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Search Results (1,458)

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Keywords = Extended Kalman Filter

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25 pages, 3077 KB  
Article
GRACE-FO Real-Time Precise Orbit Determination Using Onboard GPS and Inter-Satellite Ranging Measurements with Quality Control Strategy
by Shengjian Zhong, Xiaoya Wang, Min Li, Jungang Wang, Peng Luo, Yabo Li and Houxiang Zhou
Remote Sens. 2026, 18(2), 351; https://doi.org/10.3390/rs18020351 - 20 Jan 2026
Abstract
Real-Time Precise Orbit Determination (RTPOD) of Low Earth Orbit (LEO) satellites relies primarily on onboard GNSS observations and may suffer from degraded performance when observation geometry weakens or tracking conditions deteriorate within satellite formations. To enhance the robustness and accuracy of RTPOD under [...] Read more.
Real-Time Precise Orbit Determination (RTPOD) of Low Earth Orbit (LEO) satellites relies primarily on onboard GNSS observations and may suffer from degraded performance when observation geometry weakens or tracking conditions deteriorate within satellite formations. To enhance the robustness and accuracy of RTPOD under such conditions, a cooperative Extended Kalman Filter (EKF) framework that fuses onboard GNSS and inter-satellite link (ISL) range measurements is established, integrated with an iterative Detection, Identification, and Adaptation (DIA) quality control algorithm. By introducing high-precision ISL range measurements, the strategy increases observation redundancy, improves the effective observation geometry, and provides strong relative position constraints among LEO satellites. This constraint strengthens solution stability and convergence, while simultaneously enhancing the sensitivity of the DIA-based quality control to observation outliers. The proposed strategy is validated in a simulated real-time environment using Centre National d’Etudes Spatiales (CNES) real-time products and onboard observations of the GRACE-FO mission. The results demonstrate comprehensive performance enhancements for both satellites over the experimental period. For the GRACE-D satellite, which suffers from about 17% data loss and a cycle slip ratio several times higher than that of GRACE-C, the mean orbit accuracy improves by 39% (from 13.1 cm to 8.0 cm), and the average convergence time is shortened by 44.3%. In comparison, the GRACE-C satellite achieves a 4.2% mean accuracy refinement and a 1.3% reduction in convergence time. These findings reveal a cooperative stabilization mechanism, where the high-precision spatiotemporal reference is transferred from the robust node to the degraded node via inter-satellite range measurements. This study demonstrates the effectiveness of the proposed method in enhancing the robustness and stability of formation orbit determination and provides algorithmic validation for future RTPOD of LEO satellite formations or large-scale constellations. Full article
22 pages, 7304 KB  
Article
Adaptive Trajectory-Constrained Heading Estimation for Tractor GNSS/SINS Integrated Navigation
by Shupeng Hu, Song Chen, Lihui Wang, Zhijun Meng, Weiqiang Fu, Yaxin Ren, Cunjun Li and Hao Wang
Sensors 2026, 26(2), 595; https://doi.org/10.3390/s26020595 - 15 Jan 2026
Viewed by 215
Abstract
Accurate heading estimation is crucial for the autonomous navigation of small-to-medium tractors. While dual-antenna GNSS systems offer precision, they face installation and safety challenges. Single-antenna GNSS integrated with a low-cost Strapdown Inertial Navigation System (SINS) presents a more adaptable solution but suffers from [...] Read more.
Accurate heading estimation is crucial for the autonomous navigation of small-to-medium tractors. While dual-antenna GNSS systems offer precision, they face installation and safety challenges. Single-antenna GNSS integrated with a low-cost Strapdown Inertial Navigation System (SINS) presents a more adaptable solution but suffers from slow convergence and low accuracy of heading estimation in low-speed farmland operations. This study proposes an adaptive trajectory-constrained heading estimation method. A sliding-window adaptive extended Kalman filter (SWAEKF) was developed, incorporating a heading constraint model that utilizes the GNSS-derived trajectory angle. An enhanced Sage–Husa algorithm was employed for the adaptive estimation of the trajectory angle measurement variance. Furthermore, a covariance initialization strategy based on the variance of trajectory angle increments was implemented to accelerate convergence. Field tests demonstrated that the proposed method achieved rapid heading convergence (less than 10 s for straight lines and 14 s for curves) and high accuracy (RMS heading error below 0.15° for straight-line tracking and 0.25° for curved paths). Compared to a conventional adaptive EKF, the SWAEKF improved accuracy by 23% and reduced convergence time by 62%. The proposed algorithm effectively enhances the performance of GNSS/SINS integrated navigation for tractors in low-dynamic environments, meeting the requirements for autonomous navigation systems. Full article
(This article belongs to the Section Navigation and Positioning)
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19 pages, 7967 KB  
Article
State-of-Charge Estimation of Lithium-Ion Batteries Based on GMMCC-AEKF in Non-Gaussian Noise Environment
by Fuxiang Li, Haifeng Wang, Hao Chen, Limin Geng and Chunling Wu
Batteries 2026, 12(1), 29; https://doi.org/10.3390/batteries12010029 - 14 Jan 2026
Viewed by 138
Abstract
To improve the accuracy and robustness of lithium-ion battery state of charge (SOC) estimation, this paper proposes a generalized mixture maximum correlation-entropy criterion-based adaptive extended Kalman filter (GMMCC-AEKF) algorithm, addressing the performance degradation of the traditional extended Kalman filter (EKF) under non-Gaussian noise [...] Read more.
To improve the accuracy and robustness of lithium-ion battery state of charge (SOC) estimation, this paper proposes a generalized mixture maximum correlation-entropy criterion-based adaptive extended Kalman filter (GMMCC-AEKF) algorithm, addressing the performance degradation of the traditional extended Kalman filter (EKF) under non-Gaussian noise and inaccurate initial conditions. Based on the GMMCC theory, the proposed algorithm introduces an adaptive mechanism and employs two generalized Gaussian kernels to construct a mixed kernel function, thereby formulating the generalized mixture correlation-entropy criterion. This enhances the algorithm’s adaptability to complex non-Gaussian noise. Simultaneously, by incorporating adaptive filtering concepts, the state and measurement covariance matrices are dynamically adjusted to improve stability under varying noise intensities and environmental conditions. Furthermore, the use of statistical linearization and fixed-point iteration techniques effectively improves both the convergence behavior and the accuracy of nonlinear system estimation. To investigate the effectiveness of the suggested method, experiments for SOC estimation were implemented using two lithium-ion cells featuring distinct rated capacities. These tests employed both dynamic stress test (DST) and federal test procedure (FTP) profiles under three representative temperature settings: 40 °C, 25 °C, and 10 °C. The experimental findings prove that when exposed to non-Gaussian noise, the GMMCC-AEKF algorithm consistently outperforms both the traditional EKF and the generalized mixture maximum correlation-entropy-based extended Kalman filter (GMMCC-EKF) under various test conditions. Specifically, under the 25 °C DST profile, GMMCC-AEKF improves estimation accuracy by 86.54% and 10.47% over EKF and GMMCC-EKF, respectively, for the No. 1 battery. Under the FTP profile for the No. 2 battery, it achieves improvements of 55.89% and 28.61%, respectively. Even under extreme temperatures (10 °C, 40 °C), GMMCC-AEKF maintains high accuracy and stable convergence, and the algorithm demonstrates rapid convergence to the true SOC value. In summary, the GMMCC-AEKF confirms excellent estimation accuracy under various temperatures and non-Gaussian noise conditions, contributing a practical approach for accurate SOC estimation in power battery systems. Full article
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20 pages, 3704 KB  
Article
Accurate Position and Orientation Estimation for UWB-Only Systems Using a Single Dual-Antenna Module
by Che Zhang, Yan Li and Peng Han
Electronics 2026, 15(2), 369; https://doi.org/10.3390/electronics15020369 - 14 Jan 2026
Viewed by 137
Abstract
This paper proposes a complete cascade pipeline for accurate position and orientation estimation using a single dual-antenna UWB module. First, an extended Kalman filter (EKF) fuses distance measurements from multiple anchors to estimate the agent’s position. The estimated position is then used to [...] Read more.
This paper proposes a complete cascade pipeline for accurate position and orientation estimation using a single dual-antenna UWB module. First, an extended Kalman filter (EKF) fuses distance measurements from multiple anchors to estimate the agent’s position. The estimated position is then used to derive orientation. To overcome the critical challenge of front–back ambiguity in orientation estimation, we introduce a novel method that integrates a multi-hypothesis testing (MHT) framework with a circular likelihood metric (CLM). This method enumerates all feasible angle of arrival (AoA) hypotheses via MHT and assesses their consistency using the CLM, thereby selecting the most probable hypothesis to resolve ambiguity. Comparative simulations demonstrate that this “position-first, orientation-later” cascade enhances robustness over joint optimization by preventing the propagation of AoA noise to the position estimates. Extensive evaluations, including high-precision rotary table experiment and real-world field trials, validate the system’s efficacy in providing precise location and heading information. This work delivers a complete, low-cost, and robust solution for autonomous navigation in challenging environments. Full article
(This article belongs to the Special Issue Advanced Indoor Localization Technologies: From Theory to Application)
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34 pages, 719 KB  
Article
Prototype of Hydrochemical Regime Monitoring System for Fish Farms
by Sergiy Ivanov, Oleksandr Korchenko, Grzegorz Litawa, Pavlo Oliinyk and Olena Oliinyk
Sensors 2026, 26(2), 497; https://doi.org/10.3390/s26020497 - 12 Jan 2026
Viewed by 169
Abstract
This paper presents a prototype of an autonomous hydrochemical monitoring system developed for large freshwater aquaculture facilities, directly addressing the need for smart monitoring in Agriculture 4.0. The proposed solution employs low-power sensor nodes based on commercially available components and long-range LoRaWAN communication [...] Read more.
This paper presents a prototype of an autonomous hydrochemical monitoring system developed for large freshwater aquaculture facilities, directly addressing the need for smart monitoring in Agriculture 4.0. The proposed solution employs low-power sensor nodes based on commercially available components and long-range LoRaWAN communication to achieve continuous, scalable, and energy-efficient water quality monitoring. Each sensor module performs on-board signal preprocessing, including anomaly detection and short-term forecasting of key hydrochemical parameters. An ecological pond dynamics model incorporating an Extended Kalman Filter is used to fuse heterogeneous sensor data with predictive estimates, thus increasing measurement reliability. High-level data analysis, long-term storage, and cross-site comparison are performed on the server side. This integration enables adaptive tracking of environmental variations, supports early detection of hazardous trends associated with fish mortality risks, and allows one to explain and justify the reasoning behind every recommended corrective action. The performance of the forecasting and filtering algorithms is evaluated, and key system characteristics—including measurement accuracy, power consumption, and scalability—are discussed. Preliminary tests of the system prototype have shown that it can predict the dissolved oxygen level with RMSE = 0.104 mg/L even with a minimum set of sensors. The results demonstrate that the proposed conceptual design of the system can be used as a base for real-time monitoring and predictive assessment of hydrochemical conditions in aquaculture environments. Full article
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16 pages, 3701 KB  
Article
Real-Time Sensorless Speed Control of PMSMs Using a Runge–Kutta Extended Kalman Filter
by Adile Akpunar Bozkurt
Mathematics 2026, 14(2), 274; https://doi.org/10.3390/math14020274 - 12 Jan 2026
Viewed by 180
Abstract
Permanent magnet synchronous motors (PMSMs) are widely preferred in modern applications due to their high efficiency, high torque-to-inertia ratio, high power factor, and rapid dynamic response. Achieving optimal PMSM performance requires precise control, which depends on accurate estimation of motor speed and rotor [...] Read more.
Permanent magnet synchronous motors (PMSMs) are widely preferred in modern applications due to their high efficiency, high torque-to-inertia ratio, high power factor, and rapid dynamic response. Achieving optimal PMSM performance requires precise control, which depends on accurate estimation of motor speed and rotor position. This information is traditionally obtained through sensors such as encoders; however, these devices increase system cost and introduce size and integration constraints, limiting their use in many PMSM-based applications. To overcome these limitations, sensorless control strategies have gained significant attention. Since PMSMs inherently exhibit nonlinear dynamic behavior, accurate modeling of these nonlinearities is essential for reliable sensorless operation. In this study, a Runge–Kutta Extended Kalman Filter (RKEKF) approach is developed and implemented to enhance estimation accuracy for both rotor position and speed. The developed method utilizes the applied stator voltages and measured phase currents to estimate the motor states. Experimental validation was conducted on the dSPACE DS1104 platform under various operating conditions, including forward and reverse rotation, acceleration, low- and high-speed operation, and loaded operation. Furthermore, the performance of the developed RKEKF under load was compared with the conventional Extended Kalman Filter (EKF), demonstrating its improved estimation capability. The real-time feasibility of the developed RKEKF was experimentally verified through execution-time measurements on the dSPACE DS1104 platform, where the conventional EKF and the RKEKF required 47 µs and 55 µs, respectively, confirming that the proposed approach remains suitable for real-time PMSM control while accommodating the additional computational effort associated with Runge–Kutta integration. Full article
(This article belongs to the Special Issue Nonlinear Dynamical Systems: Modeling, Control and Applications)
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30 pages, 5328 KB  
Article
DTVIRM-Swarm: A Distributed and Tightly Integrated Visual-Inertial-UWB-Magnetic System for Anchor Free Swarm Cooperative Localization
by Xincan Luo, Xueyu Du, Shuai Yue, Yunxiao Lv, Lilian Zhang, Xiaofeng He, Wenqi Wu and Jun Mao
Drones 2026, 10(1), 49; https://doi.org/10.3390/drones10010049 - 9 Jan 2026
Viewed by 221
Abstract
Accurate Unmanned Aerial Vehicle (UAV) positioning is vital for swarm cooperation. However, this remains challenging in situations where Global Navigation Satellite System (GNSS) and other external infrastructures are unavailable. To address this challenge, we propose to use only the onboard Microelectromechanical System Inertial [...] Read more.
Accurate Unmanned Aerial Vehicle (UAV) positioning is vital for swarm cooperation. However, this remains challenging in situations where Global Navigation Satellite System (GNSS) and other external infrastructures are unavailable. To address this challenge, we propose to use only the onboard Microelectromechanical System Inertial Measurement Unit (MIMU), Magnetic sensor, Monocular camera and Ultra-Wideband (UWB) device to construct a distributed and anchor-free cooperative localization system by tightly fusing the measurements. As the onboard UWB measurements under dynamic motion conditions are noisy and discontinuous, we propose an adaptive adjustment method based on chi-squared detection to effectively filter out inconsistent and false ranging information. Moreover, we introduce the pose-only theory to model the visual measurement, which improves the efficiency and accuracy for visual-inertial processing. A sliding window Extended Kalman Filter (EKF) is constructed to tightly fuse all the measurements, which is capable of working under UWB or visual deprived conditions. Additionally, a novel Multidimensional Scaling-MAP (MDS-MAP) initialization method fuses ranging, MIMU, and geomagnetic data to solve the non-convex optimization problem in ranging-aided Simultaneous Localization and Mapping (SLAM), ensuring fast and accurate swarm absolute pose initialization. To overcome the state consistency challenge inherent in the distributed cooperative structure, we model not only the UWB noisy uncertainty but also the neighbor agent’s position uncertainty in the measurement model. Furthermore, we incorporate the Covariance Intersection (CI) method into our UWB measurement fusion process to address the challenge of unknown correlations between state estimates from different UAVs, ensuring consistent and robust state estimation. To validate the effectiveness of the proposed methods, we have established both simulation and hardware test platforms. The proposed method is compared with state-of-the-art (SOTA) UAV localization approaches designed for GNSS-challenged environments. Extensive experiments demonstrate that our algorithm achieves superior positioning accuracy, higher computing efficiency and better robustness. Moreover, even when vision loss causes other methods to fail, our proposed method continues to operate effectively. Full article
(This article belongs to the Special Issue Autonomous Drone Navigation in GPS-Denied Environments)
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18 pages, 3663 KB  
Article
Trajectory Tracking Control of a Six-Axis Robotic Manipulator Based on an Extended Kalman Filter-Based State Observer
by Jianxuan Liu, Tao Chen, Zhen Dou, Xiaojuan Li and Xiangjun Zou
Machines 2026, 14(1), 78; https://doi.org/10.3390/machines14010078 - 8 Jan 2026
Viewed by 192
Abstract
To achieve high-precision trajectory tracking for multi-joint robotic manipulators in the presence of model uncertainties, external disturbances, and strong coupling effects, this paper proposes a nonsingular fast terminal sliding mode control (NFTSMC) scheme incorporating an extended Kalman filter-based disturbance observer. First, the Kalman [...] Read more.
To achieve high-precision trajectory tracking for multi-joint robotic manipulators in the presence of model uncertainties, external disturbances, and strong coupling effects, this paper proposes a nonsingular fast terminal sliding mode control (NFTSMC) scheme incorporating an extended Kalman filter-based disturbance observer. First, the Kalman filter is combined with an extended state observer to perform the real-time observation of both internal and external disturbances in the system, accurately estimating system uncertainty and external disturbances. This approach reduces noise interference while significantly improving the correction accuracy of position and tracking errors. Second, an improved nonsingular fast terminal sliding mode controller with an optimized convergence law is introduced to ensure stability during the tracking process, effectively mitigate oscillation phenomena, and accelerate the system’s convergence speed. Finally, the convergence of the proposed method is analyzed by constructing an appropriate Lyapunov function. Simulation and experimental results strongly validate the superior performance of the proposed control strategy, demonstrating that the system can achieve high-precision trajectory tracking under the complex coupled effects of a six-axis robotic manipulator, and exhibits significant advantages in terms of accuracy and robustness. Full article
(This article belongs to the Special Issue Sensing to Cognition: The Evolution of Robotic Vision)
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24 pages, 7136 KB  
Article
Extended Kalman Filter-Enhanced LQR for Balance Control of Wheeled Bipedal Robots
by Renyi Zhou, Yisheng Guan, Tie Zhang, Shouyan Chen, Jingfu Zheng and Xingyu Zhou
Machines 2026, 14(1), 77; https://doi.org/10.3390/machines14010077 - 8 Jan 2026
Viewed by 170
Abstract
With the rapid development of mobile robotics, wheeled bipedal robots, which combine the terrain adaptability of legged robots with the high mobility of wheeled systems, have attracted increasing research attention. To address the balance control problem during both standing and locomotion while reducing [...] Read more.
With the rapid development of mobile robotics, wheeled bipedal robots, which combine the terrain adaptability of legged robots with the high mobility of wheeled systems, have attracted increasing research attention. To address the balance control problem during both standing and locomotion while reducing the influence of noise on control performance, this paper proposes a balance control framework based on a Linear Quadratic Regulator integrated with an Extended Kalman Filter (KLQR). Specifically, a baseline LQR controller is designed using the robot’s dynamic model, where the control input is generated in the form of wheel-hub motor torques. To mitigate measurement noise and suppress oscillatory behavior, an Extended Kalman Filter is applied to smooth the LQR torque output, which is then used as the final control command. Filtering experiments demonstrate that, compared with median filtering and other baseline methods, the proposed EKF-based approach significantly reduces high-frequency torque fluctuations. In particular, the peak-to-peak torque variation is reduced by more than 60%, and large-amplitude torque spikes observed in the baseline LQR controller are effectively eliminated, resulting in continuous and smooth torque output. Static balance experiments show that the proposed KLQR algorithm reduces the pitch-angle oscillation amplitude from approximately ±0.03 rad to ±0.01 rad, corresponding to an oscillation reduction of about threefold. The estimated RMS value of the pitch angle is reduced from approximately 0.010 rad to 0.003 rad, indicating improved convergence and steady-state stability. Furthermore, experiments involving constant-speed straight-line locomotion and turning indicate that the KLQR algorithm maintains stable motion with velocity fluctuations limited to within ±0.05 m/s. The lateral displacement deviation during locomotion remains below 0.02 m, and no abrupt acceleration or deceleration is observed throughout the experiments. Overall, the results demonstrate that applying Extended Kalman filtering to smooth the control torque effectively improves the smoothness and stability of LQR-based balance control for wheeled bipedal robots. Full article
(This article belongs to the Section Robotics, Mechatronics and Intelligent Machines)
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50 pages, 3579 KB  
Article
Safety-Aware Multi-Agent Deep Reinforcement Learning for Adaptive Fault-Tolerant Control in Sensor-Lean Industrial Systems: Validation in Beverage CIP
by Apolinar González-Potes, Ramón A. Félix-Cuadras, Luis J. Mena, Vanessa G. Félix, Rafael Martínez-Peláez, Rodolfo Ostos, Pablo Velarde-Alvarado and Alberto Ochoa-Brust
Technologies 2026, 14(1), 44; https://doi.org/10.3390/technologies14010044 - 7 Jan 2026
Viewed by 293
Abstract
Fault-tolerant control in safety-critical industrial systems demands adaptive responses to equipment degradation, parameter drift, and sensor failures while maintaining strict operational constraints. Traditional model-based controllers struggle under these conditions, requiring extensive retuning and dense instrumentation. Recent safe multi-agent reinforcement learning (MARL) frameworks with [...] Read more.
Fault-tolerant control in safety-critical industrial systems demands adaptive responses to equipment degradation, parameter drift, and sensor failures while maintaining strict operational constraints. Traditional model-based controllers struggle under these conditions, requiring extensive retuning and dense instrumentation. Recent safe multi-agent reinforcement learning (MARL) frameworks with control barrier functions (CBFs) achieve real-time constraint satisfaction in robotics and power systems, yet assume comprehensive state observability—incompatible with sensor-hostile industrial environments where instrumentation degradation and contamination risks dominate design constraints. This work presents a safety-aware multi-agent deep reinforcement learning framework for adaptive fault-tolerant control in sensor-lean industrial environments, achieving formal safety through learned implicit barriers under partial observability. The framework integrates four synergistic mechanisms: (1) multi-layer safety architecture combining constrained action projection, prioritized experience replay, conservative training margins, and curriculum-embedded verification achieving zero constraint violations; (2) multi-agent coordination via decentralized execution with learned complementary policies. Additional components include (3) curriculum-driven sim-to-real transfer through progressive four-stage learning achieving 85–92% performance retention without fine-tuning; (4) offline extended Kalman filter validation enabling 70% instrumentation reduction (91–96% reconstruction accuracy) for regulatory auditing without real-time estimation dependencies. Validated through sustained deployment in commercial beverage manufacturing clean-in-place (CIP) systems—a representative safety-critical testbed with hard flow constraints (≥1.5 L/s), harsh chemical environments, and zero-tolerance contamination requirements—the framework demonstrates superior control precision (coefficient of variation: 2.9–5.3% versus 10% industrial standard) across three hydraulic configurations spanning complexity range 2.1–8.2/10. Comprehensive validation comprising 37+ controlled stress-test campaigns and hundreds of production cycles (accumulated over 6 months) confirms zero safety violations, high reproducibility (CV variation < 0.3% across replicates), predictable complexity–performance scaling (R2=0.89), and zero-retuning cross-topology transferability. The system has operated autonomously in active production for over 6 months, establishing reproducible methodology for safe MARL deployment in partially-observable, sensor-hostile manufacturing environments where analytical CBF approaches are structurally infeasible. Full article
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26 pages, 3302 KB  
Article
An Autonomous Land Vehicle Navigation System Based on a Wheel-Mounted IMU
by Shuang Du, Wei Sun, Xin Wang, Yuyang Zhang, Yongxin Zhang and Qihang Li
Sensors 2026, 26(1), 328; https://doi.org/10.3390/s26010328 - 4 Jan 2026
Viewed by 383
Abstract
Navigation errors due to drifting in inertial systems using low-cost sensors are some of the main challenges for land vehicle navigation in Global Navigation Satellite System (GNSS)-denied environments. In this paper, we propose an autonomous navigation strategy with a wheel-mounted microelectromechanical system (MEMS) [...] Read more.
Navigation errors due to drifting in inertial systems using low-cost sensors are some of the main challenges for land vehicle navigation in Global Navigation Satellite System (GNSS)-denied environments. In this paper, we propose an autonomous navigation strategy with a wheel-mounted microelectromechanical system (MEMS) inertial measurement unit (IMU), referred to as the wheeled inertial navigation system (INS), to effectively suppress drifted navigation errors. The position, velocity, and attitude (PVA) of the vehicle are predicted through the inertial mechanization algorithm, while gyro outputs are utilized to derive the vehicle’s forward velocity, which is treated as an observation with non-holonomic constraints (NHCs) to estimate the inertial navigation error states. To establish a theoretical foundation for wheeled INS error characteristics, a comprehensive system observability analysis is conducted from an analytical point of view. The wheel rotation significantly improves the observability of gyro errors perpendicular to the rotation axis, which effectively suppresses azimuth errors, horizontal velocity, and position errors. This leads to the superior navigation performance of a wheeled INS over the traditional odometer (OD)/NHC/INS. Moreover, a hybrid extended particle filter (EPF), which fuses the extended Kalman filter (EKF) and PF, is proposed to update the vehicle’s navigation states. It has the advantages of (1) dealing with the system’s non-linearity and non-Gaussian noises, and (2) simultaneously achieving both a high level of accuracy in its estimation and tolerable computational complexity. Kinematic field test results indicate that the proposed wheeled INS is able to provide an accurate navigation solution in GNSS-denied environments. When a total distance of over 26 km is traveled, the maximum position drift rate is only 0.47% and the root mean square (RMS) of the heading error is 1.13°. Full article
(This article belongs to the Section Navigation and Positioning)
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37 pages, 11112 KB  
Article
Adaptive Dynamic Prediction-Based Cooperative Interception Control Algorithm for Multi-Type Unmanned Surface Vessels
by Yuan Liu, Bowen Tang, Lingyun Lu, Zhiqing Bai, Guoxing Li, Shikun Geng and Xirui Xu
J. Mar. Sci. Eng. 2026, 14(1), 88; https://doi.org/10.3390/jmse14010088 - 2 Jan 2026
Viewed by 357
Abstract
In the dynamic marine environment, the high mobility of intrusion targets, complex interference, and insufficient multi-vessel coordination accuracy pose significant challenges to the cooperative interception mission of multiple unmanned surface vehicles (USVs). This paper proposes an adaptive dynamic prediction-based cooperative interception control algorithm [...] Read more.
In the dynamic marine environment, the high mobility of intrusion targets, complex interference, and insufficient multi-vessel coordination accuracy pose significant challenges to the cooperative interception mission of multiple unmanned surface vehicles (USVs). This paper proposes an adaptive dynamic prediction-based cooperative interception control algorithm and establishes a “mission planning—anti-interference control—phased coordination” system. Specifically, it ensures interception accuracy through threat-level-oriented target assignment and extended Kalman filter multi-step prediction, offsets environmental interference by separating the cooperative encirclement and anti-interference modules using an improved Two-stage architecture, and optimizes the movement of nodes to form a stable blockade through the “target navigation—cooperative encirclement” strategy. Simulation results show that in a 1000 m × 1000 m mission area, the node trajectory deviation is reduced by 40% and the heading angle fluctuation is decreased by 50, compared with the limit cycle encirclement algorithm, the average interception time is shortened by 15% and the average final distance between the intrusion target and the guarded target is increased by 20%, when the target attempts to escape, the relevant collision rates are all below 0.3%. The TFMUSV framework ensures the stable optimization of the algorithm and significantly improves the efficiency and reliability of multi-USV cooperative interception in complex scenarios. This paper provides a highly adaptable technical solution for practical tasks such as maritime security and anti-smuggling. Full article
(This article belongs to the Section Ocean Engineering)
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25 pages, 5206 KB  
Article
Nonlinear Probabilistic Model Predictive Control Design for Obstacle Avoiding Uncrewed Surface Vehicles
by Nurettin Çerçi and Yaprak Yalçın
Automation 2026, 7(1), 10; https://doi.org/10.3390/automation7010010 - 1 Jan 2026
Viewed by 186
Abstract
The primary objective of this research is to develop a probabilistic nonlinear model predictive control structure (NMPC) that efficiently operates uncrewed surface vehicles (USVs) in an environment that has probabilistic disturbances, such as wind, waves, and currents of the water, while simultaneously maneuvering [...] Read more.
The primary objective of this research is to develop a probabilistic nonlinear model predictive control structure (NMPC) that efficiently operates uncrewed surface vehicles (USVs) in an environment that has probabilistic disturbances, such as wind, waves, and currents of the water, while simultaneously maneuvering the vehicle in a way that avoids stationary or moving stochastic obstacles in its path. The proposed controller structure considers the mean and covariances of the inputs or state variables of the vehicle in the cost function to handle probabilistic disturbances, where an extended Kalman filter (EKF) is utilized to calculate the mean, and the covariances are calculated dynamically via a linear matrix equality based on this mean and obtained system matrices with successive linearization for every sampling instance. The proposed control structure deals with non-zero-mean probabilistic disturbances such as water current via an innovative approach that treats the mean of the disturbance as a deterministic part, which is estimated by a disturbance observer and eliminated by a control term in the controller in addition to the control signal obtained via MPC optimization; the effect of the remaining zero-mean part is handled over its covariance during the probabilistic MPC optimization. The probabilistic constraints are also dealt with by converting them to deterministic constraints, as in linear probabilistic MPC. However, unlike the linear MPC, these constraints updated each sampling instance with the information obtained via successive linearization. The control structure incorporates the velocity obstacle (VO) method for collision avoidance. In order to ensure stability, the proposed NMPC adopts a dual-mode strategy, and a stability analysis is presented. In the second mode, an LQG design that ensures stability in the existence of non-zero mean disturbance is also provided. The simulation results demonstrate that the proposed probabilistic NMPC framework effectively handles probabilistic disturbances as well as both stationary and moving obstacles, ensuring collision avoidance while reaching the desired position and orientation through optimal path tracking, outperforming the conventional NMPC. Full article
(This article belongs to the Section Control Theory and Methods)
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17 pages, 921 KB  
Article
Lightweight Kalman Spoofing Detection in Platoons of Vehicles
by Dimitrios Kosmanos, Zisis-Rafail Tzoannos, Apostolos Xenakis and Costas Chaikalis
Electronics 2026, 15(1), 205; https://doi.org/10.3390/electronics15010205 - 1 Jan 2026
Viewed by 438
Abstract
Spoofing attacks remain among the most critical security threats in Connected and Autonomous Vehicles (CAVs). This work introduces a lightweight, two-level spoofing detection framework based on Kalman filtering, designed for real-time deployment in vehicular platoons that communicate over Dedicated Short-Range Communications (DSRC). At [...] Read more.
Spoofing attacks remain among the most critical security threats in Connected and Autonomous Vehicles (CAVs). This work introduces a lightweight, two-level spoofing detection framework based on Kalman filtering, designed for real-time deployment in vehicular platoons that communicate over Dedicated Short-Range Communications (DSRC). At the first level, a heuristic residual-based detector identifies abnormal measurement deviations using adaptive statistical thresholds. At the second level, a Mahalanobis distance test assesses model consistency using covariance-aware anomaly scoring at a 95% confidence level. The combination of these complementary mechanisms enables both rapid alerting and robust statistical verification without the need for machine-learning training or centralized processing. Simulation results from 20 independent nodes demonstrate that the proposed approach achieves an average F1-score of 0.92 and Area Under the ROC Curve (AUC) of 0.72, outperforming standalone detectors while maintaining low computational cost. Compared with deep learning and adaptive Extended Kalman Filter (EKF) approaches, the proposed framework achieves similar detection performance while substantially reducing computational complexity and enabling full real-time operation, making it suitable for embedded in-vehicle security modules. Full article
(This article belongs to the Special Issue Cyber Security, Design and Applications in Smart Systems)
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33 pages, 5065 KB  
Article
Delay-Compensated EKF and Adaptive Delay Threshold Weighting for AUV–MDS Docking
by Han Yan and Shuxue Yan
J. Mar. Sci. Eng. 2026, 14(1), 86; https://doi.org/10.3390/jmse14010086 - 1 Jan 2026
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Abstract
This study tackles real-time state estimation for autonomous underwater vehicle (AUV)–mobile docking station (MDS) cooperation over low-bandwidth, high-latency, jitter-dominated acoustic links, with the goal of turning delayed/out-of-sequence measurements (OOSM) into consistent and informative constraints without sacrificing online operation. We propose an integrated scheme [...] Read more.
This study tackles real-time state estimation for autonomous underwater vehicle (AUV)–mobile docking station (MDS) cooperation over low-bandwidth, high-latency, jitter-dominated acoustic links, with the goal of turning delayed/out-of-sequence measurements (OOSM) into consistent and informative constraints without sacrificing online operation. We propose an integrated scheme centered on a delay-compensated extended Kalman filter (DC-EKF): a ring buffer enables backward updates and forward replay so that OOSM are absorbed strictly at their physical timestamps; a data-driven delay threshold is learned from “effective information gain” combined with normalized estimation error squared (NEES) filtering; and dynamic confidence, derived from innovation statistics, delay, and signal-to-noise ratio (SNR) proxies, scales the measurement noise to adapt fusion weights. Simulations show the learned delay threshold converges to about 6.4 s (final 6.35 s), error spikes are suppressed, and the overall position root-mean-square error (RMSE) is 5.751 m; across the full data stream, 1067 station measurements were accepted and 30 rejected, and the fusion weights shifted smoothly from inertial measurement unit (IMU)-dominant to station-dominant (≈0.16/0.84) over time. On this basis, a cooperative augmented EKF (Co-Aug-EKF) is added as a lightweight upper layer for unified-frame cooperative estimation, further improving relative consistency. The results indicate that the framework reliably maps delayed acoustic measurements into closed-loop useful information, significantly enhancing estimator stability and docking readiness, while remaining practical to deploy and readily extensible. Full article
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