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Keywords = error state Kalman

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30 pages, 6687 KB  
Article
A Novel Shallow Neural Network-Augmented Pose Estimator Based on Magneto-Inertial Sensors for Reference-Denied Environments
by Akos Odry, Peter Sarcevic, Giuseppe Carbone, Peter Odry and Istvan Kecskes
Sensors 2025, 25(22), 6864; https://doi.org/10.3390/s25226864 - 10 Nov 2025
Abstract
Magnetic, angular rate, and gravity (MARG) sensor-based inference is the de facto standard for mobile robot pose estimation, yet its sensor limitations necessitate fusion with absolute references. In environments where such references are unavailable, the system must rely solely on the uncertain MARG-based [...] Read more.
Magnetic, angular rate, and gravity (MARG) sensor-based inference is the de facto standard for mobile robot pose estimation, yet its sensor limitations necessitate fusion with absolute references. In environments where such references are unavailable, the system must rely solely on the uncertain MARG-based inference, posing significant challenges due to the resulting estimation uncertainties. This paper addresses the challenge of enhancing the accuracy of position/velocity estimations based on the fusion of MARG sensor data with shallow neural network (NN) models. The proposed methodology develops and trains a feasible cascade-forward NN to reliably estimate the true acceleration of dynamical systems. Three types of NNs are developed for acceleration estimation. The effectiveness of each topology is comprehensively evaluated in terms of input combinations of MARG measurements and signal features, number of hidden layers, and number of neurons. The proposed approach also incorporates extended Kalman and gradient descent orientation filters during the training process to further improve estimation effectiveness. Experimental validation is conducted through a case study on position/velocity estimation for a low-cost flying quadcopter. This process utilizes a comprehensive database of random dynamic flight maneuvers captured and processed in an experimental test environment with six degrees of freedom (6DOF), where both raw MARG measurements and ground truth data (three positions and three orientations) of system states are recorded. The proposed approach significantly enhances the accuracy in calculating the rotation matrix-based acceleration vector. The Pearson correlation coefficient reaches 0.88 compared to the reference acceleration, surpassing 0.73 for the baseline method. This enhancement ensures reliable position/velocity estimations even during typical quadcopter maneuvers within 10-s timeframes (flying 50 m), with a position error margin ranging between 2 to 4 m when evaluated across a diverse set of representative quadcopter maneuvers. The findings validate the engineering feasibility and effectiveness of the proposed approach for pose estimation in GPS-denied or landmark-deficient environments, while its application in unknown environments constitutes the main future research direction. Full article
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27 pages, 2523 KB  
Article
Robust Vehicle Pose Estimation Through Multi-Sensor Fusion of Camera, IMU, and GPS Using LSTM and Kalman Filter
by Tae-Hyeok Jeong, Yong-Jun Lee, Woo-Jin Ahn, Tae-Koo Kang and Myo-Taeg Lim
Appl. Sci. 2025, 15(22), 11863; https://doi.org/10.3390/app152211863 - 7 Nov 2025
Viewed by 154
Abstract
Accurate vehicle localization remains a critical challenge due to the frequent loss or degradation of sensor data, such as from visual, inertial, and GPS sources. In this study, we present a novel localization algorithm that dynamically fuses data from heterogeneous sensors to achieve [...] Read more.
Accurate vehicle localization remains a critical challenge due to the frequent loss or degradation of sensor data, such as from visual, inertial, and GPS sources. In this study, we present a novel localization algorithm that dynamically fuses data from heterogeneous sensors to achieve stable and precise positioning. The proposed algorithm integrates a deep learning-based visual-inertial odometry (VIO) module with a Kalman filter for global data fusion. A key innovation of the method is its adaptive fusion strategy, which adjusts feature weights based on sensor reliability, thereby ensuring optimal data utilization. Extensive experiments across varied scenarios demonstrate the algorithm’s superior performance, consistently achieving lower RMSE values and reducing position errors by 79–91% compared to four state-of-the-art baselines—even under adverse conditions such as sensor failures or missing data. This work lays the foundation for deploying robust localization systems in real-world applications, including autonomous vehicles, robotics, and navigation technologies. Full article
(This article belongs to the Special Issue AI-Aided Intelligent Vehicle Positioning in Urban Areas)
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16 pages, 1252 KB  
Article
HAR-RV-CARMA: A Kalman Filter-Weighted Hybrid Model for Enhanced Volatility Forecasting
by Chigozie Andy Ngwaba
Risks 2025, 13(11), 223; https://doi.org/10.3390/risks13110223 - 6 Nov 2025
Viewed by 297
Abstract
This paper introduces a new hybrid model, HAR-RV-CARMA, which combines the Heterogeneous Autoregressive model for Realized Volatility (HAR-RV) with the Continuous Autoregressive Moving Average (CARMA) model. The key innovation of this study lies in the use of a Kalman filter-based dynamic state weighting [...] Read more.
This paper introduces a new hybrid model, HAR-RV-CARMA, which combines the Heterogeneous Autoregressive model for Realized Volatility (HAR-RV) with the Continuous Autoregressive Moving Average (CARMA) model. The key innovation of this study lies in the use of a Kalman filter-based dynamic state weighting mechanism to optimally combine the predictive capabilities of both models while mitigating overfitting. The proposed model is applied to five major Covered Call Exchange-Traded Funds (ETFs), QYLD, XYLD, RYLD, JEPI, and JEPQ, utilizing daily realized volatility data from 2019 to 2024. Model performance is evaluated against standalone HAR-RV and CARMA models using metrics such as Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Quasi-Likelihood (QLIKE), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). Additionally, the study assesses directional accuracy and conducts a Diebold-Mariano test to compare forecast performance against the standalone models statistically. Empirical results suggest that the HAR-RV-CARMA hybrid model significantly outperforms both HAR-RV and CARMA in volatility forecasting across all evaluation criteria. It achieves lower forecast errors, superior goodness-of-fit, and higher directional accuracy, with Diebold-Mariano test outcomes rejecting the null hypothesis of equal predictive ability at significant levels. These findings highlight the effectiveness of dynamic model weighting in improving predictive accuracy and offer a strong framework for volatility modeling in financial markets. Full article
(This article belongs to the Special Issue Risk Management in Financial and Commodity Markets)
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27 pages, 1702 KB  
Article
A Comparative Study of the DEKF and DUKF for Battery SOC and SOH Estimation
by Arash Seifoddini, Federico Miretti and Daniela Anna Misul
Batteries 2025, 11(11), 410; https://doi.org/10.3390/batteries11110410 - 5 Nov 2025
Viewed by 267
Abstract
The accurate estimation of the state of charge (SOC) and state of health (SOH) is essential for the safety and reliability of electric vehicle batteries. Conventional single-state Kalman filters are prone to parameter drift caused by cell aging, which leads to persistent SOC [...] Read more.
The accurate estimation of the state of charge (SOC) and state of health (SOH) is essential for the safety and reliability of electric vehicle batteries. Conventional single-state Kalman filters are prone to parameter drift caused by cell aging, which leads to persistent SOC estimation errors. This study compares two dual-estimator methods, the Dual Extended Kalman Filter (DEKF) and the Dual Unscented Kalman Filter (DUKF), for simultaneous SOC and SOH estimation using a second-order equivalent-circuit model. The process and measurement covariance matrices were tuned through a structured optimization procedure to ensure consistent performance under different drive cycles and initialization errors. To mitigate the weak voltage sensitivity to capacity, synthetic SOC–capacity coupling was introduced to enhance SOH observability and accelerate convergence. Simulations conducted under the Urban Dynamometer Driving Schedule (UDDS) and a real-world CLUST7 profile demonstrated SOC root-mean-square errors near 2% for both filters. The DUKF achieved faster and smoother convergence than the DEKF but required roughly fivefold higher computational cost. These findings provide quantitative evidence supporting dual Kalman filtering as an effective framework for accurate and robust SOC/SOH estimation in production battery management systems. Full article
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20 pages, 1597 KB  
Article
Three-Level MIFT: A Novel Multi-Source Information Fusion Waterway Tracking Framework
by Wanqing Liang, Chen Qiu, Mei Wang and Ruixiang Kan
Electronics 2025, 14(21), 4344; https://doi.org/10.3390/electronics14214344 - 5 Nov 2025
Viewed by 193
Abstract
To address the limitations of single-sensor perception in inland vessel monitoring and the lack of robustness of traditional tracking methods in occlusion and maneuvering scenarios, this paper proposes a hierarchical multi-target tracking framework that fuses Light Detection and Ranging (LiDAR) data with Automatic [...] Read more.
To address the limitations of single-sensor perception in inland vessel monitoring and the lack of robustness of traditional tracking methods in occlusion and maneuvering scenarios, this paper proposes a hierarchical multi-target tracking framework that fuses Light Detection and Ranging (LiDAR) data with Automatic Identification System (AIS) information. First, an improved adaptive LiDAR tracking algorithm is introduced: stable trajectory tracking and state estimation are achieved through hybrid cost association and an Adaptive Kalman Filter (AKF). Experimental results demonstrate that the LiDAR module achieves a Multi-Object Tracking Accuracy (MOTA) of 89.03%, an Identity F1 Score (IDF1) of 89.80%, and an Identity Switch count (IDSW) as low as 5.1, demonstrating competitive performance compared with representative non-deep-learning-based approaches. Furthermore, by incorporating a fusion mechanism based on improved Dempster–Shafer (D-S) evidence theory and Covariance Intersection (CI), the system achieves further improvements in MOTA (90.33%) and IDF1 (90.82%), while the root mean square error (RMSE) of vessel size estimation decreases from 3.41 m to 1.97 m. Finally, the system outputs structured three-level tracks: AIS early-warning tracks, LiDAR-confirmed tracks, and LiDAR-AIS fused tracks. This hierarchical design not only enables beyond-visual-range (BVR) early warning but also enhances perception coverage and estimation accuracy. Full article
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20 pages, 1442 KB  
Article
High-Precision Positioning in Power Applications Using BDS PPP-RTK for Sparse Reference Station Areas
by Xianguo Yan, Mingjie Yang, Chi Zhang, Siyuan Du and Gang Xu
Appl. Sci. 2025, 15(21), 11803; https://doi.org/10.3390/app152111803 - 5 Nov 2025
Viewed by 168
Abstract
To address the urgent demand for high-precision positioning in power industry operations within sparse reference station areas, this paper proposes a real-time kinematic positioning method integrating BeiDou multi-antenna Precise Point Positioning–Real-Time Kinematic (PPP-RTK) with inertial measurement unit (IMU) assistance. By combining the strengths [...] Read more.
To address the urgent demand for high-precision positioning in power industry operations within sparse reference station areas, this paper proposes a real-time kinematic positioning method integrating BeiDou multi-antenna Precise Point Positioning–Real-Time Kinematic (PPP-RTK) with inertial measurement unit (IMU) assistance. By combining the strengths of Precise Point Positioning (PPP) and Real-Time Kinematic (RTK) technologies, we establish a multi-antenna observation model based on State Space Representation (SSR), incorporating satellite-based augmentation signals and atmospheric correction information from sparse reference station networks. Lie group theory is employed to enhance the Extended Kalman Filter (EKF) for simultaneous estimation of position, attitude, and ambiguity parameters. The integration of IMU measurements significantly improves robustness against environmental interference in dynamic scenarios. Experimental results demonstrate average positioning errors of 3.12 cm, 3.71 cm, and 6.23 cm in the East, North, and Up (ENU) directions, respectively, with an average convergence time of 1.62 min. Compared with non-IMU-augmented single-antenna PPP-RTK solutions, the proposed method achieves accuracy improvements up to 59.6% while maintaining stability in signal-occluded environments. This approach provides centimeter-level real-time positioning support for critical power grid operations in remote areas such as desert and Gobi regions, including infrastructure inspection and precise tower assembly, thereby significantly improving the efficiency of intelligent grid operation and maintenance. Full article
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20 pages, 3365 KB  
Article
Time-Varying Current Estimation Method for SINS/DVL Integrated Navigation Based on Augmented Observation Algorithm
by Xin Chen, Hongwei Bian, Fangneng Li, Rongying Wang, Yaojin Hu and Jingshu Li
Symmetry 2025, 17(11), 1881; https://doi.org/10.3390/sym17111881 - 5 Nov 2025
Viewed by 201
Abstract
To address the problem of the bottom velocity being directly affected by the time-varying ocean currents when DVL operates in the water observation mode, it cannot be directly used for combined SINS/DVL navigation. Existing methods generally approximate small-scale, short-term currents as constant; however, [...] Read more.
To address the problem of the bottom velocity being directly affected by the time-varying ocean currents when DVL operates in the water observation mode, it cannot be directly used for combined SINS/DVL navigation. Existing methods generally approximate small-scale, short-term currents as constant; however, this assumption is inconsistent with reality over longer durations. When the conventional Kalman filter (KF) algorithm incorporates currents into the state vector, their velocities become entangled with the SINS errors, limiting estimation accuracy. This paper proposes an augmented observation algorithm (AOA) that achieves error decoupling by enhancing DVL observation and deriving the observable current velocity equation without needing external observation information. This approach effectively estimates time-varying currents. The results from simulations and shipboard tests show that, compared to the reference algorithm (Augmented Observation Quantity Filtering algorithm (AOQ)), the proposed AOA significantly decreases the root mean square error (RMSE) of time-varying current velocity estimation by more than 67%. Additionally, the RMSE of the positioning accuracy of the combined SINS/DVL navigation is improved by over 68%. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Optimization Algorithms and Systems Control)
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26 pages, 3748 KB  
Article
State of Charge Estimation for Lithium-Ion Batteries: An Online Method Combining Deep Neural Network and Adaptive Kalman Filter
by Hongwen Xu, Feng Zhao and Yun Guo
Processes 2025, 13(11), 3559; https://doi.org/10.3390/pr13113559 - 5 Nov 2025
Viewed by 396
Abstract
Electric vehicles (EVs) powered by lithium-ion batteries are crucial for sustainable transportation. Accurate State of Charge (SOC) estimation, a core function of Battery Management Systems (BMS), enhances battery performance, lifespan, and safety. This paper proposes a hybrid CNN-LSTM-AKF model integrating Convolutional Neural Networks [...] Read more.
Electric vehicles (EVs) powered by lithium-ion batteries are crucial for sustainable transportation. Accurate State of Charge (SOC) estimation, a core function of Battery Management Systems (BMS), enhances battery performance, lifespan, and safety. This paper proposes a hybrid CNN-LSTM-AKF model integrating Convolutional Neural Networks (CNN) and Long Short-Term Memory (LSTM) Neural Networks with an Adaptive Kalman Filter. CNN extracts spatial features from current, voltage, and temperature data, while LSTM processes temporal dependencies. AKF reduces output fluctuations. Trained on datasets under three operating conditions, the model was tested across various temperatures and initial SOC states. Results demonstrate that the proposed model significantly outperforms standalone LSTM and LSTM-AKF model, particularly at low temperatures. Within 0 °C to 50 °C, it achieves Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) below 1.51% and 1.18%, respectively. With an initial SOC of 80%, the model achieves an RMSE of 1.09% and MAE of 0.88%, showing rapid convergence. The model exhibits high accuracy, strong adaptability, and robust performance. Full article
(This article belongs to the Section Energy Systems)
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14 pages, 5265 KB  
Article
Non-Line-of-Sight Error Compensation Method for Ultra-Wideband Positioning System
by Bin Liang, Xuechuang Zhu, Tonggang Liu and Guangpeng Shan
Machines 2025, 13(11), 1018; https://doi.org/10.3390/machines13111018 - 3 Nov 2025
Viewed by 240
Abstract
Existing Ultra-Wideband (UWB) positioning methods are poorly suited for underground mobile devices and have limited positioning effectiveness in complex scenarios such as narrow tunnels, high dust levels, metallic structures, moving personnel, and machinery. To address this, we propose a UWB positioning method for [...] Read more.
Existing Ultra-Wideband (UWB) positioning methods are poorly suited for underground mobile devices and have limited positioning effectiveness in complex scenarios such as narrow tunnels, high dust levels, metallic structures, moving personnel, and machinery. To address this, we propose a UWB positioning method for non-line-of-sight (NLOS) error compensation, significantly improving the positioning accuracy of mobile equipment in coal mine tunnels. First, the characteristics of the impulse response waveform channel of the dataset are extracted, and the AdaBoost-based ensemble learning method is used to identify the mixture propagation channel. Then, combined with the UWB range noise model, the extended Kalman filter (EKF) algorithm is used to compensate for UWB NLOS errors. Finally, a mobile tag is used in conjunction with four positioning base stations to obtain positioning data, and the positioning effect in coal mine tunnels is simulated using a ranging noise model. The experimental results show that the EKF error compensation algorithm has good positioning accuracy and algorithm stability in different motion states in a noisy environment. Full article
(This article belongs to the Section Vehicle Engineering)
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45 pages, 5566 KB  
Article
Strengthening Structural Dynamics for Upcoming Eurocode 8 Seismic Standards Using Physics-Informed Machine Learning
by Ahad Amini Pishro, Konstantinos Daniel Tsavdaridis, Yuetong Liu and Shiquan Zhang
Buildings 2025, 15(21), 3960; https://doi.org/10.3390/buildings15213960 - 2 Nov 2025
Viewed by 396
Abstract
Structural dynamics analysis is essential for predicting the behavior of engineering systems under dynamic forces. This study presents a hybrid framework that combines analytical modeling, machine learning, and optimization techniques to enhance the accuracy and efficiency of dynamic response predictions for Single-Degree-of-Freedom (SDOF) [...] Read more.
Structural dynamics analysis is essential for predicting the behavior of engineering systems under dynamic forces. This study presents a hybrid framework that combines analytical modeling, machine learning, and optimization techniques to enhance the accuracy and efficiency of dynamic response predictions for Single-Degree-of-Freedom (SDOF) systems subjected to harmonic excitation. Utilizing a classical spring–mass–damper model, Fourier decomposition is applied to derive transient and steady-state responses, highlighting the effects of damping, resonance, and excitation frequency. To overcome the uncertainties and limitations of traditional models, Extended Kalman Filters (EKFs) and Physics-Informed Neural Networks (PINNs) are incorporated, enabling precise parameter estimation even with sparse and noisy measurements. This paper uses Adam followed by LBFGS to improve accuracy while limiting runtime. Numerical experiments using 1000 time samples with a 0.01 s sampling interval demonstrate that the proposed PINN model achieves a displacement MSE of 0.0328, while the Eurocode 8 response-spectrum estimation yields 0.047, illustrating improved predictive performance under noisy conditions and biased initial guesses. Although the present study focuses on a linear SDOF system under harmonic excitation, it establishes a conceptual foundation for adaptive dynamic modeling that can be extended to performance-based seismic design and to future calibration of Eurocode 8. The harmonic framework isolates the fundamental mechanisms of amplitude modulation and damping adaptation, providing a controlled environment for validating the proposed PINN–EKF approach before its application to transient seismic inputs. Controlled-variable analyses further demonstrate that key dynamic parameters can be estimated with relative errors below 1%—specifically 0.985% for damping, 0.391% for excitation amplitude, and 0.692% for excitation frequency—highlighting suitability for real-time diagnostics, vibration-sensitive infrastructure, and data-driven design optimization. This research deepens our understanding of vibratory behavior and supports future developments in smart monitoring, adaptive control, resilient design, and structural code modernization. Full article
(This article belongs to the Section Building Structures)
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18 pages, 10509 KB  
Article
High-Precision Mapping and Real-Time Localization for Agricultural Machinery Sheds and Farm Access Roads Environments
by Yang Yu, Zengyao Li, Buwang Dai, Jiahui Pan and Lizhang Xu
Agriculture 2025, 15(21), 2248; https://doi.org/10.3390/agriculture15212248 - 28 Oct 2025
Viewed by 337
Abstract
To address the issues of signal loss and insufficient accuracy of traditional GNSS (Global Navigation Satellite System) navigation in agricultural machinery sheds and farm access road environments, this paper proposes a high-precision mapping method for such complex environments and a real-time localization system [...] Read more.
To address the issues of signal loss and insufficient accuracy of traditional GNSS (Global Navigation Satellite System) navigation in agricultural machinery sheds and farm access road environments, this paper proposes a high-precision mapping method for such complex environments and a real-time localization system for agricultural vehicles. First, an autonomous navigation system was developed by integrating multi-sensor data from LiDAR (Light Laser Detection and Ranging), GNSS, and IMU (Inertial Measurement Unit), with functional modules for mapping, localization, planning, and control implemented within the ROS (Robot Operating System) framework. Second, an improved LeGO-LOAM algorithm is introduced for constructing maps of machinery sheds and farm access roads. The mapping accuracy is enhanced through reflectivity filtering, ground constraint optimization, and ScanContext-based loop closure detection. Finally, a localization method combining NDT (Normal Distribution Transform), IMU, and a UKF (Unscented Kalman Filter) is proposed for tracked grain transport vehicles. The UKF and IMU measurements are used to predict the vehicle state, while the NDT algorithm provides pose estimates for state update, yielding a fused and more accurate pose estimate. Experimental results demonstrate that the proposed mapping method reduces APE (absolute pose error) by 79.99% and 49.04% in the machinery sheds and farm access roads environments, respectively, indicating a significant improvement over conventional methods. The real-time localization module achieves an average processing time of 26.49 ms with an average error of 3.97 cm, enhancing localization accuracy without compromising output frequency. This study provides technical support for fully autonomous operation of agricultural machinery. Full article
(This article belongs to the Topic Digital Agriculture, Smart Farming and Crop Monitoring)
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25 pages, 6545 KB  
Article
Collaborative Estimation of Lithium Battery State of Charge Based on the BiLSTM-AUKF Fusion Model
by Rui Wang, Lele Liu, Honghou Zhang, Qifeng Qian, Lingchao Xiao, Qiansheng Qiu, Chao Tan and Fujian Yang
Energies 2025, 18(21), 5624; https://doi.org/10.3390/en18215624 - 26 Oct 2025
Viewed by 329
Abstract
To address the issue of decreased accuracy in lithium battery state of charge (SOC) estimation caused by parameter mismatches, modeling error accumulation, and sensitivity to noise, this paper proposes a collaborative estimation method. The proposed method combines a Bayesian optimization (BO)-tuned dual-input bidirectional [...] Read more.
To address the issue of decreased accuracy in lithium battery state of charge (SOC) estimation caused by parameter mismatches, modeling error accumulation, and sensitivity to noise, this paper proposes a collaborative estimation method. The proposed method combines a Bayesian optimization (BO)-tuned dual-input bidirectional long short-term memory network (BiLSTM) with an adaptive unscented Kalman filter (AUKF) based on the Sage–Husa adaptive strategy. First, a dual-input BiLSTM network is constructed using a multi-layer cascaded BiLSTM to extract time-dependent features. This network fuses both temporal and static features to perform an initial SOC prediction, while BO is employed to adaptively optimize the network’s hyperparameters. Second, the BiLSTM prediction outputs and the physical model are incorporated into the AUKF framework to achieve real-time iterative SOC estimation. Multi-scenario experiments conducted on the University of Maryland CALCE battery dataset demonstrated that the proposed method achieved a mean absolute error (MAE) below 0.6% and a root mean square error (RMSE) less than 0.8%. This method effectively enhances the robustness and noise immunity of SOC estimation in dynamic scenarios, providing a high-precision state estimation solution for battery management systems. Full article
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21 pages, 1876 KB  
Article
Adaptive Minimum Error Entropy Cubature Kalman Filter in UAV-Integrated Navigation Systems
by Xuhang Liu, Hongli Zhao, Yicheng Liu, Suxing Ling, Xinhanyang Chen, Chenyu Yang and Pei Cao
Drones 2025, 9(11), 740; https://doi.org/10.3390/drones9110740 - 24 Oct 2025
Viewed by 338
Abstract
Small unmanned aerial vehicles are now commonly equipped with integrated navigation systems to obtain high-precision navigation parameters. However, affected by the dual impacts of multipath effects and dynamic environmental changes, their state estimation process is vulnerable to interference from measurement outliers, which in [...] Read more.
Small unmanned aerial vehicles are now commonly equipped with integrated navigation systems to obtain high-precision navigation parameters. However, affected by the dual impacts of multipath effects and dynamic environmental changes, their state estimation process is vulnerable to interference from measurement outliers, which in turn leads to the degradation of navigation accuracy and poses a threat to flight safety. To address this issue, this research presents an adaptive minimum error entropy cubature Kalman filter. Firstly, the cubature Kalman filter is introduced to solve the problem of model nonlinear errors; secondly, the cubature Kalman filter based on minimum error entropy is derived to effectively curb the interference that measurement outliers impose on filtering results; finally, a kernel bandwidth adjustment factor is designed, and the kernel bandwidth is estimated adaptively to further improve navigation accuracy. Through numerical simulation experiments, the robustness of the proposed method with respect to measurement outliers is validated; further flight experiment results show that compared with existing related filters, this proposed filter can achieve more accurate navigation and positioning. Full article
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18 pages, 3538 KB  
Article
Deep Learning-Assisted ES-EKF for Surface AUV Navigation with SINS/GPS/DVL Integration
by Yuanbo Yang, Bo Xu, Baodong Ye and Feimo Li
J. Mar. Sci. Eng. 2025, 13(11), 2035; https://doi.org/10.3390/jmse13112035 - 23 Oct 2025
Viewed by 390
Abstract
This study presents a deep learning–assisted integrated navigation scheme implemented on an autonomous underwater vehicle carrying a Chinese domestically developed strapdown inertial navigation system, designed for operation in surface and littoral environments. The system integrates measurements from SINS, the global positioning system, and [...] Read more.
This study presents a deep learning–assisted integrated navigation scheme implemented on an autonomous underwater vehicle carrying a Chinese domestically developed strapdown inertial navigation system, designed for operation in surface and littoral environments. The system integrates measurements from SINS, the global positioning system, and a Doppler velocity log, while integrating a Decoder-based covariance estimator into the error state-extended Kalman filter. This hybrid architecture adaptively models time-varying processes and measurement noise from raw sensor inputs, greatly improving robustness for surface navigation in dynamic marine environments. To improve learning efficiency, we design a compact and informative feature representation that can be adapted to navigation error dynamics. The novel structure captures temporal dependencies and the evolution of nonlinear error more effectively than typical sequence models, achieving faster convergence and superior accuracy compared to GRU and Transformer baselines. The experimental results based on real sea trial data show that our method significantly outperforms model-based and learning-based methods in terms of navigation solution accuracy and stability, and the adaptive estimation of noise covariance. Specifically, it achieves the lowest RMSE of 0.0274, reducing errors by 94.6–34.6%, compared to conventional ES-EKF-integrated navigation, Transformer, GRU, and a DCE variant. These findings underscore the practical significance of integrating domain-informed filtering methodologies with deep noise modeling frameworks to achieve robust and accurate AUV surface navigation. Full article
(This article belongs to the Section Ocean Engineering)
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14 pages, 2289 KB  
Article
FPGA Implementation of Battery State-of-Charge Estimation Using Extended Kalman Filter and Dynamic Sampling
by Seungjae Yun, Jeongju Jeon, Eunseong Lee, Taeyeon Jeong and Sunhee Kim
World Electr. Veh. J. 2025, 16(10), 587; https://doi.org/10.3390/wevj16100587 - 20 Oct 2025
Viewed by 590
Abstract
The rapid increase in the adoption of electric vehicles (EVs) has highlighted issues related to the safety and efficiency of lithium-ion batteries. This study implemented a hardware module to effectively estimate the state of charge (SOC), which is a core element of the [...] Read more.
The rapid increase in the adoption of electric vehicles (EVs) has highlighted issues related to the safety and efficiency of lithium-ion batteries. This study implemented a hardware module to effectively estimate the state of charge (SOC), which is a core element of the battery management system (BMS), using an extended Kalman filter (EKF)-based approach. A method to reduce the power consumption during hardware design through adjustments to the sampling period according to the SOC range was proposed. The root mean square error was obtained as below 0.75, with only 2455 samples out of the 700,000 measurements, achieving a reduction of 99.65%. Following the evaluation of the accuracy of the software model, the results were compared through hardware implementation. Consequently, the performance was verified via synthesis using a DE2-115 FPGA board from Terasic in Taiwan. Full article
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