), such as truncation-error accumulation during repeated linearization and sensitivity to manually selected noise parameters, an integrated improvement framework is developed. Specifically, a gradient stabilizer based on state-estimation increments is introduced to alleviate estimation degradation caused by accumulated truncation errors, while the proposed MIPO algorithm is employed to adaptively optimize the process and measurement noise covariance matrices, thereby improving the robustness of parameter identification under practical measurement uncertainty. The calibration process is established on the basis of high-precision external measurement data obtained from the robotic polishing system. In benchmark-function tests, MIPO demonstrates superior convergence performance. In physical experiments based on a KUKA KR210 R2700 robot, the proposed MIPO-ARKEKF method reduces the root mean square positioning error from 0.8927 mm to 0.4858 mm, corresponding to a 45.58% improvement in accuracy. Compared with representative hybrid calibration methods, the proposed method achieves comparable compensation accuracy while reducing computation time by 34.88% to 65.08%. Practical polishing experiments on ultra-low-expansion glass lenses further verify that the proposed method effectively improves end-effector trajectory tracking accuracy and polishing quality, providing an efficient solution for high-precision robotic polishing. Full article
(This article belongs to the Section Sensors and Robotics)
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18 pages, 1752 KB  
Article
A Real-Time Inertial Sensor-Based Diagnostic Support System for Improving Angular Accuracy in Dental Implant Placement: Preclinical Experimental Validation in a 3D Haptic Simulation Model
by Raul Cuesta Román, Pere Riutord-Sbert, Daniela Vallejos Rojas, Irene Coll Campayo, Joan Obrador de Hevia and Sebastiana Arroyo Bote
Dent. J. 2026, 14(5), 296; https://doi.org/10.3390/dj14050296 - 13 May 2026
Viewed by 174
Abstract
Background: Accurate three-dimensional positioning of dental implants is critical for ensuring biomechanical stability, prosthetic passivity, and long-term clinical success. While computer-assisted navigation systems achieve high precision, their complexity and cost often limit accessibility. This study presents the development and preclinical experimental validation of [...] Read more.
Background: Accurate three-dimensional positioning of dental implants is critical for ensuring biomechanical stability, prosthetic passivity, and long-term clinical success. While computer-assisted navigation systems achieve high precision, their complexity and cost often limit accessibility. This study presents the development and preclinical experimental validation of a low-cost prototype designed to enhance angular accuracy in dental implant placement within a controlled 3D haptic simulation environment. Methods: A preclinical experimental design was implemented using a 3D haptic simulator (Virteasy, Montpellier, France). The prototype incorporated high-precision inertial measurement units (IMUs) and an Extended Kalman Filter (EKF) for real-time angular feedback. Ninety-seven simulated implant placements were performed—both freehand and with prototype assistance—under identical virtual conditions by a single experienced operator. Angular deviations in mesiodistal and buccolingual planes were recorded, combined into a composite 3D index, and analyzed using paired t-tests and linear mixed-effects models. The study was conducted in a controlled simulation environment, which does not fully replicate clinical conditions. Results: The prototype significantly reduced angular deviation from 13.49° to 2.99° in the mesiodistal plane (−77.8%) and from 13.56° to 5.59° in the buccolingual plane (−58.8%), achieving an overall 67% improvement in three-dimensional orientation (p < 0.001; Cohen’s d = 1.47). Agreement with an optical reference system (OptiTrack) was excellent (bias = +0.36°, RMSE = 0.39°). Intra-operator reliability exceeded 0.95 (ICC), confirming strong reproducibility and measurement stability. Conclusions: The proposed inertial sensor-based prototype achieved angular accuracy within the range reported for computer-guided systems while maintaining advantages of portability, low cost, and usability. Its integration into haptic simulators provides a valid tool for both educational and preclinical applications, offering real-time feedback that enhances spatial perception and psychomotor learning. Future clinical studies should validate its performance in cadaveric and patient-based contexts to determine its practical impact on surgical precision and implant success. Full article
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25 pages, 2695 KB  
Article
Robust Pose and Inertial Parameter Estimation of An Unknown aircraft Based on Variational BAYESIAN Dual Vector Quaternion Extended Kalman Filter
by Shengli Xu, Yangwang Fang and Hanqiao Huang
Entropy 2026, 28(5), 549; https://doi.org/10.3390/e28050549 - 12 May 2026
Viewed by 109
Abstract
Accurately determining the parameters of an unmodeled spacecraft is crucial. Filtering methods that are resilient to uncertainty, employing dual quaternion frameworks to ascertain orientation and position, introduce a design for an extended Kalman filter based on variational Bayesian inference and dual vector quaternions [...] Read more.
Accurately determining the parameters of an unmodeled spacecraft is crucial. Filtering methods that are resilient to uncertainty, employing dual quaternion frameworks to ascertain orientation and position, introduce a design for an extended Kalman filter based on variational Bayesian inference and dual vector quaternions (VB-DVQEKF) to carry out parameter estimation for a non-cooperative spacecraft. The system kinematics and dynamics are modeled using dual vector quaternions, rendering the representation manifestly concise. The method achieves thoroughness by accounting for the coupled interactions between translational and rotational motions. Furthermore, to address uncertainties in the measurements, a variational Bayesian approach is employed for the dependable simultaneous estimation of state parameters and measurement noise covariance. Mathematical simulations are used to verify the proposed VB-DVQEKF, and its robust capabilities are demonstrated through comparisons with several conventional parameter estimation techniques, including the conventional DVQ-EKF and the Sage–Husa adaptive DVQ-EKF (SH-DVQEKF). Quantitative results based on root-mean-square error (RMSE), convergence time, and final estimation error confirm that the proposed VB-DVQEKF achieves the smallest steady-state error among the compared methods and remains stable under white-burst, gradient (drift), and outlier-type measurement anomalies. Full article
(This article belongs to the Section Information Theory, Probability and Statistics)
18 pages, 2092 KB  
Article
An OOA-BP-EKF Integrated Framework for Maneuvering Target Tracking in WSNs
by Shaohui Li, Weijia Huang, Kun Xie and Chenglin Cai
Appl. Sci. 2026, 16(10), 4755; https://doi.org/10.3390/app16104755 - 11 May 2026
Viewed by 139
Abstract
To address tracking accuracy degradation caused by noise in sensor observations, a maneuvering target tracking algorithm based on an improved Received Signal Strength Indicator (RSSI) ranging model is proposed for Wireless Sensor Networks (WSNs). The traditional deterministic ranging model is replaced by a [...] Read more.
To address tracking accuracy degradation caused by noise in sensor observations, a maneuvering target tracking algorithm based on an improved Received Signal Strength Indicator (RSSI) ranging model is proposed for Wireless Sensor Networks (WSNs). The traditional deterministic ranging model is replaced by a backpropagation neural network optimized via the Osprey Optimization Algorithm (OOA-BP), which directly maps noisy RSSI measurements to precise physical distances. Filtering and tracking are executed using an Extended Kalman Filter (EKF) combined with a uniform circular motion model, demonstrating the robustness of the observation model across dynamic predictions. Simulation results validate the efficacy of the proposed framework. In the distance estimation phase, the OOA-BP model reduces the average ranging error to 0.04 m. During dynamic tracking, the integrated OOA-BP-EKF architecture demonstrates superior tracking performance compared to standard frameworks, reducing the Root Mean Square Error (RMSE) by 15.33% and 59.89% compared to GA-BP and standard BP algorithms, respectively. Full article
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31 pages, 48945 KB  
Article
RF-LSTM-Based Motion State Prediction for Unmanned Surface Vehicles Under Variable Operating Conditions
by Pengpeng Wan, Liming Wang, Yexin Song, Bi He, Hua Ouyang and Xing Xu
J. Mar. Sci. Eng. 2026, 14(10), 885; https://doi.org/10.3390/jmse14100885 (registering DOI) - 10 May 2026
Viewed by 215
Abstract
As a core piece of equipment for marine monitoring, search and rescue missions, and other applications, the motion state prediction accuracy of Unmanned Surface Vehicles (USVs) directly determines mission reliability and safety. However, existing methods fail to fully consider the motion characteristic differences [...] Read more.
As a core piece of equipment for marine monitoring, search and rescue missions, and other applications, the motion state prediction accuracy of Unmanned Surface Vehicles (USVs) directly determines mission reliability and safety. However, existing methods fail to fully consider the motion characteristic differences in various vessel sizes and variable-speed navigation under complex sea conditions, and struggle to capture the spatiotemporal dynamic features of state variations. This paper proposes a hybrid prediction algorithm based on Random Forest-Long Short-Term Memory (RF-LSTM), which utilizes Random Forest for key feature selection while employing LSTM to excavate temporal correlations. An intelligent routing mechanism based on the dominant frequency energy ratio (Pd) is introduced to achieve adaptive prediction mode switching, enabling comprehensive characterization of state variations. Under the 20 kn high-speed condition of a 7.5 m USV, the proposed algorithm achieves a Circular RMSE for heading prediction that is 1.9 times lower than the Extended Kalman Filter (EKF) and 1.2 times lower than a standalone LSTM, with pitch and roll prediction RMSE reduced to 0.36° and 0.85°, respectively. On a 14.5 m-long USV at 23 kn, it maintains a heading prediction accuracy of 0.10°, verifying favorable scale generalization capability. Furthermore, the algorithm demonstrates strong robustness against Gaussian white noise and synthetic ocean noise. Experimental results indicate that RF-LSTM significantly outperforms traditional methods, effectively breaking through the application limitations of fixed-architecture models, substantially enhancing USV autonomy and adaptability in complex marine environments, and providing robust guarantees for mission reliability and safety. Full article
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21 pages, 4034 KB  
Article
Low-Cost Portable Sensor Node for Gas and Chemical Leak Detection with Kalman-Filtering-Based UWB Localization
by Mohammed Faeik Ruzaij Al-Okby, Thomas Roddelkopf and Kerstin Thurow
Sensors 2026, 26(10), 2921; https://doi.org/10.3390/s26102921 - 7 May 2026
Viewed by 301
Abstract
The work environment in automated laboratories and industrial sites exposes workers to the risks associated with chemical gas and vapor leaks caused by unforeseen incidents. Such leaks may result in severe health hazards as well as damage to equipment or infrastructure at the [...] Read more.
The work environment in automated laboratories and industrial sites exposes workers to the risks associated with chemical gas and vapor leaks caused by unforeseen incidents. Such leaks may result in severe health hazards as well as damage to equipment or infrastructure at the leak site. Therefore, the development of systems capable of early detection and highly accurate localization of chemical leaks is of high importance for occupational safety. In this work, a low-cost, portable sensor node based on the Internet of Things (IoT) is proposed for the detection and localization of gas and chemical leaks in indoor environments. The sensor node features a modular design that enables flexible integration and replacement of gas and environmental sensors depending on the target application. In addition, the system includes an ultra-wideband (UWB)-based positioning and tracking unit, allowing operation across multiple indoor zones. The main contribution of this work lies in the combined integration of (i) multi-sensor-based environmental event detection and prediction and (ii) high-precision location within a dynamic multi-zone tracking architecture. The system automatically selects the most relevant anchors in each zone and applies trilateration and least-squares estimation, enhanced by Kalman filtering techniques. In particular, an extended Kalman filter (EKF) and an unscented Kalman filter (UKF) are employed, with sensor fusion incorporating inertial measurement unit (IMU) data to mitigate the effects of on-line-of-sight (NLoS) conditions and signal degradation caused by obstacles. Experimental results demonstrate that both the EKF and UKF significantly reduce positioning errors and improve tracking stability compared to baseline methods under challenging indoor conditions. The UKF shows superior performance in highly nonlinear scenarios. A quantitative evaluation using manually surveyed reference points showed that the UKF achieved the best overall performance, with a mean error of 39.72 cm and an RMSE of 43.03 cm. These findings confirm the effectiveness of Kalman filter-based sensor fusion for reliable indoor positioning and highlight the suitability of the proposed system for real-time safety monitoring applications. Full article
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27 pages, 18813 KB  
Article
Fast Prediction of Reachable Domain for High-Threat UAVs Using Space-Based Information
by Lujing Chao, Caihui Wang, Dongzhu Feng and Pei Dai
Drones 2026, 10(5), 349; https://doi.org/10.3390/drones10050349 - 6 May 2026
Viewed by 350
Abstract
Prediction of the reachable domain for high-threat unmanned aerial vehicles (UAVs) is critical for enabling cross-domain flight vehicles to perform proactive avoidance maneuvers. To address this challenge, this paper proposes a novel generic framework that integrates a Radau pseudospectral method (RPM) with a [...] Read more.
Prediction of the reachable domain for high-threat unmanned aerial vehicles (UAVs) is critical for enabling cross-domain flight vehicles to perform proactive avoidance maneuvers. To address this challenge, this paper proposes a novel generic framework that integrates a Radau pseudospectral method (RPM) with a BP neural network, supported by information acquired from satellites. The framework begins by estimating a preliminary state vector of the non-cooperative target, including its coarse position and velocity, via a Newton iterative algorithm. To refine this initial estimate and enable continuous tracking, an Extended Kalman Filter (EKF) is fused with a flight vehicle dynamics model. Subsequently, the RPM is employed to solve the trajectory planning problem, generating a comprehensive database for offline training. This database is then used to train a multilayer feedforward neural network within an offline training and online application framework, which drastically reduces computational complexity and time. Finally, numerical simulations demonstrate the method’s high prediction accuracy and strong robustness against tracking uncertainties. Crucially, the neural network predicts the reachable domain in just 0.01 s, making it highly viable for real-time online applications. Full article
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37 pages, 4082 KB  
Article
Trajectory Control for Car-like Mobile Robots via Frugal Predictive Control with Integrated Disturbance Rejection
by Luis Angel Martínez-Ramírez, Rafael Isaac Vásquez-Cruz, German Ardul Munoz-Hernandez, Gerardo Mino-Aguilar, Wuiyevaldo Fermín Guerrero-Sánchez, Roberto Carlos Ambrosio-Lázaro and José Fermi Guerrero-Castellanos
Actuators 2026, 15(5), 260; https://doi.org/10.3390/act15050260 - 2 May 2026
Viewed by 385
Abstract
This paper presents a hierarchical control architecture for high-precision trajectory tracking of a car-like mobile robot (CLMB) operating under external disturbances arising from normal and tangential wheel forces. The proposed solution addresses the critical challenge of simultaneously rejecting disturbances and accurately following a [...] Read more.
This paper presents a hierarchical control architecture for high-precision trajectory tracking of a car-like mobile robot (CLMB) operating under external disturbances arising from normal and tangential wheel forces. The proposed solution addresses the critical challenge of simultaneously rejecting disturbances and accurately following a predefined path at a determined cruise velocity. Since the vehicle is equipped with an electronic differential at the low level, a nonlinear dynamic control (NDC) scheme is implemented to regulate the speed in each wheel. This controller actively estimates and compensates for differential traction losses and other lumped disturbances in real time, ensuring robust wheel velocity tracking across varying terrain conditions. The compensated system is then governed by a high-level frugal model predictive controller (FMPC) that leverages a dynamic vehicle model to compute optimal steering and velocity commands, thereby minimizing future trajectory-tracking errors. To achieve a precise and reliable state estimation necessary for feedback control, an Extended Kalman Filter (EKF) is designed to fuse high-frequency data from wheel encoders with absolute pose measurements from a motion capture system, mitigating the drift inherent in odometry alone. Experimental results on a physical robotic platform demonstrate tracking accuracy and robust disturbance rejection under different operating conditions. Full article
(This article belongs to the Special Issue Nonlinear Control of Mechanical and Robotic Systems)
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34 pages, 12471 KB  
Article
Neural Network-Augmented Actuation Control System Designed for Path Tracking of Autonomous Underwater-Transportation Systems Under Sensor and Process Noise
by Faheem Ur Rehman, Syed Muhammad Tayyab, Hammad Khan, Aijun Li and Paolo Pennacchi
Actuators 2026, 15(5), 246; https://doi.org/10.3390/act15050246 - 30 Apr 2026
Viewed by 244
Abstract
Underwater-transportation systems have significant potential for both military and commercial applications. Neural Network (NN)-based control offers enhanced robustness for actuators to manage the states of autonomous underwater-transportation systems which include Rigid-Connection Transportation Systems (RCTSs), Flexible-Connection Transportation Systems (FCTSs) and Leader–Follower-Formation Control Transportation Systems [...] Read more.
Underwater-transportation systems have significant potential for both military and commercial applications. Neural Network (NN)-based control offers enhanced robustness for actuators to manage the states of autonomous underwater-transportation systems which include Rigid-Connection Transportation Systems (RCTSs), Flexible-Connection Transportation Systems (FCTSs) and Leader–Follower-Formation Control Transportation Systems (LFFCTSs). In this study, NN-Augmented Control (NNAC) is applied to the aforementioned three transportation systems to enable accurate path tracking by the actuators installed onboard these systems under both ideal operating conditions and in the presence of sensor and process noise. The Extended Kalman Filter (EKF) is employed to estimate the system states under noisy conditions. The results demonstrate that NNAC provides robust and adaptive control of actuators, achieving efficient trajectory tracking via the transportation systems despite the influence of sensor and process noise disturbances. NNAC predominance was also observed in comparison with the conventional PID controller. Among the transportation configurations under the NNAC strategy, the RCTS exhibited the highest tracking accuracy with the lowest power consumption by the actuators. The power consumption of actuators installed on the LFFCTS was marginally higher than that of the RCTS. However, the translational motion accuracy of the follower vehicle in the LFFCTS was the lowest due to indirect actuation control through the formation controller. In contrast, actuators in the FCTS showed the highest power consumption while motion accuracy was comparatively lowest, attributed to the increased complexity of its dynamic positioning requirements. Full article
(This article belongs to the Special Issue Fault Diagnosis and Prognosis in Actuators)
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16 pages, 2639 KB  
Article
Magnetic Heterodyne Target Proximal Distance Estimate Using Extended N-th-Pole Magnetic Dipole Model via Iterative Extended Kalman Filter
by Xuyi Miao, Yipeng Li, Zumeng Jiang, Shaojie Ma, He Zhang, Peng Liu and Keren Dai
Sensors 2026, 26(9), 2792; https://doi.org/10.3390/s26092792 - 30 Apr 2026
Viewed by 377
Abstract
Anti-collision detection technologies primarily rely on optical, radar, or laser sensors; however, their performance often deteriorates severely under adverse weather conditions (e.g., rain, snow, fog) or in scenarios involving visual occlusion. By contrast, magnetic anomaly detection leverages perturbations in the geomagnetic field induced [...] Read more.
Anti-collision detection technologies primarily rely on optical, radar, or laser sensors; however, their performance often deteriorates severely under adverse weather conditions (e.g., rain, snow, fog) or in scenarios involving visual occlusion. By contrast, magnetic anomaly detection leverages perturbations in the geomagnetic field induced by target objects (e.g., vehicles, metallic obstacles), exhibiting intrinsic all-weather operability and strong anti-interference capability. Nevertheless, conventional magnetic anomaly detection methods suffer from the limited applicability of the magnetic dipole model, which only affords coarse positioning accuracy and is predominantly suited for long-range targets. To address this limitation, this paper proposes an Extended N-th-Pole Magnetic Dipole (E-NMD) model that improves accuracy by analyzing the Lagrangian cosine term and rigorously constraining truncation errors under specific operational conditions. Experimental results demonstrate that, for steel with a relative permeability of 200, the model achieves a fitting variance of 99.87%. Furthermore, to overcome the inversion difficulties arising when the strength of short-range magnetic anomalies is comparable to sensor noise, an Adaptive Iterative Extended Kalman Filter (AI-EKF) is developed to enable robust noise suppression and precise distance estimation. Results indicate that E-NMD outperforms the traditional N-th-Pole Magnetic Dipole (NMD) model in proximal state estimation, achieving a 39.62% reduction in Root Mean Square Error (RMSE). Finally, in light of parameter uncertainty in magnetic anomaly targets under real-world conditions, a Dual-Mode Pairwise Iterative Extended Kalman Filter (DI-EKF) is introduced to jointly estimate parameters and system states, yielding an 89% reduction in RMSE compared to AI-EKF. Full article
(This article belongs to the Special Issue Smart Magnetic Sensors and Applications)
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16 pages, 1713 KB  
Article
Development and Validation of a Kinetics Prediction Model for Football Cutting Using a Single Trunk-Mounted IMU
by Inae Kim, Soo-ji Han, Joong Hyun Ryu, Sanghyuk Han, Jinsung Yoon and Jongchul Park
Sensors 2026, 26(9), 2741; https://doi.org/10.3390/s26092741 - 28 Apr 2026
Viewed by 505
Abstract
This study aimed to estimate vertical ground reaction force (vGRF) and lower-limb joint moments during football cutting movements using a trunk-mounted inertial measurement unit (IMU) combined with a Random Forest model, and to validate the feasibility of this approach. IMU data collected during [...] Read more.
This study aimed to estimate vertical ground reaction force (vGRF) and lower-limb joint moments during football cutting movements using a trunk-mounted inertial measurement unit (IMU) combined with a Random Forest model, and to validate the feasibility of this approach. IMU data collected during 45° cutting tasks were corrected using an Extended Kalman Filter (EKF). The model demonstrated good and consistent performance for vGRF (coefficient of determination, R2 = 0.766; correlation coefficient, r = 0.796) and sagittal plane moments of the ankle and knee (R2 = 0.661–0.689, r = 0.807–0.842). While Bland–Altman analysis indicated low bias and generally good agreement, precision at the individual-trial level and accuracy for non-sagittal plane moments somewhat reflected the inherent within-player trial-to-trial variability in movement execution, particularly in non-sagittal loading patterns. It should be noted that performance estimates under the current trial-based validation design may differ from those obtained using a subject-independent framework such as leave-one-subject-out cross-validation. This study demonstrates that a single trunk-mounted IMU can reliably estimate key lower-limb loading patterns, providing a practical foundation for wearable-based kinetic monitoring in applied football settings. Full article
(This article belongs to the Section Wearables)
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