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Keywords = inertial stability accuracy

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27 pages, 21019 KiB  
Article
A UWB-AOA/IMU Integrated Navigation System for 6-DoF Indoor UAV Localization
by Pengyu Zhao, Hengchuan Zhang, Gang Liu, Xiaowei Cui and Mingquan Lu
Drones 2025, 9(8), 546; https://doi.org/10.3390/drones9080546 (registering DOI) - 1 Aug 2025
Abstract
With the increasing deployment of unmanned aerial vehicles (UAVs) in indoor environments, the demand for high-precision six-degrees-of-freedom (6-DoF) localization has grown significantly. Ultra-wideband (UWB) technology has emerged as a key enabler for indoor UAV navigation due to its robustness against multipath effects and [...] Read more.
With the increasing deployment of unmanned aerial vehicles (UAVs) in indoor environments, the demand for high-precision six-degrees-of-freedom (6-DoF) localization has grown significantly. Ultra-wideband (UWB) technology has emerged as a key enabler for indoor UAV navigation due to its robustness against multipath effects and high-accuracy ranging capabilities. However, conventional UWB-based systems primarily rely on range measurements, operate at low measurement frequencies, and are incapable of providing attitude information. This paper proposes a tightly coupled error-state extended Kalman filter (TC–ESKF)-based UWB/inertial measurement unit (IMU) fusion framework. To address the challenge of initial state acquisition, a weighted nonlinear least squares (WNLS)-based initialization algorithm is proposed to rapidly estimate the UAV’s initial position and attitude under static conditions. During dynamic navigation, the system integrates time-difference-of-arrival (TDOA) and angle-of-arrival (AOA) measurements obtained from the UWB module to refine the state estimates, thereby enhancing both positioning accuracy and attitude stability. The proposed system is evaluated through simulations and real-world indoor flight experiments. Experimental results show that the proposed algorithm outperforms representative fusion algorithms in 3D positioning and yaw estimation accuracy. Full article
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23 pages, 2015 KiB  
Article
ASA-PSO-Optimized Elman Neural Network Model for Predicting Mechanical Properties of Coarse-Grained Soils
by Haijuan Wang, Jiang Li, Yufei Zhao and Biao Liu
Processes 2025, 13(8), 2447; https://doi.org/10.3390/pr13082447 (registering DOI) - 1 Aug 2025
Abstract
Coarse-grained soils serve as essential fill materials in earth–rock dam engineering, where their mechanical properties critically influence dam deformation and stability, directly impacting project safety. Artificial intelligence (AI) techniques are emerging as powerful tools for predicting the mechanical properties of coarse-grained soils. However, [...] Read more.
Coarse-grained soils serve as essential fill materials in earth–rock dam engineering, where their mechanical properties critically influence dam deformation and stability, directly impacting project safety. Artificial intelligence (AI) techniques are emerging as powerful tools for predicting the mechanical properties of coarse-grained soils. However, AI-based prediction models for these properties face persistent challenges, particularly in parameter tuning—a process requiring substantial computational resources, extensive time, and specialized expertise. To address these limitations, this study proposes a novel prediction model that integrates Adaptive Simulated Annealing (ASA) with an improved Particle Swarm Optimization (PSO) algorithm to optimize the Elman Neural Network (ENN). The methodology encompasses three key aspects: First, the standard PSO algorithm is enhanced by dynamically adjusting its inertial weight and learning factors. The ASA algorithm is then employed to optimize the Adaptive PSO (APSO), effectively mitigating premature convergence and local optima entrapment during training, thereby ensuring convergence to the global optimum. Second, the refined PSO algorithm optimizes the ENN, overcoming its inherent limitations of slow convergence and susceptibility to local minima. Finally, validation through real-world engineering case studies demonstrates that the ASA-PSO-optimized ENN model achieves high accuracy in predicting the mechanical properties of coarse-grained soils. This model provides reliable constitutive parameters for stress–strain analysis in earth–rock dam engineering applications. Full article
(This article belongs to the Section Particle Processes)
24 pages, 4820 KiB  
Article
Real-Time Wing Deformation Monitoring via Distributed Fiber Bragg Grating and Adaptive Federated Filtering
by Zhen Ma, Xiyuan Chen, Cundeng Wang and Bingbo Cui
Sensors 2025, 25(14), 4343; https://doi.org/10.3390/s25144343 - 11 Jul 2025
Viewed by 220
Abstract
To address the issues of decreased accuracy and poor stability in distributed transfer alignment caused by factors such as wing deflection and deformation in complex flight environments, this paper proposes a wing-distributed transfer alignment method based on Fiber Bragg Grating (FBG). This paper [...] Read more.
To address the issues of decreased accuracy and poor stability in distributed transfer alignment caused by factors such as wing deflection and deformation in complex flight environments, this paper proposes a wing-distributed transfer alignment method based on Fiber Bragg Grating (FBG). This paper establishes a flexural deformation model based on FBGs, establishes a coupling angle model and a dynamic lever arm model, derives the motion parameter relationship model between the main and the sub-nodes, establishes the corresponding transfer alignment filter, and proposes a federated adaptive filter based on allocation coefficients and an updated federated adaptive filter. The results show that the federated adaptive filtering algorithm based on allocation coefficients improved the pitch angle accuracy of the Inertial Measurement Unit (IMU) by 66.38% and the position estimation accuracy by 75.67%, compared to traditional algorithms. The arm estimation accuracy was also improved in the east and sky directions. Compared with traditional algorithms, the updated federated adaptive filtering algorithm improved the pitch angle accuracy of the sub IMU by 76.72%, the position estimation accuracy by 63.51%, and the lever arm estimation accuracy. Full article
(This article belongs to the Special Issue INS/GNSS Integrated Navigation Systems)
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20 pages, 3148 KiB  
Article
Performance Analysis of Stellar Refraction Autonomous Navigation for Cross-Domain Vehicles
by Yuchang Xu, Yang Zhang, Xiaokang Wang, Guanbing Zhang, Guang Yang and Hong Yuan
Remote Sens. 2025, 17(14), 2367; https://doi.org/10.3390/rs17142367 - 9 Jul 2025
Viewed by 273
Abstract
Stellar refraction autonomous navigation provides a promising alternative for cross-domain vehicles, particularly in near-space environments where traditional inertial and satellite navigation methods face limitations. This study develops a stellar refraction navigation system that utilizes stellar refraction angle observations and the Implicit Unscented Kalman [...] Read more.
Stellar refraction autonomous navigation provides a promising alternative for cross-domain vehicles, particularly in near-space environments where traditional inertial and satellite navigation methods face limitations. This study develops a stellar refraction navigation system that utilizes stellar refraction angle observations and the Implicit Unscented Kalman Filter (IUKF) for state estimation. A representative orbit with altitudes ranging from 60 km to 200 km is designed to simulate cross-domain flight conditions. The navigation performance is analyzed under varying conditions, including orbital altitude, as well as star sensor design parameters, such as limiting magnitude, field of view (FOV) value, and measurement error, along with different sampling intervals. The simulation results show that increasing the limiting magnitude from 5 to 8 reduced the position error from 705.19 m to below 1 m, with optimal accuracy reaching 0.89 m when using a 20° × 20° field of view and a 3 s sampling interval. In addition, shorter sampling intervals improved accuracy and filter stability, while longer intervals introduced greater integration drift. When the sampling interval reached 100 s, position error grew to the kilometer level. These findings validate the feasibility of using stellar refraction for autonomous navigation in cross-domain scenarios and provide design guidance for optimizing star sensor configurations and sampling strategies in future near-space navigation systems. Full article
(This article belongs to the Special Issue Autonomous Space Navigation (Second Edition))
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20 pages, 6735 KiB  
Article
Quantification of 3D Kinematic Measurements for Knee Flexion and Tibial Rotation Using an IMU-Based Sensor and Ultrasound Imaging System: A Cadaveric Study
by Hamid Rahmatullah Bin Abd Razak, Nicolas Chua and Kah Weng Lai
Sensors 2025, 25(13), 4211; https://doi.org/10.3390/s25134211 - 6 Jul 2025
Viewed by 407
Abstract
Knee rotational stability is crucial for anterior cruciate ligament (ACL) procedures, yet, current clinical assessments are subjective and lack precision. This study evaluates the accuracy and repeatability of the GATOR system, developed by PreciX Pte Ltd. and integrating ultrasound with inertial measurement units [...] Read more.
Knee rotational stability is crucial for anterior cruciate ligament (ACL) procedures, yet, current clinical assessments are subjective and lack precision. This study evaluates the accuracy and repeatability of the GATOR system, developed by PreciX Pte Ltd. and integrating ultrasound with inertial measurement units (IMUs), against a reference IMU (Xsens DOTS) for measuring knee flexion and rotation in six cadaveric specimens secured in an Oxford Knee Jig. Two experiments were conducted: (A) knee flexion from 0° to 120°, and (B) internal/external rotation at 0°, 30°, 60°, 90°, and 120° flexion. Analysis using Bland–Altman plots, root mean square error (RMSE: 3.93° for internal rotation, 6.90° for external rotation), mean biases, and paired t-tests (Bonferroni corrected) revealed that GATOR recorded lower peak flexion angles (91.49–114.65°) compared to the reference (110.31–118.49°). For rotation, internal rotation showed narrower limits of agreement than external rotation (biases: 1.91–6.88°). Over 60% of trials had errors < 5°, and 80% < 10°, indicating good agreement. Despite no isolated comparison of GATOR’s ultrasound component, findings suggest reduced soft tissue artifact due to bone-referenced sensor alignment. With optimal placement (10–15 cm from the knee center), GATOR shows promise in ACL assessment and remote rehabilitation. Full article
(This article belongs to the Section Wearables)
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19 pages, 4219 KiB  
Article
Schur Complement Optimized Iterative EKF for Visual–Inertial Odometry in Autonomous Vehicles
by Guo Ma, Cong Li, Hui Jing, Bing Kuang, Ming Li, Xiang Wang and Guangyu Jia
Machines 2025, 13(7), 582; https://doi.org/10.3390/machines13070582 - 4 Jul 2025
Viewed by 237
Abstract
Accuracy and nonlinear processing capabilities are critical to the positioning and navigation of autonomous vehicles in visual–inertial odometry (VIO). Existing filtering-based VIO methods struggle to deal with strongly nonlinear systems and often exhibit low precision. To this end, this paper proposes a VIO [...] Read more.
Accuracy and nonlinear processing capabilities are critical to the positioning and navigation of autonomous vehicles in visual–inertial odometry (VIO). Existing filtering-based VIO methods struggle to deal with strongly nonlinear systems and often exhibit low precision. To this end, this paper proposes a VIO method based on the Schur complement and Iterated Extended Kalman Filtering (IEKF). The algorithm first enhances ORB (Oriented FAST and Rotated BRIEF) features using Multi-Layer Perceptron (MLP) and Transformer architectures to improve feature robustness. It then integrates visual information and Inertial Measurement Unit (IMU) data through IEKF, constructing a complete residual model. The Schur complement is applied during covariance updates to compress the state dimension, improving computational efficiency and significantly enhancing the system’s ability to handle nonlinearities while maintaining real-time performance. Compared to traditional Extended Kalman Filtering (EKF), the proposed method demonstrates stronger stability and accuracy in high-dynamic scenarios. The experimental results show that the algorithm achieves superior state estimation performance on several typical visual–inertial datasets, demonstrating excellent accuracy and robustness. Full article
(This article belongs to the Topic Advances in Mobile Robotics Navigation, 2nd Volume)
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31 pages, 8354 KiB  
Article
The Design and Experiment of a Motion Control System for the Whole-Row Reciprocating Seedling Picking Mechanism of an Automatic Transplanter
by Jiawei Shi, Jianping Hu, Wei Liu, Junpeng Lv, Yongwang Jin, Mengjiao Yao and Che Wang
Agriculture 2025, 15(13), 1423; https://doi.org/10.3390/agriculture15131423 - 30 Jun 2025
Viewed by 335
Abstract
Aiming at the problem that the whole row of reciprocating seedling picking mechanism is prone to inertial impacts during operation due to its excessive mass, causing seedling damage and positioning errors, this study builds a motion control system with a PLC controller as [...] Read more.
Aiming at the problem that the whole row of reciprocating seedling picking mechanism is prone to inertial impacts during operation due to its excessive mass, causing seedling damage and positioning errors, this study builds a motion control system with a PLC controller as the core and proposes a composite motion control strategy based on planned S-curve acceleration and deceleration and fuzzy PID to achieve rapid response, precise positioning, and smooth operation of the seedling picking mechanism. By establishing the objective function and constraint conditions and taking into account the dynamic change of the seedling picking displacement, the S-curve acceleration and deceleration control algorithm is planned in six and seven stages to meet the requirements of a smooth transition of the speed and continuous change of the acceleration curve of the seedling picking mechanism during movement. A fuzzy PID positioning control system is designed, the control system transfer function is constructed, and fuzzy rules are formulated to dynamically compensate for the error and its rate of change to meet the requirements of fast response and no overshoot oscillation of the positioning control system. The speed and acceleration of the seedling picking mechanism under the six-segment and seven-segment S-curve acceleration and deceleration motion control conditions were simulated using MATLAB2024a simulation software and compared with the trapezoidal acceleration and deceleration motion control. The planned S-curve acceleration and deceleration control algorithm has a more stable control effect on the seedling picking mechanism when it operates under the conditions of the dynamic change of the displacement, and it meets the design requirements of seedling picking efficiency. The positioning control system was modeled and simulated using the Simulink simulation platform. When KP = 15, KI = 3, and KD = 1, the whole-row seedling picking control system ran stably, responded quickly, and had no overshoot. Compared with the PID control system with fixed parameters, the fuzzy PID control system reduced the time consumption in the rising stage by 24.5% and shortened the overall stabilization process by 17.6%. The zero overshoot characteristic was ensured, and the response speed was faster. When a disturbance signal is added, the overshoot of the fuzzy PID control system is reduced by 2.4%, and the response speed is increased by 6.8% compared with the fixed-parameter PID control system. The dynamic response rate and anti-disturbance performance are better than those of the fixed-parameter PID control system. A bench comparison test was carried out. The results showed that the S-curve acceleration and deceleration motion control algorithm reduced the average mass loss rate of seedlings by 46.19% compared with the trapezoidal acceleration and deceleration motion control algorithm, and the seedling picking efficiency met the design requirements. Fuzzy PID positioning control was used, and the maximum displacement error of the end effector during seedling picking was −1.4 mm, and the average relative error rate was 0.22%, which met the positioning accuracy requirements of the end effector in the X-axis direction and verified the stability and accuracy of the designed control system. The designed control system was tested in the field, and the average comprehensive success rate of seedling picking and throwing reached 96.2%, which verified the feasibility and practicality of the control system. Full article
(This article belongs to the Special Issue Soil-Machine Systems and Its Related Digital Technologies Application)
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29 pages, 4413 KiB  
Article
Advancing Road Infrastructure Safety with the Remotely Piloted Safety Cone
by Francisco Javier García-Corbeira, David Alvarez-Moyano, Pedro Arias Sánchez and Joaquin Martinez-Sanchez
Infrastructures 2025, 10(7), 160; https://doi.org/10.3390/infrastructures10070160 - 27 Jun 2025
Viewed by 439
Abstract
This article presents the design, implementation, and validation of a Remotely Piloted Safety Cone (RPSC), an autonomous robotic system developed to enhance safety and operational efficiency in road maintenance. The RPSC addresses challenges associated with road works, including workers’ exposure to traffic hazards [...] Read more.
This article presents the design, implementation, and validation of a Remotely Piloted Safety Cone (RPSC), an autonomous robotic system developed to enhance safety and operational efficiency in road maintenance. The RPSC addresses challenges associated with road works, including workers’ exposure to traffic hazards and inefficiencies of traditional traffic cones, such as manual placement and retrieval, limited visibility in low-light conditions, and inability to adapt to dynamic changes in work zones. In contrast, the RPSC offers autonomous mobility, advanced visual signalling, and real-time communication capabilities, significantly improving safety and operational flexibility during maintenance tasks. The RPSC integrates sensor fusion, combining Global Navigation Satellite System (GNSS) with Real-Time Kinematic (RTK) for precise positioning, Inertial Measurement Unit (IMU) and encoders for accurate odometry, and obstacle detection sensors within an optimised navigation framework using Robot Operating System (ROS2) and Micro Air Vehicle Link (MAVLink) protocols. Complying with European regulations, the RPSC ensures structural integrity, visibility, stability, and regulatory compliance. Safety features include emergency stop capabilities, visual alarms, autonomous safety routines, and edge computing for rapid responsiveness. Field tests validated positioning accuracy below 30 cm, route deviations under 15 cm, and obstacle detection up to 4 m, significantly improved by Kalman filtering, aligning with digitalisation, sustainability, and occupational risk prevention objectives. Full article
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20 pages, 4215 KiB  
Article
The Novel Gravity-Matching Algorithm Based on Modified Adaptive Transformed Cubature Quaternion Estimation for Underwater Navigation
by Tiangao Zhu, Fangjun Qin, An Li, Kailong Li, Jiujiang Yan and Leiyuan Qian
J. Mar. Sci. Eng. 2025, 13(6), 1150; https://doi.org/10.3390/jmse13061150 - 10 Jun 2025
Viewed by 306
Abstract
Gravity matching is a key technology in gravity-aided inertial navigation. The traditional Sandia inertial matching algorithm introduces linearization errors using the linear error model, which can diminish navigation accuracy. To address this issue, we propose a novel gravity-matching algorithm based on modified adaptive [...] Read more.
Gravity matching is a key technology in gravity-aided inertial navigation. The traditional Sandia inertial matching algorithm introduces linearization errors using the linear error model, which can diminish navigation accuracy. To address this issue, we propose a novel gravity-matching algorithm based on modified adaptive transformed cubature quaternion estimation (MA-TCQUE), designed for a nonlinear error model to enhance accuracy in gravity-aided navigation. Additionally, the proposed algorithm can estimate the measurement noise matrix demonstrating improved filtering stability in complex and dynamic environments. Finally, simulation and experimental results validate the advantages of the proposed matching algorithm compared to existing state-of-the-art methods. Full article
(This article belongs to the Section Ocean Engineering)
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17 pages, 11508 KiB  
Article
Adaptive Neural Network Robust Control of FOG with Output Constraints
by Shangbo Liu, Baowang Lian, Jiajun Ma, Xiaokun Ding and Haiyan Li
Biomimetics 2025, 10(6), 372; https://doi.org/10.3390/biomimetics10060372 - 5 Jun 2025
Viewed by 355
Abstract
In this work, an adaptive robust control method based on Radial Basis Function Neural Network (RBFNN) is proposed. Inspired by the local response characteristics of biological neurons, this method can reduce the influence of nonlinear errors and unknown perturbations in the extreme working [...] Read more.
In this work, an adaptive robust control method based on Radial Basis Function Neural Network (RBFNN) is proposed. Inspired by the local response characteristics of biological neurons, this method can reduce the influence of nonlinear errors and unknown perturbations in the extreme working conditions of the aircraft, such as high dynamics and strong vibration, so as to achieve high tracking accuracy. In this method, the dynamic model of the nonlinear error of the fiber optic gyroscope is proposed, and then the unknown external interference observer is designed for the system to realize the estimation of the unknown disturbances. The controller design method combines the design of the adaptive law outside the finite approximation domain of the achievable condition design of the sliding mode surface, and adjusts the controller parameters online according to the conditions satisfied by the real-time error state, breaking through the limitation of the finite approximation domain of the traditional neural network. In the finite approximation domain, an online adaptive controller is constructed by using the universal approximation ability of RBFNN, so as to enhance the robustness to nonlinear errors and external disturbances. By designing the output constraint mechanism, the dynamic stability of the system is further guaranteed under the constraints, and finally its effectiveness is verified by simulation analysis, which provides a new solution for high-precision inertial navigation. Full article
(This article belongs to the Special Issue Advanced Biologically Inspired Vision and Its Application)
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18 pages, 1927 KiB  
Article
An Adaptive Unscented Kalman Ilter Integrated Navigation Method Based on the Maximum Versoria Criterion for INS/GNSS Systems
by Jiahao Zhang, Kaiqiang Feng, Jie Li, Chunxing Zhang and Xiaokai Wei
Sensors 2025, 25(11), 3483; https://doi.org/10.3390/s25113483 - 31 May 2025
Viewed by 485
Abstract
Aimed at the problem of navigation performance degradation in inertial navigation system/global navigation satellite system (INS/GNSS)-integrated navigation systems due to measurement anomalies and non-Gaussian measurement noise in complex navigation environments, an adaptive unscented Kalman filter (AUKF) algorithm based on the maximum versoria criterion [...] Read more.
Aimed at the problem of navigation performance degradation in inertial navigation system/global navigation satellite system (INS/GNSS)-integrated navigation systems due to measurement anomalies and non-Gaussian measurement noise in complex navigation environments, an adaptive unscented Kalman filter (AUKF) algorithm based on the maximum versoria criterion (MVC) is developed. The proposed method is designed to enhance INS/GNSS-integrated navigation system robustness and accuracy by addressing the limitations of conventional filtering approaches. An adaptive unscented Kalman filter is constructed to enable dynamic adjustment of filter parameters, allowing for real-time adaptation to measurement anomalies. This ensures accurate tracking of navigation parameter states, thereby improving the robustness of the INS/GNSS-integrated navigation system in the presence of abnormal measurements. On this basis, fully considering the high-order moments of estimation errors, the maximum versoria criterion is introduced as the optimization criterion to construct a novel cost function, further effectively suppressing deviations caused by non-Gaussian disturbances and improving system navigation accuracy. The effectiveness of the proposed method was verified through vehicle navigation experiments. The experimental results demonstrate that the proposed method outperforms traditional approaches, effectively handling measurement anomalies and non-Gaussian measurement noise while maintaining robust navigation performance. Specifically, compared to the EKF, UKF, and MCCUKF, the proposed method reduces the root mean square error of velocity and position by over 60%, 50%, and 30%, respectively, under complex navigation conditions. The algorithm exhibits good accuracy and stability in complex environments, showcasing its practical applicability in real-world navigation systems. Full article
(This article belongs to the Special Issue Sensor Fusion: Kalman Filtering for Engineering Applications)
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19 pages, 4022 KiB  
Article
Evaluating Robotic Walker Performance: Stability, Responsiveness, and Accuracy in User Movement Detection
by Larisa Dunai, Isabel Seguí Verdú, Sui Liang and Ismael Lengua Lengua
Sensors 2025, 25(11), 3428; https://doi.org/10.3390/s25113428 - 29 May 2025
Viewed by 520
Abstract
This work presents the experimental evaluation of a robotic walker following the full implementation of its sensor and motorization system. The aging population and increasing mobility impairments drive the need for assistive robotic technologies that enhance safe and independent movement. The main objective [...] Read more.
This work presents the experimental evaluation of a robotic walker following the full implementation of its sensor and motorization system. The aging population and increasing mobility impairments drive the need for assistive robotic technologies that enhance safe and independent movement. The main objective was to validate the device’s behavior in real-use scenarios by assessing its stability, responsiveness, and accuracy in detecting user movement. Tests were carried out in straight-line walking and on paths involving directional changes, both with and without motor assistance, using a cohort of five test users. Principal Component Analysis (PCA) and t-SNE dimensionality reduction techniques were applied to analyze the inertial (IMU) and proximity (TOF) sensor data, complemented by motor control monitoring through wheel Hall sensors, to explore gait patterns and system performance. Additionally, synchronized measurements between the user’s and walker’s inertial units and Time-of-Flight sensors allowed the evaluation of spatial alignment and motion correlation. The results provide a foundation for future system adjustment and optimization, ensuring the walker offers effective, safe, and adaptive assistance tailored to the user’s needs. Findings reveal that the walker successfully distinguishes individual gait patterns and adapts its behavior accordingly, demonstrating its potential for personalized mobility support. Full article
(This article belongs to the Section Navigation and Positioning)
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18 pages, 3960 KiB  
Article
Pilot Study: Step Width Estimation with Body-Worn Magnetoelectric Sensors
by Johannes Hoffmann, Erik Engelhardt, Moritz Boueke, Julius Welzel, Clint Hansen, Walter Maetzler and Gerhard Schmidt
Sensors 2025, 25(11), 3390; https://doi.org/10.3390/s25113390 - 28 May 2025
Viewed by 405
Abstract
Step width is an important clinical motor marker for gait stability assessment. While laboratory-based systems can measure it with high accuracy, wearable solutions based on inertial measurement units do not directly provide spatial information such as distances. Therefore, we propose a magnetic estimation [...] Read more.
Step width is an important clinical motor marker for gait stability assessment. While laboratory-based systems can measure it with high accuracy, wearable solutions based on inertial measurement units do not directly provide spatial information such as distances. Therefore, we propose a magnetic estimation approach based on a pair of shank-worn magnetoelectric (ME) sensors. In this pilot study, we estimated the step width of eight healthy participants during treadmill walking and compared it to an optical motion capture (OMC) reference. In a direct comparison with OMC markers attached to the magnetic system, we achieved a high estimation accuracy in terms of the mean absolute error (MAE) for step width (≤1 cm) and step width variability (<0.1 cm). In a more general comparison with heel-mounted markers during the swing phase, the standard deviation of the error (<0.5 cm, measure for precision), the step width variability estimation MAE (<0.2 cm) and the Spearman correlation (>0.88) of individual feet were still encouraging, but the accuracy was negatively affected by a constant proxy bias (3.7 and 4.6 cm) due to the different anatomical reference points used in each method. The high accuracy of the system in the first case and the high precision in the second case underline the potential of magnetic motion tracking for gait stability assessment in wearable movement analysis. Full article
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16 pages, 562 KiB  
Communication
Implementation of a Low-Cost Navigation System Using Data Fusion of a Micro-Electro-Mechanical System Inertial Sensor and an Ultra Short Baseline on a Microcontroller
by Julian Winkler and Sabah Badri-Hoeher
Sensors 2025, 25(10), 3125; https://doi.org/10.3390/s25103125 - 15 May 2025
Viewed by 2412
Abstract
In this work, a low-cost low-power navigation solution for autonomous underwater vehicles is introduced utilizing a Micro-Electro-Mechanical System (MEMS) inertial sensor and an ultra short baseline (USBL) system. The complete signal processing is implemented on a cheap 16-bit fixed-point arithmetic microcontroller. For data [...] Read more.
In this work, a low-cost low-power navigation solution for autonomous underwater vehicles is introduced utilizing a Micro-Electro-Mechanical System (MEMS) inertial sensor and an ultra short baseline (USBL) system. The complete signal processing is implemented on a cheap 16-bit fixed-point arithmetic microcontroller. For data fusion and calibration, an error state Kalman filter in square root form is used, which preserves stability in case of rounding errors. To further reduce the influence of rounding errors, a stochastic rounding scheme is applied. The USBL measurements are integrated using tightly coupled data fusion by deriving the observation functions separately for range, elevation, and azimuth angles. The effectiveness of the fixed point implementation with stochastic rounding is demonstrated on a simulation, and the the complete setup is tested in a field test. The results of the field test show an improved accuracy of the tightly coupled data fusion in comparison with loosely coupled data fusion. It is also shown that the applied rounding schemes can bring the fixed-point estimates to a near floating point accuracy. Full article
(This article belongs to the Special Issue Advanced Sensors in MEMS: 2nd Edition)
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32 pages, 4186 KiB  
Article
Comprehensive Adaptive Enterprise Optimization Algorithm and Its Engineering Applications
by Shuxin Wang, Yejun Zheng, Li Cao and Mengji Xiong
Biomimetics 2025, 10(5), 302; https://doi.org/10.3390/biomimetics10050302 - 9 May 2025
Cited by 1 | Viewed by 547
Abstract
In this study, a brand-new algorithm called the Comprehensive Adaptive Enterprise Development Optimizer (CAED) is proposed to overcome the drawbacks of the Enterprise Development (ED) algorithm in complex optimization tasks. In particular, it aims to tackle the problems of slow convergence and low [...] Read more.
In this study, a brand-new algorithm called the Comprehensive Adaptive Enterprise Development Optimizer (CAED) is proposed to overcome the drawbacks of the Enterprise Development (ED) algorithm in complex optimization tasks. In particular, it aims to tackle the problems of slow convergence and low precision. To enhance the algorithm’s ability to break free from local optima, a lens imaging reverse learning approach is incorporated. This approach creates reverse solutions by utilizing the concepts of optical imaging. As a result, it expands the search range and boosts the probability of finding superior solutions beyond local optima. Moreover, an environmental sensitivity-driven adaptive inertial weight approach is developed. This approach dynamically modifies the equilibrium between global exploration, which enables the algorithm to search for new promising areas in the solution space, and local development, which is centered on refining the solutions close to the currently best-found areas. To evaluate the efficacy of the CAED, 23 benchmark functions from CEC2005 are chosen for testing. The performance of the CAED is contrasted with that of nine other algorithms, such as the Particle Swarm Optimization (PSO), Gray Wolf Optimization (GWO), and the Antlion Optimizer (AOA). Experimental findings show that for unimodal functions, the standard deviation of the CAED is almost 0, which reflects its high accuracy and stability. In the case of multimodal functions, the optimal value obtained by the CAED is notably better than those of other algorithms, further emphasizing its outstanding performance. The CAED algorithm is also applied to engineering optimization challenges, like the design of cantilever beams and three-bar trusses. For the cantilever beam problem, the optimal solution achieved by the CAED is 13.3925, with a standard deviation of merely 0.0098. For the three-bar truss problem, the optimal solution is 259.805047, and the standard deviation is an extremely small 1.11 × 10−7. These results are much better than those achieved by the traditional ED algorithm and the other comparative algorithms. Overall, through the coordinated implementation of multiple optimization strategies, the CAED algorithm exhibits high precision, strong robustness, and rapid convergence when searching in complex solution spaces. As such, it offers an efficient approach for solving various engineering optimization problems. Full article
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